CIVE 631 Engineering Fluid Mechanicsmdzahidu/turbulence_fhj.pdf · CIVE 631 Engineering Fluid...

CIVE 631 Engineering Fluid Mechanics

Term Project Report

TURBULENCE STRUCTURE DOWNSTREAM OF A FORCED

HYDRAULIC JUMP

Submitted to

N. RAJARATNAM, PhD, FASCE

Professor Emeritus Dept. of Civil and Environmental Engineering

University of Alberta

Submitted by

NAME ID MD. ZAHIDUL ISLAM 1143605 TADROS RIAD 1185682 MOHAMED EL-DALY 1134112

December 6, 2007

Table of Content

Table of Content ............................................................................................................................. 1

List of Figures .................................................................................................................................. 2

Abstract........................................................................................................................................... 3

1. Introduction ............................................................................................................................ 3

2. Objectives................................................................................................................................ 4

3. Experimental Setup................................................................................................................. 4

4. Experimental Procedure ......................................................................................................... 7

5. Data Analysis........................................................................................................................... 9

6. Result and Discussion ........................................................................................................... 10

6.1. Distribution of normalized time averaged velocity ...................................................... 10

6.2. Distribution of normalized turbulent intensity and Reynolds’ stress........................... 10

6.3. Decay of normalized time averaged velocity , and turbulence parameters ................ 11

6.4. Comparison with free jump study ................................................................................ 21

7. Conclusions ........................................................................................................................... 22

8. References ............................................................................................................................ 22

Annex A ......................................................................................................................................... 23

1

List of Figures

Figure 1: Experimental Setup for F1 =5.5 ........................................................................................ 5 Figure 2: Experimental Setup for F1 =9.0 ........................................................................................ 5 Figure 3: Acoustic Doppler Velocimeter (ADV)............................................................................... 6 Figure 4: Adjusted Coordinate system used in analysis ................................................................. 7 Figure 5: Water surface profile for different forced hydraulic jump.............................................. 8 Figure 6: Time averaged velocity vector along the centerline of the flume. ............................... 12 Figure 7: Normalized time averaged u velocity along the centerline of the flume...................... 13 Figure 8: Normalized time averaged v velocity along the centerline of the flume...................... 14

Figure 9: Normalized turbulent intensity 12 /Uu′ along the centerline of the flume................ 15

Figure 10: Normalized turbulent intensity 12 /Uv′ along the centerline of the flume. ............ 16

Figure 11: Normalized Reynolds’ stress 21/Uvu ′′− along the centerline of the flume. ............... 17

Figure 12: Effect of F1 (Upper plot without considering F1 and.................................................... 18 Figure 13: Variation of maximum normalized time averaged u velocity ..................................... 18 Figure 14: Variation of maximum normalized time averaged v velocity...................................... 19

Figure 15: Variation of maximum normalized turbulent intensity 12 /Uu

m⎟⎠⎞

⎜⎝⎛ ′ ........................ 19

Figure 16: Variation of maximum normalized turbulent intensity 12 /Uv

m⎟⎠⎞

⎜⎝⎛ ′ ......................... 20

Figure 17: Variation of maximum normalized Reynolds’ stress 21/)( Uvu m′′− ............................ 20

Figure 18: Variation of maximum normalized turbulence kinetic energy 1/)( UK m ............... 21 Figure 19: Pump ........................................................................................................................... 23 Figure 20 ADV probe and point gauge installed on channel ........................................................ 23 Figure 21 ADV probe..................................................................................................................... 24 Figure 22 Baffle blocks installed in the channel ........................................................................... 24 Figure 23 Baffle blocks installed in the channel ........................................................................... 24 Figure 24 Upstream streamlined gate opening ............................................................................ 25 Figure 25 Tailwater gate ............................................................................................................... 25 Figure 26 Flow for Fr = 4 ............................................................................................................... 26 Figure 27 Flow for Fr = 4 ............................................................................................................... 26 Figure 28 Flow for Fr = 6 ............................................................................................................... 26 Figure 29 Flow for Fr = 8 ............................................................................................................... 27 Figure 30 Flow for Fr = 9 ............................................................................................................... 27

