A New k-$\small{\varepsilon}$ Model for Prediction of Transitional Boundary-Layer Under Zero-Pressure Gradient

Title & Authors
A New k-$\small{\varepsilon}$ Model for Prediction of Transitional Boundary-Layer Under Zero-Pressure Gradient
Baek, Seong-Gu; Im, Hyo-Jae; Jeong, Myeong-Gyun;

Abstract
A modified model is proposed for calculation of transitional boundary layer flows. In order to develop the eddy viscosity model for the problem, the flow is divided into three regions; namely, pre-transition region, transition region and fully turbulent region. The pre-transition eddy-viscosity is formulated by extending the mixing length concept. In the transition region, the eddy-viscosity model employs two length scales, i.e., pre-transition length scale and turbulent length scale pertaining to the regions upstream and the downstream, respectively, and a universal model of stream-wise intermittency variation is used as a function bridging the pre-transition region and the fully turbulent region. The proposed model is applied to calculate three benchmark cases of the transitional boundary layer flows with different free-stream turbulent intensity (1%∼6%) under zero-pressure gradient. It was found that the profiles of mean velocity and turbulent intensity, local maximum of velocity fluctuations, their locations as well as the stream-wise variation of integral properties such as skin friction, shape factor and maximum velocity fluctuations are very satisfactorily predicted throughout the flow regions.
Keywords
k-$\small{\varepsilon}$ Model;Bypass Transition;Pre-Transition Region;Intermittency;Boundary-Layer;Mixing-Length;Flat Plate;
Language
Korean
Cited by
1.
수치 모사를 통한 이중원호 익렬의 성능 예측,정명균;오재민;팽기석;송재욱;

대한기계학회논문집B, 2002. vol.26. 3, pp.432-438
References
1.
Mayle, R. E., 1991, 'The Role of Laminar-Turbulent Transition in Gas Turbine Engines,' ASME J. Turbo., Vol. 113, pp. 509-537

2.
Morkovin, M. W., 'Instability, Transition to Turbulence and Receptivity,' AGARD-AG-236

3.
Cebeci, T. and Smith, A. M. O., 1974, Analysis of Turbulent Boundary Layers, Academic press, Orland, FL

4.
Rodi, W., Mansour, N. N. and Michelassi, V., 1993, 'One-Equation Near- Wall Turbulence Modeling with The Aid of Direct Simulation Data,' ASME J. Fluids Eng. Vol. 115, pp. 196-205

5.
Savill, A. M., 1995, 'A Summary Report on the COST ERCOFTAC Transition SIG Project Evaluating Turbulence Models for Predicting Transition,' ERCOFTAC Bulletin, Vol. 24, pp. 57-61

6.
Launder, B. E. and Shama, B. I., 1974, 'Application of The Energy-Dissipation Model of Turbulence to The Calculation of Flow Near A Spining Disc,' Letters in Heat and Mass Transfer, Vol. 1, pp. 131-138

7.
Rollce-Royce, 1993, transmittal by J. Coupland of data from Rollce-Royce Applied Science Laboratory

8.
Westin, K. J. A. and Henkes, R. A. W. M., 1997, 'Application of Turbulence Models to Bypass Transition,' ASME J. Fluids Engng., Vol. 119, pp. 859-866

9.
Young, T. W., Warren, E. S., Harris, J. E., and Hassan, H. A., 1993, 'New Approach for The Calculation of Transition Flows,' AIAA, Vol. 31, pp. 629-636

10.
Savill, A. M., 1995, 'The SLY RST Intermittency Model for Predicting Transition,' ERCOFTAC Bulletin, Vol. 24, pp. 37-41

11.
Cho, J. R. and Chung, M. K, 1992, 'A ${\kappa}-{\varepsilon}-{\gamma}$ Equation Turbulence Model,' J Fluids Mech., Vol. 237, pp. 301-322

12.
Mayle, R. E. and Schulz A., 1997, 'The Path to Predicting Bypass Transition,' ASME J. Turbo., Vol. 119, pp. 405-411

13.
Westin, K. J. A., Boiko, A. V., Klingmann, B. G. B., Kozlov, V. V., and Alfredsson, P. H., 1994, 'Experiments in A Boundary Layer Subjected to Free Stream Turbulence. Part 1. Boundary Layer Structure and Receptivity,' J. Fluids Mech., Vol. 281, pp. 193-218

14.
Voke, P. R. and Yang, Z., 1995, 'Numerical Study of Bypass Transition,' Phys. Fluids, Vol. 7, No.9, pp. 2256-2264

15.
Volino, R. J. and Simon, T. W., 1994, 'An Application of Octant Analysis to Turbulent and Transitional Flow Data,' ASME J. Turbo., Vol. 116, pp. 752-758

16.
Wang, T. and Zhou, D., 1996, 'Spectral Analysis of Boundary Layer Transition in A Heated on Flat Plate,' Int. J. Heat and Fluid Flow, Vol. 17, pp. 12-21

17.
Blair, M. F., 1992, 'Boundary-Layer Transition in Accelerating Flows with Intense Freestream Turbulence; Part 2-The Zone of Intermittent Turbulence,' ASME J. Fluids Eng., Vol. 114, pp. 322-332

18.
Yang, Z. and Shih, T. H., 1993, 'New Time Scale Based ${\kappa}-{\varepsilon}$ Model for Near-Wall Turbulence,' AIAA, Vol. 31, No.7, pp. 1191-1198

19.
Nagano, Y. and Tagawa, M., 1990, 'An Improved ${\kappa}-{\varepsilon}$ Model for Boundary Layer Flows,' ASME., J. Fluids Eng., Vol. 102, pp. 33-39

20.
Wilcox, D. C., 1998, Turbulence Modeling for CFD, DCW Industries, Inc., California

21.
Narashima, R., 1985, 'Subtransition in The Transition Zone,' IUTAM Symposium, Novosbirsk, USSR, p. 141