A STUDY ON THE IMPROVEMENT OF κ-εTURBULENCE MODEL FOR PREDICTION OF THE RECIRCULATION FLOW

Title & Authors
A STUDY ON THE IMPROVEMENT OF κ-εTURBULENCE MODEL FOR PREDICTION OF THE RECIRCULATION FLOW
Lee, Y.M.; Kim, C.W.;

Abstract
The standard $\small{{\kappa}-{\varepsilon}}$ and realizable $\small{{\kappa}-{\varepsilon}}$ models are adopted to improve the prediction performance on the recirculating flow. In this paper, the backward facing step flows are used to assess the prediction performance of the recirculation zone. The model constants of turbulence model are obtained by the experimental results and they have a different value according to the flow. In the case of an isotropic flow situation, decaying of turbulent kinetic energy should follow a power law behavior. In accordance with the power law, the coefficients for the dissipation rate of turbulent kinetic energy are not universal. Also, the other coefficients as well as the dissipation coefficient are not constant. As a result, a suitable coefficients can be varied according to each of the flow. The changes of flow over the backward facing step in accordance with model constants of the $\small{{\kappa}-{\varepsilon}}$ models show that the reattachment length is dependent on the growth rate($\small{{\lambda}}$) and the $\small{{\kappa}-{\varepsilon}}$ models can be improved the prediction performance by changing the model constants about the recirculating flow. In addition, it was investigated for the curvature correction effect of the $\small{{\kappa}-{\varepsilon}}$ models in the recirculating flow. Overall, the curvature corrected $\small{{\kappa}-{\varepsilon}}$ models showed an excellent prediction performance.
Keywords
Turbulence models;Backward-facing step flow;Separation flow;Recirculating region;Reattachment length;Flow prediction;
Language
Korean
Cited by
References
1.
1972, Johns, W.P. and Launder, B.E., "The prediction of Laminarization with a Two-Equation Model of Turbulence," Int J. of Heat Mass Transfer, Vol.15, p.301.

2.
1994, Myong, H.K., Han, H.T. and Paek, I.C., "Prediction of a Backward-Facing Step Flow with Modified Turbulence Models," Trans. Korean Soc. Mech. Eng. B, Vol.18, No.11, pp.3039-3045.

3.
1981, Eaton, J.K. and Johnston, J.P., "A Review of Research on Subsonic Turbulent Flow Reattachment," AIAA Journal, Vol.19, pp.1093-1100.

4.
1980, Kim, J., Kline, S.J. and Johnston, J.P., "Investigation of a Reattaching Turbulent Shear Layer : Flow Over a Backward-Facing Step," ASME J. Fluid Eng., Vol.102, pp.302-308.

5.
1980, Eaton, J. and Johnston, J.P., "Turbulent flow reattachment: an experimental study of the flow and structure behind a backward-facing step," Technical Report MD-39, Stanford University, CA.

6.
1985, Driver, D.M., Seegmiller, H. L., "Features of a reattaching turbulent shear layer in divergent channel flow," AIAA Journal, Vol.23, pp.163-171.

7.
1988, Adams, E.W. and Eaton, J.K., "An LDA study of the backward-facing step flow, including the effect of velocity bias," ASME Journal of Fluids Engineering, Vol.110, pp.275-282.

8.
1984, Adams, E.W., "Assessment of Reynolds Stress Turbulence Closures for Separated Flow over Backward-Facing Step," Ph. D. Thesis, Dept. of Mech. Eng. of Stanford Univ.

9.
1987, Nallasamy, M., "Turbulence Models and Their Applications to the Prediction of Internal Flows : A Review," Computers & Fluids, Vol.15, No.2, pp.151-194.

10.
1980, Hanjalic, K., Launder, B.E. and Schiestel, R., "Multiple-time scale concepts in turbulent shear flows," in Turbulent Shear Flows, Vol.2(L,J,S, Bradbury et al., eds.) Springer-Verlag, New York, pp.36-49.

