Mathieu Everaert, Andreas Van hulle

Common Meuse

culvert - Application to a spillway in a levee of the

Hydraulic study of a labyrinth weir integrated in a

Academic year 2014-2015

Faculty of Engineering and Architecture

Chairman: Prof. dr. ir. Peter Troch

Department of Civil Engineering

Master of Science in Civil Engineering

Master's dissertation submitted in order to obtain the academic degree of

Laboratorium), Ir. Herman Gielen (nv de Scheepvaart)

Counsellors: Ir. Stéphan Creëlle, dhr. Jeroen Vercruysse (Waterbouwkundig

Supervisor: Prof. dr. ir. Tom De Mulder

Copyright

�De auteurs geven de toelating deze masterproef voor consultatie beschikbaar te stellen en delen van

de masterproef te kopiëren voor persoonlijk gebruik. Elk ander gebruik valt onder de beperkingen van

het auteursrecht, in het bijzonder met betrekking tot de verplichting de bron uitdrukkelijk te

vermelden bij het aanhalen van resultaten uit deze masterproef.�

�The authors give permission to make this master dissertation available for consultation and to copy

parts of this master dissertation for personal use.

In case of any other, use, the copyright terms have to be respected, in particular with regard to the

obligation to state expressly the source when quoting results from this master dissertation.�

Mathieu Everaert Andreas Van hulle

June 2015

Mathieu Everaert, Andreas Van hulle

Common Meuse

culvert - Application to a spillway in a levee of the

Hydraulic study of a labyrinth weir integrated in a

Academic year 2014-2015

Faculty of Engineering and Architecture

Chairman: Prof. dr. ir. Peter Troch

Department of Civil Engineering

Master of Science in Civil Engineering

Master's dissertation submitted in order to obtain the academic degree of

Laboratorium), Ir. Herman Gielen (nv de Scheepvaart)

Counsellors: Ir. Stéphan Creëlle, dhr. Jeroen Vercruysse (Waterbouwkundig

Supervisor: Prof. dr. ir. Tom De Mulder

Foreword

A master dissertation is our final step before obtaining the degree of Master of Science in Civil

Engineering. During the past five years, we have been formed by Ghent University into the persons we

are today: reaching and striving for higher goals, increasing our mind-set and scientific background,

with this master dissertation as the icing on the cake.

Since we are both passionate about hydraulic engineering, we started this master dissertation full of

good-will and brimming with motivation. Although it was at times very challenging, pushing us to our

limits, we never lost faith in a good termination.

It is the right time to thank some people who significantly contributed to this thesis. We would like to

express our gratitude to prof. dr. ir. Tom De Mulder for his guidance, enthusiasm and corrections. PhD-

student ir. Stéphan Creëlle was always available to answer our questions straight away and to help us

out with our numerous problems. Thank you, Stéphan! Our thanks go out to PhD-student ir. Laurent

Schindfessel as well. Although he was not a supervisor of this dissertation, he could always be bothered

with questions and was always willing to help. Furthermore the technicians of the Hydraulics

laboratory , Stefaan Bliki and Davy Haerens, have contributed significantly to this thesis by constructing

and adapting our scale models for which we thank them.

Finally, we would like to thank some people, who have no direct link to this dissertation. Our parents,

for the opportunities they have given us. Furthermore, Mathieu would like to thank Charlotte Delhoux,

for supporting him whenever necessary.

Andreas & Mathieu

June 2015

Hydraulic study of a labyrinth weir integrated in a culvert - Application to a

spillway in a levee of the Common Meuse

By Mathieu Everaert and Andreas Van hulle

Master�s dissertation submitted in order to obtain the academic degree of Master of Science in Civil

Engineering

Academic year: 2014-2015

Supervisor: prof. dr. ir. Tom De Mulder

Counsellors: ir. Stéphan Creëlle, ir. Herman Gielen, ing. Jeroen Vercruysse

Faculty of Engineering and Architecture, Ghent University

Department of Civil Engineering

Chairman: prof. dr. ir. Peter Troch

Summary

To remove one of the remaining bottlenecks on the Common Meuse, a hydraulic structure needs to

be built in a levee near Heerenlaak. This document is a dissertation on the subject of this hydraulic

structure, consisting of a labyrinth weir integrated in a culvert. A tentative Qh-relation was derived by

Flanders Hydraulic Research during a desktop study. Due to the uncertainties of this study, additional

research is required.

To estimate the stage-discharge relation of the hydraulic structure, experimental measurements have

been performed on a scale model of the proposed design and a variety of other configurations.

Conclusions can be made regarding the different regimes which occur in the stage-discharge relations

by comparing the results of the different configurations. Where possible, theoretical formulas are

compared to the experimental data.

Based on the results obtained from the scale model tests and using the conclusions drawn from a

literature review, an estimation of the discharge capacity of the design is given and recommendations

for possible improvements and additional research are made.

Keywords

Labyrinth weir, culvert, stage-discharge relation, submergence effects, vortex-formation, scale model

1

Hydraulic study of a labyrinth weir integrated in a culvert �

Application to a spillway in a levee of the Common Meuse

Mathieu Everaert and Andreas Van hulle

Supervisor: prof. dr. ir. Tom De Mulder Councellors: ir. S. Creëlle, ing. J. Vercruysse, ir. H. Gielen, dr. ir. N. Van Steenbergen

Abstract

To remove one of the remaining bottlenecks on the Common Meuse in case of large floods, a hydraulic structure needs to be built in a levee near Heerenlaak. The proposed design of this structure, consisting of a labyrinth weir integrated in a culvert, requires additional research.

The main objectives of this research are to determine the stage-discharge relation of the structure and the maximum discharge capacity, and to suggest possible improvements of the design. Based upon the results retrieved from scale model testing this structure, as well as a set of variant hydraulic structures, and the knowledge acquired during a literature survey, recommendations for possible optimizations are given. Finally, an indication of the estimated increase in maximum discharge capacity of an optimized structure is given.

Keywords: labyrinth weir, culvert, stage-discharge relation, submergence effects, scale model

I. INTRODUCTION

To cope with an expected increase in discharge on the Common Meuse, a hydraulic structure needs to be constructed in the levee at Heerenlaak, Belgium. A conceptual design of this hydraulic structure has been made by nv De Scheepvaart and consists of a labyrinth weir integrated in a culvert. The construction will allow to divert part of the high discharges from the Meuse towards Heerenlaak, i.e. a pond with a downstream connection to the Common Meuse. Flanders Hydraulics Research performed a desk-top study to derive the stage-discharge relation of the proposed design. Due to the uncertainties of this tentative stage-discharge relation, it was recommended to carry out a scale model study. This is the topic of this master thesis.

II. HEERENLAAK

The proposed design for the hydraulic structure consists of a labyrinth weir with 2 cycles (further referred to as one unit) integrated in a culvert. A plan view of this design can be seen in Figure 1.

A number of these units should allow the passage of a target discharge of 300 m³/s through the Heerenlaak pond. This will lower the water level immediately downstream of the river bend in which the hydraulic structure is situated.

A. Specifics of the design

The top of the bottom slab is at 23.7 m T.A.W. (T.A.W. is the chart datum in use in Belgium). The height of the labyrinth wall (P) is 3 m, hence the crest of the weir is at 26.7 m T.A.W.. The distance between the crest of the weir and the roof of the culvert is 1 m. The roof of the culvert is supported by 3

(horizontal) beams aligned with the axis of the service road on the levee, i.e. perpendicular to the direction of the flow through the culvert. There are twelve (vertical) columns supporting the beams and the roof of the culvert. These columns and beams imply head losses and a reduction in available crest length of the weir.

The angle of the labyrinth walls with the flow direction is 8°. The total length of the crest is 58.8 m, hence an available area above the weir of 58.8 m². The inlet of the structure consists of two openings with a width of 5 m and height of 3m, thus the total inlet section is 30 m². The outlet section of the structure has an area of 30 m² as well.

Note that on both the upstream and downstream side of the structure, a U-shaped beam, with the soffit at a level of 26.7 m T.A.W. (i.e. the crest level of the weir), is present. This is shown in Figure 2. The purpose of this soffit is to prevent the ingress of floating debris in the Heerenlaak pond. This also implies that in order for water to pass through the structure, it has to dive first under the U-beam, before going up again to overtop the crest of the labyrinth weir. Hence, water only starts flowing over the weir when the water level upstream of the construction reaches the soffit of the U-beam.

Figure 2: Cross-sectional view of the labyrinth weir in a culvert

Figure 1: Plan view of the labyrinth weir in a culvert

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B. Boundary conditions

The up- and downstream water level are major factors influencing the discharge through the structure. They both depend on the discharge through the Meuse. Based on available data, it turns out that the difference between the upstream and downstream water level near Heerenlaak remains more or less constant around a value of 2 m, though it increases somewhat for higher discharges. For the optimization of the structure, several aspects have to be taken into account. The main constraint is that the optimized design should still fit within the body of the existing levee.

III. LABYRINTH WEIR

A. General concept

A labyrinth weir is a linear weir folded in plan view. As such, a longer total crest length is obtained for the same fixed width of a channel. Tullis et al. (1995) adopted the same formula as for a linear weir to calculate the discharge over a labyrinth weir.

where Q is the discharge [m³/s] Cd is the discharge coefficient [-] Lc is the total crest length of the structure [m] g is the gravitational constant [m/s²] HT is the total upstream head [m]

As can be seen from this formula, using a labyrinth weir allows the passage of a higher discharge for the same upstream head or the passage of an equal discharge for a lower head, when compared to a linear weir.

B. Variables

The main variables influencing the discharge relation of a labyrinth weir are the discharge coefficient and the crest length. In several ways, the discharge coefficient may be increased. This can be achieved by rounding the crest shape, decreasing the angle of the walls with the flow direction (although this implies a decrease in crest length), improving the approach flow conditions � However, the influence of many of these

adaptations diminishes for increasing values of HT/P.

C. Filled alveoli

The alveolus is the volume located between the walls of a labyrinth weir.

Filling the alveoli might be an effective way of reducing the construction costs of the structure. These are diminished by reducing the height of the walls, while maintaining the same level of the crest (Ben Saïd and Ouamane, 2011). This implies that hydrostatic forces are only acting on the upper portion of the wall, allowing for a smaller wall thickness and less reinforcement.

The discharge capacity of the structure is not affected by filling a limited volume of the alveolus (Ben Saïd and Ouamane, 2011). For heads HT/P > 2.5 no difference in hydraulic performance occurred for the weir with or without filling of the alveoli (Ouamane, 2013).

Filling the alveoli has the additional advantage of energy dissipation when the apron of the downstream alveoli is

designed as a stair step and may as well facilitate the construction process for the application at Heerenlaak.

IV. CULVERT

A culvert is a short channel or conduit placed through an embankment, dike, dam � Flow phenomena through culverts

are rather complex. Different flow regimes can be discerned based upon the upstream and downstream flow conditions. Only the regimes relevant to this work will be discussed.

Carter (1957) defined 6 types of flow regimes through culverts, 2 defined by inlet control and 4 by outlet control. The main parameter in the definition of these different types, is the submergence of the inlet. According to Carter, the inlet is submerged when the difference between the upstream water level and the culvert invert is smaller than 1.5 times the height/diameter of the inlet. Later on, Chow (1959) stated this to be a range of 1.2 to 1.5 times the height of the culvert. According to Henderson (1966), submergence occurs when the ratio of upstream specific energy to the barrel diameter (or barrel height) is higher than 1.2. The outlet becomes submerged when the tail water is higher than the culvert diameter/height (Carter, 1957).

The first three flow types, defined by Carter (1957), are not representative for the flow through the structure discussed, since the influence of the labyrinth determines the discharge. Type IV, V and VI, on the other hand, might be of interest.

Type IV is characterized by both ends of the culvert being completely submerged and the discharge can then be calculated by:

where Ai is the area of the inlet of the culvert [m²] Cd is the discharge coefficient [-] h1 is the piezo-metric head upstream of the culvert [m] h4 is the piezo-metric head downstream of the culvert [m] n is the roughness coefficient of Manning [s/m1/3]

L is the culvert length [m] R0 is the hydraulic radius of the culvert barrel [m]

Type V occurs when the inlet is submerged and the outlet is not. The culvert barrel flows partly full. The discharge can then be calculated by:

Type VI is similar to type V, except the barrel flows full and with free outfall.

V. TESTING

The scale model study is performed at the Hydraulics Laboratory of Ghent University. Each of the investigated scale models (scale factor 1/18) is installed in a current flume. By varying the downstream water level and increasing the discharge, the Qh-relations of the tested configurations are obtained. The water levels up- and downstream of the scale model are measured using ultrasonic water level sensors.

All data shown in this work correspond to a difference !h in upstream and downstream water level of about 2 m, unless explicitly stated otherwise. Some data in the graphs are

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obtained by interpolating between two measured data points in order to obtain the values corresponding to a !h of 2 m.

As mentioned previously, a number of variant hydraulic structures has been tested. Several abbreviations will be used throughout this work to refer to the different configurations. These abbreviations are explained in Table 1.

Table 1: Explanation of the used abbreviations

Abbreviation Explanation

LW_U_B&C

Labyrinth weir in a culvert with U-beams, internal beams and columns in the

structure. LW_U Labyrinth weir in a culvert with U-beams W_U Weir in a culvert with U-beams

LW_U_C Labyrinth weir in a culvert with U-beams,

Columns in the structure W_noU Weir in a culvert without U-beams

VI. DISCUSSION

A. LW_U_B&C

The obtained results on the scale model of the proposed design (i.e. configuration LW_U_B&C) can be seen in Figure 3.

Figure 3: Measured data and flow regimes for LW_U_B&C

Based on these results, three different flow regimes can be discerned, as indicated in Figure 3. The first flow regime is characterized by free flow over a labyrinth weir. The water flows freely over the labyrinth weir, with almost no influence of the weir being integrated in a culvert. The discharge is not dependent on the downstream water level for this regime.

At an upstream level of 28.0 m T.A.W., the inlet of the structure becomes internally drowned. This corresponds to the theoretical height at which the inlet of a culvert becomes submerged, namely when the headwater is at 1.2 to 1.5 times the height of the inlet (Chow, 1959). This second regime is comparable to Type V flow in a culvert.

A transition to a third regime occurs when the water level immediately downstream of the U-beam is at 26.7 m T.A.W. (i.e. the soffit of the downstream U-beam). For this water level the outlet becomes submerged. During this third regime, the discharge slightly declines to reach a more or less constant value for higher upstream water levels, which is consistent with Type IV flow from the culvert literature. The discharge is now depending on the difference between the water levels upstream and downstream of the construction.

B. Conclusions from other configurations

A wide variety of other configurations (linear weir, labyrinth weir, integrated in a culvert or not) were tested. Several design adaptations were made. This was done to gain insight in the Qh-relation of LW_U_B&C and to search for possible optimizations. The perceived regimes for LW_U_B&C (free flow over a weir, inlet under pressure, in- and outlet under pressure) were discerned for all tested geometries integrated in a culvert.

1) Constraining section for the discharge capacity

A comparison of a labyrinth weir and a linear weir in a

culvert (resp. LW_U and W_U) can be seen in Figure 4. In both configurations the crest is at the same level (i.e. 26.7 m T.A.W.) but W_U has a shorter crest length (11.5 m vs. 63 m) and an overflow area smaller than the inlet section of the structure (28.8 m² vs. 34.6m²).

Figure 4: Comparison between LW_U and W_U

When the overflow section above the crest of the labyrinth or linear weir is smaller than the inlet section, this overflow section of the culvert is the most restraining factor for the discharge capacity of the structure. This explains the lower discharge capacity of W_U. In case of LW_U, the most constraining factor is the inlet section. However, a higher capacity may still be reached by reducing the hydraulic losses in the structure (e.g. by removing the beams and columns supporting the roof of the culvert).

This is confirmed by comparing W_U and W_noU, for which the most constraining factor is the overflow section above the weir crest (Figure 5). These two configurations become submerged at the same moment, although the inlet section of W_noU is larger and has a larger inlet height than W_U.

Figure 5: Comparison between W_noU and W_U

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2) Removal of the beams and columns

The removal of the internal beams and columns, which support the roof of the culvert, reduces the losses and increases the overflow area between the weir crest and the roof. Also the eddies created by the beams, which reduce the capacity, disappear. Removing the beams leads to an increase in discharge of about 12 to 17 %, while the removal of both beams and columns resulted in an increase in discharge of about 15 to 20 % when compared to the LW_U_B&C configuration.

Figure 6: Comparison of LW_U_B&C, LW_U_C and LW_U

3) Removal of the U-shaped beams

Removing the U-beams of the structure causes the inlet of the structure to become drowned at higher water levels and leads to an increase in area of the inlet section. These factors explain the higher capacity of the structure without U-beams. This is illustrated in Figure 7.

Figure 7: Influence of the removal of the U-beams

4) Influence of !h over the structure

The overall head over the structure is about 2 m for most upstream water levels at the Meuse. However, this value may increase to up to 2.5 m for high upstream water levels. Testing has been performed on LW_U_B&C for different heads over the structure. The results are shown in Figure 8.

Figure 8: Results for LW_U_B&C for different !h

As can be seen from this figure, higher differences in up- and downstream water level leads to a higher capacity of the structure.

For the first regime, there is no discernible difference in capacity for different values of !h. As previously mentioned, the discharge during this regime is independent of the downstream water level.

When !h is higher, the second regime is present up to higher upstream water levels. This can be explained by recalling that the transition from the second to the third regime occurs when the outlet is drowned. Thus a higher head over the structure will result in a lower downstream water level for equal upstream water levels. Therefore, the transition occurs at higher water levels, compared to a situation with a lower head. Note that in case !h is 1 m, the second regime cannot be discerned. This is because the inlet and outlet become submerged at the same time (hupstream is 28 m T.A.W., hdownstream is 27 m T.A.W.).

During the third regime, the discharge depends on the water level difference between both sides of the structure. Hence, the higher capacity for higher values of !h.

C. Estimation of the discharge for the proposed design

There are two main reasons to assume that the maximum discharge capacity will be higher than the value of about 100 m³/s for one unit, as was shown in Figure 3.

A first reason is the minor geometrical discrepancy between the proposed design and the tested scale model LW_U_B&C. The discrepancy is caused by slightly smaller dimensions for the inlet section and slightly larger dimensions for the beams and columns, which imply a reduction in available overflow area in the structure. Therefore it is expected that the discharge of the proposed design will be 9 to 11% higher than measured on the scale model configuration LW_U_B&C.

A second reason to assume a higher discharge, in the final regime, is that for higher upstream water levels, the overall head will increase up to 2.5 m. This leads to a higher discharge capacity of the structure, as has been stated before (see Figure 8).

Taking into account these two aspects, it is assumed that a maximum discharge of 120 m³/s per unit can be reached. The influence of both factors leading to a higher discharge is shown in Figure 9.

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Figure 9: Estimation of the discharge through the proposed hydraulic structure based upon geometrical errors and a rising difference in

water level

D. Estimation of the discharge for an optimized design

A possible improvement of the proposed design is to integrate the beams supporting the roof in the ceiling of the culvert. By doing so, the hydraulic losses will decrease since there is a larger overflow area above the weir crest and less eddies will occur. Taking into account the aforementioned increase in capacity of 12 to 15% by removing the beams (see Figure 6), and considering that the capacity of the proposed design is more or less 120 m³/s (see Figure 9), a (conservative) value for the discharge capacity of 130 m³/s per unit is obtained for a design with the supporting beams integrated in the roof.

VII. CONCLUSIONS

Based upon the scale model study, three flow regimes have been discerned for the proposed design of the hydraulic structure. The first flow regime corresponds to free overflow over a labyrinth weir. The second regime starts when the upstream water level reaches a value of 28.0 m T.A.W. (i.e. when the inlet is internally drowned). This regime is comparable to the so-called Type V flow through a culvert. When the soffit of the outlet is also submerged (i.e. the water level immediately downstream of the downstream U-beam is at a level of 26.7 m), a third flow regime is perceived. Both inlet and outlet being drowned, this regime is comparable to the so-called Type IV flow through a culvert. During the third regime, however, the discharge capacity slightly decreases to reach a more or less constant value.

A peak discharge of 100 m³/s for one unit is reached at the transition of the second to the third regime. However, due to the minor geometrical discrepancies between the scale model and the proposed design, it is estimated that a discharge of 110 m³/s may be reached for the proposed design for a !h of 2 m

and up to 120 m³/s for !h equal to 2.5 m. These peak discharge values imply that 3 units of the proposed design have to be built in order to reach the target discharge for the structure of 300 m³/s.

Based upon the literature review, several aspects of the hydraulic structure may be improved (crest shape, rounded upstream abutments, rounded U-beams, filled alveoli �).

However, the impact of most of these improvements diminishes for large relative heads HT/P. The use of filled alveoli, however, seems promising since it might facilitate construction, reduce the cost and improve the dissipation of energy when the downstream apron is designed as a stair step.

Taking into account possible optimizations to the proposed design (e.g. integrating the supporting beams into or on top the roof) it is estimated that a peak discharge of 390 m³/s can be reached by constructing three units. This peak discharge is somewhat higher than the structure�s target discharge of 300

m³/s. Hence, it could be worth considering building an optimized structure with 5 labyrinth cycles instead of 6.

REFERENCES.

BEN SAÏD, M. & OUAMANE, A. (2011). Study of optimization of labyrinth weir. pp. 67-74 in: Erpicum, S., Laugier, F., Boillat, J.-L., Pirotton, M., Reverchon, B., & Schleiss, A. J. (Eds.). (2011). Labyrinth and Piano Key Weirs. CRC Press. Leiden: CRC Press/Balkema. CARTER, R.W. (1957). Computation of peak discharge at culverts US Geological Survey Circular, No. 376.

CHOW, V.T. (1959). Open Channel Hydraulics, New York: McGraw-Hill International HENDERSON, F.M. (1966). Open Channel Flow. New York: MacMillan Company OUAMANE, A. (2013). Improvement of Labyrinth Weirs Shape. pp. 15-22 in: Erpicum, S., Laugier, F., Pfister, M., Pirotton, M., Cicero, G. M., & Schleiss, A. J. (Eds.). (2013). Labyrinth and Piano Key Weirs II. CRC Press. Leiden: CRC Press/Balkema. TULLIS, P., AMANIAN, N. & WALDRON, D. (1995). Design of Labyrinth Weir Spillways. Journal of Hydraulic Engineering, ASCE, 121, nr. 3, pp. 247-255

Table of contents

CHAPTER 1: INTRODUCTION........................................................................................................ 1

1. Hydraulic structure at Heerenlaak ........................................................................................................... 1

1.1 Necessity of the structure ..................................................................................................................... 1

1.2 Heerenlaak ............................................................................................................................................. 1

2. Objectives ................................................................................................................................................ 3

CHAPTER 2: DISCUSSION OF THE DESIGN .................................................................................... 5

1. Conceptual design of the labyrinth weir in a culvert ................................................................................ 5

1.1 Bottom slab ........................................................................................................................................... 7

1.2 Inlet and outlet section.......................................................................................................................... 7

1.3 Position of the columns ......................................................................................................................... 7

1.4 Angle ...................................................................................................................................................... 8

2. Boundary conditions ................................................................................................................................ 8

2.1 Analysis of water levels ......................................................................................................................... 8

2.2 Design adaption constraints ................................................................................................................ 14

3. Q-h relation ........................................................................................................................................... 14

3.1 Weir ..................................................................................................................................................... 14

3.2 Inflow under pressure, free outflow.................................................................................................... 15

3.3 In- and outflow under pressure ........................................................................................................... 15

4. Important dimensions and levels ........................................................................................................... 16

CHAPTER 3: LITERATURE REVIEW .............................................................................................. 17

1. Scaling ................................................................................................................................................... 17

1.1 Types of similitude ............................................................................................................................... 17

1.2 Scale effects ......................................................................................................................................... 19

2. Linear Weirs ........................................................................................................................................... 22

3. Labyrinth Weirs ..................................................................................................................................... 23

3.1 General concept .................................................................................................................................. 23

3.2 Variables .............................................................................................................................................. 24

3.2.1 Crest Length Lc ................................................................................................................................. 24

3.2.2 Discharge coefficient Cd................................................................................................................... 25

3.2.3 Sidewall angle α .............................................................................................................................. 25

3.2.4 Cycle efficiency ε’ ............................................................................................................................ 26

3.2.5 Number of cycles N ......................................................................................................................... 27

3.2.6 Shape of the cycles .......................................................................................................................... 28

3.2.7 Headwater ratio HT/P ...................................................................................................................... 29

3.2.8 Vertical aspect ratio W/P ................................................................................................................ 29

3.2.9 Crest shape and wall thickness ....................................................................................................... 30

3.2.10 Ratio Wi/Wo ................................................................................................................................ 31

3.2.11 Labyrinth Weir Orientation, Placement and Cycle Configuration .............................................. 32

3.2.12 Aeration Conditions .................................................................................................................... 37

3.2.13 Filling the alveoli ......................................................................................................................... 38

3.3 Disadvantages ...................................................................................................................................... 40

3.4 Piano Key Weirs ................................................................................................................................... 40

3.5 Submergence effects ........................................................................................................................... 41

3.5.1 Influence of submergence ............................................................................................................... 41

3.5.2 Relationship by Villemonte ............................................................................................................. 42

3.5.3 Local submergence .......................................................................................................................... 43

4. Culverts .................................................................................................................................................. 44

4.1 Introduction ......................................................................................................................................... 44

4.2 Terminology ......................................................................................................................................... 44

4.3 Flow through a culvert ......................................................................................................................... 44

5. Vortices.................................................................................................................................................. 51

5.1 Introduction ......................................................................................................................................... 51

5.2 Formation and causes .......................................................................................................................... 52

5.3 Submergence ....................................................................................................................................... 54

5.4 Scale effects ......................................................................................................................................... 58

5.5 Problems .............................................................................................................................................. 60

5.6 Prevention ........................................................................................................................................... 60

6. Optimisation based on literature review and scale model testing ......................................................... 62

CHAPTER 4: EXPERIMENTAL SET-UP AND TEST PROCEDURE ..................................................... 65

1. Test facilities .......................................................................................................................................... 65

1.1 Current Flume ...................................................................................................................................... 65

1.2 Position of the scale model ................................................................................................................. 67

1.3 Honeycombs ........................................................................................................................................ 68

2. Measuring equipment............................................................................................................................ 69

2.1.1 Ultrasonic water level sensors ........................................................................................................ 69

2.1.2 Electromagnetic current meter ....................................................................................................... 70

2.2 Accuracy of surface measurements..................................................................................................... 71

3. Scale Model ........................................................................................................................................... 71

3.1 Full model ............................................................................................................................................ 71

3.2 Simple model ....................................................................................................................................... 74

3.3 Scaling .................................................................................................................................................. 75

4. Test procedure ....................................................................................................................................... 76

4.1 Stage-discharge relation ...................................................................................................................... 76

4.2 Velocity measurements ....................................................................................................................... 76

4.2.1 Testing procedure I ......................................................................................................................... 76

4.2.2 Testing procedure II ........................................................................................................................ 78

4.3 Visualization of the flow pattern using colouring dye ......................................................................... 78

5. Tested configurations of the Full and Simple models ............................................................................. 78

5.1 F_LWh_U_B&C .................................................................................................................................... 79

5.2 F_LWh_U_C ......................................................................................................................................... 80

5.3 F_LWh_U ............................................................................................................................................. 81

5.4 S_LWh_noCul ....................................................................................................................................... 82

5.5 S_LWh_U ............................................................................................................................................. 83

5.6 S_LWh_noU ......................................................................................................................................... 84

5.7 S_LWh_UMeuse .................................................................................................................................. 84

5.8 S_LWh_U_Raisedroof .......................................................................................................................... 85

5.9 S_Wh_U ............................................................................................................................................... 86

5.10 S_Wh/2_U ........................................................................................................................................... 87

5.11 S_Wh_noU ........................................................................................................................................... 88

5.12 Verification of the scale model dimensions ........................................................................................ 88

5.12.1 Full Model ................................................................................................................................... 88

5.12.2 Simple Model .............................................................................................................................. 88

CHAPTER 5: DATA PROCESSING ................................................................................................. 89

1. Remarks about the discussed data ......................................................................................................... 89

2. Data processing ..................................................................................................................................... 89

3. Accuracy of the results ........................................................................................................................... 92

CHAPTER 6: RESULTS AND DISCUSSION ..................................................................................... 95

1. Introduction ........................................................................................................................................... 95

2. Results ................................................................................................................................................... 96

2.1 S_Wh_U ............................................................................................................................................... 96

2.2 S_Wh_U and S_Wh/2_U .................................................................................................................... 103

2.3 S_Wh_U and S_Wh_noU ................................................................................................................... 106

2.4 S_LWh_noCul ..................................................................................................................................... 107

2.5 S_LWh_noU and S_LWh_noCul ......................................................................................................... 109

2.6 S_LWh_U, S_Wh_U and S_Wh/2_U .................................................................................................. 110

2.7 S_LWh_U and S_LWh_noU ................................................................................................................ 112

2.8 S_LWh_U and F_LWh_U .................................................................................................................... 114

2.9 Influence of the supporting beams and columns .............................................................................. 115

2.10 F_LWh_U_B&C for different Δh......................................................................................................... 117

2.11 Verification of the estimated stage discharge relation by FHR ......................................................... 118

2.12 Dip in the third regime ...................................................................................................................... 122

3. Optimisation ........................................................................................................................................ 123

3.1 Influence of raising the roof (S_LWh_U_Raisedroof) ........................................................................ 123

