A New Improved Formula for Calculating Trashrack Losses

A NEW IMPROVED FORMULA FOR CALCULATING TRASHRACK LOSSES

Hubert Meusburger1, Peter Volkart2 and Hans-Erwin Minor3

Laboratory of Hydraulics, Hydrology and Glaciology (VAW)

1Research engineer, 2Head of Laboratory, Dr. sc. Techn., 3Director, Prof. Dr.-Ing.

Swiss Federal Institute of Technology (ETH), CH-8092 Zurich, Switzerland

Tel. +41 1 632 11 92, Fax. +41 1 632 11 92, E-mail: [email protected]

Abstract: Practical experience during operation over the past decades has shown relevant discrepancies between measured and theoretically determined energy losses at intake trashracks of low head river power plants. On the one hand side not all loss-relevant parameters are taken into account by the usually applied equations and on the other hand, thorough comparison of field measurement data is prevented by rapidly changing flow conditions and widely varying geometrical parameters which all may have an influence on the quality of the obtained results. This contribution tries to point out how this gap can be bridged and better prognosis of trashrack losses can be reached by applying a new equation in combination with numerical analysis of the flow field in the vicinity of such trashracks.

Keywords: trashrack, energy loss, numerical flow computation, inhomogeneous inflow

1 INTRODUCTION

To prevent floating debris as well as suspended solids from entering the intake openings, trashracks are usually placed directly in front of them. Nowadays commonly used formulas to determine the energy losses caused by these trashracks origin from the early 20th century, e.g. Kirschmer [1] published in 1926. Derived under laboratory conditions, these formulas normally lack of means to take into account phenomena such as inhomogeneous velocity distributions, sectional blockage of the trashrack, turbulence or even vortice structures which all may strongly

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influence actual performance of the trashrack in practice.

This might be a reason why actually measured energy losses at prototype sites tend to be remarkably higher than the theoretically determined losses.

2 THE NEW FORMULA

To derive the new VAW-formula hydraulic model tests were conducted in an experimental set-up constructed in a 12 m long laboratory flume at a scale of 1:3. The mounted trashrack measured 500 mm in width an 700 mm in height. The implemented bars had a rectangular cross-section (s/l = 5/50 mm). In addition horizontal spacing elements were positioned at three different levels on the trashrack, just as a possible solution might look in practice. During the model tests, the following parameters were varied: the average flow velocity through the trashrack vR ( 0 . 5 m / s – 1 . 5 m / s ) , t h e h o r i z o n t a l a n g l e o f t h e i n f l o w

d (0° – 30°), and the clear spacing between the bars b (15 mm – 135 mm). The parameter are also described in Figure 1.

The so-called blockage ratio p is defined as

(1)

Where ARS is the area blocked by the bars, AAH the area blocked by the horizontal spacing elements and ARF the total area of the trashrack field. By varying b as

mentioned above, p took on values in between 0.18 and 0.54.

The empirical formula, developed from these model tests, can be written as:

[m] (2)

Where

[-] (3)

vR being the average velocity at the unblocked (gross) area at the trashrack cross-section [m/s], kF the form factor according to Kirschmer [-] (for the used cross-

section being 2.42), δ the horizontal angle of inflow [°], p the blockage ratio [-] (see eq. 1), b the clear spacing between the bars [m], l the length of the bars [m], α the vertical angle in between the main direction of the local current and the trashrack [°], B = 0.65 [-] the coefficient for the horizontal angle of inflow, C = 1.33 [-] the coefficient applicable to the blockage ratio p, D = –0.43 [-] the coefficient applicable to the ratio of b/l.



3 COMPARATIVE VIEWS

In German-speaking countries, state-of-the-art calculation of energy losses is frequently based on the relation according to Kirschmer [1] or Zimmermann [4]. Further relations, such as the ones according to Fellenius [5], Escande [6], Berezinski [7] and Ideltchik [8] are also often referred to.

Calculations according to Kirschmer, Fellenius, Escande, Spangler and Zimmermann estimate lower energy losses than the new VAW-formula does in the case of frontal inflow (δ= 0°) where the relations of Ideltchik and Berezinski lead to results overtopping the VAW-formula by 36 % and 93 % respectively (Fig. 2).

Using Berezinki’s formula, prototype peculiarities, such as the age of the power plant and different trashrack cleaning concepts, can be taken into account. The effects of such parameters can obviously influence the obtained results dramatically as shown in the example.

4 APPLICATION OF THE NEW VAW-FORMULA IN PRACTICE

For the determination of trashrack losses in practice two fundamentally differing cases are to distinguish:

Case 1 “Design Phase”: Determination for a trashrack to be designed from the scrap.

