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TECHNICAL PAPERS

On the Prediction of Axisymmetric Rotating Flows by a One-Equation Turbulence Model

[+] Author and Article Information
V. I. Vasiliev

ABB Uniturbo Ltd., 13 Ul. Kasatkina, P.O. Box 16, 129301, Moscow, Russia

J. Fluids Eng 122(2), 264-272 (Feb 09, 2000) (9 pages) doi:10.1115/1.483254 History: Received November 24, 1998; Revised February 09, 2000
Copyright © 2000 by ASME
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References

Dorfman, L. A., 1963, Hydrodynamic Resistance and the Heat Loss of Rotating Solids, Oliver and Boyd, Edinburgh.
Owen, J. M., and Rogers, R. H., 1989, Flow and Heat Transfer in Rotating-Disc Systems, Vol. 1: Rotor-Stator Systems, Research Studies Press Ltd., Taunton, England, and Wiley, New York.
Owen, J. M., and Rogers, R. H., 1995, “Flow and Heat Transfer in Rotating Disc Systems, Vol. 2: Rotating Cavities,” Research Studies Press Ltd., Taunton, England, and Wiley, New York.
Owen, J. M., and Wilson, M., 1995, “Heat Transfer and Cooling in Gas Turbines, Rotating Cavities and Disc Heat Transfer,” Von Karman Institute for Fluid Dynamics, Lecture Series 1995-05.
Stow, P., and Coupland, J., 1993, “Turbulence Modelling for Turbomachinery Flows,” 2nd International Symposium on Engineering Turbulence Modelling and Measurements, Florence, 31 May–2 June, p. 30.
Launder,  B. E. and Sharma,  B. I., 1974, “Application of the Energy Dissipation Model of Turbulence to Flow Near Spinning Disc,” Lett. Heat Mass Transfer, 1, pp. 131–138.
Morse,  A. P., 1991, “Application of a Low Reynolds Number k-ε Turbulence Model to High Speed Rotating Cavity Flows,” ASME J. Turbomach., 113, pp. 98–105.
Iacovides,  H. and Theofanopoulos,  I. P., 1991, “Turbulence Modelling of Axisymmetric Flow inside Rotating Cavities,” Int. J. Heat Fluid Flow, 12, pp. 2–11.
Virr, G. P., Chew, J. W., and Coupland, J., 1993, “Application of Computational Fluid Dynamics to Turbine Disc Cavities,” ASME-paper 93-GT-89.
Spalart, P. R., and Allmaras, S. R., 1992, “A One-Equation Turbulence Models for Aerodynamic Flows,” AIAA paper 92-0439.
Secundov,  A. N., 1971, “Application of a Differential Equation for Turbulent Viscosity to the Analysis of Plane Non-Self-Similar Flows,” Fluid Dyn., No. 5, pp. 528–840.
Gulyaev,  A. N., Kozlov,  V. Ye., and Secundov,  A. N., 1993, “A Universal One-Equation Model for Turbulent Viscosity,” Fluid Dyn., No. 4, pp. 485–494.
Bradshaw, P., Launder, B., and Lumley, J., 1991, “Collaborative Testing of Turbulence Models,” AIAA paper 91-0215.
Vasiliev,  V. I., Volkov,  D. V., Zaitsev,  S. A., and Lyubimov,  D. A., 1997, “Numerical Simulation of Channel Flows by One-Equation Turbulence Model,” ASME J. Fluids Eng., 119, pp. 885–892.
Kazarin, F. V., Secundov A. N., Vasiliev I. V., Zaitsev, S. A., 1997, “On the Bypass Transition Prediction by One-Equation Turbulence Model,” 2nd International Symposium on Turbulence, Heat and Mass Transfer. Delft, Niezerland, June.
Daily,  J. W. and Nece,  R. E., 1960, “Chamber Dimension Effects on Induced Flow and Frictional Resistance of Enclosed Rotating Disks,” ASME J. Basic Eng., 82, pp. 217–232.
Kilic,  M., Gan,  X., Owen,  J. M., 1994, “Transitional Flow Between Contra-rotating Disks,” J. Fluid Mech., 281, pp. 119–135.
Kilic,  M., Gan,  X., and Owen,  J. M., 1996, “Turbulent Flow Between Two Disks Contrarotating at Different Speeds,” ASME J. Turbomach., 118, pp. 408–413.
Schukin,  V. K. and Olimpiev,  V. V., 1976, “Experimental Investigation of Heat Transfer in Closed Rotating Cavity,” Ingenerno-Phyzichesky Zurnal, 30, No. 4, pp. 613–618.
Homsy,  G. M. and Hudson,  J. L., 1969, “Centrifugally Driven Thermal Convection in Rotating Cylinder,” J. Fluid Mech., 35, pp. 33–52.
Vasiliev,  V. I., 1994, “Computation of Separated Duct Flows Using the Boundary-Layer Equations,” AIAA J., 32, No. 6, pp. 1191–1199.

Figures

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Scheme of disk cavity and calculation grid: (a) rotor-stator system, (b) contra-rotating disks
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Swirl velocity distributions: (a) axial profiles, (b) radial distribution at the mid plane (rotor-stator system, G=0.155,r=0,Re=8×105)
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Velocity distributions in rotor-stator cavity (G=0.0685,r/R=0.1,Re=6.9×105) ⋄ experiment [[dashed_line]] Launder-Sharma model, ⋯ Morse model, – one-equation model (present calculations)
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Effect of Re on radial variation of swirl velocity in rotor-stator cavity (G=0.1,r/R=0,x/s=0.5): 1, Re=105; 2, Re=4×105; 3, Re=106; 4, Re=4×106, ⋯ Morse model, – one-equation model (present calculations)
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Computational grid for cavity with axial clearance
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Prescribed swirl velocity at the axial clearance
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Streamline maps for different swirl in the clearance (the values of streamfunction are normalized by 0.01ΩR2)
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Influence of the external flfow on the momentum friction
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(a) Velocity distributions between contra-rotating disks (G=0.12,Re=105,y/R=0.85,Γ=0;0.4). (b) Velocity distributions between contra-rotating disks (G=0.12,Re=105,y/R=0.85, Γ=0.6;1.0).
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(a) Velocity distributions between contra-rotating disks (G=0.12,Γ=0.6,Re=1.25×106) (b) Velocity distributions between contra-rotating disks (G=0.12, Γ=1.0, Re=1.25×106)
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Comparison of calculated and measured Nusselt number in rotating cavity
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Influence of Coriolis forces on the temperature distribution in rotating cavity (θ contours at G=0.12,Re=5×107m=0.005)
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Comparison of analytical and numerical solutions for rotating cavity (G=0.06,Re=107m=0.1)

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