Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Prediction of Bypass Transition Flow on Surface with Changing Pressure Gradient

압력구배가 변하는 표면 위의 Bypass 천이 유동의 예측

  • 백성구 (한국과학기술원 기계공학과) ;
  • 정명균 (한국과학기술원 항공우주공학과) ;
  • 임효재 (호서대학교 기계공학과)
  • Published : 2002.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

A modified $textsc{k}$-$\varepsilon$model is proposed for calculation of transitional boundary-layer flows with changing pressure gradient. In order to develop the model for this problem, the flow is divided into three regions; pre-transition region, transition region and fully turbulent region. The effect of pressure gradient is taken into account in stream-wise intermittency factor, which bridges the eddy-viscosity models in the pre-transition region and the fully turbulent region. From intermittency data in various flows, Narashima＇s intermittency function, F(${\gamma}$), has been found to be proportional to $\chi$$^{n}$ according to the extent of pressure gradient. Three empirical correlations of intermittency factor being analyzed, the best one was chosen to calculate three benchmark cases of bypass transition flows with different free-stream turbulence intensity under arbitrary pressure gradient. It was found that the variations of skin friction and shape factor as well as the profiles of mean velocity in the transition region were very satisfactorily predicted.

Keywords

References

  1. Mayle, R. E., 1991, 'The Role of Laminar-Turbulent Transition in Gas Turbine Engines,' ASME J. of Turbomachinery, Vol. 113, pp. 509-537 https://doi.org/10.1115/1.2929110
  2. Morkovin, M. W., 'Instability, Transition to Turbulence and Receptivity,' AGARD-AG-236
  3. Blair, M. F., 1992, 'Boundary-Layer Transition in Accelerating Flows with Intense Freestream, Turbulence; Part 2-The Zone of Intermittent Turbulence,' ASME J. of Fluids Engineering, Vol. 114, pp. 322-332 https://doi.org/10.1115/1.2910033
  4. Gostelow, J. P., Blunden, A. R., and Walker, G. J., 1994, 'Effects of Free Stream Turbulence and Adverse Pressure Gradients on Boundary Layer Trasition,' ASME J. of Turbomachinery, Vol. 116, pp. 302-404
  5. Narashima, R., Devasia, K. J., Guruani, G., and Badri Narayanan, M. A., 1984, 'Transitional intermittency in Boundary Layers Subjected to Pressure Gradient,' Experimenets in Fluids, Vol. 2, pp. 171-176 https://doi.org/10.1007/BF00571859
  6. Dey, J. and Narashima, R., 1990, 'Intergral Method for the Calculation of Incompressible Two-Dimensional Transitional Boundary-Layers,' J. Aircraft, Vol. 27, No. 10, pp. 859-865 https://doi.org/10.2514/3.45949
  7. Solomon, W. J., Walker, G. J., and Gostelow, J. P., 1996, 'Transition Length Prediction for Flows with Rapidly Changing Pressure Gradients,' ASME J. of Turbomachinery, Vol. 118, pp. 744-751 https://doi.org/10.1115/1.2840930
  8. Cebeci, T. and Smith, A. M. O., 1974, Analysis of Turbulent Boundary Layers, Academic Press, New York, pp. 234-239
  9. Sieger, K., Schiele, R., Kaufmann, F., Witting, S., and Rodi, W., 1995, 'A Two-Layer Turbulence Model for the Calculation of Transitional Boundary Layers,' ERCOFTAC Bulletin, Vol. 24, pp. 21-25
  10. Steelant, J. and Dick, E., 1996, 'Modeling of Bypass Transition with Conditioned Navier-Stokes Equations Coupled to and Intermittency Transport Equation,' Int. J. for Numerical Method in Fluids, Vol. 23, pp. 193-220 https://doi.org/10.1002/(SICI)1097-0363(19960815)23:3<193::AID-FLD415>3.0.CO;2-2
  11. 백성구, 임효재, 정명균, 2000, '압력구배가 없는 평판 천이 경계층 유동을 예측하기 위한 ${\kappa}-{\varepsilon}$ 모형의 개발,' 대학기계논문집 B권, Vol. 25, No. 3, pp. 305-314
  12. Baek, S. G., Chung, M. K., and Lim, H. J., 2001, '${\kappa}-{\varepsilon}$ Model for Predicting Transitional Boundary-Layer Flows Under Zero-Pressure Gradient,' AIAA J., Vol. 39, No. 9, pp. 1699-1706 https://doi.org/10.2514/2.1527
  13. Savill, A. M., 1995, 'The SLY RST Intermittency Model for Predicting Transition,' ERCOFTAC Bulletin, Vol. 24, pp. 37-41
  14. Cho, J. R. and Chung, M. K, 1992, 'A Proposal of ${\kappa}-{\varepsilon}-{\gamma}$ Equation Turbulence Model,' J. of Fluids Mechanics, Vol. 237, pp. 301-322 https://doi.org/10.1017/S0022112092003422
  15. Mayle, R. E. and Schulz A., 1997, 'The Path to Predicting Bypass Transition,' ASME J. of Turbomachinery, Vol. 119, pp. 405-411 https://doi.org/10.1115/1.2841138
  16. Volino, R. J. and Simon, T. W., 1994, 'An Application of Octant Analysis to Turbulent and Transitional Flow Data,' ASME J. of Turbomachinery, Vol. 116, pp. 752-758 https://doi.org/10.1115/1.2929469
  17. Wang, T. and Zhou, D., 1996, 'Spectral Analysis of Boundary Layer Transition in A Heated on Flat Plate,' Int J. of Heat and Fluid Flow, Vol. 17, pp. 12-21 https://doi.org/10.1016/0142-727X(95)00082-2
  18. Nagano, Y. and Tagawa, M., 1990, 'An Improved ${\kappa}-{\varepsilon}$ Model for Boundary Layer Flows,' ASME J. of Fluids Engineering, Vol. 102, pp. 33-39
  19. Yang, Z. and Shih, T. H., 1993, 'New Time Scale Based ${\kappa}-{\varepsilon}$ Model for Near Wall Turbulence,' AIAA J., Vol. 31, No. 7, pp. 1191-1198 https://doi.org/10.2514/3.11752
  20. Wilcox, D. C., 1998, Turbulence Modeling for CFD, DCW Industries Inc., California
  21. Rollce-Royce, 1993, transmittal by J. Coupland of data from Rollce-Royce Applied Science Lagoratory
  22. Narashima, R., 1985, 'Subtransition in The Transition Zone,' IUTAM Symposium, Novosbirsk, USSR, p. 141
  23. Abu Ghannam, B. J. and Shaw, R., 1980, 'Natural Transition of Boundary Layers-The Effects of Turbulence Pressure Gradient, and Flow History,' J. Mechanical Engineering Science, Vol. 22, No. 5, pp. 213-228 https://doi.org/10.1243/JMES_JOUR_1980_022_043_02
  24. Narashima, R. and Dey, J., 1985, 'Transitional Spot Formation Rate in Two-Dimensional Boundary Layers,' Proc. of the Third Symposium on Numerical and Physical Aspect of Aerodynamic Flows, ed. Cebeci, T., Spring-Verlag, New York, pp. 57-74