FLOW PATTERN OF AN ERODING JET

Abstract: Local scour may occur when a hydraulic structure is positioned in a channel with an erodible bed. This paper investigates experimentally the erosion and flow pattern due to a water jet passing over a channel bed. The development of the scour hole, its maximum scour depth, and length, are recorded and compared with available scour-depth relations. The distributions of the velocity vectors are presented, showing a diving free jet followed by a wall jet. Reynolds stresses were evaluated from the measured velocity fluctuations. These stresses, important in the center of the jet, are vanishingly small at the bed of the scour hole.

1 INTRODUCTION

Prediction of the local scour downstream of a hydraulic structure is of considerable engineering importance. For this reason it has been extensively researched in the past. The previous studies were mainly interested in the experimental investigation of the depth, d_s, and of the length, L_s, of the scour hole. The earliest systematic study on scour hole development due to a 2-D horizontal jet is reported by Eggenberger and Muller (1944). A summary of subsequent studies can be found in Karim and Ali (2000). More recently Ali and Lim (1986) reported detailed flow measurements in scour holes due to wall jets. Karim and Ali (2000) carried out numerical simulations of these experiments. Of interest are also the experimental studies by Ali and Neyshaboury (1991), and Balachandar et al. (2000).

In addition to 2-D wall jets, 3-D wall jets but also inclined ones have been extensively investigated. The paper by Ade and Rajaratnam (1998) summarizes the data from various sources on the development of scour holes due to wall jets. More recently Liriano and Day (2000) investigated the structure of the turbulent flow in a scour hole downstream of a pipe culvert outlet.

The present study aims at investigating experimentally the detailed structure of the 2-D flow, such as the velocity, the turbulence, and the Reynolds stress components in a scour hole formed by a plane jet. A submerged inclined plane jet was created by installing a sluice gate in a laboratory flume with a mobile bed section. The jet, initially planar with the bed, erodes the mobile bed producing erosion profiles, varying with time and reaching eventually a steady-state profile, called the asymptotic scour hole. An Acoustic Doppler Velocimeter (ADV) instrument was used to measure the instantaneous velocity components.

2 EXPERIMENTAL INSTALLATION

The experiments were carried out in the LRH, using a 17m-long tilting flume (see Fig.1) with a 0.8m-high and 0.5m-wide rectangular cross section. The upstream and downstream ends of the flume bed was artificially raised in order to create a 0.35m-deep and 3.8m-long test section, beginning at a distance of 5.0m from the inlet. The test section was filled with a uniformly graded sand with a mean diameter of d₅₀ = 2 mm. The same sand was glued on the downstream fixed-bed section. The slope of the flume bed was close to S_b» 0.

The jet issued from a vertical sluice gate, which was installed directly at the upstream end of the test section. A slightly submerged jet of Dh = h₁-h₂ was created by setting the tail-water depth, h₂, controlled by a weir at the downstream end of the flume. A constant water discharge, Q, was pumped into the flume from the general basin of the laboratory.

Prior to the experiment the test section is filled with sand and leveled to the same height as the fixed bed. The sluice-gate opening, h_v, is adjusted and the weir height is set to obtain the desired tail water depth, h₂. Paying attention not to disturb the mobile bed, the flume is slowly filled until the water level touches the gate lip. The experiment starts, t = 0, when the pump discharge is increased rapidly to the predefined discharge, Q, which is maintained constant until the formation of the asymptotic scour hole. During this period the bed profile was measured at different intervals. The water depths at the upstream and downstream of the sluice gate were also measured. After the formation of the asymptotic scour hole, the discharge was gradually decreased to zero by taking care not to disturb the bed. The channel was slowly emptied and left to dry. The scoured bed was then fixed by spraying a special glue on the sand. This allowed to have a rigid scour hole profile with the correct sand grain roughness. This asymptotic profile was measured using a point gauge installed on a carriage.

In order to measure the flow pattern in the scour hole, this same discharge, Q, was fed into the flume by keeping the sluice-gate opening and the tail-water depth as before. Using the point-gauge the water-surface elevations were checked to make sure that the flow conditions are the same. The vertical profiles of instantaneous velocity components were then measured at selected stations (see Fig.2) using an ADV. The general circulation pattern in the scour hole was visualized using dye injection and a rod with small flags.

The measuring sections located between 5< x(cm) <100, as well as the symbols used in this study are shown in Fig.2. The hydraulic characteristics of the experiment are given in Table 1. The velocity profile measurement immediately after the sluice gate, showed that the average initial jet velocity, U_o,can be estimated using the Bernoulli equation,

. The Froude number at the sluice gate is given by

. A densimetric particle Froude number was defined as

, where Dr is the difference between the density of the bed material, r_s, and the density of the fluid, r.

