Numerical Simulation and Theoretical Analysis on Hypersonic Boundary-Layer Receptivity to Wall Blowing-Suction

Abstract

Direct numerical simulations on the receptivity of hypersonic boundary layers over a flat plate and a sharp wedge were carried out with two-dimensional periodic-in-time wall blowing-suction introduced into the flow through a slot. The free-stream Mach numbers are equal to 5.92 and 8 in the cases of adiabatic flat plate and sharp wedge, respectively. The perturbation flow field was decomposed into normal modes with the help of the multimode decomposition technique based on the spatial biorthogonal eigenfunction system. The decomposition allows for the filtering out of the stable and unstable modes hidden behind perturbations of another physical nature. I. Introduction The progress being made in computational fluid dynamics provides an opportunity for the reliable simulation of such complex phenomena as laminar-turbulent transition. The dynamics of flow transition depends on the instability of small perturbations excited by external sources. Computational results provide complete information about the flow field that would be impossible to measure in real experiments. Recently, a method of normal mode decomposition was developed for two- and three-dimensional perturbations in compressible and incompressible boundary layers. 1–3 In Ref. 4, the method was applied to the theoretical analysis of the perturbation flow field in the vicinity of the blowing-suction actuator obtained from direct numerical simulation (DNS). The results demonstrated very good agreement between the amplitudes of the modes filtered out from the DNS data and those solved by linear theory of the flow receptivity to wall blowing-suction. In the present work, we apply the multimode decomposition to DNS results downstream from the blowingsuction actuator in hypersonic boundary layers past a flat plate and a sharp wedge to compare the amplitudes of the modes found from the computations with the prediction of linear stability theory. II. Outline of the multimode decomposition The method of multimode decomposition of perturbations having a prescribed frequency is based on the biorthogonal eigenfunction system for linearized Navier-Stokes equations. 3 For the clarity of further discussion, we reproduce the main definitions necessary for discussing the present work. We consider a compressible two-dimensional boundary layer in Cartesian coordinates, where x and z are the downstream and spanwise coordinates, respectively, and coordinate y corresponds to the distance from the wall. We write the linearized Navier-Stokes equations for a periodic-in-time perturbation (the frequency