The effect of Mach number on the two-dimensional boundary layer has been investigated by means of linear stability theory. The viscous compressible linear disturbance equations are solved. The resultant disturbance equations are cast as a 5 x 5 matrix eigenvalue problem. A direct spectral method using a Chebyshev series is employed to solve the eigenvalue problems of the boundary layer with adiabatic wall conditions. An Algebraic mapping function h(zeta) over the interval (zeta is greater than or equal to -1 and less than or equal to 1), where the physical domain (y is greater than or equal to 0 and less than or equal to y(sub max)) is transformed to the computational domain (zeta is greater than or equal to -1 and less than or equal to 1), is used because of robustness for the high Mach numbers instead of an exponential mapping. Results by the spectral method show a good agreement with the numerical results obtained from a shooting method developed by Mack. The direct spectral method can predict all of the unstable modes, whereas conventional shooting methods can only for a single mode at a time.
直接法による圧縮性境界層の不安定性について
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