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Numerical prediction of transition boundary-layer flows using new intermittency transport equation

Published online by Cambridge University Press:  04 July 2016

M. G. Higazy*
Affiliation:
Department of Mechanical Engineering, University of Zagazig, Cairo, Egypt

Abstract

In this paper, a new transport equation for the intermittency factor is proposed to model the transition flows. The intermittency behaviour of the transition flows is incorporated into the differential methods for solving the boundary-layer equations, which deal numerically with the basic partial differential equations. The present model accuracy and validity have been tested against a series of recent published experiments, for low Reynolds number, including flows with different freestream turbulence intensities and different pressure-gradients, such as aerofoil and flat plate flows. A comparison of the present method and two different prediction techniques is also given.

The significance of the proposed transport intermittency equation is to reproduce the streamwise variation of the intermittency factor in the transition zone. This method is found suitable and reliable to predict flows with positive or favourable pressure-gradient cases and with turbulence intensity level up to 6%.The method also confirmed the importance of estimating the start of transition, present formula. The present formula is suitable and straightforward to use. For all test cases good agreement between the computed results and the experimental data are observed.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2002 

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References

1. Larsson, L. Turbine blade heat transfer calculations using two-equation turbulence models, Proceedings of Inst of Mech Eng A, 1997, 211, pp 253262.Google Scholar
2. Suzen, Y.B. and Huang, P.G. Modeling of flow transition using an intermittency transport equation, ASME, J Fluid Eng, 2000, 122, pp 273284.Google Scholar
3. Savill, A.M. Some recent progress in the turbulence modeling of by-pass transition, 1993, Near-Wall Turbulent Flows, So, R.M.C., Speziale, C.G. and Launder, B.E. (Eds), 1993, pp 829848, Elsevier Science.Google Scholar
4. Savill, A.M. Further progress in the turbulence modeling of by pass transition, 1993, Engineering Turbulence Modeling, and Experiments 2. 1993, Rodi, W. and Martelli, F. (Eds), pp 583592, Elsevier Science.Google Scholar
5. Westin, K.J.A. and Henkes, K.A.W.M. Application of turbulence models to bypass transition, ASME, J Fluids Eng, 1997, 119, pp 859866.Google Scholar
6. Higazy, M.G. and Fraser, J.C. Numerical prediction of laminar-transition-turbulent boundary-layers, Eng Res J, 1995, 4, pp 100117.Google Scholar
7. Cebeci, T. and Smith, A.M.O. A finite-difference method for calculating compressible laminar and turbulent boundary-layers, 1971, Paper No 70-FE-A, ASME, J of Basic Eng, 1971.Google Scholar
8. Dhawan, S. and Narasimha, R. Some properties of boundary-layer during the transition from laminar to turbulent flow motion, J Fluid Mech, 1958, 3, pp 418436.Google Scholar
9. Gostelow, J.P., Blunden, A.R. and Walker, G.J. Effects of free stream turbulence and adverse pressure gradients on boundary-layer transition, ASME, J Turbomach, 1994, 116, pp 392414.Google Scholar
10. Fraser, C.J., Higazy, M.G. and Milne, J.S. End-stage boundary-layer transition models for engineering calculations, Proceedings of I of Mech Eng C, 1994, 208, (C3), pp 4758.Google Scholar
11. Solomon, W.J., Walker, G.J. and Gostelow, J.P. Transition length prediction for flows with rapidly changing pressure gradients, 1995, ASME, ASME-95-GT 241, International Gas Turbine and Aero-engine Congress & Exposition, Houston, Texas, June 1995.Google Scholar
12. Chen, K.K. and Thyson, N.A. Extension of Emmons’ spot theory to flows on blunt bodies, AIAA J. 1971, 9, (5), pp 821825.Google Scholar
13. Cho, J.R. and Chung, M.K. A k-ε-γ equation turbulence model, J Fluid Mech, 1992, 237, pp 301322.Google Scholar
14. Steelant, J. and Dick, E. Modelling of bypass transition with conditioned Navier-Stokes equations coupled to an intermittency transport equation, Int J Nume Methods Fluids, 1996, 23, pp 193220.Google Scholar
15. Suzen, Y.B. and Huang, P.G. An intermittency transport equation for modeling flow transition, 2000, AIAA Paper AIAA-2000-0287, 38th Aero space Sciences Meeting and Exhibit, Reno, NV, 10-13 January, 2000.Google Scholar
16. Cebeci, T. and Bradshaw, P. Momentum Transfer in boundary-layers, 1977, McGraw Hill, Hemisphere, Washington DC, USA.Google Scholar
17. Narasimha, R.The laminar turbulent transition zone in the boundary-layer, Prog Aerosp Sci, 1985, 22, pp 2980.Google Scholar
18. Mayle, R.F. The role of laminar-turbulent transition in gas turbine engines, ASME, J Turbomach, 1991, 113, pp 509537.Google Scholar
19. Abu-Ghannam, B.J and Shaw, R. Natural transition of boundary-layers- the effects of turbulence, pressure gradient, and flow history, J Mech Eng Sci, 1980, 22, (5), pp 213228.Google Scholar
20. Dey, J. An Integral Method for the Calculation of 2-D Transitional Boundary-Layers, 1988, PhD thesis, Indian Institute of Science, Bangalore.Google Scholar
21. Gardiner, I.D. Transition in boundary-layer Flows, 1987, PhD thesis, Institute of Technology, Dundee.Google Scholar
22. Arnal, D., Juillen, J.C. and Michell, R. Analyse et du development de la transition de la couche limite, 1977, AGARD Conf Proc 244 on Laminar-Turbulent Transition, Paper 13.Google Scholar
23. Gostelow, J.P, and Ramachandran, R.M. Some effects of free-stream turbulence on boundary-layer transition, 1983, Proceedings of Eighth Australian Conference, Paper 12-C.Google Scholar
24. Gostelow, J.P. and Blunden, A.R. Investigations of boundary-layer transition in an adverse pressure gradient, 1988, ASME paper 88-GT- 298, Amsterdam.Google Scholar
25. Blair, M.F. and Werle, M.J. Combined influence of free-stream turbulence and favourable pressure gradients on boundary-layer transition and heat transfer, 1981, United Technologies Research Center, Report R81-914388-17.Google Scholar
26. Cebeci, T. Essential ingredients of a method for low Reynolds number airfoils, A1AA J, 1989, 27, pp 16801688.Google Scholar
27. Fraser, C.J. and Milne, J.S. Integral calculation of transitional boundary-layers, Proc F Mech E, Part C, 1986, 200.Google Scholar
28. Keller, H.B. Numerical Solutions of Partial Differential Equations 2, 1970, Academic Press, New York, USA.Google Scholar
29. Emmons, H.W. and Bryson, A. E. The laminar-turbulent transition in a boundary-layer, J Aerospace Sci, 1951, 18, Part 1.Google Scholar
30. Schubauer, G.B. and Klebanoff, P.S. Contributions on the mechanics of boundary-layer transition, 1956, NACA ref 1289.Google Scholar
31. Sharma, O.P., Wells, P.A., Schlinker, P.A. and Bailey, D.A. boundary-layer development on turbine aerofoil suction surfaces, Trans ASME, J Eng for Power, 1982, 104.Google Scholar