NUMERICAL CALCULATION OF TURBULENT OPEN-CHANNEL FLOWS BY USING A MODIFIED /g-e TURBULENCE MODEL By Iehisa NEZU and Hiroji NAKAGA WA Numerical calculat
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1 NUMERICAL CALCULATION OF TURBULENT OPEN-CHANNEL FLOWS BY USING A MODIFIED /g-e TURBULENCE MODEL By Iehisa NEZU and Hiroji NAKAGA WA Numerical calculation techniques of turbulent shear flows are classified into two categories:one is k-c turbulence model and the other is large eddy simulation (LES). The standard k-s model has been established at present to predict turbulent structure in closed duct flows, while LES is being developed to predict coherent eddy structure in more simple duct flows. The standard /g-e model cannot be, however, applied to open channel surface flows, because the turbulence near the free surface is more depressed than the closed duct flows. In the present study a new modified k-e model is proposed to predict reasonably the turbulent structure in open channel flows with both of low and high Reynolds numbers. The numerical calculations indicate a splendid agreement with the experimental data which were obtained by making use of hot-film and Laser Doppler anemometers. Keywords:open-channel turbulence, numerical calculation, free surface, k-e model, turbulence model
2 P=p9(h-y)cose+P' (4 ) (5) vt=cu.2e (6) (7)
3 Up1 U-*xInyp+A (16) t(-uv)ady )=1 wvt (23) (a) Experimental Values Fig. 1 Effect of free-surface damping factor on eddy viscosity,
4 Fig. 2 Effect of free-surface damping factor on mean velocity distribution. Fig, 3 Effect of free-surface damping factor on turbulent energy k/u. Fig. 4 Effect of free-surface damping factor on energy dissipation Eh/ U*.
5 Table 1 Hydraulic conditions for numerical calculations. (a) High Reynolds-number Series (b) Low Reynolds-number Series
6 Fig. 5 Numerical results of mean velocity distributions at high Reynolds numbers (HR). Fig. 6 Turbulent energy Ic/ U* vs y/h at high Reynolds numbers. Fig. 7 Distribution of Reynolds stress -u/u. v* Fig. 8 Comparison of calculated values of energy dissipation with experimental data of Nezu (1977).
7 (a) Experimental Values (Nezu 1977) High Reynolds-number Series (HR) RUN Re Rsra O 1 2.0= =10= E ' =10' X U =10' O x ' =10" Fig. 9 Comparison of calculated values of generationdissipation relations with experimental data.
8 Low Reynolds-number Series (LR) RUN Re Rsn o 1 5.0= x x x x10 X 1 5.0x x102 O 5 1.0x x x x10 R 7 1.0= =10' Fig. 10 Numerical results of mean velocity distributions at low Reynolds numbers (LR). Low Reynolds-number Series (LR) 0 RUN Rt Rsl ' e ' ' ' X 4 S.0.10' ' o ' ' * ' ' R ' 4. I Tl0' Low Reynolds-number Series (LR) RUN Rt Rsln O ' ' e ' ' ' ' X ' '.O 5 1.0' 10' ' =10' ' ' ' Fig, 11 Calculated distribution of turbulent energy in the wall region. Fig. 12 Calculated distribution of Reynolds stress in the wall region. Low Reynolds-number Series (LR) RUN Rt Rs. O ' ' e ' ' ' ' X ' ' O ' S ' t ' 2. 22x10' R ' ' lo. Reynolds-nuwber Series (LR) O RUN R=M. 5.0x10' 1.0xt0' 2 I ' n ' ' 10' x r 5.x10' 2. 7Vx10' o * S ' 5. ax 10' ' ' x 7 I.alo ' O : E. perimentl Vlues (taufer 1954) Fig. 14 Relation between turbulent generation and dissipation in the wall region. Fig. 13 Calculated distribution of dissipation in the wall region.
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10 2) Rodi, W.: Turbulence Models and Their Application in Hydraulics, IAHR, Delft, ) Naot, D. and Rodi, W.: Calculation of Secondary Currents in Channel Flow, J. Hydraulics Div., ASCE, Vol. 108, HY-8, pp , ) Nakagawa, H., Nezu, I. and Ueda, H.: Turbulence of Open Channel Flow over Smooth and Rough Beds, Proc. JSCE, No. 241, pp , ) Celik, I, and Rodi, W.: Simulation of Free-Surface Effects in Turbulent Channel Flows, Physico-Chemical Hydrodynamics, Vol. 5, pp , ) Jones, W. P. and Launder, B. E.: The Calculation of Low-Reynolds-Number Phenomena with a Two- Equation Model of Turbulence, Int. J. Heat and Mass 10) Patel, V. C., Rodi, W. and Scheuerer, G.: Turbulence Model for Near-Wall and Low Reynolds Number Flows A Review, AIAA J., pp , ) Nezu, I. and Rodi, W.: Open-Channel Flow Measurements with a Laser Doppler Anemometer, J. Hydraulic Eng., ASCE, Vol. 112, pp , ) van Driest, E. R.: On Turbulent Flow Near a Wa!!, J. Aeron. Sci., Vol. 23, pp , ) Hussain, A. K. M. F, and Reynolds, W. C.: Measurements in Fully Developed Turbulent Channel Flow, J. Fluids Eng., ASME, Vol. 97, pp , ) Gosman, A. D., Launder, B. E, and Reece, G. J.: Computer-Aided Engineering; Heat Transfer and Fluid Flow, John Wiley & Sons, ) Eckelmann, H.: The Structure of the Viscous Sublayer and the Adjacent Wall Region in a Turbulent Channel Flow, J. Fluid Mech., Vol. 65, pp , ) Laufer, J.: The Structure of Turbulence in Fully Developed Pipe Flow, NACA, TR-1174, ) Rodi, W.: Use of Advanced Turbulence Models for Calculating the Flow and Pollutant Spreading in Rivers, 3rd Int. Symp. River Sedim., Univ. of Mississippi, pp , 1986.
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