A study of turbulence characteristics in open channel transitions as a function of Froude and Reynolds numbers using Laser technique M.I.A. El-shewey, S.G. Joshi Department of Civil Engineering, Indian Institute of Technology, Powai, Bombay 400 076, India Abstract This paper presents the results of Laser Doppler Velocimetry (LDV) investigation in open channel transitions in a horizontal rectangular channel of constant width. Experiments are carried out in sudden transition having contraction ratios of 0.3 and 0.5. To study the effect of Froude number and Reynolds number on the streamwise and vertical components of turbulence intensities u'/uo and v'/uo, the measurements are carried out along the depth at different cross sections upstream, within and downstream of all the transitions, in the longitudinal direction along the centreline and across the transition. Measurements of turbulence intensities were conducted at different values of Froude and Reynolds numbers of the free stream, for various discharges generated by altering the depth of flow. From the results, it is concluded that, an increase in the Froude number and Reynolds number decreases the turbulence intensities u'/uo and vvuo upstream slightly, followed by slight increase in the turbulence intensities downstream of the transition in the expansion zone at the same flow conditions. This effect in the turbulence occurs primarily in the wall region and the free surface region. However, in the core region there is no noticeable change in the turbulence levels upstream, within and downstream regions of the transition. Within the transition, flow tends towards the critical state (Fr approaches close to 1) with a rise in the turbulence intensities in the free surface and the wall region which may be attributed to the flow tending towards critical state. At small values of Froude number Fr ^ 0.2, the effect of Froude number on turbulence intensities and the free surface wave is negligible.
364 Advances in Fluid Mechanics 1 Introduction Flow in open channel transition being free surface flow, is governed both by gravity and the viscous forces. Hence the discussions are presented accounting both these effects in terms of Froude and Reynolds numbers. Open channel transition have been studied extensively because of their importance for reducing the energy dissipation in hydraulic structures. The turbulent flow models in open channel flows are discussed by Rodi [6], Nezu and Nakagawa [5]. Experimental investigation on turbulent structure of back facing step flow, have been reported by several investigators such as Nakagawa [3] and Ruck [7]. Simulation of turbulent flow at a Reynolds numbers, has been pointed by Antonia [1] and Bernero [2]. Measurements of turbulence characteristics in open channel flows using LDV have been reported by Nezu and Rodi [4] and others. The present research presents the results of Laser Doppler Velocimetry (LDV) investigation in open channel transitions in a horizontal rectangular channel of constant width. Experiments are carried out in sudden transition having contraction ratio of 0.3 and 0.5. To study the effect of Froude number Fr and Reynolds number Re on the streamwise and vertical turbulence intensities u'/uo and v'/uo upstream, within and downstream of the transitions, measurements were conducted at different values of Fr and Re viz. 0.230, 0.088 and 0.4x10^, and 0.16x10^ respectively, generated by altering the depth of flow. 2 Experimental set up and test procedure Experiments were conducted in a horizontal rectangular open channel flume of 7500 mm long, 300 mm wide and 500 mm height with glass wall of 6 mm thick and a steel plate bed. Figure 1 shows the layout of test facility. Water was supplied by a 15 HP pump and discharge was measured with an on-line orifice meter. In all the experiments, the discharge and the water level in the supply tanks were kept constant. Downstream water level was controlled by a tail end vertical gate. 3 Instrumentation The experimental data were collected using two color back-scatter LDV system available at the Water Tunnel Laboratory at I.I.T., Bombay. Figure 2 shows a block diagram of the two component LDV set up used for the measurements. A 5 Watt Argon-ion Laser with two Laser beams, one blue (488 nm) and one green (514.5 nm), were focused at a measuring point from one side of the channel through an optical lens. Two Burst Spectrum Analyzers (BSA) were used to evaluate the Doppler frequencies. Subsequent computer analysis consisted of velocity bias averaging and outlier rejection. The number of samples taken at every point was 5000 bursts. This corresponds to a simple averaging time of about 100 seconds. The data rate was about 40-50 per second. Before acquiring the data, the LDV signal was checked for its regular Doppler burst that correspond to a