11.
1986, Yakhot, V. and Orszag, S.A., "Renormalization group analysis of turbulence. I. Basic theory," Journal of Scientific Computing, Vol.1, pp.3-51.

12.
1988, Speziale, C.G. and Ngo, T., "Numerical solution of turbulent flow past a backward-facing step using a nonlinear k-${\epsilon}$ Model," International Journal of Engineering Science, Vol.26, pp.1099-1112.

13.
1995, Shih, T.-H., Liou, W.W., Schabbir, A., Yang, Z. and Zhu, J., "A New k-${\epsilon}$ Eddy-Viscosity Model for High Reynolds Number Turbulent Flows - Model Development and Validation," Computers Fluids, 24(3), pp.227-238.

14.
1993, Choudhury, D., "Introduction to the Renormalization Group Method and Turbulence Modeling," Fluent Inc, Technical Memorandum TM-107.

15.
1967, Bradshaw, P., Ferriss, D.H. and Atwell, N.P., "Calculation of boundary layer development using the turbulent energy equation," Journal of Fluid Mechanics, Vol.28, pp.593-616.

16.
1938, von Karman, T. and Howarth, L., "On the statistical theory of isotropic turbulence," Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol.164, No.917, The Royal Society.

17.
1941, Kolmogorov, A.N., "On the degeneration of isotropic turbulence in an incompressible viscous fluid," Dokl. Akad. Nauk SSSR, Vol.31, pp.319-323

18.
1967, Saffman, P.G., "Note on decay of homogeneous turbulence," Physics of Fluids, Vol.10, p.1349.

19.
1992, George, W.K., "The decay of homogeneous isotropic turbulence," Physics of Fluids, Vol.4, p.1492.

20.
1992, Speziale, C.G. and Bernard, P.S., "The energy decay in self preserving isotropic turbulence revisited," Journal of Fluid Mechanics, Vol.241, p.645.

21.
1976, Townsend, A., "The structure of turbulent shear flow, 2nd edn," Cambridge University Press, Cambridge.

22.
1991, Speziale, C.G., Sarkar, S. and Gatski, T.B., "Modeling of pressure-strain correlation of turbulence : an invariant dynamical systems approach," Journal of Fluid Mechanics, Vol.227, pp.245-272.

23.
1971, Comte-Bellot, G. and Corrsin, S., "Simple Eulerian time-correlation of full and narrow-band velocity signals in grid-generated, isotropic turbulence," Journal of Fluid Mechanics, Vol. 48, pp. 273-337.

24.
1997, Spalart, P.R. and Shur, M., "On the sensitization of turbulence models to rotation and curvature," Aerospace Sci. Tech., 1(5), pp. 297-302.

25.
2008, Smirnov, P.E. and Menter, F.R., "Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart-Shur correction term," ASME Paper GT 2008-50480, Berlin, Germany.

26.
2008, Dufour, G., Cazalbou, J.-B., Carbonneau, X. and Chassaing, P., "Assessing rotation / curvature corrections to eddy-viscosity models in the calculations of centrifugal-compressor flows," Journal of Fluids Engineering, Vol.130, 9, 091401.

27.
1989, Speziale, C.G. and Mac Giolla Mhuiris, N., "On the prediction of equilibrium states in homogeneous turbulence," Journal of Fluid Mechanics, Vol.209, pp.591-615.

28.
1965, Bearman, P.W., "Investigation of the flow behind a two-dimensional model with a blunt trailing edge and fitted with splitter plates," Journal of Fluid Mechanics, Vol.21, No.2, pp.241-255.

29.
1994, Jovic, S. and Driver, D.M., "Backward-facing step measurement at low Reynolds number, $Re_h$ = 5000," NASA Tech. Mem. 108807.

30.
1999, Yoder, D.A. and Georgiadis, N.J., "Implementation and validation of the chien k-epsilon turbulence model in the wind navier-stokes code," AIAA Journal, 99-0745.