2

TURBULENCE STRUCTURE DOWNSTREAM OF A FORCED

HYDRAULIC JUMP

__________________________________________________________

Abstract

Turbulence characteristics downstream of a forced hydraulic jump for Froude number 5.5 and 9

are presented. An Acoustic Doppler Velocimeter (ADV) was used to obtain the measurement of

velocities, turbulence intensities, turbulence kinetic energy and Reynolds’ stresses. Due to large

amount of air entrainment inside the jump the measurements are taken immediately downstream

of the jump. The time averaged mean velocities, turbulence intensities and found to be decrease

rapidly and then gradually along downstream. It was found that and the Reynolds’ stresses

decrease linearly. The turbulence kinetic energy at each section decreases gradually with the

longitudinal distance.

______________________________________________________________________________

1. Introduction

Turbulence in open channel flow is of great importance for the effect it has on mixing,

momentum transfer and energy dissipation in the flow. The study of turbulence and its decay in

the transition region is of no less importance. Numerous studies were conducted to study this

concept numerically and experimentally. Wu and Rajaratnum (1996) studied the transition from

the free hydraulic jump to open channel flow for Froude number ranging from 3.87 to 10.48 and

found that bed stresses decreased rapidly until they became constant. They determined the length

of this region to be approximately equal to 10 times the tail water depth. Another experimental

study conducted by Khatsuria et al. (1988) introduced a reference section where turbulence effect

on the normal flow has completely decayed. It was assumed that, this section is at a distance

20y2 from the toe of the jump where y2 is the sequent depth of the jump. Liu et al (2004) made

some turbulence measurement in the transition region at low Froude number (up to 3.32) in

addition to their turbulence measurement in the free hydraulic jump. But all those mentioned

laboratory works have been carried out for free hydraulic jump. Urban et al (2005) tested the

3

applicability of a vertically averaged mathematical model to predict the variation in turbulent

kinetic energy with distance downstream of a spillway and compared the results with

experimental measurements. To writer’s knowledge no further measurement have been made on

turbulence in forced hydraulic jump. Liu and Uwe (1994) calculated the turbulence

characteristics of forced hydraulic jump numerically by mean k-ε model. In current study the

turbulence characteristics downstream of a forced hydraulic jump for Froude number 5.5 and 9.0

is measured using an Acoustic Doppler Velocimeter (ADV) and the results are presented herein.

2. Objectives This set of experiments was designed to measure the turbulence downstream of a forced

hydraulic jump in a laboratory flume for Froude number 5.5 and 9. This study focused on the

distribution of the mean velocities, turbulence intensities, turbulence kinetic energy and

Reynolds’ stresses as well as their decay along downstream.

3. Experimental Setup

The experiments were conducted in the T. Blench Hydraulics Laboratory at the University of

Alberta. A rectangular flume 7.58 m long, 0.466 m wide and 0.60 m deep was used. The

horizontal bottom of the flume is made of aluminum while the vertical sides are made from

Plexiglas. Water flows under the control of a sluice gate with a streamline lip at the upstream end

of the flume and a tail gate at the downstream end of the flume. The gate opening was fixed at

1.9 cm (y1). A group of baffle blocks having a height of 0.05 m were installed on the channel bed

at a distance of 0.425 m from the gate opening and at a spacing of 0.05 m. Figure 1 and 2 shows

the detail experimental setup for Froude number F1 5.5 and 9.0 respectively. Water is pumped

into the channel from a head tank which is supplied directly from the sump. Discharge is

measured prior entering the flume through a magnetic flow meter installed on the supply line. At

the downstream end of the flume, the tail gate controls the tail water depth yt to ensure the

generation of the jump just at the gate opening.

