Applied Mathematics and Mechanics >
Stability analysis method considering non-parallelism:EPSE method and its application
Received date: 2015-03-20
Revised date: 2015-04-27
Online published: 2016-01-01
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 11332007, 11172203, and 91216111)
The e-N method is widely used in transition prediction. The amplitude growth rate used in the e-N method is usually provided by the linear stability theory (LST) based on the local parallel hypothesis. Considering the non-parallelism effect, the parabolized stability equation (PSE) method lacks local characteristic of stability analysis. In this paper, a local stability analysis method considering non-parallelism is proposed, termed as EPSE since it may be considered as an expansion of the PSE method. The EPSE considers variation of the shape function in the streamwise direction. Its local characteristic is convenient for stability analysis. This paper uses the EPSE in a strong non-parallel flow and mode exchange problem. The results agree well with the PSE and the direct numerical simulation (DNS). In addition, it is found that the growth rate is related to the normalized method in the non-parallel flow. Different results can be obtained using different normalized methods. Therefore, the normalized method must be consistent.
Gaotong YU, Jun GAO, Jisheng LUO . Stability analysis method considering non-parallelism:EPSE method and its application[J]. Applied Mathematics and Mechanics, 2016 , 37(1) : 27 -36 . DOI: 10.1007/s10483-016-2013-9
[1] Schubauer, G. B. and Skramstad, H. K. Laminar boundary layer oscillations and stability of laminar flow. Journal of Research of the National Bureau of Standards, 38, 251-293(1947)
[2] Gaster, M. On the effects of boundary-layer growth on flow stability. Journal of Fluid Mechanics, 66, 465-480(1974)
[3] Gaster, M. On the growth of waves in boundary layers:a non-parallel correction. Journal of Fluid Mechanics, 424, 367-377(2000)
[4] Barry, M. and Ross, M. The flat plate boundary layer, part 2:the effect of increasing thickness on stability. Journal of Fluid Mechanics, 43, 813-818(1970)
[5] Yu, X. Y. and Zhou, H. On the effect of the nonparallelism of the boundary layer flow of a flat plate on its stability characteristics. ACTA Mechanica Sinica, 18(4), 297-305(1986)
[6] Saric, W. S. and Nayfeh, A. H. Nonparallel stability of boundary layer flows. Physics of Fluids, 18, 945-950(1975)
[7] Herbert, T. and Bertolotti, F. P. Stability analysis of nonparallel boundary layers. Bulletin of American Physical Society, 32, 2079-2806(1987)
[8] Herbert, T. Parabolized stability equations. Annual Review Fluid Mechanics, 29, 245-283(1997)
[9] Chang, C. L., Malik, M. R., and Hussaini, M. Y. Compressible stability of growing boundary layers using parabolized equations. 22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference, Americam Institute of Aeronautics and Astronautics, Reston (1991)
[10] Zhang, Y. M. and Zhou, H. Verification of parabolized stability equations for its application to compressible boundary layers. Applied Mathematics and Mechanics (English Edition), 28(8), 987-998(2007) DOI 10.1007/s10483-007-0801-3
[11] Zhang, Y. M. and Zhou, H. PSE as applied to problems of secondary instability in supersonic boundary layers. Applied Mathematics and Mechanics (English Edition), 29(1), 1-8(2008) DOI 10.1007/s10483-008-0101-7
[12] Zhang, Y. M. and Zhou, H. PSE as applied to problems of transition in supersonic boundary layers. Applied Mathematics and Mechanics (English Edition), 29(7), 833-840(2008) DOI 10.1007/s10483-008-0701-8
[13] Dong, M., Zhang, Y. M., and Zhou, H. A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers-PSE+DNS. Applied Mathematics and Mechanics (English Edition), 29(12), 1527-1534(2007) DOI 10.1007/s10483-008-1201-z
[14] Zhang, Y. M. and Su, C. H. Self-consistent parabolized stability equation (PSE) method for compressible boundary layer. Applied Mathematics and Mechanics (English Edition), 36(7), 835-846(2015) DOI 10.1007/s10483-015-1951-9
[15] Zhou, H., Su, C. H., and Zhang, Y. M. Transition Mechanism and Prediction of Supersonic/Hypersonic Boundary Layer (in Chinese), Science Express, Beijing, 146-149(2015)
[16] Fedorov, A. and Tumin, A. Branching of discrete modes in high-speed boundary layers and terminology issues. 40th Fluid Dynamics Conference and Exhibit, Americam Institute of Aeronautics and Astronautics, Reston (2010)
[17] Fedorov, A. V. and Khokhlov, A. P. Prehistory of instability in a hypersonic boundary layer. Theoretical and Computational Fluid Dynamics, 14, 359-375(2001)
[18] Ma, Y. B. and Zhong, X. L. Receptivity of a supersonic boundary layer over a flat plate, part 1:wave structures and interactions. Journal of Fluid Mechanics, 488, 31-78(2003)
[19] Fedorov, A. V. and Khokhlov, A. P. Excitation of unstable modes in a supersonic boundary layer by acoustic waves. Fluid Dynamics, 9, 456-467(1991)
[20] Fedorov, A. V. and Khokhlov, A. P. Excitation and evolution of unstable disturbances in supersonic boundary layer. Proceeding of ASME Fluid Engineering Conference, 151, 1-13(1993)
/
| 〈 |
|
〉 |
Email Alert
RSS