3.2 Removal of the downstream U-beam ............................................................................................... 124

4. Flow pattern and velocity measurements ............................................................................................ 126

4.1 Flow pattern ...................................................................................................................................... 126

4.2 Velocity measurements ..................................................................................................................... 128

4.2.1 Testing procedure II ...................................................................................................................... 128

4.2.2 Testing procedure I ....................................................................................................................... 131

4.3 Velocities downstream of the structure ............................................................................................ 138

4.4 Critical remarks .................................................................................................................................. 138

5. Quantification of vortices .................................................................................................................... 139

5.1 Presence of vortices .......................................................................................................................... 139

5.2 Critical submergence ......................................................................................................................... 140

5.3 Application to the future hydraulic structure .................................................................................... 144

CHAPTER 7: CONCLUSIONS ..................................................................................................... 147

CHAPTER 8: RECOMMENDATIONS FOR FURTHER RESEARCH .................................................. 150

BIBLIOGRAPHIC REFERENCES .................................................................................................. 151

APPENDIX A: PROPOSED DESIGN OF THE HYDRAULIC STRUCTURE .......................................... 157

APPENDIX B: VALEPORT MODEL 801 ELECTROMAGNETIC FLOW METER ................................ 159

List of figures

Figure 1: Indication of the Heerenlaak-area (adapted from Bing Maps) ................................................ 2

Figure 2: Plan view of the proposed hydraulic structure ........................................................................ 3

Figure 3: Front view of the labyrinth weir in a culvert (Side of the Meuse) ........................................... 5

Figure 4: Plan view of the labyrinth weir in a culvert .............................................................................. 6

Figure 5: Longitudinal section of the labyrinth weir in a culvert ............................................................ 6

Figure 6: Illustration of the labyrinth weir angle ..................................................................................... 8

Figure 7: Water level in the Meuse and the Heerenlaak pond in function of the discharge through the

Meuse near Maaseik (Vercruysse et al., 2013) ....................................................................................... 9

Figure 8: Water level in the Meuse upstream of the labyrinth weir in function of the discharge

through the Meuse near Maaseik (Vercruysse et al., 2013) ................................................................. 10

Figure 9: Water level in the Meuse downstream of the Heerenlaak pond in function of the discharge

through the Meuse near Maaseik (Vercruysse et al., 2013) ................................................................. 11

Figure 10: Water level upstream of the labyrinth weir in function of the discharge through the Meuse

near Maaseik (Vercruysse et al., 2013) ................................................................................................. 12

Figure 11: Over flow height in function of the occurrence in days per year (Vercruysse et al., 2013) 13

Figure 12: Qh-relation as mentioned in the FHR-report (Vercruysse et al., 2013) ............................... 15

Figure 13: Sharp crested weir (Berlamont, s.d.) .................................................................................... 22

Figure 14: A 4-cycle labyrinth weir with an indication of the geometric variables (adapted from Tullis,

Amanian and Waldron, 1995) ............................................................................................................... 24

Figure 15: Cycle efficiency vs. HT/P for half-round labyrinth weirs (Crookston,2010) .......................... 26

Figure 16: Cycle efficiency vs. HT/P for quarter round labyrinth weirs (Crookston,2010) .................... 26

Figure 17: Efficacy ε vs. sidewall angle α for quarter round trapezoidal weirs (Crookston,2010)........ 27

Figure 18: Nappe interference and cycle number for an aerated nappe at low HT/P (Crookston,2010)

............................................................................................................................................................... 28

Figure 19: General classifications of labyrinth weirs: triangular (A), trapezoidal (B) and rectangular (C)

(Crookston,2010) ................................................................................................................................... 29

Figure 20: Crest shapes (Crookston,2010) ............................................................................................ 30

Figure 21: Indication of the variables Wi and Wo (adapted from Ben Saïd and Ouamane,2011) ......... 31

Figure 22: Variation of the discharge coefficient for different ratios of Wi/Wo and Lc-cycle/W =4

(adapted from Ben Saïd and Ouamane,2011) ....................................................................................... 32

Figure 23: Orientations, placements and cycle configurations (Crookston and Tullis,2011) ................ 33

Figure 24: Labyrinth weir with a rounded front wall (left) and a flat wall (right) ( Ouamane, 2013) ... 34

Figure 25: Discharge coefficient according to the entrance shape of a labyrinth weir (adapted from

Ouamane,2013) ..................................................................................................................................... 34

Figure 26: Channel with and without lateral contraction ( Ben Saïd and Ouamane,2011) .................. 34

Figure 27: Variation of the discharge coefficient for a model with and without lateral contraction

(adapted from Ben Saïd and Ouamane,2011) ....................................................................................... 35

Figure 28: Geometry of an arced labyrinth weir (Crookston,2010) ...................................................... 35

Figure 29: Cd vs. HT/P for α =6° half-round trapezoidal labyrinth weir (Crookston, 2010) ................... 36

Figure 30: Cd vs. HT/P for α =12° half-round trapezoidal labyrinth weir (Crookston, 2010) ................. 36

Figure 31: Aeration conditions for a half-round crest (Christensen,2012) ........................................... 37

Figure 32: Filling of the alveoli (adapted from Ben Saïd and Ouamane,2011) ..................................... 39

Figure 33: Rectangular labyrinth weir with a shaped entrance, partially filled alveoli and a stepped

stair in the outlet key (Ouamane, 2013) .............................................................................................. 39

Figure 34: View of a PK weir spillway of the Gloriettes Dam in France during Construction (Électricité

de France) .............................................................................................................................................. 41

Figure 35: Dimensionless relationship describing submerged labyrinth weir performance (Tullis,

Young and Chandler,2006) .................................................................................................................... 43

Figure 36: Illustration of culvert flow, explaining the different parameters (Bodhaine, 1966) ............ 45

Figure 37: Type I flow, according to Carter (1957) ................................................................................ 46

Figure 38: Type II flow, according to Carter (1957) ............................................................................... 47

Figure 39: Type III flow, according to Carter (1957) .............................................................................. 47

Figure 40: Type IV flow, according to Carter (1957) ............................................................................. 48

Figure 41: Type V flow, according to Carter (1957) .............................................................................. 49

Figure 42: Type VI flow, according to Carter (1957) ............................................................................. 49

Figure 43: Directional and structural classification of vortices (Knauss, 1987) .................................... 51

Figure 44: Sources of rotational motion according to Knauss (1987) ................................................... 52

Figure 45: Three fundamental causes of vortex formation according to Durgin and Hecker, 1978..... 52

Figure 46: Free-surface vortex classification according to Alden Research Laboratory (Knauss, 1987)

............................................................................................................................................................... 54

Figure 47: Indication of the different parameters used by Gordon (ASCE, 1995) ................................ 56

Figure 48: Recommended submergence for intakes with proper approach flow conditions (Knauss,

1987) ...................................................................................................................................................... 57

Figure 49: Floating raft (Gulliver and Rindels, 1983) ............................................................................. 61

Figure 50: Submerged raft (Gulliver and Rindels, 1983) ....................................................................... 61

Figure 51: Illustration of the inclined corners between the U-beam and the culvert soffit ................. 64

Figure 52: Current flume used during the experiments ........................................................................ 65

Figure 53: Needle of the gage to measure the discharge ..................................................................... 66

Figure 54: Qh-relation of the calibrated weir ........................................................................................ 66

Figure 55: Stilling tube with hooked gage (left) and the device to adjust the height of the needle

(right) ..................................................................................................................................................... 67

Figure 56: Cogwheel to adjust the height of the downstream weir ..................................................... 67

Figure 57: Honeycombs ......................................................................................................................... 68

Figure 58: Comparison of the water surface on both sides of the honeycombs (right: highly

fluctuating levels at the upstream side; left: calmed down free surface at the downstream side) ..... 69

Figure 59: Ultrasonic distance sensor ................................................................................................... 69

Figure 60: Indication of the position of the ultrasonic water level sensors .......................................... 70

Figure 61: The Valeport model 801 electromagnetic current meter (source:

http://www.valeport.co.uk) .................................................................................................................. 71

Figure 62: Front view (left) and top view (right) of the hydraulic structure in the current flume ........ 72

Figure 63: Front view of the scale model .............................................................................................. 72

Figure 64: Rubber sealing to prevent seepage ...................................................................................... 73

Figure 65: Model before (left) and after (right) completion with a view through the PMMA-ceiling .. 74

Figure 66: Longitudinal cross-section of the Simple model .................................................................. 75

Figure 67: Indication of the removable U-beams.................................................................................. 75

Figure 68: Indication of the transverse locations of the velocity measurements (adapted from

Vercruysse et al., 2013) ......................................................................................................................... 77

Figure 69: Electromagnetic current meter on the metal bar during the measurements ..................... 77

Figure 70: catheter used for the colouring dye experiments ................................................................ 78

Figure 71: F_LWh_U_B&C ..................................................................................................................... 80

Figure 72: Indication of the removal of the supporting beams in F_LWh_U_C .................................... 80

Figure 73: View inside the labyrinth weir without supporting beams .................................................. 81

Figure 74: Indication of the removed parts in F_LWh_U ...................................................................... 81

Figure 75: Indication of the removal of columns and beams by comparing F_LWh_U_B&C (left) with

F_LWh_U (right) .................................................................................................................................... 82

Figure 76: Front view of S_LWh_noCul (upstream) .............................................................................. 82

Figure 77: Top view of S_LWh_noCul .................................................................................................... 83

Figure 78: Longitudinal cross-section of the Simple model (S_LWh_U) ............................................... 83

Figure 79: Front view of S_LWh_U ........................................................................................................ 83

Figure 80: Front view of S_LWh_noU from the side of Heerenlaak (downstream) .............................. 84

Figure 81: Indication of the Simple model with the removed U-beams (S_LWh_noU) ........................ 84

Figure 82: Indication of the removed U-beam in S_LWh_UMeuse ...................................................... 85

Figure 83: View on downstream side of S_LWh_UMeuse with removed U-beam ............................... 85

Figure 84: Front view of S_LWh_U_Raisedroof .................................................................................... 86

Figure 85: Longitudinal cross-section of S_LWh_U_Raisedroof, with indication of the heightened roof

............................................................................................................................................................... 86

Figure 86: Longitudinal cross-section of S_LWh_UMeuse, with a linear weir with a height of 3 m ..... 87

Figure 87: Longitudinal cross-section of S_Wh/2_U, with a linear weir with a height of 1.5 m ........... 87

Figure 88: Front view of S_Wh/2_U with sight on the linear weir at half the height of the inlet ........ 87

Figure 89: Longitudinal cross-section of S_Wh_noU, without U-beams .............................................. 88

Figure 90: difference between one cycle and one unit ......................................................................... 89

Figure 91: An overview of all data measured on F_LWh_U_B&C ......................................................... 90

Figure 92: Measured data points and interpolated values (F_LWh_U_B&C) ....................................... 91

Figure 93: Measured data points with different differences in up/downstream (F_LWh_U_B&C) ..... 92

Figure 94: Comparison of data measured at different dates on the F_LWh_U_B&C ........................... 93

Figure 95: Comparison of S_Wh_U with the theoretical curves for flow over a weir .......................... 99

Figure 96: Theoretical fit of flow through a culvert on S_Wh_U ........................................................ 101

Figure 97: Schematical representation of a drowned outlet .............................................................. 101

Figure 98: Indication of the rising water level between the outlet and the downstream sensor ...... 102

Figure 99: Indication of the different regimes observed in the Qh-relation of S_Wh_U ................... 103

Figure 100: Influence of the overflow section of the weir (S_Wh_U vs. S_Wh/2_U) ......................... 104

Figure 101: Theoretical fit on S_Wh/2_U ............................................................................................ 105

Figure 102: Schematical representation of the drowned inlet ........................................................... 105

Figure 103: Impact of U-beams on Qh-relation (S_Wh_U vs. S_Wh_noU) ......................................... 106

Figure 104: Theoretical curve compared to S_LWh_noCul ................................................................. 108

Figure 105: Submergence effects, red data points are calculated based on measurements, adapted

from Tullis et al. (2005) ....................................................................................................................... 109

Figure 106: S_LWh_noCul vs. S_LWh_noU ........................................................................................ 110

Figure 107: Comparison between S_LWh_U, S_Wh_U and S_Wh/2_U ............................................. 111

Figure 108: Impact of the U-beams on a labyrinth weir in a culvert (S_LWh_U vs. S_LWh_noU) ..... 113

Figure 109: Comparison between S_LWh_U and F_LWh_U ............................................................... 114

Figure 110: Demonstration of the difference in inlet geometry between the full model (left) and the

simple model (right) ............................................................................................................................ 115

Figure 111: Comparison of F_LWh_U_B&C, F_LWh_U_C and F_LWh_U ........................................... 116

Figure 112: Interpolated values for F_LWh_U_B&C for different Δh ................................................. 118

Figure 113: Estimation of the discharge through the proposed hydraulic structure based upon

geometrical errors, in comparison with the estimated Qh-relation proposed by FHR (Vercruysse et al.,

2013) .................................................................................................................................................... 120

Figure 114: Estimation of the discharge through the proposed hydraulic structure based upon

geometrical errors and a rising up/downstream difference , in comparison with the theoretical

estimation made by FHR (Vercruysse et al., 2013) ............................................................................. 121

Figure 115: Indication of the dip in the third regime .......................................................................... 122

Figure 116: Comparison of S_LWh_U and S_LWh_U_Raisedroof ....................................................... 124

Figure 117: Comparison of S_LWh_UMeuse and S_LWh_U ............................................................... 125

Figure 118: Maximal intensity of the injected dye, injection at about 29 m T.A.W. .......................... 127

Figure 119: Maximum intensity of the injected dye, injection at about 28 m T.A.W. ........................ 127

Figure 120: Maximum intensity of the injected dye, injection at about 26 m T.A.W. ........................ 127

Figure 121: Maximum intensity of the injected dye ........................................................................... 127

Figure 122: Indication of the measured data points on the experimentally derived Qh-relation for the

F_LWh_U_B&C-configuration ............................................................................................................. 129

Figure 123: Velocity measurements for data point 1 and data point 2 .............................................. 129

Figure 124: Stationary wave pattern on the side of the Meuse ......................................................... 130

Figure 125: Indication of the measured data points on the experimentally obtained Qh-relation of the

F_LWh_U_B&C-configuration ............................................................................................................. 131

Figure 126: Velocity measurements for data point 3 and a distance of 5 m upstream of the inlet ... 132

Figure 127: Velocity measurements for data point 3 at a distance of 10 m upstream of the inlet .... 132

Figure 128: Velocity measurements for data point 3 in the middle of the flume .............................. 133

Figure 129: Velocity measurements for data point 3 in the middle of the inlet section of a single cycle

............................................................................................................................................................. 133

Figure 130: Velocity measurements for data point 3 at the side of the flume ................................... 134

Figure 131: Indication of the gap between the side of the honeycombs and the wall of the flume .. 135

Figure 132: Velocity measurements for data point 4 at the middle of the inlet section .................... 135

Figure 133: Comparison of the velocity measurements for Q = 98.7 m³/s and Q = 95.15 m³/s at the

middle of the inlet section .................................................................................................................. 136

Figure 134: Conceptual drawing indicating the contraction of the velocity profiles for data point 3 137

Figure 135: Conceptual drawing indicating the contraction of the velocity profiles data point 4 ..... 138

Figure 136: Example of a full air core vortex at a discharge of 91 m³/s and an upstream water level of

28.24 m T.A.W. .................................................................................................................................... 139

Figure 137: Graphic representation of the measured submergence, compared to the calculated

critical submergences .......................................................................................................................... 142

Figure 138: Stimulation of vorticity caused by the geometry of the structure front, top view of

F_LWh_U_B&C .................................................................................................................................... 143

Figure 139: The front of S_LWh_U ...................................................................................................... 144

Figure 140: Cross-section of the hydraulic structure inside the body of the dike .............................. 145

Figure 141: Examples of the tentative trashtests ............................................................................... 145

List of tables

Table 1: Over flow heights with corresponding water level, discharge and occurrence (Vercruysse et

al., 2013) ................................................................................................................................................ 13

Table 2: Discharge through the Meuse near Maaseik in function of the water level in the Heerenlaak

pond (Vercruysse et al., 2013)............................................................................................................... 14

Table 3: Overview of important dimensions and T.A.W.-levels ............................................................ 16

Table 4: Limiting criteria to avoid significant scale effects in various hydraulic flow phenomena

(Heller, 2011) ......................................................................................................................................... 21

Table 5: Summary of the different flow types and characteristics according to Carter (1957) ............ 45

Table 6: Explanation of the used abbreviations .................................................................................... 79

Table 7: Used abbreviations and a description of the corresponding configuration ............................ 95

Table 8: Calculation of the Cd-coefficient based on S_Wh_noU ........................................................... 97

Table 9: Calculation of the Cd-coefficient based on S_Wh/2_U ............................................................ 97

Table 10: Calculation of the Cd-coefficient based on S_Wh_U ............................................................. 97

Table 11: Comparison between the experimentally and theoretically derived Cd-coefficients ........... 98

Table 12: Calculation of the Cd-coefficient .......................................................................................... 100

Table 13: Available area above the weir for different configurations ................................................ 116

Table 14: The measured data points, corresponding to the peak discharge and discharge at the dip

............................................................................................................................................................. 128

Table 15: Discharge and corresponding hupstream and Δh for which velocity measurements have been

executed .............................................................................................................................................. 131

Table 16: Critical submergence ........................................................................................................... 141

List of symbols

Symbol Description / Explanation Unit

A Inner apex width [m]

A3 Area of section of flow at the outlet [m²]

AC Flow area at the control section [m²]

Ai Cross-sectional area of the culvert inlet [m²]

am Acceleration in model scale [m/s²]

ap Acceleration in prototype scale [m/s²]

Bi Inlet cycle cantilever length [m]

Bo Outlet cycle cantilever length [m]

bs Distance of the side wall to the centre of intake in the formula of

Gürbüzdal [m]

Cd Discharge coefficient [-]

ck Circulation constant in Knauss's formula [1/s]

Cw Discharge coefficient per unit width of the labyrinth weir [-]

D Outer apex width [m]

dc Maximum depth of water in the critical-flow section [m]

Di Diameter or characteristic dimension of the intake [m]

e Distance from the bottom of the channel to the intake invert [m]

Fm Forces in model scale [N]

Fp Forces in prototype scale [N]

Fr Froude number [-]

g Gravitational constant [m/s²]

h Water depth [m]

H0 Total upstream head for a specific discharge under free flow conditions [m]

h1 Piezo-metric water level at in front of the culvert [m]

h3 Piezo-metric water level at outlet of the culvert [m]

h4 Piezo-metric water level downstream of the culvert [m]

Hd Downstream head [m]

hd Piezo-metric head downstream [m]

he Head loss due to contraction at the inlet [m]

hf1-2 Head loss due to friction between the approach section and the inlet [m]

hf2-3 Head loss due to friction in the culvert barrel [m]

hi Depth of water above centreline of intake at face of intake [m]

hnj Difference in upstream water level between data point n and data point j [m]

hR Effective head in the Rehbock formula of flow over a linear weir [m]

HT Total upstream head measured relative to the weir crest [m]

j Data point j [-]

k Constant representing the gradient of the linear relationship in Knauss's

formula [-]

L Length of the culvert [m]

L1 Actual length of the side leg [m]

L2 Effective length of the side leg [m]

Lc Crest length [m]

Lc-cycle Centre line length for a single labyrinth weir cycle [m]

Le Effective weir length, as defined by Tullis et al. (1995) [m]

Lm Length or dimensional denotation corresponding to the model [m]

Lp Length or dimensional denotation corresponding to the prototype [m]

m Total number of data points [-]

n Data point n [-]

n Roughness coefficient of Manning [s/m1/3]

N Number of labyrinth cycles [-]

Nc Swirl number [-]

P Height of the wall of the weir [m]

Q Discharge [m³/s]

Qf Free flow discharge related with a driving head HT [m³/s]

Qi Discharge of intake [m³/s]

Qj Measured discharge corresponding to data point j [-]

Qn, Measured discharge corresponding to data point n [-]

Qn, theoretical Theoretical, smoothened discharge corresponding to data point n [-]

Qs Submerged discharge related with a driving head HT [m³/s]

Qsw Specific discharge [m³/s/m

]

r Radius of the vortex [m]

R Hydraulic radius of the culvert barrel [m]

Rcrest Weir crest radius [m]

Re Reynolds number [-]

S Submergence factor (Hd/HT) [-]

Sc Submergence above the top of the intake [m]

Si Slope of the inlet cycle [-]

So Slope of the outlet cycle [-]

tm Time in model scale [s]

tp Time in prototype scale [s]

tw Wall thickness at the crest [m]

V1 Mean velocity in the approach section [m/s]

V3 Velocity at the outlet of the culvert [m/s]

V∞ Uniform approach flow velocity [m/s]

Va Approach speed [m/s]

Vi Average velocity through the inlet [m/s]

Vm Velocity in model scale [m/s]

Vp Velocity in prototype scale [m/s]

Vt Tangential velocity of approach flow [m/s]

W Width of one cycle [m]

WC Width of the approach channel [m]

We Weber number [-]

Wi Width of the inlet [m]

wnj Weigh factor for data point j to calculate the theoretical discharge for

data point n [-]

Wo Width of the outlet [m]

WT Width of the labyrinth weir [m]

z Height of the culvert inlet [m]

zi Submergence depth at intake [m]

α Sidewall angle [°]

α 1 Velocity-head coefficient at the approach section [m]

α a Scale factor with regard to acceleration [-]

α F Scale factor with regard to forces [-]

α L Scale factor with regard to length or in general a value of dimension [-]

α t Scale factor with regard to time [-]

α v Scale factor with regard to velocity [-]

β Approach flow angle [°]

ε Cycle efficacy [-]

ε' Cycle efficiency [-]

εmean Mean error on the measurements [-]

εn Relative error corresponding to data point n [-]

ν Kinematic viscosity [m²/s]

νm Kinematic viscosity in model scale [m²/s]

νp Kinematic viscosity in prototype scale [m²/s]

ρ Density [kg/m³]

σ Surface tension [N/m]

Abbreviations

Abbreviation Explanation

B&C The beams and columns in the internal structure are present.

C The columns supporting the roof are present in the internal structure. The

beams supporting the roof are not present.

F Full model

LWh Labyrinth weir with a wall height of 3 m

noCul The structure is not integrated in a culvert.

noU There are no U-beams.

Raisedroof In comparison to the other configurations, the roof is raised by 1 m. The height

of the U-beam changes from 1 m to 2 m.

S Simple model

U There are U-beams on both sides of the structure.

UMeuse There is a U-beam on the side of the Common Meuse. There is no U-beam on

the side of the Heerenlaak pond.

Wh Linear weir with a wall height of 3 m

Wh/2 Linear weir with a wall height of 1.5 m

1

Chapter 1: Introduction

The subject of this master dissertation is the hydraulic study of a labyrinth weir integrated in a culvert.

This dissertation is situated within the context of removing the remaining bottlenecks on the Common

Meuse, more specifically at Heerenlaak, Belgium. To attain this, a hydraulic structure has been

designed by nv De Scheepvaart. This hydraulic structure features a labyrinth weir integrated in a

culvert.

The necessity of the hydraulic structure will be explained and a brief overview of the specifics of the

design of the labyrinth weir in a culvert will be given, followed by the objectives of this master

dissertation.

1. Hydraulic structure at Heerenlaak

1.1 Necessity of the structure

The Common Meuse is a part of the river Meuse situated on the border between Belgium and the

Netherlands under the supervision of nv De Scheepvaart. Nv De Scheepvaart is an autonomous, public

agency responsible for the maintenance, operation, management and commercialization of the Albert

Canal, the Campine Canals, the Scheldt-Rhine River connection and the Common Meuse.

Nowadays the dikes and structures on the Common Meuse are designed for a discharge up to 3000

m³/s. The discharge is expected to increase to more than 4000 m³/s in the future. To cope with this

increased discharge, measures have to be taken. One of these measures concerns the area of

Heerenlaak, which is discussed below.

1.2 Heerenlaak

Heerenlaak is a recreational pond, situated between two consecutive bends of the Common Meuse

(see Figure 1). Heerenlaak is also the subject of a project concerning the removal of the bottlenecks on

the Common Meuse. This project consists of two modifications, among which the construction of a

hydraulic structure, which is the subject of this dissertation.

The first modification to the current situation is the relocation of the downstream connection between

the Heerenlaak area and the Common Meuse. The reason for this relocation is to avoid unwanted

sedimentation which takes place nowadays, since the current connection is located between two river

2

bends. By relocating the connection, the outflow will be directed more parallel to the Meuse, instead

of rather perpendicular to it. The repositioning of the connection is shown in Figure 1.

Figure 1: Indication of the Heerenlaak-area (adapted from Bing Maps)

The second modification, situated more upstream, is the construction of a structure which allows the

entrance of water from the Common Meuse to the Heerenlaak area. Through the hydraulic structure,

a flow of approximately 300 m³/s should be discharged from the Meuse into the Heerenlaak area and

from the Heerenlaak pond through the relocated connection back into the Meuse. This should result

in a lower discharge through the Common Meuse near the bend and therefore a lower water level.

The conceptual design of the hydraulic structure has been made by ir. H. Gielen (nv De Scheepvaart).

A plan view of the structure is shown in Figure 2. The design features a labyrinth weir integrated in a

culvert. A labyrinth weir can be seen as a linear weir folded in plan-view. By doing so, a higher discharge

can be dealt with for the same upstream water level or the same discharge for a lower upstream water

level, in comparison to a linear weir.

Further details of the proposed design can be found throughout this report or in Appendix A.

Heerenlaak

Position of the current

connection

Position of the relocated

connection

Position of the future hydraulic

structure

3

Figure 2: Plan view of the proposed hydraulic structure

2. Objectives

The main objective of this dissertation, is to verify by means of a scale model study how much discharge

can pass through the hydraulic structure proposed by ir. H. Gielen. This knowledge will allow nv De

Scheepvaart to make a well substantiated estimation of the required number of labyrinth weir cycles

in the hydraulic structure, in order to safeguard the Common Meuse and its river banks.

Besides the assessment of the maximal discharge, other objectives are pursued as well:

(1) Gain in-depth knowledge about labyrinth weirs, culverts and labyrinth weirs integrated in

culverts through a literature review.

(2) Verify the stage-discharge or Q-h-relation for the future hydraulic structure deduced from a

desk-top study by FHR (Flanders Hydraulic Research; Vercruysse et al., 2013). This verification

is done by performing a scale model study of the proposed design.

Axis of the road

Meuse

Heerenlaak

4

(3) Make a comparative scale model study of the performance of the proposed design with a

variety of other hydraulic structures in order to acquire insight into the stage-discharge

relation of the proposed design.

(4) Compare the abovementioned experimentally obtained results with theoretical formulas from

literature and try to explain the correspondence and differences between those.

(5) Try to optimize the geometry of the proposed design were possible and formulate

recommendations for further research.

5

Chapter 2: Discussion of the design

This chapter will elaborate on the specifics (dimensions and T.A.W.-levels1) of the proposed design.

How the relevant dimensions and levels have been obtained will be explained and the boundary

conditions of Heerenlaak will be discussed as well. The aim of this chapter is to increase the insight of

the reader in the future hydraulic structure and the Heerenlaak area. The theoretical regimes, which

have been discerned in the FHR report concerning the labyrinth weir in a culvert, are given as well. To

conclude, a table with an overview of important dimensions and T.A.W.-levels is given.

1. Conceptual design of the labyrinth weir in a culvert

As can be seen from Figure 3 and Figure 4, the proposed design consists of a labyrinth weir integrated

into a culvert. In the figures two cycles of a labyrinth weir are shown, but to reach the required flow

rate of 300 m³/s, more cycles may be needed. One can argue whether the cycles are triangular or

trapezoidal in plan shape, since the columns supporting the culvert roof have a certain width.

Figure 3: Front view of the labyrinth weir in a culvert (Side of the Meuse)

1 T.A.W. is the chart datum used in Belgium. It roughly corresponds to an average low water level at Ostend (situated along the Belgian North Sea shore).

6

Figure 4: Plan view of the labyrinth weir in a culvert

Figure 5: Longitudinal section of the labyrinth weir in a culvert

Axis of the road

Meuse

Heerenlaak

1 cycle

Meuse

Sheetpiles Spillway

Heerenlaak pond

7

1.1 Bottom slab

The bottom slab has a length of 22 m and a width of 16 m. The lowest point of the labyrinth weir will

be constructed at a height of 23.2 m T.A.W., which corresponds to a discharge of 10 m³/s in the river

Meuse at Maaseik, in order to avoid the need for drainage during the construction of the structure.

The thickness of the floor slab is 0.5 m. Since the walls of the weir have a height of 3 m, the crest of

the weir is at a level of 26.7 m T.A.W..

1.2 Inlet and outlet section

The inlet section at the side of the Common Meuse consists out of two rectangular openings, each

having a width of 5 m and a height of 3 m, making the total area of the inlet section 30 m².

Once the water has flown through the inlet section, it has to pass over the crest of the labyrinth weir.

The flow area above the crest of one cycle consists out of 2 rectangles having a length of 14.7 m and a

height of 1 m. Thus the available flow area above the crest of one cycle is 29.4 m² or almost double

the inlet section of one cycle. As a result, the velocities in the flow area above the labyrinth weir are

about half of the velocities in the inlet section.

The soffit of the inlet section and the crest of the labyrinth weir are at equal elevation (26.7 m T.A.W.).