Advances in Fluid Mechanics 365 Transactions on Engineering Sciences vol 9, 1996 WIT Press, www.witpress.com, ISSN 1743-3533 particle passing through the measuring volume. The measurements were taken at nine different cross sections upstream, within, and downstream of the transitions. Figure 3 shows the location grid of the measuring stations. 4 Results and discussion Figures 4, 5, and 6 depict the profiles of streamwise and vertical components of turbulence intensities u'/uo and v'/uo with relative water depth y/yo in sudden transition at different locations upstream, within and downstream the transition at contraction ratios Ab/b of 0.3 and 0.5 for discharges of 15 1/s and 39 1/s. Clearly, the trend of variation in streamwise and vertical turbulence intensities u'/uo and v'/uo are similar in all the cases. In all cases both u'/uo and v'/uo, the maximum turbulence intensities occur close to bed, following a gradual fall in the wall region defined by y/yo < 0.2, reaching the minimum in core region defined by 0.2 3 y/yo < 0.6. Turbulence increases in the free surface region defined by 0.6 < y/yo < 1.0, reaching up to the free surface. Generally, maximum streamwise and vertical turbulence intensities u'/uo and v'/uo occur at the same location of the profiles of transition. Also, as a comprehensive observation, it is noted that the streamwise turbulence u'/uo is always stronger compared to the vertical turbulence v'/uo. In the wall region defined by y/yo 30.2 the turbulence intensities u'/uo and v'/uo have substantially large magnitude closer to the wall (wall effect). With the increasing distance from the boundary, both the turbulence intensities decrease in wall region tending towards a minimum in the intermediate region (core region) defined by 0.2 s y/yo s 0.6, where the location of the minimum value of the turbulence consistently corresponds to that of maximum streamwise mean velocity reaching a higher value in the free surface. Figures 4, and 5 depict the variation of u'/uo and v'/uo in the^transition for different Fr and Re viz. 0.230, 0.088 and 0.4x10 and 0.16x10, for free stream respectively at Ab/b = 0.3. Comparison of u'/uo and v'/uo upstream, within and downstream the transition, indicates that an increase in the Froude number and Reynolds number, decreases the turbulence intensities u'/uo and v'/uo upstream and within the transition slightly with a slight increase in the turbulence intensities downstream of the transition in the expansion zone at the same flow conditions. This slight decrease in the turbulence intensities u'/uo and v'/uo with increasing Fr and Re occur in the wall region and the free surface region and slight corresponding increase occurs in the downstream region. However, in the core region no noticeable change in the turbulence levels upstream, within the downstream region of the transition occurs. This increase or decrease in Fr and Re is not associated with the drastic change in the nature of turbulence intensity profiles maintaining the similarity of turbulence profiles with Fr or Re in the transition. This observation is consistent with the observation reported by Nezu
366 Advances in Fluid Mechanics Transactions on Engineering Sciences vol 9, 1996 WIT Press, www.witpress.com, ISSN 1743-3533 and Nakagawa [5]. Figure 6 depict the turbulence intensity profiles along the depthwise and channel axis, for contraction ratio Ab/b = 0.5. In the upstream region of the transition, the Froude and Reynolds numbers are 0.22 and 3.8x10 on an average respectively, turbulence is relatively lower compared to the turbulence within and downstream regions of the transition. It has been observed during this experimentation, that surface waves play an important role in the turbulence production. Upstream of the entrance to the transition, surface waves were relatively mild. Within the transition, the Reynolds and Froude number increased to 6.7x10 and 0.6 on average respectively. As the flow approaches critical state as indicated by Fr reaching close to unity, it tends to be unstable due to higher wave disturbance, although the flow in transition is not exactly critical at Fr = 0.6. In addition, oblique surface waves are seen during experimentation within the transition and few centimeters, about 20-30 cms downstream of the exit of the transition. The combined influence of these surface waves in the subcritical flow and the oblique waves due to constriction could have enhanced, the turbulence intensities in the free surface and wall region at the centre x/b = 0, and beyond up to exit section at x/b = 0.9. This surface wave disturbance effect appears predominant from the centre and at all subsequent sections downstream. At the centre itself at x/b = 0, however, in the core region turbulence is minimum. This may be attributed to the high linear velocity generated due to constriction and reduced depth. Downstream of the transition in the expansion zones, the conditions of the flow at the inlet of the expansion zones cause undirectional distortion of the fluid elements which may be expected to produce high nonhomogeneous and anisotropic turbulence downstream of the transition. Under the action of dynamic process, the turbulence is produced to some degree all over the field. A high level of turbulence intensities u'/uo and v'/uo in all expansion zone occurs compared to the upstream sections as seen in the Fig.6. Specifically the maximum turbulence intensities u'/uo and v'/uo can be seen to occur either close to the free surface or close to the bed. Even in this region, turbulence intensities u'/uo and region are relatively low. v'/uo in core 5 Conclusions The conclusions arising out of this study can be summarized as follows: (1) An increase in the Froude number and Reynolds number, decreases the turbulence intensities u'/uo and v'/uo upstream slightly, followed by slight increase in the turbulence intensities downstream of the transition in the expansion zone at the same flow conditions. This effect in the turbulence occurs primarily in the wall region and the free surface region. However, in the core region no noticeable change in the turbulence levels upstream, within and downstream regions of the transition occurs, (2) Within the transition, flow tends towards the critical state (Fr approaches close to 1)