4

Figure 1: Experimental Setup for F1 =5.5

Baffle Piers

At X/y2 =3.06

End of Stilling Basin

At X/y2 =21.64

Gate Opening

a) Plan View

Baffle Piers at X/y2 =3.06

Gate Opening

y1=1.9 cm

yt/y2=6.85

h/y2=0.361

b) Elevation

Baffle Piers at X/y2 =1.83

Gate Opening

y1=1.9 cm

yt/y2=9.625

h/y2=0.215

b) Elevation

Baffle Piers

At X/y2 =1.83

End of Stilling Basin

At X/y2 =12.9

Gate Opening

a) Plan View

Figure 2: Experimental Setup for F1 =9.0

5

Flow depths are measured with point gauges. An ADV as shown in Figure 3 was used to

measure the velocity profile downstream the forced hydraulic jump. The ADV used in this

experiment was manufactured by SONTEK. It is a 25 MHz down looking ADV. The ADV was

connected to a PC with data acquisition software ADVLab. The transmitter sends the sound and

it is reflected from the sampling volume to the three receivers. The receiver painted red indicates

the direction of positive x axis and vertical is the z axis. However the coordinate system was

adjusted as shown in Figure 4. The received signals are used to compute 3 dimensional velocity

components at the sampling volume. The standard sampling volume is a cylinder of water with a

diameter of 6 mm and height of 9 mm. The distance of the sampling volume is 5.7 cm from the

acoustic transmitter.

Figure 3: Acoustic Doppler Velocimeter (ADV)1

The ADV is mounted on a mechanical setting placed over the flume. This setting has a

horizontal and a vertical roller over which the position of the ADV can be changed horizontally

or vertically. This setting is connected to a driver which controls the horizontal and vertical

1 Source http://www.sontek.com/product/adv/advxdsc.htm#advxds1

6

http://www.sontek.com/product/adv/advxdsc.htm#advxds1

sliding of the ADV. There are four knobs in the driver to change the position vertically up and

down and horizontally left and right. There are two wheels in the setting near the ADV one of

which indicates the amount of vertical movement and the other horizontal movement.

Figure 4: Adjusted Coordinate system used in analysis

4. Experimental Procedure

To visualize the flow behavior a set of test runs were conducted for Froude number ranging from

4 to 9.6. At every case the water surface measurement were taken and the flow profile was

drawn. Figure 5 shows the water surface profile for F1 4 to 9.6 in both non-dimensional and

dimensional form. The non-dimensional from was obtained by normalizing the longitudinal

distance and vertical depth by sequent depth of subsequent free jump (y2) and initial depth (y1)

respectively. After visualizing the flow behavior two set of experiments were conducted with

velocity and turbulence measurement. The experimental conditions are summarized in Table 1.

Table 1: Experimental condition

Experiment F1 y1 (cm) U1 (cm/s) yt (cm) y2 (cm)

1 5.5 1.9 237.5 13.01 13.86

2 9 1.9 388.6 18.29 23.25

Flow

X , u

z , w

y , v

7

a) Non-dimensional

b) Dimensional

Figure 5: Water surface profile for different forced hydraulic jump

8

Data were collected at 25 Hz frequency with a sampling duration of 5 minutes. For Froude

number 5.5 measurements were made at 12 verticals starting from x/y2 5.0 to 20.9. In case of

higher Froude number 9.0 measurement were taken at 11 verticals where x/y2 ranging from 4.7

to 12.5. For each set of experiment, first the required discharge is applied to the pump, and

after about 10 minutes for water level being stabilized, the tail water gate is adjusted such that

the jump begins just at the edge of the gate opening, this was made to confirm the non-

submergence at one hand, and on the other hand to ensure the approximation that the y1 used for

calculations is actually the gate opening. Then the water surface profile is measured at intervals

ranging from 5 cm in the longitudinal direction near the gate, and 20 cm away from the jump.

5. Data Analysis

ADV data contain spikes caused by aliasing of the Doppler signal. The phase shift between the

outgoing and incoming pulse lies outside the range between -180° and +180° and there is

ambiguity, causing a spike in the record (Goring and Nikora, 2002). So it’s necessary to despike

the original ADV data. In this study it was done by WinADV software which applies the phase

space threshold despiking method of Goring and Nikora (2002). This method uses the concept of

a three-dimensional Poincare Map or phase-space plot in which the variable and its derivatives

are plotted against each other. The points are enclosed by an ellipsoid defined by the Universal

criterion and the points outside the ellipsoid are designated as spikes. The method iterates until

the number of good data becomes constant or equivalently, the number of new points identified

as spikes falls to zero (Goring and Nikora, 2002). It was found that almost 96 to 97 % of the

original data retained after filtering. The data analyses were done in Matlab. In analysis the

distribution of the time averaged velocity, turbulence kinetic energy (K), Reynolds’ stresses and

subsequent turbulence intensities as well as their decay along the downstream direction were

considered.