This implies that, in order to pass through the structure, the water has to flow first under the soffit of

the inlet, which consists of a U-shaped beam, and then over the crest of the labyrinth weir. The purpose

of this is to prevent the ingress of floating debris from the Meuse into the Heerenlaak pond.

The outlet section consists out of 3 openings. One central opening, having a width of 5 m and a height

of 3 m and two openings on the side of the structure, each having a width of 2.5 m and a height of 3

m. Thus the area of the in- and outlet section is equal.

1.3 Position of the columns

The columns in the design, meant to support the roof of the culvert, have a square cross section with

the length of one side chosen equal to 0.4 m. They support three horizontal beams, having a square

cross section with a side of 0.4 m, placed perpendicular to the direction of flow. The position of the

columns is chosen in such a way that they are symmetrical with respect to the axis of the service road

on top of the dike. Their main purpose is to provide support for the service road on top of the hydraulic

structure. The twelve columns are indicated with blue circles in Figure 4.

8

A second aspect which has been taken into account for the positioning of the columns is the length of

the walls between each column. This distance should be limited to make sure that the heavy and long

prefabricated panels can still be transported by trucks towards the construction site. For the proposed

design this distance is maximum 5.2 m.

The columns are believed to act as breakers providing aeration of the nappe falling over the crest of

the weir.

1.4 Angle

The angle of the labyrinth walls with the longitudinal axis of the structure is 8°. This is illustrated in

Figure 6.

Figure 6: Illustration of the labyrinth weir angle

2. Boundary conditions

2.1 Analysis of water levels

The water level upstream of the labyrinth weir is one of the major factors influencing the discharge

through the structure. This upstream water level depends on the discharge flowing through the Meuse

upstream of the Heerenlaak area.

8 °

9

The water level downstream of the hydraulic structure can also have an impact when it exceeds the

level of the crest of the weir (i.e. 26.7 m T.A.W.) and is discussed further on. This downstream water

level equals the water level in the Heerenlaak pond.

The Hydrological Information Centre (HIC, a subdivision of Flanders Hydraulics Research, Antwerp,

Belgium) collects data on water levels of the navigable rivers. Based on these data and on a study

carried out by Arcadis, a brief analysis of the water levels upstream and downstream of the Heerenlaak

area is given in Vercruysse et al. (2013).

Figure 7: Water level in the Meuse and the Heerenlaak pond in function of the discharge

through the Meuse near Maaseik (Vercruysse et al., 2013)

Figure 7 consists of data compiled by the HIC during the period from 10/01/2008 to 01/07/2013 and it

shows the water level in the Meuse (at km 52.7), the water level in the Heerenlaak pond (in the centre

of the pond) and the difference between these two water levels.

From Figure 7 it follows that the difference between the water level upstream and downstream of the

(future) labyrinth weir remains more or less constant around a value of about 2 m, though it increases

somewhat for higher discharges. This will influence the discharge through the structure and is one of

the most important boundary conditions.

Water level Meuse

Water level Heerenlaak

Dif

fere

nce

up

/do

wn

stre

am

wa

ter

lev

el

[m]

Wa

ter

lev

el

[m

TA

W]

Discharge through the Meuse [m³/s]

Difference

10

Note that (for a given discharge through the Meuse) the scatter of the water level in the Meuse is less

than for the water level in the Heerenlaak pond. This is caused by the damping capacity of the pond of

100 ha which has to be filled or emptied every time the water level in the Meuse rises or lowers. The

maximum water level measured in Maaseik during this period is 31.2 m T.A.W..

Figure 8: Water level in the Meuse upstream of the labyrinth weir in function of the discharge

through the Meuse near Maaseik (Vercruysse et al., 2013)

The graph shown in Figure 8 is based on a study of Arcadis. Arcadis made a numerical modelling

analysis studying the impact of different modifications on the water level in the Common Meuse. The

graph shows the water level in the Meuse, upstream of the (future) hydraulic structure, as a function

of the discharge through the Meuse near Maaseik. The different curves represent:

- HIC 2008-2012: The water level in function of the discharge in Maaseik based on the data of

the HIC

- Arcadis – HS: The current situation based on the study of Arcadis

- Arcadis – AO: The current situation with autonomous development

- Arcadis – VKA_HS: The preferential situation: the water level with the labyrinth weir in a

culvert and relocated connection, based on the current situation

Wa

ter

lev

el

[m T

AW

]

Discharge through the Meuse [m³/s]

11

- Arcadis – VKA_AO: The preferential situation: the water level with the labyrinth weir in a

culvert and relocated connection, with autonomous development

The same graph has been made for the water level near the relocated connection of the Heerenlaak

area and the downstream part of the Common Meuse.

Figure 9: Water level in the Meuse downstream of the Heerenlaak pond in function of

the discharge through the Meuse near Maaseik (Vercruysse et al., 2013)

From Figure 8 and Figure 9 it can be concluded that the preferential situation, with the labyrinth weir

in place and the relocated connection, leads to lower water levels upstream of the weir and

downstream of the pond. However, the differences with the current situation are limited. Based upon

the relation between the water level in the Meuse near Maaseik ( km 52.7) and upstream of the

labyrinth weir (km 53.0), the data near Maaseik is converted into water levels upstream of the weir.

These are shown in Figure 10. Note that the difference of the water level just upstream of the weir and

the water level near Maaseik (km 52.7) is very limited with a maximal difference of 0.09 m.

Wa

ter

lev

el

[m T

AW

]

Discharge through the Meuse [m³/s]

12

Figure 10: Water level upstream of the labyrinth weir in function of the discharge

through the Meuse near Maaseik (Vercruysse et al., 2013)

Compiling the data from these graphs (HIC-data), the overflow height with reference to the crest height

of the weir (+ 26.7 m T.A.W.) can be found in function of the number of days. This is shown in Figure

11 and Table 1. From the graph and the table, it can be concluded that the labyrinth weir will work

during 19.2 days per year (water level higher than 26.7 m T.A.W.). During 63% of these 19.2 days (12.1

days), the water remains under the level of the ceiling of the weir (27.7 m T.A.W.). During 7.2 days, the

water level is higher than the level of the ceiling.

Discharge through the Meuse [m³/s]

Wa

ter

lev

el

[m T

AW

]

13

Figure 11: Over flow height in function of the occurrence in days per year (Vercruysse et al., 2013)

Table 1: Over flow heights with corresponding water level, discharge and occurrence (Vercruysse et al., 2013)

Over flow height [m] Water level [m TAW] Discharge [m³/s] Occurrence [days/year]

0.0-0.5 26.7 - 27.2 735 - 869 7.1

0.5-1.0 27.2 - 27.7 869 - 1012 5

1.0-1.5 27.7 - 28.2 1012 - 1167 2.6

1.5-2.0 28.2 - 28.7 1167 - 1310 1.9

2.0-2.5 28.7 - 29.2 1310 - 1470 0.8

2.5-3.0 29.2 - 29.7 1470 - 1660 0.9

3.0-3.5 29.7 - 30.2 1660 - 1850 0.4

3.5-4.0 30.2 - 30.7 1850 - 2040 0.2

4.0-4.3 30.7 - 31.0 2040 - 2180 0.4

The discharges corresponding to a water level of the Heerenlaak pond equal to the crest height and

the ceiling of the labyrinth weir in a culvert are given in Table 2. A minimal and maximal discharge are

given because of the water storage capacity of the pond which causes a certain lag when comparing

the water level of the Meuse and the Heerenlaak pond. Construction of the labyrinth weir will reduce

this lag, making the minimal discharges more representative.

Occ

urr

en

ce [

da

ys/

ye

ar

]

Over flow height [m]

14

Table 2: Discharge through the Meuse near Maaseik in function of the water level in the Heerenlaak pond (Vercruysse et al., 2013)

Height of water level in the Heerenlaak

pond

Minimal discharge

[m³/s]

Maximal discharge

[m³/s]

Crest height: 26.70 m TAW 1170 1400

Ceiling level: 27.70 m TAW 1610 1770

2.2 Design adaption constraints

Several requirements which have to be taken into account while making changes to the original design

are listed below.

- The length and width of the foundation slab may vary, as long as the structure still fits within

the body of the dike. The same is applicable to the height of the structure. Thus a structure

with a shorter length can have a larger opening above the wall, since it will still fit within the

boundaries of the dike.

- As mentioned before, the position of the columns has to be chosen in such a way that the

forces from the road above may be dealt with in a safe way.

- The length of the prefabricated panels has to stay limited, in order to avoid the need for special

transport.

3. Q-h relation

The discharge through the construction depends on the upstream- and downstream water levels.

Considering these levels, three different situations are being discerned in the FHR-report concerning

the hydraulic structure at Heerenlaak (Vercruysse et al., 2013). These different regimes are:

- free flow over a weir

- inflow under pressure, free outflow

- in- and outflow under pressure

The formulas and their theoretical background will not be repeated here. The reader is being referred

to Vercruysse et al., 2013.

3.1 Weir

When the water level in the construction stays below the level of the top plate (i.e. the ceiling of the

culvert), the construction will act as a weir.

15

3.2 Inflow under pressure, free outflow

This situation occurs when the piezometric head in the construction is higher than the level of the

ceiling (which implies that the inflow is under pressure; this occurs at a water level of 28.0 m T.A.W.)

but the downstream level in the area of Heerenlaak is still below the crest height of the spillway.

3.3 In- and outflow under pressure

This situation occurs when, compared to the situation described in 3.2, the downstream water level

rises above the crest of the spillway (i.e. at 26.7 m T.A.W.).

Figure 12: Qh-relation as mentioned in the FHR-report (Vercruysse et al., 2013)

0

20

40

60

80

100

120

140

160

180

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

h upstream [ m T.A.W.]

Based upon simulations of submerged in- and outlet

Weir regime

Submerged inlet

Submerged inlet and outlet

16

4. Important dimensions and levels

An overview of some important dimensions and T.A.W.-levels is given in Table 3.

Table 3: Overview of important dimensions and T.A.W.-levels

Floor of the culvert 23.7 m T.A.W.

Invert of the U-beam 26.7 m T.A.W.

Crest of the weir 26.7 m T.A.W.

Ceiling of the culvert 27.7 m T.A.W.

Area of culvert inlet section 30 m²

Area of culvert outlet section 30 m²

Crest length of labyrinth weir 58.8 m

Available area above the crest 58.8 m²

17

Chapter 3: Literature Review

To get a full understanding of the proposed design for the hydraulic structure and the parameters

which may impact the flow through the structure, a thorough literature review is performed. This

literature review focusses on the main aspects deemed useful such as scaling, the hydraulic

characteristics of labyrinth weirs and flow through culverts. The behaviour of weirs under submerged

conditions and the presence of vortices and their effect on the discharge capacity are briefly discussed

as well.

1. Scaling

The behaviour of labyrinth weirs is influenced by many variables, which makes it very difficult to make

an accurate prediction of the discharge capacity of a proposed design. This explains why for many

projects a scale model is tested in a laboratory preceding the start of the construction process. The

theory of similitude permits to scale the characteristics of flow from prototype to model.

1.1 Types of similitude

There exist three types of similitude, namely geometric similitude, kinematic and dynamic similitude.

Geometric similitude implies that the length ratios of the prototype and the model are equal. Also the

different angles in the model are equal to those of the prototype. A such, the model has the same

shape as the prototype, while the dimensions are scaled proportionally.

With

is a scale factor with regard to length or in general a value of dimension (subscript ‘L’) [-]

L is the length or a dimensional denotation, where subscript ‘m’ and ‘p’ stand for model and

prototype respectively [m]

When 2 models are kinematically similar, the ratio of the prototype and model velocities is equal.

Consequently, the time ratio and length ratio are equal:

and

18

Hence,

and

In other words, the flow conditions should be the same. Dynamic similitude indicates similitude of

forces. The ratio of forces at similar locations of the model and prototype should be a constant value

in dynamically similar systems. The following scale factors will determine a dynamically similar scale

model:

The forces acting on a hydraulic structure or scale model can be generated by pressure, gravity,

viscosity or surface tension. Giving the variety of these forces, perfect dynamic similitude is not

possible, for example because of the viscosity of the fluids. Therefore the dynamic similitude of the

dominant forces must be ensured. This is done by scaling based upon the laws of similarity (or

dimensionless numbers).

The most important dimensionless numbers regarding free-surface flow and applied to the structure

at Heerenlaak are the Froude number, the Reynolds number and the Weber number.

The Froude number is defined as the ratio of inertia forces to the gravitational forces:

Where

is the Froude number [-]

V is the velocity [m/s]

g is the gravitational acceleration, i.e. 9.81 m/s²

L is the characteristic length [m]

19

The law of Froude is most often used in systems with free-surface flow, when gravity is the

most dominant force. Scaling according to Froude’s law is done as follows:

à à

The Reynolds number is defined as the ratio of inertial forces to the viscous forces:

Where,

is the Reynolds number [-]

is the kinematic viscosity of the fluid [m²/s]

Reynolds law is most often used for flow under pressure or where the viscosity of the fluid has

a non-negligible influence. When scaling is done with respect to Reynolds law, the velocity can

be found:

à à

The Weber number is defined as the ratio between surface tension and velocity.

Where,

is the Weber number [-]

is the density of the fluid [kg/m³]

is the surface tension [N/m]

Weber’s law is to be applied when the surface tension is a significant factor in the hydraulic

process, which occurs when a water-air interface is present (e.g. vortices). However, in open

channel flow this is rarely the case (except for capillary waves).

1.2 Scale effects

In order to have similitude between two systems with a free surface, the Reynolds number and the

Froude number should be equal in both systems. Because the ratios of the viscosities and the densities

20

of the fluids in the two systems are usually equal to 1, it is impossible to have a model that is perfectly

dynamically similar. These ratios are usually 1 because the fluids are the same in the prototype as well

as in the model, namely water. Therefore, the most dominant mechanism is modelled, implying the

gravity effects of the free surface flow (Froude), while the Reynolds number will differ.

When the dimensionless parameters between the model and the prototype are not equal, the

performance of the scale model might be different than that of the prototype leading to discrepancies

in the results. These deviations are known as scale effects (Webber, 1979). Scale effects can be

negligible, depending on the relative values of the differing dimensionless numbers. However, thought

should be given to these distortions to keep them negligible.

Avoidance of significant scale effects is usually done by use of limiting criteria (Heller, 2011). These

criteria define a range of force ratios which a scale model must satisfy, so that the effects of scaling

are negligible with respect to the parameter or phenomenon being researched. In the same manner,

limiting scale size criteria can be applied to avoid significant scale effects. These limiting criteria and

limiting scale size criteria are the result of experimental tests or theoretical analysis.

For example, by considering a perfect fluid (viscous forces are zero), the equality of the Reynolds

number is not required anymore. The only parameter that has to be equal is the Froude number. This

consideration is only valid in case the viscosity forces are small, compared to the inertial forces, i.e.

when the Reynolds number is high enough. Hence, scale effects should be a minor influence when the

Reynolds number is above a certain limitation.

When air transport takes place in the model, scale effects will have a larger impact, because dynamic

similarity is impossible for geometrically similar models (Chanson, 2009). Chanson established that

since there are too many relevant dimensionless parameters when air transport takes place. Again,

keeping in mind certain limits considering the Weber and Reynolds number, these scale effects can be

minimized. Pfister and Chanson (2012) suggest that for high-speed air-water two-phase flows, scaled

by use of the Froude similitude, the necessary limitations are either or .

Heller (2011) assembled a table containing the limiting criteria and limiting scale size criteria leading

to moderate (not necessary negligible) scale effects, from which the criteria applicable to the structure

at Heerenlaak are shown in Table 4.

21

Table 4: Limiting criteria to avoid significant scale effects in various hydraulic flow phenomena (Heller, 2011)

Investigation Phenomenon Rule of thumb Reference

Air-entraining free vortex

at horizontal intake Flow conditions

and

Anwar el al.

(1978)

Broad-crested weir Discharge coefficient Overfall height ≥ 0.07 m Hager (1994)

Sharp-crested weir Lower nappe profile Overfall height ≥ 0.045

m

Ghetti and

D’Alpaos (1977)

Spillway

Amount of air

entrainment from

aerator

Rutschmann

(1988)

Stepped spillway Flow velocity profile air–

water mixture Scale ≥ 1 : 15 Boes (2000)

In the table above, following notations are used:

is the discharge of intake [m³/s]

is the submergence depth at intake [m]

is kinematic viscosity of water [m²/s]

is the density of water [kg/m³]

is the cross-sectional area of intake [m²]

is the surface tension between air and water [N/m]

h is the water depth [m]

22

2. Linear Weirs

A weir or spillway is a structure which allows the passage of water over it. Weirs are built for several

purposes such as measuring the discharge, increasing the water level, releasing the excess flood water

of storage basins… Based upon the shape of the weir, several types can be discerned ( sharp crested

weir, broad crested weir, overflow spillway) (Berlamont, 2003).

Figure 13: Sharp crested weir (Berlamont, s.d.)

The formula below gives the discharge over a sharp crested weir.

Where

Q is the discharge over the hydraulic structure [m³/s]

Cd is the discharge coefficient [-]

Lc is the crest length [m]

g is the gravitational constant [m/s²]

HT is the total upstream head [m]

This formula is derived from the formula proposed by Weissbach by assuming that the approach speed

Va of the flow is small and the velocity head becomes negligible when compared to HT. Other

assumptions made when deriving this formula are a uniform pressure distribution above the crest,

negligible head losses, the contraction of the flow above the weir crest ... (De Mulder, 2015). These

assumptions are not always fulfilled. Therefore a discharge coefficient is introduced.

The afore mentioned formula is often simplified by replacing HT by h, the upstream water level, leading

to Poleni’s formula:

23

3. Labyrinth Weirs

3.1 General concept

A labyrinth weir is a linear weir folded in plan view in a repetitive manner. By doing so, a higher total

crest length for a given overall spillway width is obtained. This allows the passage of a higher discharge

for a given total upstream head and total overall width or the passage of the same discharge for a

lower head. This can be seen from the equation giving the discharge of a linear weir, mentioned above.

Labyrinth weirs are particularly advantageous when the available width and the flood surcharge space

(i.e. the available space above the crest of the weir, which can be limited due to the presence of e.g. a

bridge) are limited and large discharges must be passed. (Lux and Hinchliff, 1985)

Another advantage of labyrinth weirs, besides the substantial increase in crest length, is the economic

cost of construction when compared to the standard weir. A disadvantage is the disturbed three-

dimensional flow at each discontinuity of the weir axis and the interference of the jets of adjacent

crests which reduce somewhat the performance of the labyrinth weir (Ouamane, 2013).

A common application of labyrinth weirs is the rehabilitation of an existing spillway when the capacity

has to be increased (Delleur, 2013). This increase in capacity can be required by an increase in

precipitation rate when compared to the precipitation rate anticipated during the design of the

structure or by a governmental desire for a design capable of dealing with floods with a higher return

period. Another application is the use of labyrinth weirs as energy dissipators, applied to control water

quality by aerating or de-aerating the flow (Falvey, 2003). Blanc and Lempérière (2001) advise the use

of a labyrinth weir for specific discharges less than 50 m³/(s·m). For higher specific discharges, the

labyrinth weir requires high walls, which imply a greater wall thickness and greater reinforcement.

The discharge of a labyrinth weir depends on many geometric variables, which are discussed below.

Also other, non-geometric variables play a role when determining the QH-relation of a labyrinth weir.

Tullis et al. (1995) adopted the afore mentioned equation for linear weirs to describe the QH-relation

of labyrinth weirs. This means that the capacity of a labyrinth weir is a function of the crest coefficient

Cd, the crest length Lc and the total head HT. Another equation which is also commonly used is given

below:

24

In this equation Cw stands for the discharge coefficient per unit width of the labyrinth weir. WT is the

overall width of the labyrinth weir, as can be seen in Figure 14. Sometimes the factor 2/3 is not included

in the formula and is taken into account in the value of Cw. Other formulae have been developed in the

past as well (Lux and Hinchliff (1985), Lux (1984)) but will not be mentioned here.

3.2 Variables

3.2.1 Crest Length Lc

As can be seen from Poleni’s formula, the discharge is proportional to the crest length. Thus, based on

this formula, an increase in crest length would lead to a proportional increase in discharge for a given

total upstream head. The total crest length can be calculated as follows (Delleur, 2003):

Where

L1 is the actual length of the side leg [m]

A is the inner apex width [m]

D is the outer apex width [m]

These variables are also explained in Figure 14.

Figure 14: A 4-cycle labyrinth weir with an indication of the geometric variables (adapted from Tullis, Amanian and

Waldron, 1995)

25

In the simplified design method, developed by Tullis et al. (1995), the total weir length is replaced by

an effective weir length Le. This is a more physical based approach to take into account for apex

influences on discharge efficiency rather than the “black box mixing” of all influences in the discharge

coefficient, which will be discussed below. The effective weir length is given by the following formula,

where L2 stands for the effective length of the side leg, as can be seen in Figure 14 (Schleiss, 2011).

Seamons (2014) reported that the effective weir length Le does not completely account for all

efficiency losses due to nappe interference and therefore recommends the use of the total crest length

Lc. This is consistent with the recommendation by Crookston and Tullis (2013). The losses due to nappe

interference are taken into account by the Cd-coefficient when using Lc.

3.2.2 Discharge coefficient Cd

Cd is a dimensionless discharge coefficient, influenced by weir geometry, flow conditions and aeration

conditions of the nappe. There are four different aeration conditions which can be discerned for the

nappe: clinging, aerated, partially aerated and drowned (Crookston and Tullis, 2011). These aeration

conditions will be discussed further on. The Cd value takes into account the effects of nappe collisions,

submergence and the assumptions mentioned when deriving the formula for Q. The values for Cd are

usually presented in terms of HT/P with P being the height of the wall of the weir. The value for Cd is

always smaller than 1.

3.2.3 Sidewall angle α

The sidewall angle α is 90° for a linear weir. When the sidewall angle is 0°, the walls are parallel with

the flow direction. The smaller the sidewall angle, the larger the developed crest length and the larger

the maximum discharge. However, the afore mentioned discharge coefficient Cd decreases with

decreasing sidewall angle, yet the increase in crest length compensates for the reduction in discharge

coefficient (Crookston and Tullis, 2011). According to Tullis et al. (1995) a labyrinth weir can increase

the discharge Q by 3 to 4 times.

For linear weirs the streamlines are perpendicular to the crest and two-dimensional. For labyrinth weir,

the streamlines in the nappe are almost perpendicular to the crest, whereas at the free water surface

the streamlines are directed in the downstream direction. For a decrease in angle between the crests,

there is an increase of the interference of the jets from adjacent crests (Khode and Tembhurkar, 2010).

26

3.2.4 Cycle efficiency ε’

A useful variable to combine the effects of the increase in crest length and the decrease in discharge

coefficient for decreasing sidewall angles, is the cycle efficiency. This concept was developed by

Willmore (2004). This variable is given by the following formula:

Where Lc-cycle stands for the centreline length for a single labyrinth weir cycle and W is the width of a

single labyrinth weir cycle, as can be seen in Figure 14.

The cycle efficiency is a useful design tool because it facilitates the comparison of hydraulic

performance of several acceptable spillway designs against other significant spillway factors, such as

construction costs associated with increasing or decreasing the weir length and apron size (Crookston

and Tullis, 2011).

Figure 15: Cycle efficiency vs. HT/P for half-round labyrinth weirs (Crookston,2010)

Figure 16: Cycle efficiency vs. HT/P for quarter round labyrinth weirs (Crookston,2010)

27

From Figure 15 and Figure 16 it can be seen that ε’ increases as α decreases and that the benefits of

smaller α angles decrease with increasing HT/P. When considering only discharge capacity, it seems

beneficial to select a small sidewall angle. No sidewall angles smaller than 6° are tested but probably

there is a limiting value below which the cycle efficiency begins to decrease.

Another variable, closely related to the cycle efficiency ε’ is the efficacy ε, given by the following

equation:

The efficacy is thus the cycle efficiency divided by the discharge coefficient of the linear weir. The

efficacy is a useful tool to compare the hydraulic performance of a labyrinth weir to that of a linear

weir. Results obtained by Crookston (2010), shown in Figure 17, exhibit an increasing trend in efficacy

ε with decreasing values of α. However, due to the requirement of linear weir data (Cd90°), which

complicates the procedure, it is advised to use the cycle efficiency rather than the efficacy when

optimizing labyrinth weirs.

Figure 17: Efficacy ε vs. sidewall angle α for quarter round trapezoidal weirs (Crookston,2010)

3.2.5 Number of cycles N

The larger the number of cycles, the more nappe interference will occur, which will reduce the

efficiency of the structure due to a relative decrease in the effective length of the weir crest. The nappe

collision also depends on the nappe aeration condition, which will be discussed further on. When

28

maintaining a constant length, the spillway footprint can be reduced by increasing the number of

cycles. However, a 4-cycle labyrinth will be more efficient than an 8-cycle labyrinth of equal length due

to the increase in the number of apexes and consequently a reduction in the length of weir crest due

to the higher amount of colliding nappes according to Crookston (2010). This is illustrated in Figure 18.

Figure 18: Nappe interference and cycle number for an aerated nappe at low HT/P (Crookston,2010)

However, Kozák and Sváb (1961) concluded that a larger number of small cycles is more efficient and

economical than a labyrinth weir of equivalent length composed of fewer cycles. It is important to note

that this study was conducted for small operating heads where discharge capacity is not significantly

reduced by sidewall angle and nappe interference. Waldron (1994) concluded that Cd is independent

of N, for the data tested (α = 12°).

3.2.6 Shape of the cycles

The cycles can have different shapes in plan view: rectangular, triangular or trapezoidal. A trapezoidal

or rectangular shape would be beneficial for ease of construction to provide a minimum required

workspace and would also minimize nappe interference and local submergence effects. A triangular

shape allows for larger crest lengths when comparing to a rectangular shaped labyrinth weir with the

same width (Schleiss, 2011).

Ouamane (2013) reported that the rectangular shape can be as effective as the trapezoidal shape and

is even more effective for relative heads lower than 0.5. Blancher, Montarros and Laugier (2010)

concluded the same with numerical models: the trapezoidal-shaped labyrinth is more efficient in terms

of specific discharge Qsw (i.e. discharge per unit width) for higher upstream heads thanks to its reduced

29

sensitivity to downstream submergence while the rectangular-shaped cycles are more efficient for

lower heads due to the longer total crest length.

Figure 19: General classifications of labyrinth weirs: triangular (A), trapezoidal (B) and rectangular (C) (Crookston,2010)

The proposed design for Heerenlaak consists out of trapezoidal cycles.

3.2.7 Headwater ratio HT/P

In general, an increasing driving head causes a decrease in discharge efficiency, quantified by the

discharge coefficient, with the exception of smaller HT/P values (Amanian, 1987). Both Hay & Taylor

(1970) and Lux (1989) recommend an upper limit for HT/P based upon the reduction in discharge

coefficient for increasing headwater ratios. Tullis et al. (1995) recommend an upper limit of 0.9, but

this was solely based upon the limit of the experimental results. Further research for higher headwater

ratios is required according to Crookston (2010). For the structure at Heerenlaak, headwater ratio will

exceed the recommended value of 0.9 when there is a high water level in the Meuse.

3.2.8 Vertical aspect ratio W/P

The vertical aspect ratio, also referred to as cycle width ratio, is the ratio of the width of one cycle of

the labyrinth (denoted by W) to the height of the walls, which is denoted by P. Lux (1984) and Tullis

(1995) both recommend a minimum aspect ratio of 2 to 3. Hay and Taylor (1970) showed that the

aspect ratio has no significant effect if it is greater than 2. For this value of the vertical aspect ratio the

negative effects of nappe interference on the discharge efficiency are avoided (Seamons, 2014).

Magalhães and Lorena (1989) recommended vertical aspect ratios greater than 2.5. Lux (1989) also

found from his experiments that the discharge coefficient decreased as W/P decreased. The proposed

30

design for the structure at Heerenlaak has an aspect ratio of 5/3, or 1.66 which is below the

recommended values.

3.2.9 Crest shape and wall thickness

A wide variety of crest shapes is available: sharp, flat, quarter-round, half-round, elliptical, truncated

ogee and WES crest shapes. Some of these crest shapes are presented in Figure 20.

Figure 20: Crest shapes (Crookston,2010)

Crookston and Tullis (2011) and Amanian (1987) noted higher Cd-values for the half-round (HR) crest-

shape when comparing to the quarter-round (QR) crest shape for HT/P < 0.4. The explanation given for

this is that a crest which is rounded on the downstream face helps the flow to stay attached (i.e.

clinging flow) to the weir wall, thus increasing discharge efficiency. For increasing values for HT/P the

difference between both crest shapes diminishes and becomes negligible when HT/P > 1. Willmore

(2004) concluded that the most hydraulically efficient crest shape from the ones depicted in Figure 20

was an ogee-type crest, with a leading radius of 1/3 tw and a trailing radius of 2/3 tw. The reason for

this is again that the geometry helps the nappe to cling to the downstream face of the weir at low

heads. He also stated that a half-round crest shape is more efficient than a quarter-round crest shape.

Blancher, Montarros and Laugier (2010) concluded, using numerical models, that an increase in wall

thickness leads to a decrease in specific discharge for Piano Key Weirs (PKW). Piano Key Weirs will be

briefly discussed further on.

Cicero and Delisle (2013) state, based on experimental testing that the efficiency of a PKW can be

increased by 10 to 20% using a QR or HR crest instead of a flat-topped shape.