An Acoustic Doppler Velocimeter (ADV Nortek, side–looking probe) was used to measure the three components of the instantaneous point velocity. Referring to Fig.3, the emitter generates a short ultrasonic pulse at a fixed carrier frequency that insonifies the water column. The acoustical wave backscattered from the targets moving with the flow, such as air bubbles or solid particles, is captured simultaneously by three receivers. The captured signals are shifted in frequency due to the Doppler effect. Frequency demodulation is applied to the signals in order to evaluate the three frequencies and the corresponding target velocities. The pulses are repeated with a frequency of 200-250Hz. This pulse repetition frequency is equal to the sampling frequency of the local Doppler signal. Each quasi-instantaneous velocity measurement is obtained by averaging over a certain number of pulses. In the present experiment, the number of pulses used for computing one quasi-instantaneous velocity is equal to 14. This results in a final velocity sampling frequency of 200/14 =15 Hz. The Win ADV post-processing program was used to analyze the velocity signals.

To measure the water velocity the head of the ADV must be inserted into the water. Generally, the presence of the probe does not influence the measurement because the sensing volume is located 5-6cm centimeters away from the probe body. The measuring volume can be approximated by a cylindrical volume. In the present experiment, the diameter and the length of the measuring volume are equal to f = 0.6cm and Dl = 0.6cm (see Fig.3).

Vertical velocity profiles were measured at 5, 10, 20, 30, 40, 50, 60, 70, 80 and 90cm downstream of the sluice gate. A distance of 1cm is taken between each point in one vertical profile. Due to the instrument configuration, the data can not be obtained in regions closer to 1.2cm from the bed and 5 to 6cm from the water surface (see Fig.3 and Fig.5).

Q [m³/s]

h_v

[cm]

U_o [m/s]

Fr_o

[-]

h₁

[cm]

h₂

[cm]

d₅₀ [mm]

Fr_d

[-]

d_s

[cm]

L_s

[cm]

0.015

5.0

0.875

1.25

16.2

12.1

2.0

4.9

25.5

100

3 DEVELOPMENT OF SCOUR HOLE

The present experiment used the clear-water scour condition, when there is no sediment transport into the scouring region during the experiment (Graf and Altinakar, 1998). The observation of the growth of the scour hole was done during the experiment. The evolution of the scour depth, d_s, as well as the rate of change of the scour depth, d(d_s)/dt, are plotted in Fig.4. As can be seen, the asymptotic state— a definition also used by Rajaratnam and Macdougall (1983) — was reached after 5510 min or 91.8h. At this stage there was no sediment transport throughout the measuring section. The length of the scour hole was measured as being L_s = 100cm corresponding to a maximum scour depth of d_s = 25.5cm (see Fig.4). It should be noted that, almost 80% of the maximum scour depth occurred at about 13% of time. The scour hole is followed by a deposition ridge on its downstream side.

When the experiment begins the jet is parallel to the bed. Since the sluice gate is positioned at the extremity of the upstream fixed-bed, the apron length was zero. As the scour hole became deeper, the jet became more and more deflected towards the bed. When the asymptotic profile was reached, the jet was making an angle of 25° with the horizontal. The measured velocity vectors plotted in Fig.5 show the inclined trajectory of the jet.

The depth and the length of the scour hole obtained in the present experiment was compared with the relationships proposed by Eggenberger and Muller (1944) for submerged horizontal jet scour, given by:

The value of the coefficient, w_e = 21.4 s^0.6/m^0.3, for the present experiment is larger than the one originally proposed by the authors, which is w_e=10.35 s^0.6/m^0.3. The present experiment yields a value of f_e »3, which is smaller than the proposed one, f_e »6.

A similar discrepancy is observed when the measured scour depth is compared with the one obtained from the expression proposed by Ali and Lim (1986, Fig.5), which summarizes the results of various studies with 2-D and 3-D horizontal jets by:

Here, R is the ratio of the jet area (gate opening) to its perimeter and v_ss represents the mean fall velocity of the sediment. The measured scour depth is twice the one predicted by eq.2.

The larger scour depth, d_s, and the smaller scour length, L_s of the present experiment are attributed to the inclined entry of the jet into the scour hole. The same tendency was also observed in an experiment by Ali and Neyshaboury (1991) and in another one by Balachandar et al. (2000).

4 DISTRIBUTION OF VELOCITY VECTORS

The velocity vectors measured in the central plane of the flume in several sections along the scour hole are shown in Fig.5. Supplementary velocity profiles measured in the quarter-width planes showed that the highly turbulent flow in the scour hole is reasonably two-dimensional over almost the entire flume width.

