| Citation: | TU Guohua, ZHAO Lei, WAN Bingbing, et al. Simplified linear stability theory for boundary layer of three-dimensional curved surface[J]. Journal of Aerospace Power, 2023, 38（11）：2583-2590 doi: 10.13224/j.cnki.jasp.20210378
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The magnitude orders of the terms of the linearized perturbation equations (LPEs) in body-fitted three-dimensional curvilinear orthogonal coordinates were analyzed. Results showed that most of the curvature-related terms were represented by high-order small quantities. The LPEs in body-fitted curvilinear orthogonal coordinates were greatly simplified by neglecting the high-order small quantities, which resulted in the simplified LPEs. The tedious derivation of the fully LPEs in curvilinear orthogonal coordinates was no longer needed. The simplified LPEs can be easily obtained by extending the Cartesian LPEs to body-fitted curvilinear orthogonal coordinates for the convenience of beginners. The simplified linear stability theory (LST) suitable for boundary layers with surface curvatures was developed based on the simplified LPEs. The accuracy of the simplified LST was validated in the boundary layers on the curved surfaces of a subsonic sweep wing and a hypersonic sharp-nose cone. For the former, the growth rate of crossflow instability predicted by the simplified LST deviated from the result predicted by the full form LST less than 4×10−5; for the later, the simplified LST accurately predicted the effect of circumferential curvature on the neutral line of the Mack mode. Numerical results showed that the simplified LST had almost the same accuracy with the full form LST.
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