31

Matthews (1963) studied the effects of curvature on weirs with a round-crest (i.e. QR, HR, ogee,…) and

concluded that weirs with a small radius of curvature would have a larger Cd than weirs with a large

radius of curvature, at a given head. An important ratio to take into account the effects of curvature is

the radius of curvature, given by HT/Rcrest, with Rcrest standing for the radius of the crest (i.e. tw/2, with

tw being the thickness of the weir wall). Most studies concerning the discharge coefficient for different

crest shapes include the effects of HT/Rcrest inherently on the physical models tested, i.e. the influence

of varying values for HT/Rcrest is taken into account in the Cd-coefficient (Crookston,2010).

For the future hydraulic structure at Heerenlaak, the proposed design consists of a flat crest.

3.2.10 Ratio Wi/Wo

The definition of the variables Wi and Wo can be seen from Figure 21. Wi stands for the width of the

inlet and Wo stands for the width of the outlet. Ben Saïd and Ouamane (2011) reported an increase in

labyrinth weir performance with an increase of the ratio Wi/Wo, although the number of tested

configurations was limited.

Figure 21: Indication of the variables Wi and Wo (adapted from Ben Saïd and Ouamane,2011)

32

The measured data can be seen in Figure 22. The difference between the models decreases with

increasing upstream head.

Figure 22: Variation of the discharge coefficient for different ratios of Wi/Wo and Lc-cycle/W =4 (adapted from Ben Saïd and

Ouamane,2011)

3.2.11 Labyrinth Weir Orientation, Placement and Cycle Configuration

Factors as the spillway orientation and placement, the inlet section and cycle configuration may

influence the flow capacity of a labyrinth spillway. Houston (1983) reported an increase in discharge

by 10.4 % for the Partially Projecting orientation when compared to the flush orientation for similar

entrance conditions and that the Normal orientation had a 3.5 % greater discharge than the Inverted

orientation. Crookston and Tullis (2011) compared a Normal and Inverse oriented labyrinth weir with

a sidewall angle of 6° and reported no change in hydraulic performance.

33

Figure 23: Orientations, placements and cycle configurations (Crookston and Tullis,2011)

In general, the discharge efficiency of the weir may be improved by orienting the cycles to the

approaching flow. Case studies by Babb (1976) and Houston (1983) reported that curved abutment

walls upstream of the labyrinth weir minimized the loss of efficiency caused by flow separation and

thus increase the capacity of the weir. Crookston (2010) stated that the relative increase in hydraulic

efficiency of the rounded abutment walls diminishes as N increases. The rounded inlet reduces flow

separation and turbulent flow over the crest when compared to projecting weirs. This leads to an

increase in nappe stability and an improved discharge efficiency (Christensen, 2012).

Ben Saïd and Ouamane (2011) reported a decrease in labyrinth weir performance (i.e. a decrease in

discharge coefficient) for a channel with contraction. This decrease in performance tends to increase

for increasing heads, as can be seen from Figure 27.

Blanc and Lempérière (2001) proposed a rounded front wall to improve the hydraulic performance of

the labyrinth weir. Ouamane (2013) reported an increase in performance of about 10 % when

comparing two models, one with a flat entrance and another with a profiled entrance. The explanation

for this is that the profiled shape facilitates the flow on each side of the front wall. The rounded shape

also eliminates the discontinuity points and thus reduces the disturbance effects at the top of the weir.

34

Figure 24: Labyrinth weir with a rounded front wall (left) and a flat wall (right) ( Ouamane, 2013)

Figure 25: Discharge coefficient according to the entrance shape of a labyrinth weir (adapted from Ouamane,2013)

Figure 26: Channel with and without lateral contraction ( Ben Saïd and Ouamane,2011)

35

Figure 27: Variation of the discharge coefficient for a model with and without lateral contraction (adapted from Ben Saïd

and Ouamane,2011)

A possible way of increasing the discharge capacity are arced labyrinth weir configurations. The cycles

of the labyrinth weir are now no longer following a straight axis, but are laying on a curved axis. They

are orienting the cycle to take advantage of the converging nature of the reservoir approach flow and

they further increase the weir crest length. The geometric layout of an arced labyrinth weir can be

seen in Figure 28.

Figure 28: Geometry of an arced labyrinth weir (Crookston,2010)

Figure 29 and Figure 30 clearly show an increase in discharge coefficient for the arced configuration.

36

Figure 29: Cd vs. HT/P for α =6° half-round trapezoidal labyrinth weir (Crookston, 2010)

Figure 30: Cd vs. HT/P for α =12° half-round trapezoidal labyrinth weir (Crookston, 2010)

This increased efficiency is attributed to the improved orientation of the cycles to the approaching

flow. However, local submergence limits the gains in discharge efficiency. Local submergence develops

sooner for arced labyrinth weirs because these geometries discharge more flow into the downstream

cycles and channel than a linear cycle configuration for a given HT (Crookston,2010). Local

submergence is discussed further on.

37

For most applications of a labyrinth weir, the approach flow is perpendicular to the weir axis. Dabling

(2014) conducted research on the discharge efficiency of a 4-cycle, 15° labyrinth weir with a

channelized approach flow and three different approach angles β (0°, 15° and 45°). He reported no

measurable loss in discharge efficiency for approach flow angles less than 15° and a decrease in

capacity of up to 10° for the 45° approach flow angle at the higher HT/P values. He also noted that at

low HT/P values there is little impact on hydraulic efficiency by the angled approach flow.

3.2.12 Aeration Conditions

As mentioned previously, there are four different aeration conditions: clinging, aerated, partially

aerated and drowned. However, different terms may be found in literature as well. Some labyrinth

weirs do not exhibit all aerations conditions. Aeration conditions are influenced by the crest shape, HT,

the momentum and trajectory of the flow passing over the crest, the depth and turbulence of flow

behind the nappe and the pressure behind the nappe (sub-atmospheric for non-vented or atmospheric

for vented nappes.) Some structures artificially aerate the nappe, creating a vented condition

(Crookston and Tullis, 2011). This is also the case for the proposed design: the columns act as breakers

and provide artificial aeration.

Figure 31: Aeration conditions for a half-round crest (Christensen,2012)

As HT increases, the nappe of a labyrinth weir will transition from clinging to aerated to partially

aerated and finally to a drowned condition. A clinging nappe refers to a nappe adhering to the

downstream face of the weir. An aerated nappe occurs when there is an air cavity behind the nappe.

An aerated nappe will transition to a partially aerated nappe when the air cavity behind the nappe

becomes unstable i.e. varies spatially and temporally. The behaviour of a partially aerated nappe can

be characterized as follows: the air cavity oscillates between labyrinth weir apexes, increasing or

decreasing the length of the sidewall that is aerated. An unstable air cavity causes fluctuating pressures

38

at the downstream face of the weir. A drowned nappe occurs for large values of HT/P and is

characterized by a large, thick nappe with no air cavity (Crookston, 2010).

Nappe interference occurs when two or more nappes collide. For labyrinth weirs this mainly happens

at the upstream apex and this may cause wakes downstream of the apex and standing waves. Nappe

interference reduces the local labyrinth weir discharge capacity (Crookston, 2010).

Increasing the upstream apex width by using trapezoidal or rectangular cycles instead of triangular

cycles may diminish the nappe interference and thus increase the discharge capacity. The downside of

increasing the apex width is a decrease of the overall crest length for a fixed channel width and a fixed

sidewall angle. Therefore increasing the apex width does not necessarily lead to an increase in

discharge capacity. Seamons (2014) reported that in general the reduction in nappe interference does

not outweigh the reduction in crest length. He states that the apex width should be as small as possible

while still maintaining the minimal space needed for construction.

Aeration conditions have a significant influence on the discharge capacity of a labyrinth weir.

Generally, a clinging nappe is more efficient than an aerated nappe. For increasing sidewall angles α

the inception of the drowned conditions begins at higher values of HT/P. Also the shape of the crest

has a large influence on the range of HT/P values for which a certain aeration conditions occurs

(Crookston, 2010).

3.2.13 Filling the alveoli

The alveolus is the volume located between the walls of a labyrinth weir. This is indicated in Figure 32.

A distinction is made between upstream or inlet alveoli and downstream or outlet alveoli. Filling of the

alveoli may be an effective way of reducing the construction costs of the weir. These are diminished

by reducing the height of the walls while maintaining the same height of the weir (Ben Saïd and

Ouamane, 2011). The reduction in free height of the walls allows to have hydrostatic pressure forces

only acting on the upper portion of the wall. This allows for a smaller wall thickness and less

reinforcement. However, the volume of concrete of the apron becomes larger (Ouamane, 2013).

Ben Saïd and Ouamane (2011) reported that filling ¼ of the length of the alveoli has no impact on the

discharge coefficient, regardless of the height of filling. When filling half the length of the alveoli and

for a filling height higher than P/3 the discharge starts to be affected, i.e. the discharge coefficient

starts to decrease.

39

Figure 32: Filling of the alveoli (adapted from Ben Saïd and Ouamane,2011)

Ouamane (2013) also reported that alveoli filling has no effect except for low heads. For heads HT/P >

2.5 no difference in hydraulic performance occurred for the weir with or without filling of the alveoli.

Another advantage of filling the alveoli is the dissipation of some energy, when the apron of the

downstream alveoli is designed as a stair step.

Willmore (2004) found the effects of an upstream ramp in trapezoidal labyrinth weirs to be negligible.

Figure 33: Rectangular labyrinth weir with a shaped entrance, partially filled alveoli and a stepped stair in the outlet key

(Ouamane, 2013)

40

3.3 Disadvantages

There are three main drawbacks for labyrinth weirs. A first disadvantage are the high reinforced

concrete quantities. A second downside is that the efficiency declines for high heads and high

discharges caused by the flow interference from the jets of adjacent crests. Labyrinth weirs also require

a massive basis. The recently developed Piano Key Weirs ( PKW, to be discussed further on) combine

the advantages of a traditional labyrinth weir with a reduced footprint (Lempérière, Vigny and

Ouamane, 2011).

Labyrinth weirs also cause a decrease in reservoir attenuation of flood waves and an increase in peak

outflows, caused by the increased hydraulic capacity. A solution for this problem is creating a staged

labyrinth weir. A staged weir is a weir for which different sections of the weir have different crest

levels.

3.4 Piano Key Weirs

Piano Key Weirs are a relatively new type of weir, which evolved from the traditional labyrinth weir. A

PKW is similar to a labyrinth weir since it consists out of a rectangular shape repeated in plan view. The

main difference is that the apexes are inclined, thus leading to a smaller footprint in comparison to a

traditional labyrinth weir. The discharge capacity of a PK weir depends on more variables than that of

a labyrinth weir. Some of the additional parameters are the slope of the inlet cycle Si, the slope of the

outlet cycle So, the inlet cycle cantilever length Bi, the outlet cycle cantilever length Bo and the height

of the parapet walls. These parapet walls are placed on the crest of the PK weir and transform the

upper part into a rectangular labyrinth weir. These walls help to increase the discharge capacity since

they improve the stream line pattern of the approaching flow and increase the outlet key volume

(Vermeulen et al., 2011).

41

Figure 34: View of a PK weir spillway of the Gloriettes Dam in France during Construction (Électricité de France)

3.5 Submergence effects

When the downstream water level is sufficiently low (i.e. lower than the crest of the weir, or more

precisely than the level positioned a critical water depth above the crest), the discharge over the weir

is independent of the downstream water level and the weir is said to operate in modular flow regime.

However, when the downstream water level exceeds the aforementioned level, the weir is said to be

submerged. For a submerged weir, the discharge is both a function of the upstream and the

downstream water level. This implies that the upstream water level (or head) increases for a given

discharge, or conversely that the discharge decreases for a given upstream head, relative to a free

discharge condition.

During the early days of the labyrinth weir, researchers assumed that the effect of submergence would

be much greater on labyrinth weirs than on linear weirs. Therefore labyrinth weirs were not designed

for submerged conditions (Tullis, Young and Chandler, 2006). Taylor (1968) disproved this assumption

and found that the effect of submergence on labyrinth weirs was less than for linear weirs. This was

later confirmed by Tullis, Young and Chandler (2006) and by Belaabed and Ouamane (2013).

3.5.1 Influence of submergence

Taylor (1968), Tullis et al. (2006) and Lopes et al. (2009) found that submersion has no impact on the

capacity of the structure until the downstream water level exceeds the weir crest. When the

42

downstream water level continues to increase and equals the upstream water level, the structure will

no longer work as a control structure.

3.5.2 Relationship by Villemonte

Villemonte (1947) developed a relationship describing the effects of submergence on the hydraulic

performance of rectangular weirs. He developed a flow reduction factor Qs/Qf for submerged sharp-

crested linear weirs as a function of a submergence ratio Hd/HT. Qs and Qf stand respectively for the

submerged and free-flow discharge rates associated with a driving head equal to HT. The equation

which Villemonte developed is as follows:

The exponent of 0.385 takes into account interaction effects and is determined by the method of

algebraic averages. Results of seven types of weirs tested by Villemonte have shown that the exponent

should be equal to 0.385 for a range of submergence practice from 0.00 to 0.90.

Taylor (1968) used the equation by Villemonte when comparing the performance of a submerged

linear weir to that of a submerged labyrinth weir. Falvey (2003) reported that Villemonte’s equation is

conservative in terms of capacity (head required to pass a given flow) for labyrinth weirs. Therefore he

recommended further research. Tullis, Young and Chandler (2005) conducted research on

submergence effects on three labyrinth weirs with differing geometries. They noted an average error

of 8.9 % and a maximum error of 22% in Villemonte’s equation for predicting submerged labyrinth weir

performance. They also reported a good agreement of Villemonte’s equation for linear weirs. A

dimensionless relationship between Hd/H0 and HT/H0 describing submerged labyrinth weir

performance was developed. H0 stands for the upstream head required for a fixed discharge in free-

flow conditions. This is shown in Figure 35. The submerged upstream head approaches the free-flow

head as the submergence level, Hd/H0, goes to zero and the tailwater depth approaches the head water

depth as the submergence levels increase. With a sufficient level of submergence, Hd will equal Hu and

the labyrinth weir will cease to function as a control.

43

Figure 35: Dimensionless relationship describing submerged labyrinth weir performance (Tullis, Young and Chandler,2006)

3.5.3 Local submergence

Local submergence occurs when the downstream water level locally exceeds the weir crest elevation.

Local submergence differs from the traditional submergence in that it does not necessarily encompass

the entire labyrinth weir. Local submergence is caused by the inflow exceeding the local outflow

capacity of the outlet cycle, resulting in a local increase in downstream water level. The local

submergence region develops downstream of the upstream apex and increases in size as the weir

discharge increases (Crookston, 2010). Local submergence occurs sooner (i.e. at lower HT/P values) for

smaller sidewall angles and can locally decrease the discharge efficiency (Belaabed and Ouamane,

2013).

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4. Culverts

Flow through the hydraulic structure can be compared with flow through a culvert when either the

inlet or the in- and outlet of the structure is drowned. Because of the presence of a labyrinth weir in

the hydraulic structure, this comparison is not so straightforward. Nevertheless, a good knowledge of

culverts is required to try and understand the different characteristics of the hydraulic structure. Hence

part of the literature review is devoted to flow through culverts.

4.1 Introduction

A culvert is a short channel or conduit placed through an embankment, dike, dam … Culverts are built

for different reasons and consequently have many different definitions. The most common definition

found in literature is that culverts are designed to transport water underneath embankments or

roadways. A culvert can also be used to restrict flow for upstream detention and/or reduce the

influence of flood waves downstream of the culvert, which would be the main objective in case of the

proposal for the hydraulic structure at Heerenlaak.

4.2 Terminology

A culvert consists out of three mains parts, namely the entrance or inlet, the barrel and the outlet. The

most common cross-sectional shapes of the barrel are circular (i.e. pipe) or rectangular (i.e box

culvert). Considering the structure at Heerenlaak, the main focus will be on rectangular culverts.

The invert is defined as the bottom of the barrel while the barrel roof is called the soffit or obvert.

Further important notions to be considered are the upstream water level (i.e. the headwater) and the

downstream water level (i.e. the tailwater).

4.3 Flow through a culvert

Flow phenomena through culverts are complex. Different flow regimes can be discerned based upon

the upstream and downstream flow conditions. The control section of the flow or terminal section can

be at the inlet or at the outlet and the governing parameters can change unpredictably, causing

relatively sudden rises in headwater.

When the type of flow is known, the well-known equations for orifice, weir, or pipe flow and backwater

profiles can be applied to determine the relationship between head and discharge (Blaisdell, 1966).

45

Modern culvert design nomographs and computer programs which are based on the theory and

experiments are also available.

Carter (1957) defined a classification system of 6 types of flow through culverts based on the location

of the control section and the relative heights of the headwater and tailwater surfaces. The main

characteristics of each type are shown in Table 5. The different types are differentiated according to

type of barrel flow, the location of the control section (upstream or downstream) and the main factor

influencing the discharge and headwater level (i.e. kind of control). For each type, discharge equations

have been defined based upon the continuity and energy equations. The explanation of the different

parameters is given in Figure 36.

Figure 36: Illustration of culvert flow, explaining the different parameters (Bodhaine, 1966)

Table 5: Summary of the different flow types and characteristics according to Carter (1957)

Flow

type

Type of

barrel flow

Location of

control

section

Kind of control Culvert

slope

I Partly Full Inlet Critical Depth Steep < 1.5 < 1 1

II Partly Full Outlet Critical Depth Mild < 1.5 < 1 1

III Partly Full Outlet Tailwater Mild < 1.5 > 1 1

IV Full Outlet Tailwater Any > 1 > 1

V Partly Full Inlet Entrance

geometry Any 1.5 1

VI Full Outlet Entrance and

barrel geometry Any 1.5 1

46

Types I and II are defined by flow at critical depth, which in case of type I occurs at the upstream part

of the culvert and in case of type II at the downstream end of the culvert. The critical depth, dc , is the

depth at the point of minimum specific energy for a given discharge and cross section. The position of

the critical depth section depends on the headwater elevation, the slope of the invert, and the

tailwater elevation. For types I and II to occur, the headwater elevation above the upstream invert

must be less than 1.5 times the diameter or height of the culvert, .

Figure 37: Type I flow, according to Carter (1957)

TYPE I: Type I flow is characterized by a critical depth section near the culvert entrance and

the culvert barrel flows partly full. For type I to occur, the slope of the culvert barrel, S0, must

be greater than the critical slope, Sp , and the tailwater elevation, , must be less than the

elevation of the water surface at the control section, . The discharge equation is

Where

is the discharge coefficient [-]

is the flow area at the control section, defined as [m]

g is the gravitational constant, defined as 9.81 m/s²

is the piezo-metric water level at position 1 [m]

z is the height of the culvert [m]

V1 is the mean velocity in the approach section [m/s]

is the velocity-head coefficient at the approach section [-]

is the maximum depth of water in the critical-flow section [m]

is the head loss due to friction between the approach section and the inlet [m]

47

Figure 38: Type II flow, according to Carter (1957)

TYPE II: The second type is characterized by a partly full flowing barrel with a critical depth

section at the culvert outlet. The slope of the culvert S0 is less the critical slope Sc and the

tailwater elevation does not exceed the elevation of the water surface at the control section

. The discharge equation remains the same as type I with an adaptation considering

the barrel friction loss.

Where

is the head loss due to friction in the culvert barrel, from location 2 to 3 on Figure 38

[m]

For types III and IV, critical depth does not occur in the culvert and the tailwater elevation controls the

headwater level for a given discharge. The culvert can flow partly full, if , which is

defined as type III. Type IV on the other hand, is characterized by both ends of the culvert being

completely submerged which is denoted as full flow through the barrel.

Figure 39: Type III flow, according to Carter (1957)

48

TYPE III: For type III to occur, the headwater-diameter ratio should be less than 1.5 and the

tailwater should exceed the elevation of critical depth at the control section (either at the inlet

or at the outlet), but the outlet must not be submerged. The culvert barrel flows partly full. It

is further assumed that equals . The discharge equation for this type of flow is

Where

is the area of the section of flow at the outlet (position 3) [m²]

is the piezo-metric head at location 3 [m]

Figure 40: Type IV flow, according to Carter (1957)

TYPE IV: Type IV is characterized by both the entrance as well as the outlet being submerged

as is shown Figure 40. The culvert flows full and the discharge can be computed directly from

the energy equation between sections 1 and 4. Leading to the following discharge equation:

And

With

is the area of the inlet of the culvert [m²]

is the piezo-metric head at position 4, indicated at Figure 40 [m]

is the head loss due to the contraction at the inlet [m]

49

V3 is the velocity at position 3, indicated at Figure 40 [m/s]

n is the roughness coefficient of Manning [ s / m1/3]

L is the culvert length [m]

is the hydraulic radius of the culvert barrel [m]

Types V and VI are defined as flow under high head (Bodhaine, 1968) and will occur if the tailwater is

below the soffit of the culvert at the outlet and the headwater is equal or higher than 1.5 times the

diameter, .

Figure 41: Type V flow, according to Carter (1957)

TYPE 5: In type V the headwater elevation is higher than 1.5 times the inlet diameter. The

water flows rapidly at the inlet and the tailwater elevation is below the soffit at the outlet. The

culvert barrel flows partly full and at a depth less than critical. The discharge equation is

Figure 42: Type VI flow, according to Carter (1957)

TYPE 6: In type VI the barrel of the culvert flows full, under pressure and with free outfall. The

headwater-diameter ratio exceeds 1.5 and the tailwater does not submerge the culvert outlet.

The discharge equation between sections 1 and 3, neglecting and , is

50

The difficulty in applying this formula is the necessity of determining , varying from a point

below the centre of the outlet to its top, even though the water surface is at the top of the

culvert. This variation in piezometric head is a function of the Froude number.

Hee (1969, see Chanson, 1995) and Henderson (1966) established that for free surface flow in the

barrel, the ratio of upstream specific energy to the barrel diameter (or barrel height) should be less

than 1.2. This has been experimentally confirmed by Chanson (1995a). According to Chow (1959), the

entrance will be submerged when the headwater is less than a certain critical value, namely 1.2 to 1.5

times the height of the culvert, depending on the entrance geometry, barrel characteristics, and

approach condition.

51

5. Vortices

5.1 Introduction

During the measurements performed on the scale model, swirling motion of water and the formation

of vortices were noticed at the intake of the labyrinth weir in a culvert. These vortices can have a

negative impact on the flow through the structure and the structure itself.

Vortices can be divided in two classes, free surface vortices and sub-surface vortices (Hydraulic

Institute, 1998). Since the flow through the labyrinth weir in a culvert only triggers free surface

vortices, the main focus will be directed to free surface vortices.

Vortices can also by classified according to the direction and position of the intake. This classification

was made by Knauss (1987) and is shown in Figure 43. For the proposed design, only the horizontal

intake will be considered.

Figure 43: Directional and structural classification of vortices (Knauss, 1987)

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5.2 Formation and causes

Swirls and vortices are formed by rotational motions of fluid regions. Hence they find their origins in

discontinuities in the flow pattern. These discontinuities cause swirling which can grow into vortices

when strong enough. Discontinuities leading to swirling are mostly found in the form of asymmetrical

flow areas. Knauss (1987) listed six different types of sources leading to rotational motion. These are

shown in Figure 44, where they are divided in rotational motion caused by symmetry (a) and caused

by a change in direction of the borderlines (b).

Figure 44: Sources of rotational motion according to Knauss (1987)

Durgin and Hecker (1978) defined the causes of vortices more generally in three fundamental types,

being:

- non-uniform approach flow to the intake due to geometric orientation

- the existence of velocity gradients

- obstructions near the intake

Figure 45: Three fundamental causes of vortex formation according to Durgin and Hecker, 1978

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The physical processes behind the formation of vortices are explained by Wu et al. (2006). They

attribute the compressing/expanding and the shearing process to be the two fundamental processes

behind fluid dynamics, such as vortex formation. Both processes are present when water flows through

an intake or in this case a submerged inlet.

The spinning motion is caused by shear stresses in the fluid. In ideal fluids with no viscosity, shear

stresses would force the different layers to slide over each other without any resistance. In real fluids,

viscosity is present which means that the fluid elements have some resistance against shearing stresses

putting the fluid elements into spinning motion.

The compression process is created by a sufficient amount of water above the intake, otherwise known

as submergence. This submergence provides enough pressure head to support the shearing process

and has thus a lower limit. However, higher submergence means the core length of the vortices is

extended, as a result the amount of circulation is larger and the amount of water required to be set in

a spinning motion to support the vortex structure is larger (Knauss, 1987). Hence, there exists a

submergence depth at which vortex formation starts and a submergence depth where the vortices

disappear.

The shape of the vortex is caused by the centripetal acceleration generating a drop of pressure in the

centre of the vortex. This pressure drop results in a local depression of the free surface. The magnitude

of the drop in the water surface depends on the equilibrium of gravity forces, centripetal acceleration

forces and surface tension, ranging from a dimple (strong circulation) to a vortex with a full air core

over the whole depth of submergence.

A dimple is a description of the appearance of the water surface, classified according to the Alden

Research Laboratory or ARL (Hecker, 1981). The ARL drafted a classification system of free surface

vortices to define the strength of different types of free surface vortices. The classification consists of

six stages which are shown in Figure 46.

This classification is based on visual observations. Classification of the intake vortices can also be

accomplished by measuring vortex related quantities, related to the strength of vorticity. Examples of

these quantities are the magnitude of swirl inside an inlet pipe, determination of the amount of

ingested air, changes in discharge coefficients and free surface velocities around the vortex core. Since

vortices are time dependent, fluctuate in strength and shift in position, the reliability of the

measurements can be low, the correlation between vortices and a selected parameter weak and the

selected parameters depend upon other parameters (Knauss, 1987).

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Figure 46: Free-surface vortex classification according to Alden Research Laboratory (Knauss, 1987)

5.3 Submergence

As explained before, there is a range of submergences in which vortices appear. This submergence is

one of the most determining factors in the creation of vortices. After the water rises above the intake,

vortices rapidly start to develop and they grow with increasing submergence until they reach a

maximum intensity. Afterwards, the intensity of the vorticity decreases again with increasing water

level. When the submergence increases even more, a critical submergence is reached.

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A considerable amount of research has been performed concerning this critical submergence. This

concept is defined by Jain et al. (1978) as the smallest depth at which strong and objectionable vortices

will not form anymore. Gordon (1970, cited from ASCE, 1995) defines it to be the submergence level

required to prevent air – entraining vortex formation. According to Yildirim and Kocabaş (1995) it is

“the value of submergence of the intake when air-entraining vortex just occurs”. For most research, it

is the threshold at which air-entraining vortices change into non air-entraining vortices. When studying

the critical submergence, attention must be paid to the definition of the different parameters, which

are determined by the researcher.

Several empirical and analytical formulas have been suggested to define the submergence at which

vortices appear. Only the main formulas will be discussed here. Gordon (1970, see Baykari, 2013)

explained the influencing aspects on the formation of vortices to be the geometry of the approach

flow to the intake, the velocity at the intake, the size of the intake and the submergence. He proposed

a formula which relates the submergence to the average velocity V through the inlet and the diameter

of the inlet. After transformation to SI-units, following formulas are obtained:

For symmetrical approach flow conditions:

For asymmetrical approach flow conditions:

In which

is the submergence above the top of the intake [m]

is the diameter of the intake [m]

is the average velocity through the inlet [m/s]

is the Froude number, defined as [-]

Gordon’s research was based on a study of 29 hydroelectric intakes. A disadvantage of Gordon’s

formula is that the parameters are not dimensionless thus it cannot be considered a universal

relationship for all intake designs (Rindels and Gulliver, 1983).

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Figure 47: Indication of the different parameters used by Gordon (ASCE, 1995)

The formula proposed by Knauss (1987, see ASCE, 1995) for the critical submergence is based on the

Froude number at the inlet and the direction of the intake (horizontal, vertical or inclined intake).

Where

k is a constant representing the gradient of the linear relationship [-]

is the depth of water above centerline of intake at face of intake [m]

is the diameter or characteristic dimension of the intake [m]

is the intake velocity [m/s]

Fr is the Froude number, defined as [-]

is the circulation constant, defined as [m²]

is the tangential velocity of approach flow [m/s]

r is the radius of vortex [m]

is the swirl number, defined as [-]

Knauss (1987) further recommended the minimum design submergences for well operating prototypes

with normal approach flow and proposed the curve shown in Figure 48. He recommends a

submergence depth of 1 up to 1.5 times the intake height/diameter for large size intakes, while for

medium and small size installations the following formula is proposed:

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With

is the depth of the water above the centre line of the intake [m]

is the Froude number, defined as [-]

Figure 48: Recommended submergence for intakes with proper approach flow conditions (Knauss, 1987)

More recent studies were done by Ahmad et al. (2008) concerning horizontal intakes. Ahmad et al.

performed an analytical and experimental study regarding critical submergence for a 90° horizontal

intake in an open channel flow. They found that the critical submergence depends on the (intake)

Froude number, ratio of intake velocity and channel velocity, Reynolds number and the Weber

number, with a more pronounced influence of the Froude number and the ratio of intake velocity and

channel velocity. Furthermore, they presented a predictor for the critical submergence when the

bottom clearance from intake to the bottom is equal to zero or half of the diameter, with satisfactory

results. The formulas for critical submergence are:

When the bottom clearance is zero (e = 0),

And when the bottom clearance is equal to half of the diameter (e = D/2),

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Where

e = the distance from the bottom of the channel to the intake invert [m]

= intake velocity [m/s]

= uniform approach flow velocity [m/s]

Gürbüzdal (2009) proposed a formula which included the Reynolds number based on experiments on

horizontal intakes to study the possible scale effects on the vortex formation. Another parameter of

influence incorporated in the proposed formula is the side wall clearance.