The inclined plane jet issuing from the sluice gate has a free-jet like velocity distribution with weak return flows at the top and the bottom. The jet impinges on the bed at about 50cm from the gate. The flow is partly diverted backwards to form a circulation zone near the bed. A larger fraction of the flow leaves the scour hole as an upward-inclined wall jet and reaches the water surface at about 80cm from the gate. At this point the flow is partly diverted backwards to form a circulation zone near the water surface. A larger fraction of the flow continues downstream and establishes a uniform open-channel flow profile. The return flow regions are eye fitted in gray in Figs 5 and 8.

Ali and Neyshaboury (1991) observed a similar flow pattern in an experiment where the slightly inclined, 2D plane-jet had also an impingement point in the scour hole. Liriano and Day (2000), who studied 3-D erosion downstream of a pipe culvert outlet, report a weak return current near the surface for some of their experiments with a jet slightly inclined towards the bed. On the other hand, Rajaratnam and Berry (1977, p.282) do not observe any return current in the scour holes formed by 3-D air jets.

The gray line in Fig.5 indicates the position of the local maximum velocity, u_m, in each section. The decay of the normalized maximum velocity, plotted in Fig.6, shows three distinct regions. In the free-jet region the maximum velocity decays almost linearly. It is interesting to note that the potential core is extremely short, ~1h_v , compared to the one in an unbounded free jet, 5-6h_v. A transition region covers the impingement zone. The maximum velocity in the wall jet increases up to the end of the transition zone due to a stagnation pressure and then it decreases.

The dimensionless velocity distribution in the free-jet region is plotted in Fig.7. The centerline, z = 0, coincides with the height z where the velocity is maximum and b represents the value of z where the velocity is equal to half the maximum velocity, u = 1/2 u_m (note, this u is the horizontal component of the inclined velocity vector). Overall, these distributions compare favorably with the theoretical distribution (Rajaratnam, 1976, p. 22) of a free jet.

The measured turbulence intensities in the three directions showed the turbulent flow to be non-isotropic. The longitudinal components dominated throughout the scour hole. The transversal components were always the less important ones.

5 DISTRIBUTION OF REYNOLDS STRESSES

Since the turbulence components of the velocity were measured the Reynolds stress,

, could readily be calculated. The measured Reynolds stresses, normalized with ru_m², are presented in Fig.8, for the different sections in the scour hole. Qualitatively these distributions compare with available data, reported by Rajaratnam (1976). The maximum is usually situated at the line of maximum velocity. In the vicinity of the bed they are vanishing considerably, implying the incapacity of transporting sediments.

Negative Reynolds stresses are measured in the layer close to the water surface and this throughout the entire distance investigated. Our observations agree roughly with measurements at culvert outlets by Liriano and Day (2000).

6 CONCLUSIONS

A slightly submerged 2-D jet issuing from a sluice gate and creating a scour hole was experimentally investigated. The temporal evolution of the scour depth was recorded at regular intervals until the asymptotic scour profile is reached. The asymptotic scour hole of the present experiment is found to be twice deeper and half shorter than the predictions with the available formulae. This discrepancy is attributed to the inclined entry of the jet into the scour hole due to the absence of an apron downstream of the sluice gate.

After the establishment of the asymptotic scour hole, the bed was fixed by spraying a glue. The profiles of the three components of the instantaneous velocity were then measured at several stations in the central plane of the flume using an Acoustic Doppler Velocimeter (ADV). The flow in the scour hole was found to be reasonably two-dimensional. The measurements show that the jet issuing from the sluice gate has a free-jet like velocity profile. The jet has an extremely short potential core and the maximum velocity decays almost linearly until the jet impinges on the bed. Downstream of the point of impingement the flow leaves the scour hole as an inclined wall jet. Velocity measurements and flow visualization reveal the existence of two permanent circulation cells, one below and one above the jet.

In the free-jet region, the normalized Reynolds stresses in the longitudinal direction are quite large in the center of the jet, indicating a strong turbulence in the scour hole. They are however vanishingly small at the boundary of the channel bed. Downstream of the impingement point, in the transition and wall-jet regions, negative Reynolds stresses are measured especially above the maximum velocity line. Measured turbulence intensities indicate that the longitudinal component is dominant and the turbulence is non-isotropic.

The authors would like to thank all members of LRH for contributions in the different aspects of this research. Our special thanks go to Prof. N. Rajaratnam, for friendly discussions and extensive comments during his stay at the EFPL as visiting professor.

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