Numerical Simulation on a Planar Supersonic Free Shear Layer Secondary Instability

Abstract

The secondary instability of a planar supersonic shear layer at Mc=0.5 has been simulated and studied with a direct numerical simulation (DNS) method. In the present numerical method, Navier-Stokes equations in the perturbation form are solved with a finite difference method of the third order accuracy, and the stability is analyzed on the evolution of disturbance wave simulated in the shear layer. At first, verification is made to DNS computations with LST results for the linear spatial problem of a two-dimensional supersonic free shear layer, by which the accuracy of the DNS results is proved. With the present DNS method, the three-dimensional nonlinear spatial problem of a planar supersonic mixing layer is solved by introducing a two-dimensional disturbance wave on the lateral middle line of the inflow boundary. Along with the development of two-dimensional unstable perturbation wave in the shear layer, the secondary instability takes place and develops in the downstream of the shear layer flow. With different frequencies of disturbance waves, the developments of secondary instability are different. For the disturbance circular frequency of 200.0, the secondary instability takes place and grows rapidly, but for the disturbance circular frequency of 100.0, the secondary instability does not grow.