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Flow and Turbulence Characteristics of Open Channel Flow over a Mobile Bed

Prashanth Reddy Hanmaiahgari, Vesselina Roussinova, Ram Balachandar and Tirupati Bolisetti Department of Civil and Environmental Engineering, University of Windsor

Windsor, Canada

Abstract— The particle image velocimetry (PIV) technique has been used to study turbulence characteristics of the flow over a mobile sand bed in an open channel flow (OCF). Initially, the flow is in the fully rough regime and the bed is non-mobile. As the flow velocity is increased, bed becomes mobile. This paper presents preliminary results for the vertical distributions of the velocity, turbulence intensities and Reynolds shear stress, in a region above y+ = 20 on the non-mobile and mobile rough bed. The present experiments are compared with previously reported data on a smooth bed.

Keywords-PIV; mobile-bed; OCF; turbulence; log-law

I. INTRODUCTION

Current knowledge of flow and turbulence characteristics

over a rough sand bed is still unable to explain the mechanisms by which dunes are formed. Most of the previous experimental studies on dunes were based on studying turbulence characteristics over fixed dunes where the role of mobile sediment was ignored. In natural flows, bed is continuously changing and bed forms such as dunes and ripples are formed as a result of the continuous sediment transport. Analysis of turbulence characteristics of mobile bed in open channel flow is very important in order to quantify bed resistance, Reynolds shear stresses and secondary flows. The turbulence generation in a non-mobile, but porous sand bed still needs to be understood. The state of knowledge regarding the turbulence characteristics due to mobility of the bed is very sparse. This paper presents experimental results obtained using a particle image velocimeter (PIV) to characterize flow field and turbulence in open channel flow over a mobile sand bed. Results of the present experiments are verified with the previously published data on flow over smooth bed.

Experimental investigations have produced increasingly detailed and consistent information for the turbulence structure of smooth open channel flows (e.g., Nakagawa and Nezu [1]; Tachie, Bergstrom and Balachandar [2]; Balachandar and Patel [3]; Krampa-Morlu and Balachandar [4]) and boundary layer flows (e.g., Tachie, Bergstrom and Balachandar [5]; Jimenez [6]). Bigillon, Niño and Garcia [7] studied turbulence characteristics of flow over a sand layer glued to the smooth channel bottom using a PIV. However, studies of the effect of roughness on turbulence characteristics in a mobile sand bed

are very limited. Most of the earlier studies reported pointwise turbulence measurements obtained by using hot-film anemometry (e.g., Antonia and Krogstad [8]), laser Doppler velocimetry (e.g., Tachie, Bergstrom and Balachandar [2]; Balachandar and Patel [3]) and acoustic Doppler velocimetry (e.g.,Nikora and Goring [9]). PIV provide velocity information in multiple points in the plane, allowing investigation of the spatial variation of the velocity (Hyun, Balachandar, Yu and Patel [10]; Manes, Pokrajac, and McEwan [11]) and vorticity fields.

This paper investigates the double averaged turbulence characteristics of OCF on a mobile sand bed using PIV. Results for the mean flow, turbulence intensities and Reynolds shear stress are compared with previous results obtained on a smooth bed using laser Doppler velocimetry (LDV) technique.

II. EXPERIMETNS

A. Experimental setup

The experiments were conducted in a rectangular open channel flume 12.0 m long, 0.61 m wide, and 1.0 m high. The test section was located 3.5 m downstream from the start of sand bed which was sufficiently long for the flow to attain a fully developed state. A ramp was build at the start of the sand bed to avoid any disturbances in approaching flow (Fig. 1) and smoothly transition the flow onto the bed. The sand bed was 5.8 m long and 0.15 m thick spanning the width of the flume. The mean size diameter ( ) of the sand grains was 0.7mm. The roughness height ( ) is considered equal to , i.e.

=0.7 mm. A centrifugal pump of 25 HP was used to control and recirculate the water in the flume.

The PIV experiments were conducted in a vertical central plane of the channel and the size of the observation field of view (FOV) was 0.075 m 0.075 m. A Nd-YAG laser with 300 mJ/ pulse was used to illuminate the flow. The particle images were recorded using a 4M pixels camera and synchronized with the laser. The camera resolution was 2048 x 2048 pixels and it was able to capture two consecutive images of the FOV with small time separation (Δ ). The flow was continuously seeded with spherical hollow glass particles of mean diameter 12m with a specific gravity of 1.13 manufactured by Potters Industries Inc.

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For each test, a series of 2000 pairs of images was recorded and analyzed. The images were analyzed with the TSI Inc Insight software. The velocity at any point is determined by measuring the movement of the particles between two consecutive recorded images using a two dimensional cross-correlation technique. Each frame was split up into a grid of small interrogation areas (IA) where the correlation analysis is performed. The details of the correlation technique are provided by Westerweel [12]. There was a 50% overlap of the neighboring IA such that a grid containing about 127 x127 velocity vectors was produced for the flow field on each image with a resolution of about five wall units. The spurious vectors, estimated to be less than 2%, were eliminated on the base of a range filter and a median filter. The PIV data yield instantaneous vector fields for the whole field of view, for each pair of images analyzed. Turbulence characteristics were computed by double averaging of the velocity data ([13]) and the results are presented in the following sections.