Advances in Fluid Mechanics 367 Transactions on Engineering Sciences vol 9, 1996 WIT Press, www.witpress.com, ISSN 1743-3533 with a rise in the turbulence intensities u'/uo and v'/uo in the free surface and the wall region which may be attributed to the flow tending towards critical state, (3) At small values of Froude number Fr s 0.2, the effect of Fr on turbulence intensities u'/uo and v'/uo and the free surface wave is negligible, (4) As a comprehensive observation, it is noted that, the streamwise turbulence u'/uo is always greater compared to the vertical turbulence v'/uo, (5) The turbulence intensities u'/uo and v'/uo are higher nearer the bed in the wall region defined by y/yo < 0.2 due to wall effect and the free surface region defined by y/yo > 0.6 due to free surface effect, (6) In the intermediate core region defined by 0.2 < y/yo < 0.6, minimum turbulence intensities u'/uo and v'/uo occur, and (7) With the increasing contraction ratio Ab/b, the streamwise and vertical variation of turbulence intensities u'/uo and v'/uo increased and become pronounced within and downstream of the transition, changing rapidly in the wall, core and the free surface regions. 6 Nomenclature b Channel width Ab Channel contraction Fr Froude number g Gravitation acceleration Q Flow discharge H Horizontal distance along the channel length Re Reynolds number u' Streamwise turbulence intensity component in x-direction (RMS) Uo Streamwise mean free stream velocity (averaged over the cross section) V Vertical distance along the channel width v' Vertical turbulence intensity component in y-direction (RMS) x Longitudinal axis along channel length y Transverse axis along channel height yo Free stream water depth z Lateral axis along channel width References 1. Antonia, R.A., and RajagopaIan, S., "Reynolds dependence of the structure of a turbulent boundary Prof. J. Fluid Mechanics, 121: pp.121-140, 1982. number layer", 2. Bernero, S., and Munukutla, S., "Developing turbulent pipe flow at low Reynolds numbers", Proc. Sixth Asian Congress of Fluid Mechanics, Ed., Chew, Nanyang Technological University, Nanyang Avenue, Singapore, 2263, 1995. 3. Nakagawa, H., and Nezu, I., "Experimental investigation on turbulent structure of back facing step flow in an open channel", J. Hydraulic Research, IAHR, 25, pp.67-88, 1987. 4. Nezu, I., and Rodi, W., "Open channel flow measurements with a Laser Doppler Velocimetry", J. Hydraulic Engg., ASCE, 112, pp.335-355, 1986
368 Advances in Fluid Mechanics S.Nezu, I., and Nakagawa, H., "Turbulence in open channel flows", IAHR- Monograph, A.A. Balkema Publishers, Old Post Road, Brookfield, VT 05036, USA, 1993. G.Rodi, W., "Turbulence Models and their application in hydraulics", IAHR Monograph, A. A. Balkema Publishers, Old Post Road, Bookfield, VT 05036, USA, 1994. 7.Ruck, B., and Makiola, B., "Flow over a single-sided backward facing step with step angle variation", Proc. 3rd Int. Conference of Laser Anemometry, BHRA, Springer-Verlag, UK, pp.369-378, 1990. H- ioo-«figure 1. Schematic of test facility BLUE COLOURED BEAMS (**» n } GREEN COLOURED BEAMS (514.5 n ) TRANSMITTING OPTICS CONSISTING A) BEAM SPLITTER Of B) BRAGG CELL Figure 2. Block diagram of the Laser Doppler Velocimetry (LDV)
Advances in Fluid Mechanics 369 [6X7 # ##. *"'.' f3)(o Figure 3. Schematic showing the grid cross sections for measurements of the transition o-o o-i o-o 0-1 o-o o-i U/Uo,v'/Uo o -a L ) 0 01 D- 0 0-1 0-0 0-1 U/Uo,v'/Uo Figure 4 Continued
370 Advances in Fluid Mechanics 0 0 0-1 )-0 0-1 0-1 )-0 01 0-8 250 # U'/Uo O v'/ Uo Vo = 32 0 mm Uo = 60 cm/5 Ab /b = 0-3 L / b z 1-7 tz SUDDEN TRANSITION o-o 0-1 u/ue,v'/uo Figure 4. Variation of streamwise and vertical components of turbulence intensities u?u<>and v?u<, with y/y,at different locations for Q=39 1/S at Ab/b=0.3 (Fr=0.23 and Re=0.4x10^for free stream) I. 0-25 b Figure 5 Continued 0-1 0-2,V/U*
Advances in Fluid Mechanics 371 u'/uo O v'/uo y<, = 320mm UQ = 1 6-8 cm / S Ab/b = 0-3 L / b = 1-7 SUDDEN TRANSITION 0-0 0-1 o o-i U/Uo,V/Uo Figure 5. Variation of streamwise and^ vertical components of turbulence intensities u/uoand v/uo with y/'yoat different locations for Q=15 1/S at Ab/b=0.3 (Fr=0.088 and Re=0.16x10*for free stream) *'-' * 00 01 02 0" 0 0-1 0-2 0-0 01 02 O'O O'l o-o o-i o-2 o-o o-i oo oi 0-0 O-I 0-2 u'/uo, i Figure 6 Continued
372 Advances in Fluid Mechanics 00 o-1 0-2 0-0 0-1 0-2 03 0-0 0-2 0 3 0-4 0-5 0-6 0-0 01 0-2 03 u/uo,v'/uo Figure 6. Variation of streamwise and vertical components of turbulence intensities u^uoand v^u with y^y^at different locations for Q=39 1/S at Ab/b=0.5 (Fr=0.23 and Re=0.4xlO*for free stream)