Case 2 “Refurbishment”: Determination for a trashrack which is to be replaced.

Subsequently for both of these cases an application example of the VAW-formula for a specific power plant is presented and afterwards compared with corresponding calculations according to Kirschmer and Zimmermann. Additionally interpretation of field measurement data gathered at this power plant regarding the above mentioned results is done.

4.1 The power plant

The focused on prototype is a so-called bay power plant located at the river Fulda north-east of the city of Kassel in Germany. The installed Kaplan-turbine (flow rate: 60 m3/s) was originally protected by a trashrack featuring a clear spacing b of 60 mm. Due to ecological demands (fishery etc.) the clear spacing b had to be reduced to 20 mm which lead to a replacement of the original trashrack. The necessary parameters for the calculations are indicated in Table 1.

4.2 Case 1: “design phase”

In this case, determination of the energy losses is a sequence of three steps. In a first step, applying “Hydro2de”, a program developed at the VAW which solves the shallow water equations on a structured computational grid, the flow to the intake is calculated in a wider area, consisting of the power station intake, the weir system and



about 100 m of the flume upstream. As initial conditions the total discharge, the weir and turbine discharge and the water level are given. The results of this step, basically the obtained flow field, enter the following three-dimensional calculations carried out using “CFX-F3D” as initial and boundary conditions. For this step, the model area is reduced and investigation focuses on the two trashrack fields, a short part of the turbine inlet and a cantle of the river approx. 20 m long and 15 m wide. Having gone through these procedures, the velocity field in front of each of the trashracks is now determined.

In a final stage each of the trashracks is subdivided into 18 partial fields in which the mean values for the angle of the inflow and inflow velocity are evaluated. Based on these values the empirical relations according to Kirschmer and to Zimmermann as well as the VAW-formula can be applied and the energy losses for each of the 18 partial fields be determined. The total energy loss for the trashrack field can finally be found by calculating the mean value over all 18 partial fields (Table 2).

4.3 Case 2: “refurbishment”

Prognosis of future trashrack losses in this case is not only rather easy but also, within certain not very confining limits, accurate. First of all collecting field data will allow for a precise determination of the actual energy losses caused by the current layout. Subsequently a calculation of the actual and of the future energy losses is to be done using the VAW-formula. At this stage it is rather important to evaluate the blockage ratio of both trashracks (the installed one at present and the future one) precisely, while the horizontal angle of inflow may be estimated roughly.

Multiplying the results from the field measurements by the so-called “E-Factor” (increase factor, Table 3), which represents the ratio of the δ-values of both trashracks, finally equals the expected future energy losses.

Applying this procedure to the test case mentioned earlier, estimation of the energy losses would lead to the following differences of water levels in front and behind the future trashrack (b = 20 mm): according to Kirschmer 654 mm, according to Zimmermann in between 246 and 654 mm and using the VAW-Formula 420 mm. All these values are basing on a measured difference of water levels at the old trashrack (b = 60 mm) of 150 mm.

In the following discussion these results are to be compared also with field data gathered at the new trashrack (b = 20 mm) where the water level difference accounted for 370 mm.

5 DISCUSSION



As seen above, applying the VAW-Formula to the test case lead to a water level difference at the new trashrack of 420 mm which matches the actually measured difference (370 mm) rather well. Therefore, in the case of a refurbishment, this method seems to be an appropriate way to estimate future water level differencies.

Nevertheless this water level difference is not to be confused with the actual energy loss. If the intake loss (31 mm, loss that would occur also without having a trashrack placed) and the difference in the velocity potential (120 mm) are subtracted from the measured water level difference (370 mm) an effective loss of energy of 219 mm results. Comparing this value with the value for the loss of energy calculated using the VAW-Method (being 100 mm, see Tab. 3), a difference of 119 % is observed.

There are several reasons for that difference. Negative pressure, resulting from the strongly curved shape of the intake and separation effects at the edge of the dam beam slot may lead to a lower water level exactly at the reading point which was placed in the dam beam slot.

Furthermore it might well be, that the assumed flow rate through the trashrack and therefore the flow velocity were smaller than the actual values during the field campaign. The latter were calculated from performance values of the generator under certain assumptions for the efficiency factor of the machinery.

The fact that the water level differences calculated according to 4.3 match the measured values well, implies, that those parts of the water level differences which are not easy to explain are independent of the blockage ratio and the horizontal angle of inflow. Regarding the above explanations the conclusion can be drawn, that these residual discrepancies depend only on not directly measurable velocity differences.