B. Experimental conditions

The present experiments were carried out under uniform flow conditions for non-mobile bed where the flow depth was 0.08 m. For mobile bed conditions, only velocity is increased and all other flow conditions were same. The aspect ratio (width of the channel to depth ratio) is 7.63 which is large enough to avoid side wall effects. Reynolds number / based on the total depth ( ) and maximum free stream velocity ( ) were 16696 and 26713 respectively. The Froude number for these two experiments was 0.27 and 0.44 which corresponds to subcritical flow regimes.

The value of the friction velocity was obtained using two different methods. The first method fits the velocity defect equation proposed by Krogstad, Antonia and Browne [14] to the measured velocity distribution in the outer region y/h > 0.1 which is referred here as ∗ . Krogstad, Antonia and Browne [14] proposed an equation for the outer layer velocity distribution of the velocity in a fully developed rough turbulent boundary layer given by:

2Π1

12Π

1 6Π

1 4Π1

(1) Here, is the boundary layer thickness, is the wall normal location; is the virtual origin located below the top of the roughness elements and is the von Karman constant 0.41. Equation 1 has been adopted for the flow in straight open channel flow on smooth and rough beds (Balachandar, Blakely, Tachie, and Putz [15]; Tachie, Bergstrom and Balachandar [2]). The non-dimensional quantity Π is called the wake parameter and it is a measure of the deviation of the velocity distribution from the logarithmic law of the wall. Cardoso, Graf and Gust [16] reported values of Π that varied from -0.27 to +0.2 for the smooth, uniform open channel flow. In present rough open channel flow, Π values are negative and varied from -0.103 to -0.259. The second method uses a linear regression fit of the measured Reynolds shear stress in the region 0.2 < y/h < 0.7 where the contribution from the viscous stress is negligible. The value of the Reynolds shear stress is extrapolated to the wall and this value is used to find another estimate for the friction velocity denoted as ∗ . A summary of experimental conditions is shown in Table 1. When the bed starts to move the validity of the friction velocity as a characteristic velocity scale becomes questionable since the classical law of the wall is derived for a smooth bed. In this paper, scaling with the friction velocity was used to compare the present velocity distribution on the mobile bed with the previous reported data assuming validity of the universal logarithmic law of the wall. Equation 1 computes higher values for the friction velocity compared to the Reynolds shear stress method as shown in Table 1. Since the values of the ∗ and ∗ listed in Table 1 were within a ± 37% error for non-mobile bed and 112% for mobile bed, the ∗ was chosen to scale velocity, turbulent intensities, and

Reynolds stress distributions. Note that in the following text, the superscript ‘‘+’’ denotes quantities made dimensionless with the viscous length scale ∗/ or viscous velocity scale 1/ ∗.

Fig. 1 Schematic of experimental set-up

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III. MEAN FLOW

The vertical distribution of the mean streamwise velocity, , was computed from the PIV data using a double averaging procedure. The velocity fields are first averaged over time and then spatially averaged over constant vertical slices. The velocity distributions in the logarithmic law format are shown in Figure 2. Fig 2 Velocity distributions of smooth bed, rough non- mobile

bed rough mobile bed

From the graph, it is noted that the flow resistance of the run with a mobile bed is higher than that of the non-mobile bed with identical roughness characteristics. It was also noted that the velocity distribution of mobile bed is not exactly parallel to the theoretical log law line. It appears that application of log law of the wall to flow over the mobile bed is rather difficult and may not be correct.

IV. TURBULENT INTENSITIES

Figure 3 shows vertical distributions of the streamwise turbulence intensity, where denotes streamwise turbulence intensities in inner scaling. Nezu and Nakagawa [17] proposed an empirical equation (Eq. 2) describing the vertical distribution of the streamwise turbulence intensities of the rough open channel flow.

∗ ∗

2.3 exp ⁄1 ⁄ 2Π

21 ⁄ 8.5

(2)

Fig 3 Distributions of streamwise turbulence intensity as a function of the outer variable

This equation is included for comparison in Figure 3 along with the calculated turbulence intensities over rough non-mobile and mobilebed, respectively. Figure 3 presents distribution of non-mobile bed, mobile bed, smooth wall (Roussinova, Biswas and Balachandar [18]) and as well as with theoretical curve plotted for non-mobile bed given by the Eq. 2. Equation 2 is a function of and relative value of / . Experimental data of mobile and non-mobile beds show a reasonably good agreement with smooth wall and Eq. 2. As expected, Eq. 2 nicely reproduces the plot of of non-mobile bed and Eq. 2 lies below the distribution of mobile bed. The decrease in distribution of

of mobile bed with increase in ⁄ is less than the non-mobile bed may be due to production of higher turbulence on mobile bed. The distribution for mobile bed reaches a maximum value of about 5.0 for 0 < ⁄ < 0.1. Measured

values for mobile bed near the wall slightly above the curve given by Eq. 2. Peak values of are matching with that of eq. 2 for smooth wall case, and non-mobile bed. Measurements of decrease near the wall for < 10 for mobile and non-mobile beds.