Where

= distance of the side wall to the centre of intake (symmetrical geometry) [m]

This formula is valid for

The bottom clearance in the experiments was zero (e = 0). Further observations concerning the side

wall clearance showed that the critical submergence becomes independent of the side wall clearance

when the ratio of the side wall clearance to the intake diameter ( / ) exceeds a value of 6.

5.4 Scale effects

Surface tension and the velocity and viscosity of the fluids are of importance for the research

concerning vortex formation. Consequently the Froude, Reynolds and Weber numbers come into play

when model studies are performed. Unfortunately, the laws of similitude cannot be satisfied

simultaneously, which can lead to discrepancies between the results of the scale model and the

prototype (see also paragraph 1, concerning scaling), also known as scale effects (Webber, 1979).

Hence, Froude and Reynolds similitude are impossible to fulfil simultaneously. The Froude number is

found to be the most influencing factor in all experiments conducted up to now and Froude similitude

is customary to be used as basis.

A lot of research has been done regarding the relative significance of the different parameters in the

vortex formation process. Surface tension and viscosity are parameters which are investigated

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extensively. From these studies, it was concluded that surface tension and viscosity effects are

negligible if the Reynolds and Weber number attain certain values.

Dagget and Keulegan (1974) demonstrated that surface tension does not influence the

formation of vortices when the Reynolds number is in the range from to

(no tests outside this region were performed). This conclusion was based upon a

comparison of different fluids (glycerine-water and oil mixtures) in a cylindrical tank.

Research done by Jain et al. (1978, cited in Yildirim and Kocabaş, 1995) showed that surface

tension has no influence on the formation of vortices when the Weber number is in the range

from to (with ). This research was based on vertical inlets.

For horizontal and vertical intakes in a long flume, surface tension does not affect the

formation of vortices when the Weber number is larger than (with ,

h being the submergence based upon the centre line of the intake), according to Anwar (1981,

cited in Rindels and Gulliver, 1983).

Further research done by Anwar (1978, cited in Rindels and Gulliver, 1983) on horizontal

intakes in a flume showed that viscous effects had no influence on the flow of a free surface,

if the Reynolds number is higher than (with and h defined as the

submergence from the centre line of the intake ).

According to Odgaard (1986), the criterion for neglecting the surface tension is a Weber

number exceeding 720. The criterion for neglecting the viscous effects is a Reynolds number

exceeding . Odgaard’s research is based on a free-surface, air-core vortex model.

Padmanabhan and Hecker (1984) found above a Weber number of 600 and a Reynolds number

of no significant scale effects when operating according to Froude similitude,

meaning that the surface tension and viscosity effects are negligible. These experiments were

conducted on a sump pump.

Summarizing the past research and experiments, surface tension can be neglected in case of the

Heerenlaak scale model when the Weber number is higher than 720 and the

viscosity can be neglected if the Reynolds number ( ) is higher than . This

prescribed Reynolds number increases with increasing Froude number. (Gürbüzdal, 2009)

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5.5 Problems

The formation of vortices is related with the risk of air entrainment at the inlet. This might be a source

of different problems which could impact the life time of the structure. According to Knauss (1987),

air-entraining vortices can be the cause of two hydraulic problems at intakes:

- Unfavourable vibrations

- Transport of trash through the closed channel

The most serious and relevant problems caused by vortices concerning the hydraulic structure at

Heerenlaak will be:

- Increase of head loss

- Reduction of intake discharge:

- Ingress of trash or debris

- Air entrainment

5.6 Prevention

The prevention of vortex formation is usually based upon providing enough submergence at the intake

and improvement of the approach flow conditions (avoid separation of flow, induced by abrupt

changes in the geometry of the boundaries, removal of obstacles …). Structural measures can be taken

such as lowering the Froude number by enlarging the inlet area. Unfortunately, these options are

difficult to apply in case of the Heerenlaak structure. Another solution to prevent the formation of

vortices is to use anti-vortex devices.

Gulliver and Rindels (1983) compiled a list of available anti-vortex devices, based upon the works of

Denny and Young (1957) and Ziegler (1976). The first anti-vortex device is a floating raft shown in

Figure 49. The intention of the raft is to disrupt the angular momentum at the water surface.

Experiments done by Ziegler (1976) found that the floating rafts disrupted the converging circular

water surface currents normally present in an organized vortex. In a developed vortex, the motion of

the water surface currents is a spiralling inflow toward the centre of the vortex. The raft prevented the

converging portion of this motion, but a very substantial circular motion still remained as swirl beneath

the raft.

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Figure 49: Floating raft (Gulliver and Rindels, 1983)

Ziegler (1976) performed tests on both floating as well as submerged rafts. He found that both rafts

prevented formation of air-entraining vortices. However, a raft submerged only by a small distance

below the water surface reacted on the upper portion of a vortex with a similar result to a floating raft,

while a raft submerged a substantial distance below the water surface reacted on the lower portion of

the vortex. The submerged rafts were perceived to be slightly better than the floating rafts. Ziegler

found that there was an optimum depth of submergence at which the rafts were most efficient.

Figure 50: Submerged raft (Gulliver and Rindels, 1983)

Trashracks can also be used to disrupt the angular momentum of the flow and can be used as anti-

vortex devices. According to Ziegler’s research, vortex formation is dependent on the size of the

trashrack. However, for the proposed hydraulic structure at Heerenlaak, thrashracks are not desirable

because of trash congestion at the inlet and the accompanying maintenance.

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6. Optimisation based on literature review and scale model testing

Based upon the literature, some recommendations and (possible) improvements of the proposed

design can be made. These improvements mainly aim at increasing the maximum discharge of the

hydraulic structure.

As mentioned in the literature review, rectangular-shaped labyrinth weirs are more effective for low

relative heads (HT/P<0.5) due to their longer total crest length, while trapezoidal-shaped labyrinth

weirs are more efficient for higher relative heads due to their reduced sensitivity to downstream

submergence (Ouamane, 2013, Schleiss, 2011 and Blancher, Montarros and Laugier, 2010). Assuming

an upstream water level of 32.0 m T.A.W., which corresponds to a discharge of ± 3000 m³/s through

the Meuse near Maaseik (see Figure 8), a relative head of 1.77, when neglecting the velocity head, is

obtained. Since the maximum discharge of the hydraulic structure is more essential to the design than

the Qh-relation, it is thus not deemed useful to adapt the design and replace the trapezoidal cycles by

rectangular cycles.

Increasing the inner and outer apex width of the current design will reduce the interference losses.

However, Seamons (2014) states that the reduction in interference losses does not outweigh the

reduction in crest length. Therefore no changes to the shape of the structure are recommended.

No consistent advice regarding the impact of a higher / smaller amount of cycles for an identical

spillway footprint can be given (Crookston, 2012, Waldron, 1994 and Kozák and Sváb, 1961).

Decreasing the amount of cycles while maintaining the same value for the overall crest length by

increasing the size of the cycles (by using the same scale factor for the direction perpendicular and

parallel to the axis of the road) is not an option at Heerenlaak, since the structure would then no longer

fit within the body of the existing levee.

Creating a larger amount of small cycles (while maintaining the same value for the overall crest length)

would increase the interference losses and would further decrease the vertical aspect ratio W/P, which

has a value of 1.66 in the proposed design whereas a value larger than 2 is recommended (Lux, 1984

and Tullis et al., 1995). However, this would offer the opportunity to increase the available area above

the weir. Due to the shorter length of the bottom slab, the height above the weir (which is limited by

the dimensions of the dike body) may be larger.

The crest of the labyrinth weir in the proposed design is of the flat crest type. Using a quarter-round,

half-round or an ogee type crest can increase the capacity significantly (Crookston and Tullis, 2011,

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Amanian, 1987, Willmore, 2004). However, the influence of the crest shapes manifests itself especially

at low heads, and disappears for higher heads. Therefore, replacing the flat crest of the proposed

design will lead to a better performance at low heads, but will most likely have little to no influence

for high heads during drowned conditions. Since the maximum discharge is the main interest for

making design adaptations, it is not beneficial to replace the crest in order to obtain a higher maximum

discharge.

Filling of the up- and downstream alveoli is a possible design adaptation worth considering. Filling the

alveoli up to a certain extent (i.e. limited height and length) has only an effect for low heads (Ben Saïd

and Ouamane, 2011) but, as has been mentioned before, this is not the main area of interest for the

discussion of the proposed design. Therefore, if filling the alveoli would lead to a cost reduction of the

hydraulic structure, this option is worth considering. For being an economical solution, the reduction

in cost of the walls should outweigh the cost for filling the alveoli. The cost for constructing the walls

declines since lower hydrostatic pressures act on the walls, allowing a smaller thickness. This implies

that at a certain location prefabricated panels with a smaller thickness can be used. A smaller thickness

of the walls will also lead to a higher capacity of the structure in comparison to structures with thicker

walls. Filling the alveoli also may facilitate the construction process. The prefabricated panels for the

walls may be attached to the alveoli.

Ir. H. Gielen has expressed the concern for the dissipation of energy of the discharge through the

hydraulic structure when it enters the area of Heerenlaak. Constructing the downstream alveoli as a

stair step, as shown in Figure 33Figure 32, might serve this purpose. This stair step reduces the cost of

constructing measures to dissipate energy downstream of the structure. Thus this saving in cost may

also be taken into account when considering to fill the alveoli or not.

Several measures can be taken to facilitate the flow towards the structure. Research showed that

rounding the upstream front wall may increase the performance of the structure with almost 10 %.

However, this increase diminishes and becomes negligible for higher heads. Rounding the external

edges of the upstream U-beam is another measure which may facilitate the flow. Facilitating the flow

may also imply that floating debris goes through the inlet section and enters the area of Heerenlaak.

Using an arced or projecting configuration is not an option at Heerenlaak, since these configurations

would then no longer fit within the body of the existing dike.

64

Dabling (2014) mentioned that for increasing approach flow angles, the capacity of the structure

declines and that this decline is larger for higher values of HT/P. Considering that the future hydraulic

structure will be located in a bend of the Meuse and taking into account the results obtained by

Dabling, the change in hydraulic capacity of the approach conditions at Heerenlaak requires attention.

There are several possible design adaptations which will increase the discharge of the structure at a

given head. However, the influence of most of these adaptations diminishes for higher heads, and thus

the adaptations become useless. Nevertheless, the use of filled alveoli has quite some advantages,

being the dissipation of energy, a smaller wall thickness, a faster and more straightforward

construction process and possibly a cheaper cost of the hydraulic structure and the measures to

dissipate energy downstream.

From analysing the culvert regimes and corresponding formulas, enhancing the discharge through the

structure can be done by enlarging the inlet area, increasing the head over the structure and reducing

the hydraulic losses through the culvert. These losses can be reduced by rounding the edges of the U-

beams or the beams inside the structure, by preventing the formation of eddies (e.g. removing void

areas where eddies can form, by use of an inclined corner between the U-beam and culvert soffit, as

illustrated in Figure 51). Other possibilities in reducing hydraulic losses exist as well.

Figure 51: Illustration of the inclined corners between the U-beam and the culvert soffit

The formation of vortices at the inlet section is also a source of hydraulic losses, which has to be

avoided. These vortices can also lead to unwanted vibrations and ingress of trash through the

structure. Several possibilities exist to reduce the formation of vortices. The geometry and approach

conditions are of importance, because they can create rotational motion which enhances formation of

vortices. Furthermore the use of trashracks or submerged / floating rafts can be implemented to

reduce this formation of vortices. However, for the structure at Heerenlaak, this might not be an

option.

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Chapter 4: Experimental set-up and test procedure

In this chapter an overview will be given of the test facilities which were used to perform the

experimental measurements. Consequently, the measurement devices and testing procedure will be

discussed, followed by an overview and description of the configurations which were tested.

1. Test facilities

1.1 Current Flume

The scale model study is performed at the Hydraulics Laboratory of Ghent University, in a current flume

with a length of approximately 15 m, a width of ca. 0.70 m and a height of 0.68 m. A picture of the

current flume is shown in Figure 52. To provide the discharge through the flume, three different pumps

are available with a combined maximal flow rate of 500 l/s.

Figure 52: Current flume used during the experiments

The discharge through the flume is measured by means of a calibrated sharp-crested, rectangular weir.

The height of the water above the weir can be determined using a hooked gage submerged in a stilling

66

tube connected to the reservoir. To do so, the needle of the gage needs to be positioned near the

water surface until the tip of the needle touches the free surface. Since the needle approaches the

water surface from underneath the free surface, a higher accuracy is reached because surface tension

is eliminated. The accuracy of the gage is about 0.3 mm. However, given the formula of the calibrated

weir, a measuring error of mm results in discharge error of only 1.1%.

Figure 53: Needle of the gage to measure the discharge

The calibration curve of the current flume is known and is depicted in Figure 54.

Figure 54: Qh-relation of the calibrated weir

0

20

40

60

80

100

120

140

160

180

200

0 50 100 150 200 250

Q [

l/s]

h-h0 [mm]

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Figure 55: Stilling tube with hooked gage (left) and the device to adjust the height of the needle (right)

The water level downstream of the flume can be controlled by means of an inclined rectangular weir.

The crest level of this weir can be changed by adjusting the teeth of the cogwheel connected to the

weir.

Figure 56: Cogwheel to adjust the height of the downstream weir

1.2 Position of the scale model

The respective scale models are simply mounted in the (downstream half of) the flume, with the

longitudinal axis of the structure in-line with the flume axis. As a consequence, the scaled-down

structure is subjected to a relatively uniform approach flow. The rationale behind this approach is that

in the scale model only two cycles of the labyrinth weir are integrated in the culvert, whereas in the

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prototype a multiple of these cycles will be needed to attain the target discharge. Hence, the results

of this scale model study will be more representative for the inner cycles of the construction (which

have indeed an approach flow aligned with the structure) rather than for the outer cycles. The latter

might somewhat suffer from side effects, dependent on the detailed geometry of the diversion

between the river Meuse and the construction. Yet, nv de Scheepvaart is willing to shape this diversion

in order to have approach flow conditions which are as uniform as possible.

1.3 Honeycombs

Due to the presence of another scale model (related to another master thesis) in the upstream half of

the flume, honeycombs have been mounted at a certain distance upstream of the hydraulic structure,

in order to calm down the flow and the water level disturbances and to make the flow more uniform.

No flow streamliners are used on the downstream side of the structure since they might influence the

discharge capacity of the structure. The use of these streamliners is illustrated in Figure 57 and Figure

58. Streamliners are also used in the reservoir upstream of the calibrated weir, thus allowing to

determine the discharge more accurately.

Figure 57: Honeycombs

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Figure 58: Comparison of the water surface on both sides of the honeycombs

(right: highly fluctuating levels at the upstream side; left: calmed down free surface at the downstream side)

2. Measuring equipment

The equipment used to measure water levels and velocity profiles will be described below.

2.1.1 Ultrasonic water level sensors

By using ultrasonic water level sensors (Maxbotix LV-MaxSonar-EZ4) positioned above the water

surface, the distance of the latter relative to the sensor is registered. The sensor emits high frequency

sound waves which reflect when hitting a surface. This echo is then registered by the receiver of the

sensor. By measuring the time that it takes between emitting a signal and receiving, the ultrasonic

sensor can determine the distance between the sensor and the surface. The sensor then averages the

measured distances over a time period of 1 second and emits this signal wirelessly to a receiver

connected to a laptop.

Figure 59: Ultrasonic distance sensor

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There are two sensors used in the experiments: one located at the upstream side of the structure, at

a distance of 1.52 m with respect to the inlet section and one at the downstream side of the structure,

at a distance of 1.58 m with respect to the outlet section of the hydraulic structure.

Figure 60: Indication of the position of the ultrasonic water level sensors

2.1.2 Electromagnetic current meter

For the determination of velocity profiles, an electromagnetic current meter is used, more specific the

Valeport model 801 (see Appendix B). This device offers velocity measurements at a high precision

(±0.5% of reading plus 5 mm/s) over a velocity range from -5 m/s to 5 m/s.

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Figure 61: The Valeport model 801 electromagnetic current meter (source: http://www.valeport.co.uk)

2.2 Accuracy of surface measurements

Because of water surface fluctuations (+/- 5 mm), caused by ripples and waves, the accuracy of the

water level measurements is limited. The accuracy depends on the discharge, since for high discharges

the fluctuations of the surface are much larger than for low flow discharges. The ultrasonic sensors

allow determining the distance between the sensor and the water surface with an accuracy of 1 mm,

but because of the method of measuring the distance the real accuracy is 3 to 4 mm.

3. Scale Model

In the course of this scale model study experiments have been performed on two different scale

models, scaled with the same scale factor but having different features.

3.1 Full model

In the model that will be further referred to as the “Full model”, experimental measurements are

performed on an exact scale model of the design made by nv De Scheepvaart. Pictures of this model

and its position in the current flume can be seen in Figure 62 and Figure 63. A geometrical scale factor

of 18 is chosen such that the model will occupy almost the complete width of the current flume.

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Figure 62: Front view (left) and top view (right) of the hydraulic structure in the current flume

Figure 63: Front view of the scale model

73

The model is made out of Medium-Density Fibreboard (MDF). Poly Methyl Methacrylate (PMMA) is

used to create the ceiling of the structure. The PMMA-ceiling has the advantage that it is transparent,

allowing to observe the flow patterns through the ceiling of the hydraulic structure. The columns and

beams in the scale-model are made out of stainless steel (Figure 65). Under the bottom slab a rubber

sealing is applied to mitigate the flow of water under the structure as much as possible. Also between

the side walls of the model and the flume, there is a rubber sealing to prevent the seepage of water

(Figure 64). The model is finished with grey paint (Figures 12 to 14).

Figure 64: Rubber sealing to prevent seepage

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Figure 65: Model before (left) and after (right) completion with a view through the PMMA-ceiling

3.2 Simple model

A second model was made to allow testing on a wider variety of hydraulic structures, that were

deemed useful for comparison purposes. This second model, that will be further referred to as the

“Simple model”, offers the possibility of testing a linear weir and a labyrinth weir. Since the simple

model has a removable ceiling, these weirs can be tested as such or integrated in a culvert.

An additional advantage of the Simple model is that the U-shaped beams (U-beams), indicated in black

on Figure 66 and also shown in Figure 67, can be removed (contrary to what is the case in the Full scale

model). This allows investigating the possible effect of these U-beams on the discharge through the

hydraulic structure. Moreover, the ceiling of the culvert in the Simple model can be positioned at

different heights (contrary to what is the case in the Full scale model).

The hydraulic structure is again scaled with a factor 18. In this second model, no beams and columns

for supporting the roof of the culvert are present, which can be seen in Figure 66.

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Figure 66: Longitudinal cross-section of the Simple model

Figure 67: Indication of the removable U-beams

3.3 Scaling

As mentioned previously, the Froude number for the model and prototype remains the same (Froude

scaling). Considering this, the scaled velocities can be calculated.

The flow rate in the scale model can be calculated as:

Hence the flow rate in the scale model is a factor smaller than in the prototype at Heerenlaak.

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4. Test procedure

4.1 Stage-discharge relation

Before each testing session (i.e. once or twice a working day), the sensors are recalibrated when no

discharge flows through the flume. The water surface is then a level surface used as reference to

determine the position of the sensors relative to the base plate of the model. The height of the water

surface relative to the top of the base slab of the hydraulic structure is measured manually for both

the upstream and the downstream sensor and the distance between the sensor and the water surface

is denoted for the upstream and downstream sensor. In that way, the position of the sensor relative

to the top of the base slab is known. These values are then converted to an upstream and downstream

water level at prototype scale.

Subsequently a certain flow rate is set and once the water levels upstream and downstream of the

model are stabilized, the corresponding distances measured by the ultrasonic distance sensors are

denoted. Because of the fluctuating water level, the values given by the sensors fluctuate as well. An

average value is denoted. By use of the weir downstream of the flume, the downstream water level

can be raised in order to attempt to reach the target difference in water level between the river Meuse

and the Heerenlaak pond.

4.2 Velocity measurements

Velocity measurements have been executed during two separate testing sessions on the

F_LWh_U_B&C-configuration. Each session had some differences in testing procedure. The specifics

of each testing session will be explained further on. For all measurements, the Valeport Model 801

electromagnetic current meter has been used. A brief description of this device can be found in

paragraph 2.1.2 or in Appendix B. During a period of 1 minute, a velocity measurement was done every

second, after which the fixed average and the standard deviation are calculated by the electromagnetic

current meter.

4.2.1 Testing procedure I

Measurements upstream of the scale model were executed for two different data points (Q, hupstream,

Δh). For the first data point, velocity measurements are performed at three transverse locations (i.e.

perpendicular to the flow direction): in the middle of the current flume (indicated with A in Figure 68),

77

close to the side of the current flume (C in Figure 68) and in the middle of the inlet section of a single

cycle (B in Figure 68), i.e. in between the two previous locations.

Figure 68: Indication of the transverse locations of the velocity measurements (adapted from Vercruysse et al., 2013)

For all locations, measurements are executed at different heights above the bottom of the current

flume in order to cover the complete section of the flume, both in height and width of the flume. The

height of the current meter is varied by stepwise moving it up or down on a steel bar. The final height

of the current meter is measured with a yardstick. The afore described testing method is executed for

two different longitudinal locations in front of the inlet section of the hydraulic structure (i.e. at 5 m

and 10 m upstream of the inlet of the hydraulic structure).

For the second data point, velocity measurements are only carried out at location B, i.e. in the middle

of the inlet section of a single cycle. The height of the device and its longitudinal position are again

being varied.

Figure 69: Electromagnetic current meter on the metal bar during the measurements

78

4.2.2 Testing procedure II

During the second testing session, measurements are carried out for a fixed height of the measuring

device, while the longitudinal position of the current meter is varied. The transverse position

corresponds to location B as indicated in Figure 68. Thus graphs showing the measured time-average

velocity for different distances relative to the inlet of the structure are obtained. This is done for two

separate data points, namely the peak discharge and the discharge at the dip of the third regime. The

fixed height of the device is at ± 1.2 m (prototype) below the upstream water level. This implies that

the height of the current meter depends on the data point being measured.

4.3 Visualization of the flow pattern using colouring dye

The colouring dye is injected at a certain distance below the water surface using a catheter. The

catheter has a length of 5 ¼ inches, i.e. 13.335 cm and an opening of 14 gauge, i.e. 1.98 mm. The

injection takes place in front of the middle of the inlet section at a distance of about 5 m upstream of

the structure. The colouring dye used in the experiments is Patent Blue V (also known as Food Blue 5

or Sulphan Blue). The injected volume of colouring dye is roughly between 5 and 10 mm³ for each test.

Figure 70: catheter used for the colouring dye experiments

During the injection of the dye, the flow pattern is being filmed. Using the image processing package

Fiji Is Just ImageJ these records are being processed to obtain a visualization of the flow pattern.

5. Tested configurations of the Full and Simple models

Besides the model of the design made by nv De Scheepvaart (i.e. the Full model), other configurations

were developed and tested in the Simple model. The latter configurations were tested in order to

elucidate the different factors influencing the Qh-relation of the hydraulic structure as well as to find

possible improvements of the designed structure. The results of these tests will be discussed further

79

on. All these configurations are obtained by modifying the two models (Full and Simple) which have

been discussed previously. Throughout this document, these configurations are referred to by well-

chosen abbreviations. These abbreviations are explained in Table 6 and the corresponding

configurations will be explained in this section.

Table 6: Explanation of the used abbreviations

Abbreviation Explanation

F Full model

S Simple model

LWh Labyrinth weir with a wall height of 3 m

Wh Linear weir with a wall height of 3 m

Wh/2 Linear weir with a wall height of 1.5 m

noCul The structure is not integrated in a culvert.

U There are U-beams on both sides of the structure.

noU There are no U-beams.

UMeuse There is a U-beam on the side of the Common Meuse. There is no U-beam on

the side of the Heerenlaak pond.

Raisedroof In comparison to the other configurations, the roof is raised by 1 m. The

height of the U-beam changes from 1 m to 2 m.

B&C The beams and columns in the internal structure are present.

C The columns supporting the roof are present in the internal structure. The

beams supporting the roof are not present.

5.1 F_LWh_U_B&C

This configuration concerns the Full model as designed by nv de Scheepvaart. This model features a

Labyrinth Weir in a culvert, the roof of which is supported by Beams and Columns and which has U-

beams both on the side of Heerenlaak and on the side of the Common Meuse.

80

Figure 71: F_LWh_U_B&C

5.2 F_LWh_U_C

In comparison to the previous model the beams supporting the roof are removed from the structure,

but the columns are still present. This implies enlarging the available area through which water can

flow inside the structure. The area increases with 3.27 %, in comparison to F_LWh_U_B&C (30.36 m²

vs. 29.4 m², both figures being on prototype scale). The removal of the three beams might also alter

the flow patterns in the structure.

Figure 72: Indication of the removal of the supporting beams in F_LWh_U_C

Meuse Heerenlaak pond

81

Figure 73: View inside the labyrinth weir without supporting beams

5.3 F_LWh_U

In comparison to F_LWH_U_B&C, both the beams and columns are removed from the structure. This

further increases the available area inside the structure in comparison with F_LWh_U_C. The available

area is now 31.8 m², i.e. an increase of 8 % compared to F_LWH_U_B&C. This configuration is tested

to investigate the influence of further enlarging the available section inside the structure. From a pure

practical point of view, this configuration is not relevant since columns are adopted in the proposed

design to support the roof, limit the length of the prefabricated wall elements and provide breaking of

the nappe.

Figure 74: Indication of the removed parts in F_LWh_U

Meuse Heerenlaak pond

82

Figure 75: Indication of the removal of columns and beams by comparing F_LWh_U_B&C (left) with F_LWh_U (right)

5.4 S_LWh_noCul

This configuration is tested on the Simple model. It is a labyrinth weir without a roof on top of it. The

labyrinth weir has the same wall height of 3 m as the labyrinth weir in the Full model. Pictures of this

configuration can be seen in Figure 76 and Figure 77.

Figure 76: Front view of S_LWh_noCul (upstream)

83

Figure 77: Top view of S_LWh_noCul

5.5 S_LWh_U

This configuration is tested on the Simple model. It features a labyrinth weir with a height of 3 m,

integrated in a culvert with U-beams. This configuration should be identical to F_LWh_U, although

there are some minor differences in dimensions between the Full and Simple models, which will be

discussed further on (see paragraph 5.12). This configuration is shown in Figure 79.

Figure 78: Longitudinal cross-section of the Simple model (S_LWh_U)

Figure 79: Front view of S_LWh_U

84

5.6 S_LWh_noU

This configuration is tested on the Simple model. It features a labyrinth weir with a height of 3 m,

integrated in a culvert without U-beams. This increases the inlet and outlet section from 30 m² to 41

m². This is an increase of 36.6 %.

Figure 80: Front view of S_LWh_noU from the side of Heerenlaak (downstream)

Figure 81: Indication of the Simple model with the removed U-beams (S_LWh_noU)

5.7 S_LWh_UMeuse

In comparison to S_LWh_U, the U-beam at the downstream side of the structure, i.e. at the side of

Heerenlaak pond, is removed. This implies that there is only a U-beam at the side of the Common

Meuse. This is indicated in Figure 82. The upstream U-beam needs to prevent the ingress of floating

debris from the Meuse into the Heerenlaak pond, but the downstream U-beam is believed to have no

such function.

85

Figure 82: Indication of the removed U-beam in S_LWh_UMeuse

Figure 83: View on downstream side of S_LWh_UMeuse with removed U-beam

5.8 S_LWh_U_Raisedroof

This configuration features a labyrinth weir with a height of 3 m in a culvert in the Simple model. The

roof of the structure (i.e. the culvert ceiling) is raised over a distance of 1 m. The soffit of the U-beams,

however, remains at the crest level of the weir, i.e. at + 26.7 m T.A.W.. Due to heightening the roof of

the structure, the height of the U-beam increases to 2 m. A cross section is shown in Figure 85. By

heightening the roof of the structure, the available area over which the water can flow in the structure

doubles to 134 m². However, the area of the inlet and outlet sections remains unchanged and is still

equal to 30 m².

Note that this configuration does not fit within the dike with its current dimensions. This can be solved

by reducing the length of the structure, which will lead to a different crest length over the weir, a

different angle between the walls of the labyrinth and the longitudinal axis, … However, to make a

well-based comparison, the length of this configuration remains the same as for the other

configurations. As a result, this configuration has no direct practical use for the hydraulic structure at

Upstream

(Meuse)

Downstream

(Heerenlaak)

86

Heerenlaak. Nevertheless, testing this configuration might provide additional insight with regard to

improvements.

Figure 84: Front view of S_LWh_U_Raisedroof

Figure 85: Longitudinal cross-section of S_LWh_U_Raisedroof, with indication of the heightened roof

5.9 S_Wh_U

This configuration of the Simple model features a linear weir with a height equal to 3 m in a culvert

with U-beams, i.e. the same height as the labyrinth weir in the Full model. This configuration implies

that the available area in the structure is the same as the area of the inlet and outlet section. The

location of the linear weir is in the middle of the culvert. This weir has a length of 11 m, in prototype

dimensions. Thus the available section above the weir is 11 m².

Upstream

(Meuse)

Downstream

(Heerenlaak)

87

Figure 86: Longitudinal cross-section of S_LWh_UMeuse, with a linear weir with a height of 3 m

5.10 S_Wh/2_U

In comparison to S_Wh_U, the height of the linear weir is divided by two, i.e. 1.5 m. The crest level of

the weir is then at + 25.2 m T.A.W. The available area in the structure then becomes 27.5 m², in theory.

