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The Reliability of the Improved e-N Method for Transition Prediction as Checked by PSE Method

Authors: Caihong Su


Transition prediction of boundary layers has always been an important problem in fluid mechanics both theoretically and practically, yet notwithstanding the great effort made by many investigators, there is no satisfactory answer to this problem. The most popular method available is so-called e-N method which is heavily dependent on experiments and experience. The author has proposed improvements to the e-N method, so to reduce its dependence on experiments and experience to a certain extent. One of the key assumptions is that transition would occur whenever the velocity amplitude of disturbance reaches 1-2% of the free stream velocity. However, the reliability of this assumption needs to be verified. In this paper, transition prediction on a flat plate is investigated by using both the improved e-N method and the parabolized stability equations (PSE) methods. The results show that the transition locations predicted by both methods agree reasonably well with each other, under the above assumption. For the supersonic case, the critical velocity amplitude in the improved e-N method should be taken as 0.013, whereas in the subsonic case, it should be 0.018, both are within the range 1-2%.

Keywords: Boundary layer, e-N method, PSE, Transition

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[1] T. Cebeci, J. P. Shao, H. H. Chen, et al., "The Preferred Approach for Calculating Transition by Stability Theory", Institute for Numerical Computation and Analysis, In: Proceeding of International Conference on Boundary and Interior Layers, France, Toulouse, 2004.
[2] C. H. Su, H. Zhou, "Transition prediction of a hypersonic boundary layer over a cone at small angle of attack´╝ìwith the improvement of e-N method", China Sci Ser G, vol. 52, no. 1, pp. 115-123, 2009.
[3] C. H. Su, H. Zhou, "Transition prediction for supersonic and hypersonic boundary layers on a cone with angle of attack", China Sci Ser G, vol. 52, no. 8,pp. 1223´╝ì1232, 2009.
[4] F. P. Bertolotti, "Compressible Boundary Layer Stability Analyzed with the PSE Equation", AIAA Paper 91-1637.
[5] F. P. Bertolotti, Th. Herbert, et al., "Linear and nonlinear stability of the Blasius boundary layer", Journal of fluid mechanics, vol. 242, pp. 441-474, 1992.
[6] F. P. Bertolotti, Th. Herbert, "Stability analysis of nonparallel boundary layers", J. Bull. Am. Phy. Soc., vol. 32, pp. 2079-280, 1987.
[7] F. P. Bertolotti, Th. Herbert, "Analysis of the linear stability of compressible boundary layers using the PSE", Theroretical and computational fluid dynamics, vol. 3, pp. 117-124, 1991.
[8] F. P. Bertolotti, "Compreesible boundary layer stability analyzed with the PSE equation", AIAA paper 91-1637.
[9] V. Estahanian, K. Hejrantar, et al., "Linear and nonlinear PSE for stability analysis of the Blasius boundary layer using compact scheme", Journal of Fluids Engineering, vol. 123, pp. 545-550, 2001.
[10] C. L. Chang, M. R. Malik, et al., "Linear and nonlinear PSE for compressible boundary layers", NASA Contractor Report 191537, 1993.
[11] R. D. Joslin, C. L. Streett, et al., "Spatial direct numerical simulation of boundary-layer transition mechanisms: Validation of PSE theory", Theoretical and Computational Fluid Dynamics, vol. 4, no. 6, pp. 271-288, 1993.
[12] Y. M. Zhang, H. Zhou, "PSE as applied to problems of transition in compressible boundary layers", Applied Mathematics and Mechanics-English Edition, vol. 29, no. 4, pp. 833-840, 2008.
[13] Th. Herbert, "Parabolized stability equations", Annual Reviews, vol. 29, pp. 245-283, 1997.