The Interaction Between 2D Freestream Disturbance And An Oblique Shockwave

The prediction of laminar-turbulent transition of the boundary layer is of great popular in hydromechanics.For the super/hypersonic flying vehicles,the free-stream disturbances would pass the shock ahead of the body first to trigger the disturbances behind the shock,and then the disturbances behind the shock could enter boundary layer to trigger transition.So the first investigation about receptivity is the interaction between the free-stream disturbances and shock,which is the important part.In this paper,the interaction of small amplitude free-stream disturbances with an oblique shock was investigated.Considering the real situation,we focus on the generation of acoustic wave,especially the generation of slow acoustic wave,which is proved to be more efficient to excite boundary layer modes,by the incidence of entropy/vertical wave.Our main concern is if shock-capturing scheme can be used for the numerical simulation of this problem,because otherwise,shock-fitting method has to be adopted,which usually is difficult to be used in 3-D problem.There have been people using shock-capturing scheme for this purpose,but with no convincing discussion that the results were reliable.First,theoretical analysis is performed to obtain the relationship between the free-stream disturbances and the disturbances downstream of the shock.Second,DNS is performed to check the accuracy of the shock-capturing method by comparing with the theoretical results.The main conclusions are as follows:1.When the flow behind the shock is subsonic,only fast acoustic wave can be generated.When the flow is supersonic behind the shock(of course the component normal to the shock is subsonic),slow acoustic wave can also be generated.Whether fast or slow acoustic wave is generated behind the shock is dependent on the incident angle of the entropy/vortical wave.We provide the range of the incident angle for generating fast or slow acoustic wave.These have significance for the investigation about receptivity.2.The comparison of the incident angle,wavelength and amplitude of the disturbance behind shock shows good agreements.Especially for the pressure fluctuation,DNS gives fairly satisfactory results.Therefore,the shock-capturing method can faithfully reproduce the fluctuations behind the shock.And it can be used in the DNS of transition problem to simulate the interaction of the free-stream disturbances and the shock.The comparison of generation coefficients for the incident entropy wave and vortical wave shows that vortical wave is more efficient to generate acoustic wave.