Relationship between vortex and sound in under-expanded supersonic impinging jets

摘要

The study of an under-expanded supersonic jet impinging on a flat plate by using large-eddy simulation is reported. A third-order upwind compact difference and a fourth-order symmetric compact scheme are employed to discretize the nondimensional axisymmetric compressible Favre-filtered Navier-Stokes equations in space, whereas the third-order Runge-Kutta method with the total variation diminishing property is adopted to deal with the temporal discretization. The numerical simulation successfully captures the shock wave and vortex structures with different scales in the flow field. Waves with high and low frequencies traveling forward and reflecting back, and sound sources in different locations can be observed. By comparison with the frequency of the impinging tone from the experiment, it can be deduced that the change of pressure and swirling strength in the shear layer, pressure change on the impinging plate, and vortex merging in the jet shear layer are interdependent with the impinging tone. The effects of nozzle lip thickness on the impinging jet flow field have been investigated. The results show that the values of pressure fluctuation and vortex swirling strength in the shear layer near the nozzle have an extremum with the variation of the nozzle lip thickness. The results provide a theoretical foundation for the design of supersonic nozzles.