1. 1 26-05-15 22nd Canadian Hydrotechnical Conference Simulation of flow past an open channel floor slot J. Qu 1, D. Vo 2 & A. S. Ramamurthy 2 1. KGS Group, Winnipeg, Manitoba, 2.Concordia university, Montreal Fig.1. Flow past an open channel floor slot 1

2. 1.1Summary 2 Floor slots in channels divert flows from streams. In the past, slot flows were solved by experimental or analytical procedures. In this study, a free-surface turbulence model is used to get pressure, velocity & surface profiles. Simulation results are validated using test data. A properly validated model predicts flow behavior for differing field boundary conditions. This avoids need for expensive test procedures. 2

3. 1.1 Introduction 4 Floor outlets or bottom racks are frequently used to divert flow from one stream to another (Fig. 1). Floor slots are also used as horizontal trash racks in hydro power plants & street curb outlets (Brune et al.1975 & Venkataraman 1977) Venkataraman (1977, 1978) found the angle of the diverted jet, for slot flows, in rectangular channels. Nasser et al. (1980) determined Cd for slot outflows. Satish & Ramamurthy (1986) measured pressure & velocity distributions for open channeslot flows. Chow (1959) has summarized earlier floor slot studies. 3

4. Recently, Mohapatra et al.(2001) used Youngs’ 3 volume of fluid technique to predict pressure & velocity for slot flows & validated the inviscid model using data of Satish & Ramamurthy, 1986. It gave good predictions of pressure. As expected, the inviscid model failed to predict velocity distribution Fig.1. Flow past an open channel floor slot STN denotes measuring stations 4

5. 1.2 Experimental procedures 5 A contraction & screens at the entrance ensured smooth flow in the approach section. Slot & channel discharges were measured by V-notches Velocity and pressure distributions across the channel section were recorded at regular intervals. A 3 mm diameter Pitot tube measured the total head & a static probe with a flattened end gave static pressure. Velocity & pressure were collected at channel center as the flow was assumed to be 2-dimensional. For details see a related publication: Satish, thesis 1986 For slot flows, Venkataraman (1978) has presented many water surface profile data. 5

6. 1.2 Turbulence Model 6 The model solves the 2-d RANS eqns. for turbulent unsteady flow using 2-eqn. k-ω model (Wilcox 2000). Control volume (CV) technique is used to convert governing eqns. to algebraic eqns. to solve numerically using collocated-grid approach. Pressure-velocity coupling is achieved using the PISO algorithm (Issa 1986). Discretized eqns. are solved with a tridiagonal solver. More details are in Qu’s thesis (ref. section) Free Surface Method In the VOF method, besides conservation equation for mass and momentum, introduce a variable c to denote volume fraction of phase in the computational cell. In each control volume, volume fractions of all phases sum to unity. The fields for all flow variables and properties represent volume- averaged values.Depending upon volume fraction (Ferziger & Peric, 2002) c = 1 for control volumes (CVs) filled by liquid and c = 0 for CVs filled by air. Eq. (1) denotes the change of c. 6

7. Here, ujdenotesaveragevelocity( j=1,2 in 2d); xj denotes coordinates ( j = 1, 2 in 2-d. Treating bothfluidsas 1 fluid space (Ferziger&Peric 2002), one obtains Eq. (2). Subscripts1 & 2 denote 2 fluids. Boundary Conditions At wall, the wall-functionapproachof Launder& Spalding (1974) was used. For log law, outside the viscous sub layer, Here, u = velocity at the first cell, uτ = friction velocity, κ= 0.41; and C = 5.0 for smooth surfaces. Near the wall, turbulent kinetic energy k & dissipation rate ω are specified (assume local equilibrium of turbulence : Wilcox 2000): 7

8. At inlet (Fig. 2), known velocities and turbulent quantities are prescribed. Outlet HI far d/s of slot BO & outlet TF of slot (Fig. 2) are pressure boundaries to let water flow freely. All air boundaries are pressure boundaries with zero pressure. A M J H G F B Q T S Y X O Fig. 2 Domain for flow past a slot 8

9. 9 Solution Procedure Channel u/s of slot AB is 3.0 m long in the x - direction. The channel d/s of slot QH is 1.2m long. Channel bed, ABQH (Fig. 2) is 0.08m above bottom of computational domain. Hence, ST = GF = 0.08 m. The slot width L = 0.0192m, 0.04m, 0.055m and 0.074m. Cartesian body fitted coordinates are used. Four meshes SM1 to SM4 are generated for various slot widths (Table 1). The flow domain is meshed with a power law function to generate a fine mesh near boundary. Grid cells next to boundary are within turbulent region. Flow parameters for different computational cases are also shown in Table 1. The flow mode is supercritical. Through time-dependent simulation, water flows on open channel.

10. 10 Results were checked for grid independence. Program execution time was close to 10 hours. Table 1. Grid cells and flow parameters (time step = 0.001 second) Mesh No. Slot Width L (m) Discharge q (m 3 /s.m) Initial Flow Depth H (m) Fr Number Number of grid cells X upstream X downstream X slot Y open channel SM10.01920.13780.07662.075120100830 SM20.04000.08320.08501.0721201001630 SM30.05500.0850 1.0961201002030 SM40.07400.08480.08501.0921201002430

11. 11 RESULTS Pressure and Axial Velocity data near Slot Fig. 3 compares computed pressure & velocity for slot width L = 0.0192 m with data (Satish & Ramamurthy 1986). Deviation of pressure head from the hydrostatic distribution (Fig. 3) is due to streamline curvature. For u/s sections, pr. head distribution is similar to test data (Fig. 3). For stns. 4 and 5 d/s of slot follow trend of measured pressure except in wall region. All velocity profiles agree very well with measured values (Fig. 3). Acceleration of flow and resulting reduction in boundary layer thickness ahead of slot are captured by test data & simulation (Fig. 3).

12. 12 Surface Profile Fig. 4 shows good agreement between computed and experimental profiles (L= 0.0192m, Satish, 1986), Figs. 4b to 4d refer to profiles measured by Venkataraman (1978) in a large number of tests (L = 0.040m, 0.055m and 0.740m). The comparison is very good. For supercritical flow, water surface decreases with discharge/unit width in the d/s as one would expect. Floor slot a) b) Floor slot c) Floor slot d) Floor slot Figure 4 Water surface profiles

13. 13 CONCLUSIONS 2-d 2 eqn. k-ω turbulence model with VOF method simulates faithfully slot flow in a open channels. Experimental data (past & present) validate the model. Validated data cover water surface profiles besides distribution of pressure head and axial velocity. Water depth predictions provide guidance for wall height design in diversion works related to drainage systems and power channels of hydroelectric development. Due to lower time and cost demand of modeling, it offers an advantage in engineering practice.