This represents an increase of 150 % in comparison to S_Wh_U. Note that for this configuration the

water does not necessarily need to dive under the U-beam and then go over the crest of the weir. This

is indicated in Figure 87. For this model, the available section in the inside of the structure is 83.33%

of the inlet section, which is 33 m².

Figure 87: Longitudinal cross-section of S_Wh/2_U, with a linear weir with a height of 1.5 m

Figure 88: Front view of S_Wh/2_U with sight on the linear weir at half the height of the inlet

Upstream

(Meuse)

Downstream

(Heerenlaak)

Upstream

(Meuse)

Downstream

(Heerenlaak)

88

5.11 S_Wh_noU

In comparison to S_Wh_U, the U-beams are removed from the culvert, thus increasing the in- and

outlet section.

Figure 89: Longitudinal cross-section of S_Wh_noU, without U-beams

5.12 Verification of the scale model dimensions

5.12.1 Full Model

In order to manufacture the Full scale model at a limited cost, the technical staff of the laboratory has

made use of readily (commercially) available MDF-plates and stainless steel bars. This implies that the

geometry in the scale model is not exactly equal to the one in the design proposed by nv de

Scheepvaart. The MDF-plates used to construct the model have a thickness of approximately 1.85 cm,

which corresponds to a thickness of 33.3 cm in the prototype, whereas nv de Scheepvaart suggested

a value of 30 cm in the conceptual design. As a consequence, the inlet area of the Full model is 27.32

m² at the scale of the prototype, which is 9% smaller than the value of 30 m² suggested in the

conceptual design. The columns and beams in the scale model have a square cross-section with a side

of 2.5 cm, which corresponds to a side of 45 cm for the prototype, whereas the conceptual design

suggested a value of 40 cm. This means that there is a reduction in the available flow area over the

labyrinth weir with 2 %.

5.12.2 Simple Model

The area of the inlet section of the Simple Model is 27.81 m² at prototype scale, which is 9% smaller

than the value of 30 m² suggested in the design. The area of the outlet section is 28.83 m² at prototype

scale, which is 4% smaller than the suggested value of 30 m². The MDF-plates used to construct the

model have a thickness of 1.6 cm while for the Full model this was 1.85 cm. The thickness of 1.6 cm

corresponds to a thickness of 28.8 cm at prototype scale. The suggested value is 30 cm.

Upstream

(Meuse)

Downstream

(Heerenlaak)

89

Chapter 5: Data Processing

1. Remarks about the discussed data

An important remark concerning the data and the processing of it, is that the values used for

comparisons and explanations are already converted from model to prototype-scale. Hence all

discussed data will be based upon the values as they would appear in the real-life structure at

Heerenlaak.

Furthermore, all data discussed, corresponds to the discharge over a labyrinth weir of two cycles or a

structure with an equivalent width. This is indicated in Figure 90.

Figure 90: difference between one cycle and one unit

2. Data processing

During the experiments, a lot of data is gathered which is not relevant for the actual analysis of the

hydraulic structure or still has to be processed. Hence, a selection of the useful data is made. The

specific reason and method of selection and processing, will be explained in this chapter,

demonstrated on the data of the original model of the hydraulic structure (F_LWh_U_B&C).

1 cycle

1 unit

90

For the original model, the water heights upstream and downstream of the labyrinth weir in a culvert

are measured according to the method explained before. An overview of all data points measured for

the original configuration of the model, is shown in Figure 91. In this graph, the discharge Q is shown

in function of the upstream water height hupstream.

Figure 91: An overview of all data measured on F_LWh_U_B&C

After setting a certain target discharge and measuring the upstream and downstream water level, the

downstream water level is increased and the upstream and downstream levels are measured again.

This process of raising the downstream level is repeated several times. Afterwards, the discharge is

increased and this process is repeated.

Executing the measurements in this manner, makes that the different data points on this graph cannot

be compared with each other. The reason for this is that for the same upstream water level, several

discharges through the structure are possible, depending on the downstream water level. Hence the

data points can only be compared with each other when the difference between the up- and

downstream water level is the same.

The difference between the Meuse upstream and the Heerenlaak pond downstream of the hydraulic

structure is at a more or less constant value of 2 m, as explained in chapter 2, paragraph 2.1 (Figure 7).

Hence the data points selected to analyse the structure, will be the ones with a water level difference

of 2 m.

0

20

40

60

80

100

120

140

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

hupstream [ m T.A.W.]

F_LWh_U_B&C

91

However, given the test facilities it is practically impossible to reach exactly the value of 2 m. Therefore,

the values measured having an up/downstream difference close to 2 m will be used to interpolate in

order to reach a constant up/downstream difference of 2 m which can be used for solid comparisons.

This is illustrated in Figure 92 were the data measured having an up/downstream difference of 2 m +/-

0.05m are interpolated to reach a constant difference of 2 m.

Figure 92: Measured data points and interpolated values (F_LWh_U_B&C)

Besides the practical difficulty in reaching the exact difference in up/downstream level of 2 m, also a

structural difficulty prevented reaching the 2 m difference. This is because the height of the

downstream water level is dependent on the discharge through the flume and the height of the weir

at the downstream end of the flume (see chapter 4, paragraph 1.1). When this weir is flat (at the level

of the flume base), the downstream water level for a given discharge cannot be lowered anymore.

When the upstream water level related to that given discharge is less than 2 m higher than the

mentioned downstream water level, reaching the target difference of 2 m is not possible. This problem

is often encountered in the first part of the Qh-relation of the tested models, when the water flows

freely over the labyrinth weir or rectangular weir. When parts of the structure start to work under

pressure, for example in case of a drowned inlet, the aforementioned problem disappears.

Since in this first part of the Qh-relationship the downward water level does not have an influence on

the upstream water level, it is not necessary to aim for a constant difference of 2 for comparison with

0

20

40

60

80

100

120

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

hupstream [ m T.A.W.]

2 m +/- 0.05 m

Interpolation 2 m - curve

92

data from other models. This is illustrated in Figure 93, where the first part of the curve has the same

trend for various differences between up- and downstream water level, while for higher upstream

water levels the corresponding curves start to deviate. This transition will be further elaborated in the

results section.

Figure 93: Measured data points with different differences in up/downstream (F_LWh_U_B&C)

In conclusion, for the analysis and discussion of the data taken on different configurations, only the

interpolated data having a constant difference in up/downstream water level of 2 m will be displayed

together with the data from the first part of the curve where the downstream water level does not yet

influence the upstream water level.

3. Accuracy of the results

The accuracy of the results is demonstrated in Figure 94 by comparing data measured on

F_LWh_U_B&C on different occasions during the year. In between those different testing sessions, the

ultrasonic level sensors have been replaced or repositioned. Hence, a systematic measuring error

based on the location of the sensors, is excluded.

0.00

20.00

40.00

60.00

80.00

100.00

120.00

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

hupstream [ m T.A.W.]

1 m +/- 0.05 m

1.5 m +/- 0.05 m

2 m +/- 0.05 m

2.5 m +/- 0.05 m

93

Figure 94: Comparison of data measured at different dates on the F_LWh_U_B&C

Figure 94 illustrates that over a period of time of 3 months, similar data values were measured. During

this period, the scale model was modified and moved, as well were the measuring sensors. This

indicates that the measurements were taken accurately and are reproducible, notwithstanding the

accuracy of the equipment.

To quantify the average error of the measurements, a kernel interpolation has been applied in order

to attain a smooth curve through this data. By applying this kernel, a theoretical, smoothened value

for the discharge, corresponding to each upstream height (in total 105 data points) for which

measurements have been performed, is calculated. This theoretical value is calculated by attributing a

weighing factor to each data point. This weighing factor depends on the square of the inverse of the

difference in upstream water level between two points: the point for which a theoretical discharge is

calculated and the point for which the weighing factor is calculated. After calculating the weighing

factor for each point, the weighing factors are scaled so the sum is 1. Thus the formula to calculate the

weighing factor is given by:

In which

0

20

40

60

80

100

120

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

hupstream [ m T.A.W.]

9-11 februari 23 - 26 februari 15 - 16 april 23-27 april

94

n is the data point for which a theoretical discharge is calculated [-]

j is one of the other data points, i ranges from 1 to 105 and cannot be equal to n [-]

is the weigh factor for data point i to calculate the theoretical discharge for data point n [-]

m is the total number of data points, 105 in total [-]

hni is the difference in upstream water level between data point n and data point j [m]

The smoothened theoretical discharge corresponding to data point n is found by applying the weighing

factors on the discharges i:

is the smoothened value of the discharge, corresponding to data point n [m³/s]

is the measured discharge corresponding to data point j [m³/s]

These theoretical discharges are compared to the measured discharges, corresponding to a given n,

and the difference in discharges is expressed relative to the theoretical discharge. This is the relative

error of data point n. Since this value can either be negative or positive, the absolute value is taken:

is the relative error corresponding to data point n

Afterwards, the mean error is found by taking the mean of the relative errors of all data points.

The resulting mean error is 2.05 %, indicating that the tests have been performed with a good accuracy,

and were repeatable over the entire measurement period.

95

Chapter 6: Results and discussion

1. Introduction

The culvert with an integrated labyrinth weir is a complex structure and the presence of the U-shaped

beams even enhances the complexity of the proposed design. A simple understanding of this structure

is not evident when solely based upon the scale model tests of the proposed design (F_LWh_U_B&C).

Therefore, several more simple configurations have been defined and tested in order to meticulously

investigate the influence of the different aspects of the structure and to obtain, if possible, full insight

in the structure and its Qh-relation. Throughout this chapter, an overview of the tested configurations

and the obtained results will be given, followed by a discussion and comparison of the different

configurations.

The tested configurations have been described in detail in chapter 4, paragraph 5. In Table 7

underneath, a brief overview of the used abbreviations and a description of the corresponding

configurations is repeated for the sake of readability of this chapter.

Table 7: Used abbreviations and a description of the corresponding configuration

Abbreviation Description of the configuration

S_Wh_U Simple model, linear weir in a culvert with U-beams

S_Wh/2_U Simple model, linear weir in a culvert with a height equal to 1.5 m,

with U-beams

S_Wh_noU Simple model, linear weir in a culvert, no U-beams

S_LWh_noCul Simple model, labyrinth weir, not in a culvert

S_LWh_noU Simple model, labyrinth weir in a culvert, no U-beams

S_LWh_U Simple model, labyrinth weir in a culvert with U-beams

S_LWh_U_Raisedroof Simple model, labyrinth weir in a culvert with a raised roof.

S_LWh_UMeuse Simple model, labyrinth weir in a culvert with a U-beam on the side of the

Meuse

F_LWh_U_B&C Full model, labyrinth weir in a culvert with U-beams, with beams and

columns

F_LWh_U_C Full model, labyrinth weir in a culvert with U-beams, only columns

F_LWh_U Full model, labyrinth weir in a culvert with U-beams, no beams and

columns

96

As previously mentioned, the simple model is constructed without beams and columns in the internal

structure, in contrast to the full scale model F_LWh_U_B&C.

2. Results

2.1 S_Wh_U

One of the most basic and understandable hydraulic structures, is a simple, rectangular sharp-crested

weir. To investigate the influence of such a linear weir being in a culvert, tests are performed on the

S_Wh_U-configuration. By comparing the experimental data with the theoretical formula for a sharp-

crested weir, the impact of the culvert and the U-beams on the Qh-relation may be assessed. The Qh-

relation of such a weir is given by the following formula:

In this formula is the upstream head relative to the crest level of the weir. However, since the

velocity head is negligible compared to the total upstream head, it will be neglected. In that case the

formula is reduced to the formula of Poleni.

The crest length of the weir in the simple model is ± 0.64 m, which is ± 11.52 m on prototype scale. A

Cd-coefficient of the weir can be calculated by transforming the previous formula to the following form:

The Cd-coefficient of the linear weir will be calculated below not only for the S_Wh_U configuration

(Table 10) but for comparison purposes also for the S_Wh_noU (Table 8) and S_Wh/2_U (Table 9)

configuration.

For the S_Wh_noU configuration, water starts to flow over the structure before the upstream water

level reaches the soffit of the culvert at 27.7 m T.A.W.. Hence only data points for upstream water

levels below 27.7 m T.A.W. are taken into account when determining the Cd-coefficient.

97

Table 8: Calculation of the Cd-coefficient based on S_Wh_noU

S_Wh_noU

Q [m³/s] hupstream [m T.A.W.] h [m] Cd [-]

7.91 27.19 0.49 0.67

20.17 27.46 0.76 0.89

Average: 0.78

For the S_Wh/2_U-configuration, water flows freely over the weir for an upstream water level in the

range from 25.2 m T.A.W. (crest level of linear weir) to 26.7 m T.A.W. (the soffit of the U-beam).

Table 9: Calculation of the Cd-coefficient based on S_Wh/2_U

S_Wh/2_U

Q [m³/s] hupstream [m T.A.W.] h [m] Cd [-]

12.77 25.81 0.61 0.80

30.27 26.27 1.07 0.80

46.62 26.65 1.45 0.78

Average: 0.79

For the S_Wh_U configuration, water only starts flowing over the linear weir when the water level

reaches the soffit of the U-beam. This might influence the Cd-coefficient. For higher upstream water

levels, the internal structure becomes submerged and the flow pattern changes.

Table 10: Calculation of the Cd-coefficient based on S_Wh_U

S_Wh_U

Q [m³/s] hupstream [m T.A.W.] h [m] Cd [-]

5.10 27.07 0.37 0.68

7.41 27.17 0.47 0.67

12.28 27.30 0.60 0.78

21.45 27.59 0.89 0.75

Average: 0.72

The average Cd-coefficients corresponding to S_Wh/2_U and S_Wh_noU are very similar (0.79 and

0.78) whereas the Cd-coefficient of S_Wh_U is circa 10 % lower (0.72). According to the theory (see

below), the Cd-coefficient of S_Wh/2_U is supposed to have a higher value. However, no conclusions

will be made out of this, since a systematic increase of the linear weir height with 2 mm during the

experiments (e.g. caused by swelling of the wood or a calibration error), would imply a 10% increase

in the Cd-coefficient.

98

These experimentally obtained Cd-coefficients are compared with Cd-coefficients found in the

literature. Rehbock (1929) proposed a formula for the calculation of the discharge over a rectangular,

sharp-crested weir.

With hR being the effective head given by:

Since hR is used in this formula, the Cd-coefficients are also derived from the data (Table 11) using this

definition. For this formula, Rehbock proposes a theoretical determination of the Cd-coefficients:

In this formula, P is the height of the weir. This formula is valid for 0.003 < h < 0.75 m, h/P < 1, b > 0.3

and P>0.1. These criteria are fulfilled for the data shown in Table 11 on the S_Wh_U and the

S_Wh/2_U-configuration, whereas data for which these conditions are not fulfilled is left out. In this

table, a comparison between the theoretically and experimentally derived Cd-coefficients is given.

Table 11: Comparison between the experimentally and theoretically derived Cd-coefficients

S_Wh_U

Q [m³/s] h [m] Theoretical Cd [-] Experimental Cd [-]

5.10 0.37 0.61 0.67

7.41 0.47 0.62 0.66

12.28 0.60 0.62 0.77

S_Wh/2_U

Q [m³/s] h [m] Theoretical Cd [-] Experimental Cd [-]

12.77 25.81 0.72 0.79

The theoretical Cd-coefficients are underestimated by about 10 % compared to the experimental Cd-

coefficients. However, as is mentioned before, a systematic error of 1 or 2 mm would already imply an

increase in discharge coefficient of 5 to 10 %. Moreover, the weir inside the scale model cannot be

considered to be a sharp-crested weir, given the finite crest width of the weir (i.e. a MDF – plate of 16

mm).

99

The theoretical formulas of a sharp-crested weir are plotted on a graph with both a Cd-coefficient equal

to 0.72 and 0.79 and are compared with the experimental results of the S_Wh_U – configuration. This

graph is shown in Figure 95.

Figure 95: Comparison of S_Wh_U with the theoretical curves for flow over a weir

A good correspondence between the theoretical curves and the measured data can be seen for

upstream water levels smaller than about 27.7 m T.A.W., meaning that the structure acts as a simple

rectangular weir. The discharge only depends on the upstream level, more specifically on the upstream

head above the weir crest, and is independent of the difference between the up- and downstream

level. At higher upstream water levels, the influence of the U-beam is noticeable.

Starting from an upstream water level of 28.0 m T.A.W., the theoretical curve and measurements begin

to diverge. A second flow regime is perceived. In configuration S_Wh_U, the constraining flow section

is the overflow section between the weir crest and the culvert roof, as will be explained further on. As

such, it is considered to act as the inlet of the culvert (instead of the actual inlet) and becomes

submerged at an upstream level of 28.0 m T.A.W.. This is conform with the literature (e.g. Chow, 1959),

stating that the inlet of a culvert is submerged when the upstream water level is at 1.2 to 1.5 times the

inlet height (i.e. 26.7 m T.A.W. + 1.2 x 1 m = 27.9 m T.A.W. to 28.2 m T.A.W.). The structure acts

comparable to flow through a culvert in regime V.

0

20

40

60

80

100

120

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

hupstream [ m T.A.W.]

S_Wh_U Theoretical formula, Cd=0.72 Theoretical formula, Cd=0.79

100

This can be verified by use of the theoretical formulas for flow through a culvert, regime V (see chapter

3, paragraph 4.3). The Cd-coefficient is derived from data on S_Wh_U.

- For flow through a culvert, regime V:

This leads to:

With being the height of the upstream water level and z the height of the culvert invert.

Since in configuration S_Wh_U, the constricting overflow area is the overflow area between the roof

of the culvert and the crest of the weir, this is considered to be the inlet of the culvert in this formula,

with section .

Table 12: Calculation of the Cd-coefficient

Flow through a culvert (Regime V)

Q [m³/s] hupstream [m T.A.W.] hdownstream [m T.A.W.] Cd [-]

47.99 28.31 26.31 0.74

50.03 28.56 26.56 0.72

Average: 0.73

The formula of flow through a culvert is valid from the moment the upstream water level is above

approximately 28.0 m T.A.W. and as long as the downstream water level does not exceed a height of

26.7 m T.A.W. (i.e. the level of the soffit of the U-beams).

When comparing these results (red curve in Figure 96) with the experimental results, again a good fit

is obtained.

101

Figure 96: Theoretical fit of flow through a culvert on S_Wh_U

S_Wh_U eventually reaches a maximum discharge of 52.6 m³/s at an upstream water height of 29.25

m T.A.W.. This maximum is reached when the outlet is not yet fully drowned. The water level still flows

underneath the downstream U-beam. Figure 97 shows what is meant by ‘a drowned outlet’.

Figure 97: Schematical representation of a drowned outlet

An important remark concerning the drowned outlet is that a downstream water level, measured

during the experiments, higher than 26.7 m T.A.W. does not necessarily imply a drowned outlet. When

high discharges pass through the structure, a high flow velocity is reached at the outlet of the hydraulic

structure, where also a contraction takes place caused by the downstream U-beam. The measured

downstream water level is thus usually higher than the water level at the outlet, since the downstream

level is measured in the flume approximately 1.5 m behind the outlet.

0.00

20.00

40.00

60.00

80.00

100.00

120.00

26.70 27.70 28.70 29.70 30.70 31.70 32.70 33.70

Q [

m³/

s]

hupstream [ m T.A.W.]

S_Wh_U Theoretical formula, Cd=0.87

Theoretical formula, Cd=0.79 Flow through a culvert

Upstream Downstream

26.7 m T.A.W.

27.7 m T.A.W.

23.7 m T.A.W.

Outlet drowned

102

This is the reason why for S_Wh_U, the outlet is drowned at a registered downstream water level of

27.25 m T.A.W. instead of 26.7 m T.A.W.. Therefore, the determination of whether the outlet is

drowned or not, is mainly visually.

Figure 98: Indication of the rising water level between the outlet and the downstream sensor

For upstream water levels higher than 29.25 m T.A.W., the outlet of S_Wh_U is fully drowned. The

water level just downstream of the hydraulic structure reaches or exceeds the soffit of the U-beam, as

illustrated in Figure 97. The discharge diminishes again and reaches a minimum of 43.6 m³/s for an

upstream water level of 31.41 m T.A.W.. This regime seems comparable to flow through a culvert, type

IV (see chapter 3, paragraph 4.3).

Beyond this water level, the discharge increases slightly and finally becomes constant. The reason for

this ‘dip’ in the curve is not yet understood. A possible explanation could be the presence of the U-

beams, or the formation of eddies inside the structure. More about this local minimum is explained in

section 2.12.

In conclusion, three different flow regimes can be discerned on the Qh-relation of the linear weir in a

culvert with U-beams. First, a regime where the water can flow freely over the weir. Secondly, a regime

in which the constraining inlet section is submerged. Finally, a regime in which both the constraining

inlet section and outlet are submerged. This third regime has a local minimum when the upstream

water level is at a height of 31.4 m T.A.W.. This is clearly illustrated in Figure 99.

103

Figure 99: Indication of the different regimes observed in the Qh-relation of S_Wh_U

2.2 S_Wh_U and S_Wh/2_U

To investigate which parameter is the most restricting on the discharge through the linear weir in a

culvert with U-beams (S_Wh_U), experiments have been performed on the same model but with a

weir crest which is lowered in the culvert (S_Wh_U/2). Lowering the height of the weir crest with 1.5

m increases the available area through which water can flow in the hydraulic structure with 150%,

while the in- and outlet section remain identical for both models.

Based upon the results, shown in Figure 100, a considerably higher discharge can be noticed for a

certain upstream water level for S_Wh/2_U in comparison to S_Wh_U. The maximum measured

discharge for S_Wh/2_U is 147.7 m³/s for an upstream water level of 29.22 m T.A.W.. For S_Wh_U this

is 52.6 m³/s for an upstream water level of 29.25 m T.A.W..

The peak discharge for both models seems to occur at similar upstream water levels, confirming that

the peak discharge is reached when the outlet becomes submerged. At the peak discharge, the

downstream water level is at a height of about 27.2 m T.A.W..

0

10

20

30

40

50

60

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

hupstream [ m T.A.W.]

S_Wh_U

Regime 1:

Free overflow

over labyrinth

Regime 3:

Inlet and outlet submerged

Regime 2:

Inlet

submerged

Local minimum in regime 3

104

Figure 100: Influence of the overflow section of the weir (S_Wh_U vs. S_Wh/2_U)

For the data measured on the S_Wh/2_U-configuration, the peak is much sharper when compared to

S_Wh_U. This is because the target difference in up/downstream water level of 2 m could not be

reached. At 25.2 m T.A.W., the upstream level reaches the height of the low-crested weir and water

starts to flow over the weir. Because the height of the weir crest is very low compared to the bottom

of the current flume, the downstream water level already reaches the crest of the weir when the

upstream water level is approximately 26 m T.A.W.. From that moment on, the weir acts as a

submerged weir and the discharge over the weir is constrained by the downstream water level.

The theoretical formula for the discharge over a submerged weir (Villemonte, 1947) is used to verify

this:

The Cd-coefficient of the unsubmerged weir is required for this calculation (S_Wh/2_U), which was

determined previously and found equal to 0.79. However, since this Cd-coefficient is based on only 2

data points, a better match could be obtained with a Cd-coefficient of 0.83. These theoretical curves

are shown in Figure 101 with as input the values measured for hupstream and Δ h and as output, the

theoretical discharge based on the formula of Villemonte.

0

20

40

60

80

100

120

140

160

25.2 26.2 27.2 28.2 29.2 30.2 31.2 32.2 33.2

Q [

m³/

s]

hupstream [ m T.A.W.]S_Wh/2_U S_Wh_U

105

Figure 101: Theoretical fit on S_Wh/2_U

This curve is valid until an upstream water level of approximately 28 m T.A.W., i.e. when the inlet

becomes submerged. In this case, the inlet section of the culvert is the most constraining factor, since

the overflow area between the crest of the weir and the roof of the culvert is larger than the inlet of

the culvert. A description of the inlet of the culvert being submerged is shown in a conceptual drawing

in Figure 102. However, the inflexion point indicating a transition from the 1st to the 2nd regime, is

almost undiscernible.

Figure 102: Schematical representation of the drowned inlet

At upstream water levels higher than 29.2 m T.A.W., the outlet of the culvert is again fully drowned

and the discharge lowers until reaching a more or less constant value at an upstream height of 31.2 m

T.A.W..

0

20

40

60

80

100

120

140

160

25.2 26.2 27.2 28.2 29.2 30.2 31.2 32.2 33.2

Q [

m³/

s]

hupstream [ m T.A.W.]

S_Wh/2_U Flow over submerged weir, Cd=0.79 Flow over submerged weir, Cd=0.83

Upstream Downstream

26.7 m T.A.W.

27.7 m T.A.W.

23.7 m T.A.W.

± 28 m T.A.W. Inlet internally drowned

106

At approximately 31.2 m T.A.W., a dip in the curve is observed at a similar location as for S_Wh_U. The

average discharge after this dip is 46.69 m³/s for S_Wh_U and 119.63 m³/s for S_Wh/2_U. This is an

increase of 156%.

2.3 S_Wh_U and S_Wh_noU

By comparing S_Wh_U with S_Wh_noU, the influence of the removal of the U-shaped beams on the

flow over a linear weir in culvert may be analysed.

Figure 103: Impact of U-beams on Qh-relation (S_Wh_U vs. S_Wh_noU)

The same regimes as described previously are still present. During the first regime, no increase in

discharge is perceived by the removal of the U-shaped beams.

During the second, and definitely in the third regime, an increase in discharge occurs due to the

absence of the U-shaped beams. Removing the U-beams results in less losses and thus a higher

discharge for the same upstream head.

The change from the first to the second regime occurs again for an upstream water level of

approximately 28 m T.A.W.. The peak of the data occurs at higher upstream water levels for S_Wh_noU

(54.43 m³/s at 29.62 m T.A.W in comparison to 52.62 m³/s at 29.25 m T.A.W.)

0

10

20

30

40

50

60

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

hupstream [ m T.A.W.]S_Wh_noU S_Wh_U

107

The transition from the first to the second regime occurs at the same upstream water level for both

configurations. This indicates that the main restraining factor is the overflow area between the weir

crest and the soffit of the culvert. As such, the discharge is not significantly influenced by enlarging the

inlet of the culvert. This also confirms the assumption of this overflow area acting as the inlet of the

culvert. Otherwise the transition would occur at an upstream level of about 28.5 to 29.7 m T.A.W.. (i.e.

1.2 to 1.5 times the height of the culvert inlet according to Chow, 1959).

The third regime is again characterized by the presence of a local minimum as is also observed in the

Qh-relation of S_Wh_noU. Several tests confirm the presence of this dip in the curve. By comparing

S_Wh_U with S_Wh_noU, it can be concluded that the U-beams do not have an impact on this dip and

on the shape of the Qh-relation in general.

2.4 S_LWh_noCul

Since the proposed hydraulic structure consists of a labyrinth weir in a culvert, the theoretical specifics

of this labyrinth weir are also verified by use of a scale model, consisting of just a labyrinth weir

(S_LWh_noCul).

The theoretical curve, describing the Qh-relation of a labyrinth weir is compared to the data measured

on S_LWh_noCul. The theoretical Qh-relation is calculated as follows:

HT is again the upstream head, relative to the crest of the labyrinth weir (26.7 m T.A.W.). In the graph,

Hupstream will be used, which equals HT + 26.7 m. In this case, the upstream velocity head is not negligible

and will be used in the formulas.

Cd is calculated based on the trend lines composed by Tullis et al. (1995):

However, this formula is valid for an apex width t ≤ A ≤ 2t, HT / P < 0.9, t ≈ P/6 and a quarter-round

crest shape with radius R = P/12. These conditions are mostly not fulfilled, but for the sake of the

comparison, this formula has been applied anyhow.

The crest length is calculated as follows (see chapter 3, Figure 14):

108

N, the number of cycles, is two for this configuration. L1 is 89.4 cm, the inner apex width is 1.8 cm and

the outer apex width is 5.3 cm. These dimensions are measured on the scale model. Thus they need

to be multiplied with the scale factor of 18 to obtain the dimensions on the scale of the prototype. The

theoretical curve and the measured data can be seen in Figure 104.

Note that the data for S_LWh_noCul do not correspond to the target water level difference of 2 m,

since it was practically not possible to attain this difference in the current flume (see chapter 5,

paragraph 2). However, as has been mentioned in the literature review (chapter 3, paragraph 3.5) and

as can be seen from the formula giving the QH-relation of a labyrinth weir, it is only the upstream

water level which plays a role, as long as the weir is not submerged downstream.

Figure 104: Theoretical curve compared to S_LWh_noCul

The theoretical curve and the measured data only correspond for low discharges. As explained before,

the conditions for applying the formula of Tullis are not fulfilled, which might be the cause.

For fixed discharges (among others Q = 66.3 m³/s and Q = 149.4 m³/s) the downstream water level was

varied by increasing the height of the downstream weir to investigate the influence of increasing

downstream water levels on the discharge. As long as the downstream water level does not exceed

0

50

100

150

200

250

300

26.7 27.2 27.7 28.2 28.7 29.2

Q [

m³/

s]

Hupstream [ m T.A.W.]

S_LWh_noCulvert Theoretical formula for labyrinth weir

109

the crest of the weir, the upstream water level remains unaffected and submergence has no impact

on the capacity of the structure. This is consistent with the research conducted by Taylor (1968), Tullis

et al. (2006) and Lopes et al. (2009). Thus, by avoiding submergence of the hydraulic structure, a

significant increase in capacity can be obtained.