It can be assumed, that the influence of the angle of inflow, the blockage ratio and the geometry of the bars are considered accurately using the VAW-Method and that therefore evaluation of energy losses is reliably performed.

6 CONCLUSIONS

Data from many field measurements have shown that the flow conditions in the vicinity of trashracks are fully three-dimensional, turbulent and locally transient. The velocity field is inhomogeneous and local velocity peaks may overtop the average velocity substantially. Asymmetric operational regimes of more than one turbine and the actual position of the power plant relative to the main currents in the river may intensify these inhomogenities.

The relevant parameters of energy losses are: approach velocity vR, angle of inflow δ, blockage ratio p, clear spacing between bars b, thickness of bars s, length of bars l, shape of bars kF, inclination of the trashrack α, and local blockage of the trashrack.

Using common relations the energy loss at trashracks is normally substantially underestimated.

The water level difference in front and behind the trashrack does not



correspond directly to the energy loss caused by the trashrack. Mainly the local geometry may influence the water levels by causing negative pressure and separation effects.

The proposed VAW-Method leads to results accurate enough for reliable prognosis of energy losses in both cases, the new design of a trashrack and refurbishment.

The practical example shown underlines that reducing the clear spacing b from 60 mm down to 20 mm increases the energy losses caused by the trashrack significantly. The increase factor is around 2.5 or 2.8 for measured values or calculated values (using the VAW-Method) respectively.

References

[1] Kirschmer, O. (1926): Untersuchungen Uber den Verlust an Rechen, Mitteilungen Hydraulisches Institut Munchen, Nr. 1

[2] Meusburger, H. - Volkart, P. (1999) Untersuchung Uber den Einfluß der Geometrie und Anstromung von Einlaufrechen auf den Betrieb von Wasserkraftwerken (unveroffentlicht). Untersuchungsbericht der Versuchsanstalt fur Wasserbau, Hydrologie und Glaziologie der Eidgenossischen Technischen Hochschule Zurich, Nr. 4109, im Auftrag der Vereinigung Deutscher Elektrizitatswerke-VDEW-e.V.

[3] Zimmermann, J. (1969): Widerstand schrag angestromter Rechengitter, Universitat Fridericana Karlsruhe, Theodor-Rhebock-Flubbaulaboratorium, Mitteilungen Heft 157.

[4] Fellenius, W. - Lindquist, E. (1929): Verluste an Rechen, Hydr. Lab. Practice, ASME, NY.

[5] Escande, L. (1947): Pertes de charge a la traversee des grilles, Complements d’Hydraulique 1.

[6] Mostkov, M.A. (1954): Hydraulisches Handbuch, Moskau.

[7] Spangler, J. (1928): Untersuchung Uber den Verlust an Rechen bei schrager Zustromung, Mitteilung des hydraulischen Instituts der TH Munchen, H2.

[8] Ideltchik, J. (1960): Formeln der hydraulischen Fliebverluste, Moskau.

[9] VAW; Beffa, C. (1997): Benutzerhandbuch Version 1.4, Beffa Hydrodynamik, Schwyz.

[10] CFDS, (1995): Flow Solver User Guide, Computational Fluid Dynamics Service.



Fig. 1 Parameters of trashrack geometry and of the flow in hydraulic model invstigations

Fig. 2 Comparison of the trashrack loss ΔhR according to different authors for frontal

inflow (δ = 0°, vR = approach velocity) with the new VAW equation.

Table 1 Parameter of the original and new trashrack

Parameter kF [-] b

[mm] s [mm] l [mm] p [-] α [°] δ [°] vR

[m/s] Trashrack old

2,42 60 10 120 0,250 90 0 ; 30 1,11

Trashrack new

2,42 20 8 100 0,381 90 0 ; 30 1,11



Table 2 Calculated energy losses according to different equations in combination with numerical computation

Table 3 Calculated energy losses according to different equations with specification of the E-factor

Kirschmer Zimmermann VAW ΔhR ΔhR ΔhR [mm] [mm] [mm]

Trashrack old 15 31 36 Trashrack new 66 114 100

Kirschmer Zimmermann VAW ΔhR ζR ΔhR ζR ΔhR ζR [mm] [-] [mm] [-] [mm] [-] δ = 0° δ = 0° δ = 0° δ =

30°δ = 0° δ = 30° δ = 0° δ =

30°δ = 0° δ = 30°

Trashrack old 14 0,22 14 111 0,22 1,77 32 45 0,52 0,71 Trashrack new

60 0,96 60 183 0,96 2,91 91 125 1,45 1,99

E-Factor 4,36 E-Factor 4,36 1,64 E-Factor 2,78 2,80



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A New Improved Formula for Calculating Trashrack Losses