TABLE 1 Summary of the experimental conditions

Runs ∗ (m/s)

[14] (m) Π (m)

(m/s) Reynolds number

∗ (m/s) (Reynolds

stress method)

Non-mobile bed 0.0137 -0.00067 -0.1035 0.0586 0.240 16696 0.010

Mobile bed 0.051 -0.00073 -0.259 0.0632 0.384 26713 0.024

0

5

10

15

20

25

50 500 5000

u+

y+

non‐mobile bed

mobile bed

log law

smooth bed

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.2 0.4 0.6 0.8 1

uRMS+

y/h

non‐mobile bed

mobile bed

Nezu & Nakagawa (1993)

smooth bed

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Fig 4 vertical distributions of vertical turbulence intensity as a

function of the outer variable ⁄

1.14exp 0.76 ⁄ (3)

Figure 4 shows the distributions of the vertical turbulence intensity for mobile and non-mobile beds and as well as for smooth wall data (Roussinova, Biswas and Balachandar [18]). The present results are reasonably well described by the relationship (Eq. 3) developed for rough open channel flows by Song, Graf and Lemmin [19]. Present results are also matching well with smooth wall data (Roussinova, Biswas and Balachandar [18]) except for ⁄ > 0.5 where decrease of

on the smooth bed is more than that of non-mobile and mobile bed experiments. This could be attributed to higher turbulence generated in the region ⁄ > 0.5 in non-mobile and mobile bed experiments. Values ⁄ in the intermediate region, (0.1 < ⁄ < 0.8) for non-mobile bed are ranging between 1.4 to 2.15 while higher values are obtained on the mobile bed ranging between 2.0 to 6.7. Theoretical equations 2 and 3 give ⁄ values in the range of 1.4 to 2.34 which is in good agreement with values obtained on the non-mobile bed. It is observed that ⁄ is very high in the case of mobile bed where increase of the flow anisotropy is evident.

V. REYNOLDS STRESS

The vertical distributions of Reynolds shear stress, ∗⁄ ⟨ ⟩ is plotted in Figure 5. In the

region / > 0.2, good collapse is noted between present results and experimental data (Roussinova, Biswas and Balachandar [18]), corresponding to smooth bed, and with the trend given by 1 / . In the wall region, the Reynolds stress attains a maximum and decreases towards the bed for smooth bed data as well as rough non-mobile bed data. This trend of the scaled Reynolds stress variation with / is conforming to the trend available in the literature. In the case of smooth walls this behavior is due to the viscous effects, while for rough walls it can be explained by the existence of a roughness sub-layer where additional mechanisms for momentum extraction exists (Nikora and Goring [9]). The peak of Reynolds stress

for data on the mobile bed is occurring in the region / > 0.2. Another important observation in the present studies is that, as the Reynolds number increases, the peak of Reynolds stress is decreasing and curve is becoming flatter near the wall. The difference between theoretical line and experimental Reynolds stress is very high near the bed in the case of mobile bed, because viscous effects are dominant near the bed in high Reynolds number flows. This behavior could be expected as the theoretical line corresponds to the total stress while the experimental data correspond only to the Reynolds stress. Fig 5 vertical distribution of the Reynolds shear stress as a function of the y/δ

VI. CONCLUSIONS

The objective of this paper was to experimentally investigate the turbulence characteristics of open channel flows under conditions of rough wall with mobile and non-mobile bed. For this purpose, vertical distributions of the turbulent intensities of streamwise and vertical velocities and Reynolds stress have been investigated using PIV measurements over a non-mobile and mobile rough sand bed. The present data are compared with previous results obtained on smooth bed as well as theoretical equations available in the literature. It appears from the data analysis that logarithmic law may not be applicable to flows during mobile bed. It is also concluded that turbulence and bed resistance increases drastically during mobile bed. The peak of the scaled Reynolds shear stress decreases with increase in Reynolds number of flow. Finally, the results prove that the PIV technique can be successfully applied to investigate turbulence in open channel flow over rough mobile bed.

REFERENCES

[1] Nakagawa, H. and Nezu, I. (1977). "Prediction of the contributions to

the Reynolds stress from bursting events in open-channel flows," J Fluid Mech., April, 80, part.l, 99-128.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

v RMS+

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1.14exp(‐0.76y/h)

0

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0.9

1

0 0.2 0.4 0.6 0.8 1

UV+

y/δ

non‐mobile bed

1‐y/δ

mobile bed

smooth bed

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