9

6. Result and Discussion

6.1. Distribution of normalized time averaged velocity

The time averaged velocity vector in the centerline of the flume for the Froude number 5.5 and 9

are shown in Figure 6. The depth and the longitudinal distance are normalized by the initial

depth of the jump (y1) and sequent depth (y2) calculated for the corresponding free jump

obtained from Belenger equation. The plotting indicated the presence of upward velocity for x/y2

up to 7.2 and 6.0 for Froude number 5.5 and 9 respectively. The velocity vectors become

horizontal as it moves towards downstream. In Figure 7 and 8, the normalized time averaged u

and v velocity have been plotted in different verticals for both Froude numbers. It was found that

the distribution of the longitudinal velocity component become uniform as it moves downstream

which clearly indicate the transition from the hydraulic jump to the open channel flow. If we

look at the distribution of the vertical component of the velocity (Figure 8), it was observed that

up to a distance of x/y2 around 7 the vertical component is significant at near the surface while it

eventually close to zero near the bed and as approach further downstream.

6.2. Distribution of normalized turbulent intensity and Reynolds’ stress

Figure 9 and 10 shows the normalized turbulent intensities 12 /Uu′ and 1

2 /Uv′ at different

verticals for Froude number 5.5 and 9.0. Again the longitudinal distances and vertical depths are

normalized by y2 and y1 respectfully. It was found that both the turbulent intensities higher near

the jump and decreases as it moves downstream. It was observed that 12 /Uu′ decrease

rapidly than 12 /Uv′ . Also the intensities are higher close to the water surface than close to the

bottom, however the eventually become uniform as move further downstream. Similar types of

results were found in the study of Liu et al. (2004) for free jump. Figure 11 shows the similar

type of plotting for normalized Reynolds’ stress 21/Uvu ′′− . It was found that for Froude number

5.5 the stresses are positive having a lower value near the jump at x/y2 = 5.0 to 6.0. But at x/y2 =

10

6.5 the stresses are significant and which eventually decrease along downstream. Similar type of

results was observed for Froude number 9.0 except the stresses become significant at x/y2 =5.2,

which indicate that the distribution depends on the initial Froude number F1.

6.3. Decay of normalized time averaged velocity , and turbulence parameters

In order to see the variation of maximum values of different parameters as,

1/Uu , 1/Uv , 12 /Uu′ , 1

2 /Uv′ , 21/Uvu ′′− , 1/UK , they need to be plotted against a

dimensionless distance scale as x/y2. As beyond the jump the Froude number plays an important

rule, so the effects of Froude number on these plots were investigated first. It was done by

plotting the dimensionless parameter against x/y2 twice, first plotted their usual values and

secondly plotted by multiplying them with their corresponding Froude number. It was found that

all the parameter are sensitive to F1 , which implies when the parameters multiplied by their

corresponding Froude number they become well fitted for both Froude number in a general curve

that eventually lead to a better understanding. Figure 12 shows how the 12 /)( Uv m′ fitted well

for both F1 when they multiplied by their corresponding F1.

Based on the above discussion, the maximum values of all the parameters were multiplied by

their corresponding Froude number and plotted against dimensionless distance scale x/y2. They

are shown in Figure 13 to 18. It was observed that 11 /)( UuF m is almost constant along

downstream though a slight higher values were found near the jump at an x/y2 equals 4.0 to 5.0.

On the other hand 11 /)( UvF m shows a sharp change between x/y2 = 4.5 to 6.0 and become

eventually constant further downstream. In case of the normalized dimensionless turbulence

intensities it was found that there is a sharp change occurred in 12

1 /)( UuF m′ , 12

1 /)( UuF m′

between x/y2 =4.5 to 6.0 and after x/y2 = 6.0 it decreases gradually along downstream. Similar

type of relationship was found for the case of turbulence energy per unit mass K (Figure 18). The

variation of maximum Reynolds’ stresses as shown in Figure 17 implies that it decreases almost

linearly as move towards downstream which is quite significant.