For several fixed discharges, both submerged and modular flow conditions have been tested. For these

discharges, a graph with Hd/H0 vs. HT/H0 is created to verify whether the measurements correspond to

the graph describing submergence effects on labyrinth weirs developed by Tullis, Young and Chandler

(2005). This graph can be seen in Figure 105. H0 is the head required for a fixed discharge under

modular flow conditions. H0 is not calculated by transforming the formula giving the discharge over a

labyrinth weir, but is known from the measured data corresponding to modular flow conditions.

Figure 105: Submergence effects, red data points are calculated based on measurements, adapted from Tullis et al. (2005)

2.5 S_LWh_noU and S_LWh_noCul

The labyrinth weir in a culvert without U-beams (S_LWh_noU) is tested to investigate the impact of

the culvert ceiling on the Qh-relation over a pure labyrinth weir (S_LWh_noCul). The absence of U-

beams implies that S_LWh_noU starts to be submerged when the upstream water level exceeds a

Submergence effects

110

value of approximately 28.5 to 29.7 m T.A.W. (i.e. 1.2 to 1.5 times D, according to Chow, 1959). Hence,

for lower upstream water levels, there should be no discernible difference in Qh-relation. This is indeed

confirmed by the measurements, as can be seen in Figure 106.

Figure 106: S_LWh_noCul vs. S_LWh_noU

The peak discharge of S_LWh_noU is assumed to be around 184 m³/s, based upon the surrounding

values and comparisons with other configurations. However, this discharge could not be reached

during the experiments due to logistic reasons. No further conclusions can be drawn from this graph.

2.6 S_LWh_U, S_Wh_U and S_Wh/2_U

The next step in understanding the future hydraulic structure, is the addition of the U-beams to the

labyrinth weir in a culvert (S_LWh_U) and to evaluate whether or not the same trends can be discerned

as for the linear weirs in a culvert (S_Wh_U and S_Wh/2_U). The obtained data are shown in Figure

107.

0

20

40

60

80

100

120

140

160

180

200

26.7 27.2 27.7 28.2 28.7 29.2 29.7 30.2 30.7 31.2 31.7

Q [

m³/

s]

hupstream [ m T.A.W.]

S_LWh_noCul S_LWh_noU

111

Figure 107: Comparison between S_LWh_U, S_Wh_U and S_Wh/2_U

From an upstream water level of 26.7 m T.A.W., i.e. when water starts to flow over the structure, until

an upstream water level of approximately 28 m T.A.W., the first regime can be discerned for S_LWh_U.

This regime is similar to the first regime observed in S_Wh_U and S_Wh/2_U. However, the slope of

the Qh-relation is much steeper for the labyrinth weir compared to the rectangular weir, hence allows

for a larger discharge for equal upstream water levels. A larger crest length, allowing more water to

flow over the labyrinth weir is the cause of this difference in slope between S_Wh_U and S_LWh_U.

S_Wh/2_U has a similar slope during the first regime as S_Wh_U, but starts to flow over at an upstream

height of 25.2 m T.A.W., whereas in case of S_Wh_U this is at 26.7 m T.A.W.; hence the difference in

discharge between S_Wh_U and S_Wh/2_U, as explained before.

The transition from the first to the second regime takes places at an upstream water level of

approximately 28 m T.A.W. for all three configurations. For S_LWh_U and S_Wh/2_U, this is the result

of the inlet of the culvert being drowned. For an inlet with U-beams, this is at an approximate upstream

water level of 28 m T.A.W. (i.e. 1.2 to 1.5 times the height of the inlet). For S_Wh_U, however, the

overflow area between the crest of the weir and the soffit of the culvert is the most constraining

section. The transition occurs at about 28 m T.A.W. as well, but in this case it is the result of the most

restraining flow section being submerged, as was indicated before.

0

20

40

60

80

100

120

140

160

25.2 26.2 27.2 28.2 29.2 30.2 31.2 32.2

Q [

m³/

s]

hupstream [ m T.A.W.]

S_LWh_U S_Wh_U S_Wh/2_U

112

The transition point from the second to the third regime differs between S_LWh_U on the one hand

and S_Wh_U and S_Wh/2_U on the other hand. For S_LWh_U, this transition appears at an upstream

level of approximately 29.7 m T.A.W. and a downstream level of 27.7 m T.A.W., whereas for S_Wh_U

and S_Wh/2_U this upstream water level is 29.25 m T.A.W. and downstream level of 27.25 m T.A.W.

(the soffit of the downstream U-beam is at 26.7 m T.A.W.). However, in both cases this transition takes

place when the outlet is on the verge of drowning. Because of the high flow velocities and the presence

of the downstream U-beam, a contraction at the outlet was observed. This explains why the transition

from the second to the third regime occurs at different downstream water levels, while it was

determined visually that in all three configurations the outlet became submerged at that particular

moment.

In the third regime, the discharge of S_LWh_U remains more or less constant around a value of 130

m³/s, which is consistent with the formula of flow through culverts, regime IV (see chapter 3, paragraph

4.3). However, a local minimum is found, which is for all three different configurations at an

approximate upstream water level of 31.2-31.4 m T.A.W.. This local minimum is further discussed in

paragraph 2.12.

The maximal discharge through S_Wh/2_U is about 11% higher than the maximal discharge through

S_LWh_U. This can partially be caused by a larger inlet section of about 20%, considering that the

labyrinth weir reduces the inlet section partially (i.e. by the presence of the upstream apex). However,

since the overflow section between the weir and the culvert soffit is smaller for S_Wh/2_U (approx.

29 m²) compared to the overflow area in S_LWh_U (approx. 66.9 m²), higher energy losses will

decrease this maximal discharge.

In conclusion, the labyrinth weir in a culvert allows for a much higher discharge than a linear weir

during the first regime. In the second regime, the restraining factor is the smallest section through

which the flow needs to pass, in combination with the accompanying energy losses through the

structure.

2.7 S_LWh_U and S_LWh_noU

The impact of the U-beams on the labyrinth weir in a culvert can be assessed by comparing the data

of a labyrinth weir in a culvert with U-beams (S_LWh_U) to the data of the model without U-beams

(S_LWh_noU). This comparison is shown in Figure 108.

113

Figure 108: Impact of the U-beams on a labyrinth weir in a culvert (S_LWh_U vs. S_LWh_noU)

The peak discharge of the S_LWh_noU-configuration is assumed to be about 184 m³/s, based upon the

surrounding values. However, this discharge could not be reached during the experiments due to

logistic reasons.

Removing the U-beams (S_LWh_noU) leads to a higher discharge capacity in comparison to S_LWh_U,

which was also observed on the model with a rectangular weir (S_Wh_U vs. S_Wh_noU). The cause of

this increase in discharge is twofold.

On the one hand, the height of the inlet increases with 33 % by removing the U-beams. As a result, the

inlet in the S_LWh_noU-configuration becomes drowned at an upstream water level which is higher

than in the S_LWh_U-configuration (approx. 28.5 m T.A.W. vs. 28 m T.A.W.) and thus the second

regime starts at higher upstream water levels. This results in a much higher discharge going through

the S_LWh_noU-configuration.

On the other hand, removing the U-beams increases the area of the inlet section with 36%, as has been

mentioned in chapter 4. This also enhances the discharge through the structure. Assuming that the

second regime is comparable with flow through a culvert (regime V), this would result (based on the

formula for flow through a culvert, regime V, see chapter 3, paragraph 4.3) in a discharge which is also

36 % higher. By comparing the discharges of the second regime for both configurations, it was found

that the increase in discharge was about 35% to 40 %, which supports this theory.

0

20

40

60

80

100

120

140

160

180

200

26.7 27.7 28.7 29.7 30.7 31.7 32.7

Q [

m³/

s]

hupstream [m T.A.W.]

S_LWh_U S_LWh_noU

114

Due to a lack of data, no clear-cut remarks can be made concerning the third regime. For high upstream

water levels (> 31.0 m T.A.W.), the S_LWh_U-configuration gives a discharge which is 37 to 40 % higher

than for the S_LWh_noU configuration.

2.8 S_LWh_U and F_LWh_U

The Simple model gives the possibility to test a wide variety of hydraulic structures, as has been

illustrated in the previous sections. However, there are some features of the proposed design which

are not incorporated in the simple model. Therefore a comparison is made in this paragraph between

the S_LWh_U configuration of the Simple model and the F_LWh_U configuration of the Full model. A

comparison of the measurements on both configurations is shown in Figure 109.

Figure 109: Comparison between S_LWh_U and F_LWh_U

During the first regime, there are only small differences between both configurations, which could be

attributed to minor differences in geometry or to the accuracy of the measurements. However, during

the second, and definitely in the third regime, the S_LWh_U-configuration seems to have a higher

discharge capacity than the F_LWh_U configuration.

The main reason for this discrepancy is assumed to be the difference in the design of the inlet of both

models. The different geometries can be seen in Figure 110. For the F_LWh_U-configuration, the U-

0

20

40

60

80

100

120

140

160

26.7 27.7 28.7 29.7 30.7 31.7 32.7

Q [

m³/

s]

hupstream [ m T.A.W.]

S_LWh_U F_LWh_U, difference of 2 m +/- 0.08 m

115

shaped beam is fabricated according to the proposed design (i.e. as a U-shape), while for the S_LWh_U-

configuration, there is a straight vertical wall at the location of the U-beam. This leads to different flow

patterns in both models. The U-beam from the Full model, creates a dead zone of water above the

inlet, in which the water has almost no velocity and has a lot of swirling motion caused by this

geometry. In contrast, on the Simple model this dead zone of water and the swirling motion is reduced

significantly. This could (partially) explain the lower discharge capacity for the F_LWh_U-configuration.

Figure 110: Demonstration of the difference in inlet geometry between the full model (left) and the simple model (right)

Another difference in inlet geometry, is that for the S_LWh_U-configuration the U-beams have

rounded edges, which is not the case for the F_LWh_U-configuration. This leads to higher losses for

the latter and could explain the less steep curve for this configuration.

Visual observations in the model show that for the S_LWh_U-configuration the occurrence of vortices

is significantly lower than for the F_LWh_U-configuration. These vortices also imply a decrease in

discharge. The occurrence of these vortices is most likely related with the differences in inlet geometry,

enhancing the swirling motion and thus the formation of vortices in case of the Full model. This is

discussed further in paragraph 5.

A last explanation given for the higher capacity of the S_LWh_U-configuration is the larger size of the

inlet-section (2.6 %) and the outlet section (2.3 %) in comparison to the F_LWh_U-configuration.

2.9 Influence of the supporting beams and columns

The last step in the process of experimenting is the verification of the impact of the beams and

columns, supporting the roof of the culvert, on the discharge capacity of the structure. Therefore, the

F_LWh_U_B&C-configuration is being compared to the F_LWh_U_C and F_LWh_U configurations. The

removal of these structural elements will increase the available flow area over the labyrinth weir and

116

will decrease the aeration (in case the columns act as artificial breakers of the falling nappe). The

influence of the removal of the beams and columns on the available area over the weir can be seen in

Table 13.

Table 13: Available area above the weir for different configurations

Configuration Available area [m²] per cycle

F_LWh_U_B&C 29.4

F_LWh_U_C 30.4

F_LWh_U 31.8

Figure 111: Comparison of F_LWh_U_B&C, F_LWh_U_C and F_LWh_U

The previously described regimes also occur in the F_LWh_U_C and the F_LWh_U_B&C configurations,

around similar water levels as mentioned before.

In the first regime, a very small difference can be noticed in the discharge of the F_LWh_U_B&C-

configuration as compared to the F_LWh_U_C and F_LWh_U configurations, which can be attributed

to the small difference in overflow length.

In the second regime, the slope is steeper for the F_LWh_U_C and for the F_LWh_U configuration. The

explanation for this is the reduction of hydraulic losses when no supporting beams and columns are

present. The F_LWh_U configuration should be steeper than the F_LWh_U_C configuration, although

0

20

40

60

80

100

120

140

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

h upstream [ m T.A.W.]

F_LWh_U, 2 m +/- 0.08 m F_LWh_U_C F_LWh_U_B&C

117

the accuracy of the measurements and quantity of the data in the second regime, does not allow to

make any definite conclusions on the steepness of the curve.

The influence of the columns on the discharge is small, since the difference in discharge between the

configuration with and without columns (F_LWh_U vs. F_LWh_U_C) is limited. When the supporting

beams are present, a more significant decrease in discharge is noticed in comparison with F_LWh_U_C

and F_LWh_U. The presence of the beams causes much more hydraulic losses in the culvert, resulting

in a lower discharge through the structure for similar upstream water levels.

Another important conclusion is that the curves visibly start diverging at an upstream water level of

about + 27.5 m T.A.W., until the outlet becomes submerged. They stay more or less at a constant offset

(of about 14.5 m³/s) for higher upstream water levels.

In the third regime, again the presence of a local minimum is observed. This is discussed in 2.12.

2.10 F_LWh_U_B&C for different Δh

Besides testing with a target difference in upstream and downstream water levels Δh equal to ± 2 m

(as was the case in the previous paragraphs), the F_LWh_U_B&C-configuration has also been tested

with other target values: Δh = 1m, 1.5 m and 2.5 m. The reasons for this are twofold. Firstly to gain

additional insight in the stage-discharge relation of the hydraulic structure at Heerenlaak. A second

reason is to anticipate on the design of future, similar hydraulic structures at other locations in the

Common Meuse, which are characterized by other Δh values. The same hydraulic structure might have

a different Qh-relation and performance at different locations. The resulting graph is shown in Figure

112 below.

118

Figure 112: Interpolated values for F_LWh_U_B&C for different Δh

Several conclusions can be drawn based upon these measurements. A first main conclusion is that for

higher differences in water level Δh, the structure will have a higher discharge capacity. The outlet is

drowned at a higher upstream water level, allowing the discharge to increase during the second

regime.

A second conclusion is that for the first regime, the capacity is independent of the difference in water

level. The only influencing parameter is the upstream water level.

A third conclusion is that for the measurements corresponding to a difference in water level of Δh = 1

m, the second regime as defined previously for the case of Δh = 2 m does not occur. The explanation

for this is that, due to the limited difference in water level, the outlet starts to be submerged when the

inlet is drowned. Therefore the second regime, where the inlet is submerged with free outflow, is not

present.

2.11 Verification of the estimated stage discharge relation by FHR

The data measured on the F_LWh_U_B&C configuration can now be compared to the tentative Qh-

relation based on a desk-top study by FHR (Vercruysse et al., 2013) prior to the present scale model

study.

0

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26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

hupstream [ m T.A.W.]

Δh = 2 m Δh = 2.5 m Δh = 1 m

119

As indicated in chapter 4, paragraph 5.12, the Full model has some small differences in geometry

compared to the proposed hydraulic structure. Prior to obtaining the best estimation of the discharge

of the proposed structure, the impact of these differences will be discussed.

Firstly, the inlet section of the Full model is 9% smaller than the suggested value of 30 m² in the design

of the hydraulic structure. As is concluded in the comparison between S_LWh_U and S_LWh_noU,

enlarging the inlet section should result in a discharge which is higher. The resulting discharge through

the proposed hydraulic structure is thus assumed to be about 9 % higher than for F_LWh_U_B&C,

based on the aforementioned conclusions.

Secondly, the columns and beams in the scale model have a square cross-section corresponding to a

side of 45 cm on prototype scale, whereas the conceptual design suggested a value of 40 cm. This

means that the scale model has a reduced flow area over the labyrinth weir. Moreover, the beams

create high hydraulic losses inside the structure. Based upon the comparison between F_LWh_U_C

and F_LWh_U_B&C, an estimation of the discharge through the prototype is made, given that the

discharge through F_LWh_U_C was about 15 % higher than through F_LWh_U_B&C. For a scale model

with more accurate dimensions of the beams, the stage-discharge relation should be in between that

of F_LWh_U_B&C and F_LWh_U_C. When evaluating the increase in overflow area of F_LWh_U_C

compared to F_LWh_U_B&C, an estimation of the increase in discharge capacity, for a model with

more accurate beam dimensions (i.e. reducing the beam dimensions in F_LWh_U_B&C), can be made.

This is done by taking the ratio of the absolute increase in overflow area of the more accurate model

to the absolute increase of the F_LWh_U_C when compared to F_LWh_U_B&C and multiplying this

with the afore mentioned increase of 15%. Thus the discharge through the prototype is assumed to be

about 1.5 to 2 % higher than the discharge through F_LWh_U_B&C.

Furthermore, the walls of the labyrinth are 3 cm thicker in F_LWh_U_B&C, than on the design of the

proposed structure. As is mentioned in the literature review about labyrinth weirs, an increase in wall

thickness leads to a decrease in specific discharge (Blancher, Montarros and Laugier, 2010). However,

this decrease is not quantified in the latter publication and the possible increase on the discharge

through the proposed structure is assumed to be negligible compared to the discharge through

F_LWh_U_B&C.

120

In conclusion, the discharge through the future hydraulic structure is assumed to be about 9 to 11 %

higher than is measured on the F_LWh_U_B&C-configuration. A comparison between the original and

the corrected (i.e. 9 to 11% higher) data measured on the F_LWh_U_B&C-configuration and the

estimated stage-discharge relation, based upon a desk-top study by FHR (Vercruysse et al., 2013) is

shown in Figure 113.

Figure 113: Estimation of the discharge through the proposed hydraulic structure based upon geometrical errors, in

comparison with the estimated Qh-relation proposed by FHR (Vercruysse et al., 2013)

For the first regime (i.e. the weir regime), the desktop-based curve somewhat underestimates the

discharge. This can be attributed to the fact that conservative assumptions have been made in the

desktop study, to account for the large uncertainties concerning the different influence factors on the

hydraulic structure.

When the second regimes starts (i.e. at 28.0 m T.A.W.), there agreement between the desktop-based

QH-relation and the measured one becomes very poor . Yet, the transition from the second to the third

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26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

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h upstream [ m T.A.W.]

FHR: simulations of submerged in- and outlet FHR: Weir regimeFHR: Submerged inlet FHR: Submerged inlet and outletF_LWh_U_B&C Estimation based on geom. differences, 9 %Estimation based on geom. differences, 11 %

121

regime occurs at a similar upstream water level (i.e. at ± 29.2 m T.A.W., when the outlet is submerged

as well).

The desktop-based curve takes into account the rising of the head (i.e. the difference between the up-

and downstream level) from 2 m to approximately 2.5 m for high discharges at the Meuse, and

corresponding high upstream water levels, as shown in chapter 2, Figure 7. This is an additional

explanation for the poor agreement between the desktop-based and the measured Qh-relation. The

influence of the rising difference between the Meuse and the Heerenlaak pond, can be incorporated

in the result, by evaluating the curve with a Δh of 2.5 m (see 2.10). When considering that Δh changes

from 2 m at an upstream water level of 29.5 m T.A.W. to 2.5 m at an upstream water level of 31 m

T.A.W., an estimation can be made which incorporates the geometrical errors and the rising value of

Δh over the construction. This estimation is shown in Figure 114. It is obvious that the agreement with

the desktop-based values is somewhat better.

Figure 114: Estimation of the discharge through the proposed hydraulic structure based upon geometrical errors and a

rising up/downstream difference , in comparison with the theoretical estimation made by FHR (Vercruysse et al., 2013)

0

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180

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

h upstream [ m T.A.W.]

FHR: simulations of submerged in- and outlet FHR: Weir regime

FHR: Submerged inlet FHR: Submerged inlet and outlet

F_LWh_U_B&C Final estimation, 11 %

Final estimation, 9 %

122

It should be mentioned that the report on the desktop-study (Vercruysse et al. 2013) clearly states that

the estimated Qh-relation is afflicted with a lot of uncertainties and therefore recommended that the

hydraulic structure would be tested in a scale model study, which is the subject of the present master

thesis. Thanks to this scale model testing it becomes clear that the maximum discharge through the

construction is less than what was estimated based upon the desktop-study.

2.12 Dip in the third regime

During the evaluation of the data, a local minimum in the third regime was consistently observed in

the tests concerning a labyrinth or linear weir integrated in a culvert. In some cases, this local minimum

is very pronounced, while in other cases it is but a peculiarity in the curve of the third regime.

Considering the hypothesis of flow through a culvert (regime IV) is valid in the third regime , the

discharge should remain more or less constant. However, the corresponding formula of flow through

a culvert (regime IV) incorporates a Cd-coefficient, hence hydraulic losses may influence the discharge.

The data for different configurations are shown in Figure 115. The fact that this dip was observed

consistently, signifies that it cannot be related to the accuracy of the measurements or errors during

measuring.

Figure 115: Indication of the dip in the third regime

0

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80

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180

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

s]

hupstream [ m T.A.W.]

S_LWh_U F_LWh_U_C F_LWh_U, 2 m +/- 0.08 mF_LWh_U_B&C S_Wh_U S_Wh_noUS_Wh_UMeuse S_LWh_U_Raisedroof

123

While testing, some possible theories about the origin of this phenomenon were tested. The first

theory was that this local minimum was due to the formation of eddies inside the labyrinth weir, close

to the apex. However, this theory could be discarded when comparing the experiments on the

labyrinth weir in a culvert with the experiments on a linear weir in a culvert. The presence of this dip

in the curves of these configurations (i.e. with a linear weir), counteracts this theory.

A second theory, was that the presence of the dip was related to the presence of the U-beams.

However, tests were performed on a linear and labyrinth weir inside a culvert with and without U-

beams. In both cases, the dip was observed in the results, discarding this theory.

A third theory is based on observations during testing. At high discharges, in the third regime, a zone

of water with a return current was perceived near the water level downstream of the outlet of the

scale models, indicating that the culvert might be lengthened hydraulically. This could explain the

decrease in discharge. These observations were done on the S_Wh_noU-configuration. However, this

was not investigated further, but might require additional research.

3. Optimisation

Two additional configurations, which may have practical use for the further optimisation of the design

of the structure at Heerenlaak, have been built and tested, i.e.. the S_LWh_U_Raisedroof configuration

and the S_LWh_UMeuse-configuration.

3.1 Influence of raising the roof (S_LWh_U_Raisedroof)

Raising the roof implies doubling the available area above the labyrinth weir, in comparison to

S_LWh_U. As was mentioned before, the removal of the beams and columns (F_LWh_U in comparison

to F_LWh_U_B&C) also causes an increase in available flow area above the weir and leads to a higher

discharge capacity. Based on these measurements and conclusions, one would expect an increase in

capacity of the structure due to raising the roof of the structure. A comparison of S_LWh_U and

S_LWh_U_Raisedroof is presented in Figure 116.

124

Figure 116: Comparison of S_LWh_U and S_LWh_U_Raisedroof

The measurements show a decrease in capacity of the structure by raising the roof, which is not in

accordance with the expectations. The afore described regimes do occur for the S_LWh_U_Raisedroof

configuration but the stage-discharge relations of S_LWh_U and S_LWh_U_Raisedroof begin to diverge

from an upstream water level of 28.7 m T.A.W. The maximum capacity of the S_LWh_U_Raisedroof

configuration is 117 m³/s. The surprising decrease in capacity might have several explanations. One

possible explanation is that the larger amount of available area in the structure facilitates the creation

of eddies, which in turn increases the head losses, hence a decrease of the overall capacity of the

structure.

3.2 Removal of the downstream U-beam

A second configuration, tested to obtain an improved discharge capacity with respect to the proposed

design, is the S_LWh_UMeuse-configuration. This model has only a U-shaped beam at the inlet (i.e.

the Meuse side) while the U-beam at the outlet (i.e. the Heerenlaak side) is removed.

The reason for removing the downstream U-beam is threefold. First, the costs of the future hydraulic

structure could be reduced. Secondly, the utility of the downstream U-beam is questioned. Given the

water level difference between the Meuse and the Heerenlaak pond, the flow through the structure

0

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26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

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hupstream [ m T.A.W.]

S_LWh_U S_LWh_U_Raisedroof

125

will always be directed from the Meuse to the Heerenlaak pond. Hence, no ingress of floating debris is

possible from the downstream side and if debris from the Meuse would have flown into the structure,

the presence of the downstream U-beam could make it more difficult to remove this debris. A third

reason, is that by removing the downstream U-beam, the flow at the outlet is not forced to contract

in the downward direction, improving the conditions for the bottom protection at the outlet.

The influence of the removal of the U-beam on the side of Heerenlaak (S_LWh_UMeuse) in comparison

to the proposed design (S_LWh_U) can be seen in Figure 117.

Figure 117: Comparison of S_LWh_UMeuse and S_LWh_U

The removal of the downstream U-beam leads to an increase in capacity when compared to the

S_LWh_U configuration. This increase occurs in the second regime, where the curve is much steeper

in case of S_LWh_UMeuse, because removing the downstream U-beam reduces the hydraulic losses

inside the structure.

The outlet is drowned at an upstream water level which is somewhat higher. Given the larger outlet

section, this is a logic result.

0

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26.7 27.7 28.7 29.7 30.7 31.7 32.7

Q [

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hupstream [ m T.A.W.]

S_LWh_U S_Wh_UMeuse

126

The third regime has the same shape for both configurations, but the higher discharge of the

S_LWh_UMeuse configuration that was built up during the second regime remains present as a

constant offset throughout the third regime.

In conclusion, the S_LWh_UMeuse configuration is believed to have some (economic and practical)

advantages over the S_LWh_U-configuration and allows a larger maximum discharge through the

future hydraulic structure. This could mean a reduction in number of required units. Hence, this option

is worth considering in the presumption that this U-beam is not required for a retaining, bearing or

other function.

4. Flow pattern and velocity measurements

Velocity measurements are performed to gain insight in the flow pattern upstream of the structure

(mainly the contraction of the flow) and to be able to give an estimation of the specifics of the bottom

protection. The location of the contraction is of importance for nv De Scheepvaart in order to fine-tune

the approach flow conditions towards the hydraulic structure. Note that the velocity measurements

have been performed on the F_LWh_U_B&C – configuration, which is according to the design of nv De

Scheepvaart, and that the position of the bottom of the flume is at 22.3 m T.A.W. in prototype

dimensions. Thus the tested situation does not correspond to the boundary conditions of the future

hydraulic structure.

4.1 Flow pattern

To visualize the flow pattern towards the structure, experiments using colouring dye were performed

and recorded. These experiments were performed for the peak discharge of 99.8 m³/s and an

upstream water level of 29.24 m T.A.W.. The injections were done at varying depths. The maximum

intensity of the injected dye can be seen in Figure 118, Figure 119,Figure 120 and Figure 121. Two

figures are provided for the same flow pattern to be able to discern both the flow pattern and the

colouring dye.

127

Figure 118: Maximal intensity of the injected dye, injection at about 29 m T.A.W.

Figure 119: Maximum intensity of the injected dye, injection at about 28 m T.A.W.

Figure 120: Maximum intensity of the injected dye, injection at about 26 m T.A.W.

Figure 121: Maximum intensity of the injected dye

128

From these figures, it can be seen that for injection at higher levels, a vertical contraction of the flow

takes place towards the inlet section. For heights, in between 23.7 m T.A.W. and 26.7 m T.A.W. (i.e.

the level of the top of the bottom slab and the soffit of the U-beam), the contraction becomes less

noticeable.

4.2 Velocity measurements

4.2.1 Testing procedure II

By executing the experiments with colouring matter, a good insight in the location of the contraction

was obtained. This location is further concretized by performing velocity measurement at a constant

height underneath the water surface. These measurements were taken at different longitudinal

positions upstream of the hydraulic structure. About the test procedure, more explanation is given in

Two different data point were measured in the stage-discharge relation, having a given upstream

height and discharge. The corresponding values are given in Table 14, where hmeasurement is the height

at which the velocity is measured.

Table 14: The measured data points, corresponding to the peak discharge and discharge at the dip

Nr. Q [m³/s] hupstream [m T.A.W.] hmeasurement [ m T.A.W.]

1 99.89 29.298 28.074

2 91.33 30.972 29.874

In the table above, h measurement stands for the height at which the velocity is being measured. This is at

a level roughly 1.2 m below the upstream water level. The data points mentioned in Table 14, are

indicated on the experimentally obtained Qh-relation in Figure 122.

129

Figure 122: Indication of the measured data points on the experimentally derived Qh-relation for the F_LWh_U_B&C-

configuration

The resulting graph is shown in Figure 123.

Figure 123: Velocity measurements for data point 1 and data point 2

0.8

0.9

1

1.1

1.2

1.3

0 5 10 15 20 25

velo

city

[m

/s]

distance relative to inlet section [m]

Data point 2 (hupstream = 30.97 m T.A.W. and Q = 91.3 m³/s)

Data point 1 (hupstream = 29.3 m T.A.W., Q = 99.9 m³/s)

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26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Q [

m³/

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hupstream[ m T.A.W.]

F_LWh_U_B&C

1 2

130

From Figure 123 can be seen that for data point 1 (corresponding to a peak discharge of 99.9 m³/s and

an upstream water level of 29.3 m T.A.W.), higher velocities occur in comparison to the discharge at

the dip (91.3 m³/s). Note that both measurements are taken at different heights relative to the bottom

of the flume, but at the same height below the upstream water level. The cause of these lower

velocities is because of a higher upstream water level for data point 2 (30.97 m T.A.W. vs. 29.3 m

T.A.W.), which leads to a larger flow section, combined with a lower discharge (91.3 m³/s vs. 99.9

m³/s).

