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Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

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Abstract

The nth-order expansion of the parabolized stability equation (EPSEn) is obtained from the Taylor expansion of the linear parabolized stability equation (LPSE) in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE (EPSE1) and the second-order EPSE (EPSE2) are used to study the crossflow instability in the swept NLF(2)-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory (LST), the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE. In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient eN prediction tool for the crossflow instability in swept-wing boundary-layer flows.

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Abbreviations

(X, Y, Z):

incoming-flow coordinate system

(x, y, z):

chordwise coordinate system

(x s, y s, z):

body-fitted coordinate system

(x t, y s, z t):

crossflow coordinate system

u 0 :

streamwise velocity

v 0 :

normal velocity

w 0 :

spanwise velocity

w t :

crossflow velocity

U X :

incoming-flow-direction velocity

Re :

Reynolds number

Re c :

chord-length Reynolds number

α :

eigenvalue

β :

spanwise wavenumber

ω :

frequency

σ :

growth rate

\(\tilde \alpha \) :

complex streamwise wavenumber

Ã:

complex amplitude

A :

amplitude

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Authors and Affiliations

  1. Department of Mechanics, Tianjin University, Tianjin, 300072, China

    Xuezhi Lu & Jisheng Luo

Authors
  1. Xuezhi Lu
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  2. Jisheng Luo
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Correspondence to Jisheng Luo.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11332007)

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Lu, X., Luo, J. Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers. Appl. Math. Mech.-Engl. Ed. 38, 981–996 (2017). https://doi.org/10.1007/s10483-017-2214-6

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  • DOI: https://doi.org/10.1007/s10483-017-2214-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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