11

(a) For Froude No. 5.5

(b) For Froude No. 7

Figure 6: Time averaged velocity vector along the centerline of the flume.

12



Figure 7: Normalized time averaged u velocity along the centerline of the flume.

13



Figure 8: Normalized time averaged v velocity along the centerline of the flume.

14



Figure 9: Normalized turbulent intensity 12 /Uu′ along the centerline of the flume.

15



Figure 10: Normalized turbulent intensity 12 /Uv′ along the centerline of the flume.

16



Figure 11: Normalized Reynolds’ stress 21/Uvu ′′− along the centerline of the flume.

17

Figure 12: Effect of F1 (Upper plot without considering F1 and

Lower plot multiplying the dimensionless parameter by F1)

Figure 13: Variation of maximum normalized time averaged u velocity

18

Figure 14: Variation of maximum normalized time averaged v velocity

Figure 15: Variation of maximum normalized turbulent intensity 12 /Uu

m⎟⎠⎞

⎜⎝⎛ ′

19

Figure 16: Variation of maximum normalized turbulent intensity 12 /Uv

m⎟⎠⎞

⎜⎝⎛ ′

Figure 17: Variation of maximum normalized Reynolds’ stress 21/)( Uvu m′′−

20

Figure 18: Variation of maximum normalized turbulence kinetic energy 1/)( UK m

6.4. Comparison with free jump study

Some of the results were compared with the similar type of study for free jump (Liu et al., 2004).

It was found the normalized turbulent intensities 12

1 /)( UuF m′ and 12

1 /)( UvF m′ decrease in

a higher rate than that in free jump. This might be because of the presence of the baffle pier. The

Reynolds’ stresses diminish sharply in free jump whereas in case of forced jump it decreases

almost linearly along downstream direction.

21

7. Conclusions

In present study the mean flow and turbulence characteristics downstream of a forced hydraulic

jump in a laboratory flume for Froude number 5.5 and 9.0 are presented. The distribution of

mean velocities, turbulent intensities and Reynolds’ stresses at different verticals clearly

indicates the transition from forced hydraulic jump to open channel flow. It was found that

Froude number F1 is an important scale along with the inlet velocity U1 at the downstream of the

jump. The variation of the maximum values of the normalized time averaged velocity, turbulence

intensity, Reynolds’ stresses and turbulence kinetic energy per unit mass was observed and to

some extent they vary in a similar manner. While comparing to the free jump results it was found

that the turbulent intensities decrease in a higher rate than free jump and the decay of Reynolds’

stresses become linear along downstream whether it was curvilinear in free jump.

8. References Goring, D.G., and Nikora, V.I, 2002, Despiking Acoustic Doppler Velocimeter Data, Journal of Hydraulic Engineering, Vol. 128, No. 1, 117-126. Liu, Q. and Uwe, D.,1995, Turbulence characteristics in free and forced hydraulic jump, Journal of Hydraulic Research, Vol. 32, No. 6, 877-898.

Liu, M. Rajaratnam, N., and Zhu, D.Z., 2004, Turbulence structure of hydraulic jumps of low Froude numbers, Journal of Hydraulic Engineering, 2004, 511-520.

Urban, A.L., Wilhelms, S.C., and Gulliver, J.S., 2005, Decay of turbulence downstream of a

stilling basin, Journal of Hydraulic Engineering, 2005, Vol. 131 No. 9, 825-829.

Wu, S. and Rajaratnam, N., 1995, Transition from hydraulic jump to open channel flow, Journal of Hydraulic Engineering, 1995, Vol. 122 No. 9, 526-528

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Annex A

Figure 19: Pump

Figure 20 ADV probe and point gauge installed on channel

23

Figure 21 ADV probe

Figure 22 Baffle blocks installed in the channel

Figure 23 Baffle blocks installed in the channel

24

Figure 24 Upstream streamlined gate opening

Figure 25 Tailwater gate

25

Figure 26 Flow for Fr = 4



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