From these curves, especially for data point 2, it can be seen that there is a contraction of the flow in

vertical direction. Then the velocity decreases, as Figure 123 indicates. For data point 2, the contraction

is noticed around a distance of 8 m upstream of the inlet of the structure. For data point 1, this

contraction seems to occur around a distance of ± 5 m relative to the inlet section. These locations are

also indicated on Figure 123. Hence, for higher upstream levels, the contraction takes place more

upstream of the structure.

Throughout the measurements on the F_LWh_U_B&C-configuration, a small number of stationary

waves were observed upstream of the inlet of the hydraulic structure. These are shown in Figure 124.

Figure 124: Stationary wave pattern on the side of the Meuse

Visual observations of the wave pattern in combination with the results from Figure 123, indicate that

the longitudinal position at which the vertical contraction takes place, is at the location of the

stationary waves. Since the measurements from Figure 123 were taken about 1.2 m below the water

surface, the location of the contraction in these curves, is at a small distance downstream of the

stationary waves.

The observations on these stationary waves indicated that the position of the waves relative to the

inlet, depends on the upstream water level. The higher the water level, the larger the distance between

131

the inlet and the waves. Confirming the conclusions from Figure 123, that the higher the upstream

water level, the further upstream the contraction occurs.

These observations suggest the presence of a region with almost no velocity towards the scale model

and a contraction of the flow starting on the water surface near the location of the waves. This region

will also have an impact on the formation of vortices, which is discussed in chapter 3, paragraph 5.2.

4.2.2 Testing procedure I

Furthermore, velocity profiles were measured to verify velocities upstream of the structure. The

measurements have been executed according to testing procedure I, which was described previously

in chapter 4, paragraph 4.2.1. The measured data points (Q, hupstream) are named 3 and 4 and are shown

in Table 15.

Table 15: Discharge and corresponding hupstream and Δh for which velocity measurements have been executed

Nr. Q [m³/s] hupstream [m T.A.W.]

3 98.70 29.23

4 95.15 31.71

To situate these points, they are indicated in Figure 124 on the experimentally obtained Qh-relation of

the F_LWh_U_B&C-configuration.

Figure 125: Indication of the measured data points on the experimentally obtained Qh-relation of the F_LWh_U_B&C-

configuration

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Q [

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hupstream[ m T.A.W.]

F_LWh_U_B&C

3 4

132

4.2.2.1 Data point 3

The velocity measurements on data point 3 (29.2 m T.A.W.) can be seen in Figure 126, showing the

velocity on the x-axis against the height at which the measurement was taken (hmeasurement). These

velocities were measured at a longitudinal distance of 5 m upstream of the inlet of the structure. The

same graph for a longitudinal distance of 10 m upstream of the inlet of the structure can be seen in

Figure 127. The location of the bottom slab of the hydraulic structure is indicated on these graphs by

a black line.

Figure 126: Velocity measurements for data point 3 and a distance of 5 m upstream of the inlet

Figure 127: Velocity measurements for data point 3 at a distance of 10 m upstream of the inlet

22.7

23.7

24.7

25.7

26.7

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28.7

1.05 1.1 1.15 1.2 1.25 1.3

h m

easu

rem

ent[m

T.A

.W.]

V [m/s]

Data point 3, 5 m upstream of the inlet

middle of the flume middle of the inlet section side of the flume

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28.7

1.05 1.1 1.15 1.2 1.25 1.3

h m

easu

rem

ent[m

T.A

.W.]

V [m/s]

Data point 3, 10 m upstream of the inlet

middle of the flume middle of the inlet section side of the flume

133

As can be seen from these figures, the velocity is higher close to the water surface and decreases in

depth for most of the measured points. The velocity is slightly higher at the middle of the flume than

at the middle of the inlet section of a single cycle. The measurements at the side of the flume show a

lot of variation. No clear trend can be discerned for the measurements at the side of the flume. Figures

comparing the data at a different longitudinal location at a fixed transverse location can be seen in

Figure 128, Figure 129 and Figure 130.

Figure 128: Velocity measurements for data point 3 in the middle of the flume

Figure 129: Velocity measurements for data point 3 in the middle of the inlet section of a single cycle

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28.7

1.05 1.1 1.15 1.2 1.25 1.3

h m

easu

rem

ent

[m T

.A.W

.]

V [m/s]

Data point 3, middle of the flume

5 m relative to the inlet 10 m relative to the inlet

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1.05 1.1 1.15 1.2 1.25 1.3

h m

easu

rem

ent

[m T

.A.W

.]

V [m/s]

Data point 3, middle of the inlet section of a single cycle

5 m relative to the inlet 10 m relative to the inlet

134

Figure 130: Velocity measurements for data point 3 at the side of the flume

These figures show that the velocities in the middle of the flume and the middle of the inlet section

are lower at a distance of 10 m relative to the inlet section, compared to a similar measurement at a

distance of 5 m relative to the inlet section. It is also noted that the difference between both 5 m and

10 m relative to the inlet, decreases in height. The differences imply that for an upstream distance of

5 m, the velocities should be smaller at the side of the flume (since more discharge passes through the

centre of the flume) when compared to the velocities at the side of the flume at a distance of 10 m

upstream of the inlet section. However, based on Figure 130, no real conclusions can be made on this

matter. Distortion may be caused by effects due to the presence of the wall of the flume or due to a

narrow gap between the side of the honeycombs, located more upstream in the flume, and the wall

of the flume. This is shown in Figure 131.

22.7

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26.7

27.7

28.7

1.05 1.1 1.15 1.2 1.25 1.3

h m

easu

rem

ent

[m T

.A.W

.]

V [m/s]

Data point 3, side of the flume

5 m relative to the inlet 10 m relative to the inlet

135

Figure 131: Indication of the gap between the side of the honeycombs and the wall of the flume

4.2.2.2 Data point 4

For the data point 4 (hupstream of 31.71 m T.A.W.), velocities have only been measured at the centre of

the inlet section of a single cycle.

Figure 132: Velocity measurements for data point 4 at the middle of the inlet section

For the data corresponding to a distance of 10 m relative to the inlet, the velocities increase in height.

The velocities are again smaller, or have approximately the same magnitude for a relative distance of

10 m compared to a relative distance of 5 m to the inlet section.

22.7

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30.7

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

h m

easu

rem

ent

[m T

.A.W

.]

V [m/s]

Data point 4, middle of the inlet section

5 m relative to inlet 10 m relative to inlet

136

4.2.2.3 Comparison of both data points

When comparing the measurements on data point 3 (hupstream of 29.2 m T.A.W.) and data point 4

(hupstream of 31.71 m T.A.W.) for the middle of the inlet section, the graph in Figure 133 is obtained.

Figure 133: Comparison of the velocity measurements for Q = 98.7 m³/s and Q = 95.15 m³/s at the middle of the inlet

section

From this figure, it can be seen that lower velocities occur for data point 4 (hupstream = 31.71 m T.A.W.,

Q = 95.15 m³/s) than for data point 3 (hupstream = 29.2 m T.A.W., Q = 98.7 m³/s). This can be explained

by the higher upstream water level at data point 4, leading to a larger section through which the water

flows, combined with a slightly lower discharge.

When comparing the measurements from data point 4 for an upstream distance of 5 m and 10 m,

several conclusions can be made. The velocity increases in the lower half of the flume (i.e. from the

bottom of the flume up to a height of ± 27.0 m T.A.W.) from a distance of 10 m relative to the inlet to

a distance of 5 m relative to the inlet. This can be explained by the contraction of the flow in vertical

direction towards the inlet section. Note that the soffit of the U-beam (i.e. the top of the inlet section)

is at 26.7 m T.A.W.. The velocities close to the water level have approximately the same value, while

at lower height the velocity at 5 m is higher than the velocity at 10 m. This indicates that more discharge

goes through the section at 5 m than at 10 m. A possible hypothesis for this, is that besides a vertical

contraction also a contraction in horizontal direction occurs towards both openings of the inlet.

No velocity measurements for this data point (i.e. data point 4, hupstream = 31.71 m T.A.W., Q = 95.15

m³/s) at the middle of the flume are available to check this theory concerning the horizontal

22.7

23.7

24.7

25.7

26.7

27.7

28.7

29.7

30.7

0.54 0.64 0.74 0.84 0.94 1.04 1.14 1.24 1.34

h m

easu

rem

ent

[m T

.A.W

.]

V [m/s]

Middle of the inlet section of a single cycle

Data point 4, 5 m relative to inlet Data point 4, 10 m relative to inlet

Data point 3, 5 m relative to inlet Data point 3, 10 m relative to inlet

137

contraction. The measurements from data point 3 do not confirm this theory. However for data point

3, less difference in velocity is measured between the section at 5 m and the section at 10 m, than for

data point 4. Additionally, no contraction in vertical direction was observed data point 3.

Assuming that the stationary waves indicate the location of the flow contraction in vertical direction,

as explained in paragraph 4.2.1, an explanation for the absence of vertical flow contraction for data

point 3 (hupstream = 29.2 m T.A.W., Q = 98.7 m³/s) can be given. The stationary waves are located at a

distance less than 5 m upstream of the structure for data point 3. For data point 4, the waves are

located further upstream, conform to the theory explained in paragraph 4.2.1. This explains why no

vertical contraction is noticed for data point 3. The contraction starts at approximately 5 m upstream

of the structure, as was indicated at Figure 123 from paragraph 4.2.1. For data point 4, the

measurements are influenced by the wave pattern. Two conceptual drawings, sketching the situation

for both discharges, can be seen in Figure 134 and Figure 135.

Figure 134: Conceptual drawing indicating the contraction of the velocity profiles for data point 3

Data point 3 (hupstream = 29.2 m T.A.W., Q = 98.7

m³/s)

V [m/s] V [m/s]

138

Figure 135: Conceptual drawing indicating the contraction of the velocity profiles data point 4

4.3 Velocities downstream of the structure

No velocity measurements have been executed on the downstream side of the structure.

Whitecapping on the downstream side of the hydraulic structure disappears at a distance of 15 to 20

m more downstream, for the peak discharge (i.e. ± 99 m³/s). Hence, the turbulence at the outlet, is

limited to a region of 18 to 20 m downstream of the structure. This value is obtained based on visual

observations.

4.4 Critical remarks

Two (main) critical remarks concerning the velocity measurements have to be made. They concern the

interpretation of the velocities measured on the scale model in the flume in function of the structure

at Heerenlaak.

Firstly, the presence of a standing wave pattern in front of the structure influences the velocity

measurements, as was stated above. Questions can be raised whether this standing wave pattern will

occur for the structure at Heerenlaak, since the labyrinth weir in a culvert is not located in a canal or

Data point 4 (hupstream = 31.71 m T.A.W., Q = 95.15

m³/s)

V [m/s] V [m/s]

139

wave flume, and the flow approach conditions at Heerenlaak do not match these of the tested

configuration. A second remark concerns the position of the bottom of the flume relative to the height

of the bottom slab. During the scale model test, the bottom of the current flume is at 22.7 m T.A.W..

Since no details concerning the bottom of the Meuse at the location are available, the influence of the

embankment on the velocities is not included in the velocity measurements on the scale model study.

5. Quantification of vortices

During some experiments, the formation of vortices was noticed. Consequently, this phenomenon was

investigated based upon the most important findings stated in the literature review. The presence and

the different types of vortices are investigated and the application of the theories given in the literature

about vortices is explored.

5.1 Presence of vortices

For the experiments in the F_LWh_U_B&C configuration at different upstream water levels (keeping

the difference with the downstream level at a constant value of 2 m), observations are made. If

present, vortices are classified according to the classification system of Knauss (1987), as discussed in

the literature review.

Figure 136: Example of a full air core vortex at a discharge of 91 m³/s and an upstream water level of 28.24 m T.A.W.

For low flows, no vortices were observed. At an upstream level of approximately 27.4 to 27.5 m T.A.W.

(i.e. the water level is 0.8 to 0.9 m above the soffit of the U-beams) and a discharge of 50 to 60 m3/s,

surface dimples (type II) start to appear. At higher flows, full air core vortices (type VI) appear. These

140

are observed when the upstream water level reaches a height of 28.2 to 28.3 m T.A.W., corresponding

to a discharge of about 92 m3/s. These findings are consistent with the literature, stating that the

formation of vorticity starts rapidly after the inlet section becomes submerged and grow in intensity

with increasing submergence.

The intensity of the vortices is highest for flows of about 92 to 98 m³/s, corresponding to an upstream

water level of 28.5 to 29.4 m T.A.W.. For even higher flows, the intensity of the vortices diminishes

again.

5.2 Critical submergence

As explained in the literature, the critical submergence is defined by different researchers in a

somewhat different manner. The definition used in this paragraph is the one adopted in most research,

i.e. the threshold at which air-entraining vortices change into non air-entraining vortices. The definition

of critical submergence is thus partly based on subjective evaluation of the presence and the type of

the vortices and is as a result subject to uncertainty.

Numerous formulas for the determination of the critical submergence have been proposed by the

different researchers. Some formulas take into account more influence factors than others. The

formulas applied to the data from the hydraulic model are given below with further explanation in

Table 16.

- The formula of Gordon (1970) for symmetrical approach flow conditions:

- The formula of Ahmad et al. (2008) used when the bottom clearance is zero (e = 0):

and for when the bottom clearance is equal to half of the diameter (e = D/2):

- The formula of Gürbüzdal (2009) :

141

is the critical submergence above the top of the intake [m]

is height of the intake [m]

is the average velocity through the inlet [m/s]

is the intake Froude number, given by [-]

e is the distance from the bottom of the channel to the intake invert [m]

is the distance of the side wall to the centre of intake for a symmetrical geometry [m]

is the Reynolds number, given by [-]

is the Weber number, given by [-]

The formulas of Ahmad et al. are drafted for a distance between the bottom of the approach channel

and the invert of the intake of either 0 or Di/2. In case of the model tested in the flume, this distance

is equal to 1/3 Di. The submergence should thus be in between both formulas of Ahmed et al.

The critical submergence of the scale model is velocity dependent, which is derived through the known

discharge:

For each measurement of the Qh-relation, the critical submergence is calculated and compared with

the actual submergence of the inlet. When the calculated submergence is smaller than the measured

submergence, air-entraining vortices should not be present anymore. These thresholds are given in

Table 16 and a graphical representation is given in Figure 136.

Table 16: Critical submergence

Formula Utilized parameters * Critical submergence

Gordon (1970)

29.8 m T.A.W.

Ahmad et al. (2008) , for e = 0

29.69 m T.A.W.

142

Ahmad et al. (2008), for e = D/2

e = D/2 = 1.5 m

28.81 m T.A.W.

Gürbüzdal (2009)**

29.42 m T.A.W.

*In the table above, is the width of the flume, rescaled with a factor 18 for comparison in

prototype values. The same remark is applicable on , which is the upstream water level

relative to the bottom of the flume, rescaled with a factor 18 for comparison in prototype values

** In case of the formula by Gürbüzdal, the accompanying boundary condition of

is not fulfilled, hence the results of this formula might be incorrect.

Figure 137: Graphic representation of the measured submergence, compared to the calculated critical submergences

0

1

2

3

4

5

6

7

26.7 27.7 28.7 29.7 30.7 31.7 32.7 33.7

Sub

mer

gen

ce [

m]

hupstream [m T.A.W.]

Experimentally measured submergence Critical Submergence by Gordon (1970)Critical submergence by Ahmad (e=0) Critical submergence by Ahmad (e=D/2)Critical submergence by Gurbuzdal

Observed critical submergence

143

In our observations, the threshold between air entraining vortices and non-air entraining vortices (i.e.

the critical submergence) was denoted at an upstream water level of about 31.5 m T.A.W.. This

corresponds to a submergence of 3.8 m. Note that, as explained before, defining the critical

submergence is based on a subjective evaluation of the presence and strength of the vortices. Above

the denoted critical submergence, small vortices were still present but they were very weak, with no

air-entrainment.

As the results in Table 16 and Figure 137 indicate, the critical submergence of the scale model is a lot

higher than the theoretical values proposed by Gordon, Ahmad et al. and Gürbüzdal would suggest.

This means the vortices still remain present at high upstream water levels.

The most likely explanation is that this is caused by the geometry of the front of the hydraulic structure.

In the literature review about vortices, it was mentioned that vortices are formed by rotational motions

of fluid regions and they find their origins in discontinuities in the flow pattern. Gordon (1970, see

Baykari, 2013) explains one of the influencing aspects on the formation of vortices to be the geometry

of the approach flow to the intake. Since the U-beam creates the possibility for the water to rotate in

a water zone with no velocity, swirling motion and hence vorticity is stimulated significantly. This is

illustrated in Figure 138.

Figure 138: Stimulation of vorticity caused by the geometry of the structure front, top view of F_LWh_U_B&C

144

This was established before (see section 2.8), by comparing two identical scale models having a

different front section. In the scale model with a flat front geometry (S_LWh_U, see, Figure 139)

significantly less vortices were observed. However, no systematic classification of the vortices in the

S_LWh_U configuration has been made.

Figure 139: The front of S_LWh_U

Since all the formulas mentioned above have been based upon intakes with a flat front surface (i.e. a

vertical plane with an orifice), this could explain the poor agreement in critical submergence between

the theory and observations.

5.3 Application to the future hydraulic structure

When considering the observed vortices on the scale model, it is verified whether scale effects could

play an important role. In the literature review about vortices (chapter 3, paragraph 5.4), it was

concluded that the surface tension of water can be neglected when the Weber number

is higher than 720 and the viscosity can be neglected if the Reynolds number ( ) is

higher than . The Reynolds number and Weber number of the data in the scale model were

calculated, reaching higher values than the prescribed ones at a discharge of about 85 m³/s and an

upstream water level of 27.86 m T.A.W. and higher. Thus, it can be concluded that scale effects should

be negligible when researching the critical submergence of the vortices.

Because the future hydraulic structure is built inside a dike (Figure 140), the rotational motion above

the inlet may even be enhanced, considering the flow of the Meuse is perpendicular to the flow

145

through the structure. This flow through the Meuse could create extra angular momentum on the

water above the U-beam, which could enhance the presence of vortices and their strength. However,

this is dependent on the actual construction and flow conditions, thus care should be given after the

implementation on the Meuse.

Figure 140: Cross-section of the hydraulic structure inside the body of the dike

By the presence of vortices, debris could be drawn inside the structure. The U-beams are designed to

prevent the ingress of floating debris, but the vortices might suck this floating debris inside, diminishing

the effectiveness of the U-beams. To verify this, some tentative tests were performed by use of floating

polypropylene-particles with a diameter of about 3 mm and paper lumps (diameter of about 1.5 – 2

cm). These tests confirm the possibility of trash intake caused by vortices. It must be remarked,

however, that these tests were tentative and no scaling was done to verify this.

Figure 141: Examples of the tentative trashtests

Meuse

Sheetpiles Spillway

Heerenlaak pond

146

Trash intake by vortices must be avoided for structural, maintenance and environmental reasons.

Some possibilities for vortex mitigation are given in the literature review, such as trashracks, floating

or submerged rafts, … However, for the future hydraulic structure, nv de Scheepvaart is not in favour

of trash racks, while the other solutions might hinder the intended function of the U-beams, namely

to intercept debris of the Meuse. Small adaptions to the surrounding geometry at the inlet might be a

solution, in order to decrease the rotational motion of the water.

147

Chapter 7: Conclusions

To remove one of the remaining bottlenecks in the Common Meuse, a hydraulic structure has been

designed by ir. H. Gielen (nv de Scheepvaart) to be built in a levee near the Heerenlaak pond. This

structure consists of a labyrinth weir integrated in culvert and consists of two labyrinth cycles, further

referred to as one unit (see chapter 2, paragraph 1). The intention is to implement a number of these

units to discharge water from the Meuse through the Heerenlaak pond, at times of high discharges in

the Meuse.

The Q-h relation of the proposed structure and the corresponding maximum discharge capacity, have

been estimated by means a desktop study by Flanders Hydraulics Research (FHR, Vercruysse et al.,

2013). Given the many uncertainties, it was recommended to make a scale model study of the

hydraulic structure. This was the main objective of the present master thesis. In the Hydraulics

Laboratory of Ghent University, a study (at scale 1 to 18) has been carried out, in cooperation with FHR

and nv De Scheepvaart. To acquire more insight into the Qh-relation, a literature survey has been

carried out as well as a scale model study of variant configurations of the proposed design. The latter

was also meant to explore possible optimizations of the design.

The main conclusions derived from the scale model study of the proposed design are:

(1) The stage-discharge relation of the hydraulic structure consists out of 3 regimes. The first

regime corresponds to free overflow over a labyrinth weir, in which the discharge only

depends on the upstream water level. The second regime starts when the inlet of the structure

becomes internally drowned, i.e. at an upstream water level of 28.0 m T.A.W.. This regime

seems comparable to flow through a culvert, regime V. The third regime starts when the outlet

of the hydraulic structure is submerged as well, i.e. when the downstream water level reaches

the soffit of the downstream U-beam. During this regime, the discharge capacity of the

structure decreases slightly before reaching a more or less constant value for high upstream

water levels. In the third regime, the capacity depends on the difference in water levels

upstream and downstream of the structure and seems comparable to flow through culverts,

regime IV. This difference is about 2 m at Heerenlaak, although it slightly increases for higher

discharges through the Common Meuse.

(2) A peak discharge of 100 m³/s was reached at the transition from the second to the third

regime, i.e. when the downstream water level is at the soffit of the outlet. This value, however,

148

is somewhat underestimated, since the tested model geometry has some minor discrepancies

with the proposed design (which were induced by choices of commercially available scale

model components, with slightly different thicknesses and sizes as the dimensions suggested

by the conceptual design). When taking into account the effect of these discrepancies, it is

estimated that the capacity of the structure might increase up to 10%. Thus a capacity of 110

m³/s may be reached.

Other conclusions, which were made based on a comparative testing of a wide variety of related

hydraulic structures (integrated in a culvert or not) are:

(1) When the inlet section of the culvert is smaller than the available area over the weir, integrated

in the culvert, the culvert section is the most limiting factor for the capacity of the structure.

However, by reducing the head losses inside the structure the discharge capacity can be

increased.

(2) The occurrence of vortices at the inlet, as well as the presence of eddies inside the structure,

can decrease the capacity of the hydraulic structure. As such, measures preventing the

creation of these vortices could increase the discharge capacity of the structure. Punctilious

design of both the inlet section and the U-beam at the Meuse side of the structure could

ensure this.

(3) Experiments have proven that removing the beams, supporting the roof structure, out of the

flow area between the culvert ceiling and the crest of the labyrinth weir –meaning those

beams have to be integrated either into or on top of the ceiling slab of the culvert –leads to a

discharge increase of 12 to 17%. This is due to the afore mentioned reduction in head losses.

(4) An increase in discharge of about 14% can be reached by removing the downstream U-beam

of the structure, as was demonstrated in the experiments.

(5) Higher differences in Δh between the water levels upstream and downstream of the structure,

result in higher discharge capacities.

Based on the literature review, it is concluded that the proposed design can possibly be improved in

several respects (crest shape, rounded upstream abutments, rounded U-beams, filled alveoli …). Yet,

the influence of most improvements diminishes for large ratios of the total upstream head HT to the

height of the labyrinth weir P. Nonetheless, the use of filled alveoli and its corresponding merits

(smaller required wall thickness, the possibility to use a stair step and facilitating the practical

construction process) seem to be promising for the structure at Heerenlaak.

149

For the proposed design, 3 units (each consisting out of two labyrinth weir cycles) are required to allow

the passage of the target discharge of 300 m³/s. It is expected that these three units will have a

maximum capacity of about 320-330 m³/s. Taking into account possible improvements to this design

(e.g. integrating the supporting beams into or on top the roof) and the fact that for higher upstream

levels, the difference between the upstream and downstream side of the structure increases, it is

believed that a discharge of 390 m³/s can be reached. This implies that a total of 5 cycles will be

sufficient to allow the passage of 300 m³/s (assuming a discharge capacity of 65 m³/s for each cycle).

However, it is unknown if this is practically possible.

During the scale model experiments, the approach flow was uniform and aligned with the longitudinal

axis of the culvert. When finalizing the design, the approach channel between the river Meuse and the

hydraulic structure should preferably be made such that comparable approach flow conditions are

present. Otherwise, the abovementioned number of units to reach the target discharge of 300 m³/s

should be taken with caution.

150

Chapter 8: Recommendations for further research

Several aspects regarding the hydraulic structure at Heerenlaak have been investigated. The

experimental measurements highlighted some new areas of interest, while other facets of the

structure still remain unaddressed. Therefore some recommendations for further research can be

made.

Scale model testing on the S_LWh_U_Raisedroof configuration showed, somewhat surprisingly, a

decrease in discharge capacity of the structure. The explanation given for this is the creation of eddies

in the structure. Therefore it is highly recommended to further investigate the occurrence of these

eddies and possible measures of preventing them.

In the different configurations, where a linear or labyrinth weir is incorporated in a culvert, a slight

decrease in discharge was noticed in the third regime. Afterwards the discharge increased again slightly

and/or became constant. This dip in the Qh-relation was discussed in chapter 6, paragraph 2.12, where

some possible theories were given and some disproved. However, the origin of this dip was not

investigated further, hence it might interesting to conduct additional research.

The experimental scale model tests have been executed as described in chapter 4. The scale model is

inserted in a channel and the height of the bottom slab of the tested hydraulic structure to the bottom

of the current flume is small ( < 1 m, on prototype scale). The influence of the embankment of the dike

and the approach flow conditions of the Common Meuse (the hydraulic structure is located in a bend,

see chapter 1, Figure 1) are not taken into account during the experimental tests. Additional research

concerning the influence of the approach section could be an interesting topic for further research.

Proceeding on these approach conditions, it might be worth investigating more in depth the formation

of vortices on the Heerenlaak structure. These vortices were observed during the experiments and it

was concluded that they impacted the discharge through the structure. Moreover, the inlet geometry

is assumed to have a major influence on their presence. Hence, researching the specific influence of

the geometry could result in possible improvements of the hydraulic structure.

151

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Appendix A: Proposed design of the hydraulic

structure

158

159

Appendix B: Valeport Model 801 Electromagnetic Flow

Meter

As part of our policy of continuing development, we reserve the right to alter at any time, without notice, all specifications, designs, prices and conditions of supply of all equipment

MODEL 801 Electromagnetic Flow Meter

Datasheet Reference: MODEL 801 version 2A, Feb 2011

The Model 801 Electromagnetic Flow Meters measure the speed of

water in Open Channel environments with exceptional accuracy. Two

sensor types are available, to suit different application requirements,

but both offer excellent durability, reliable accurate data, and are

suitable for use in clean water and dirty or difficult environments.

Specifications

Model 801 - Cylindrical Type

Range: -5m/s to +5m/s

Accuracy: ±0.5% of reading plus 5mm/s

Zero Drift: <5mm/s

Sensing Volume: Sphere of approx 12cm diameter around sensor

Minimum Depth: 15cm

Model 801 - Flat Type

Range: -5m/s to +5m/s

Accuracy: ±0.5% of reading plus 5mm/s

Zero Drift: <5mm/s

Sensing Volume: Cylinder of approx 20mm Ø x 10mm high

Minimum Depth: 5cm

Calibration

Both instruments are calibrated to NAMAS traceable standards at

Valeport’s own premises up to speeds of 1m/s. Higher speed

measurements are based on linear extrapolation. Specific high speed

calibrations can be arranged at a third party facility on request.

Display Unit

Size: 244mm x 163mm x 94mm, 2kg

Environmental: Sealed to IP67

Power: 8 x alkaline C cells, lasting for up to 37 hours

Operating Temp.: -5°C to +50°C (display unit)

-5°C to + 40°C (sensor)

Configuration

Both instruments are available for use as hand held “Wading Sets” only,

with the operator standing in the channel, holding the instrument in position.

The system is supplied with 1.5m wading rod (3 x 0.5m sections),

graduated in cm, and a 3m cable from instrument to display unit.

Alternatively, a “top-setting” wading rod system is available, which allows

the vertical position of the instrument to be set without removing the wading

rods from the water.

Software

System is supplied with CDUExpress Windows based PC software, for data

extraction from display unit. CDU Express is license free.

Shipping

Standard: 62 x 42 x 34cm, 9kg (wading set)

Ordering

0801001 Single axis cylindrical sensor, c/w 3m cable, control

display unit (with logging facility), and operation

manual. Supplied in ABS transit case.

0801002 Single axis flat sensor, c/w 3m cable, control display

unit (with logging facility), and operation manual.

Supplied in ABS transit case.

0801003 Wading rod set c/w 3 x 0.5m graduated rods, base,

direction knob, and canvas carrying bag.

0801011 Option - Large transit case to take instrument and

wading rods.

What’s the Difference?

The smaller sampling volume of the flat sensor makes it very much more

suitable for shallow flows, or measurements in confined spaces. However,

it is also very much more sensitive to turbulent flows, which may manifest

as apparently noisy real time readings. This effect can be minimised by

using a long (>30secs) average period. The larger sampling volume of the

cylindrical sensor effectively eliminates the turbulence noise, but also

means that a greater depth of water is required for measurements.

Data Acquisition

The Model 801 Flow Meters are supplied with a dedicated surface display

unit, which both drives the sensor and provides data display of the

measured water velocity.

Data is updated at 1Hz, and may be averaged over any number of seconds

from 1 to 600. The display will show real time speed data at a resolution of

1mm/s, as well as the result of the data average, and a Standard Deviation

figure to give added data confidence. A solid state memory records all

results (up to 999 averaged readings), and the data may be downloaded to

PC using the RS232 interface lead supplied.