Prediction and understanding of three-dimensional screech phenomenon from a circular nozzle

A three-dimensional computational aeroacoustic procedure is developed to simulate the screech phenomenon from a supersonic circular jet. The three dimensional Navier-Stokes equations and a modified two equations standard k - ε turbulence model are solved in the generalized curvilinear coordinate system. The dispersion-relation-preserving scheme is utilized for space discretization. The 2N storage low-dissipation and low-dispersion Runge-Kutta scheme is applied for time marching. Numerical results are presented at Mach number range from 1.17 to 1.60. It is shown that the predicted wavelengths and amplitudes of the flapping and helical modes are in good agreement with experimental data by Ponton et. al. The predicted shock cell structure and radial density profiles agree well with the measured results by Panda & Seasholtz. And it is found that the instantaneous flow fields dominating the flapping and helical jet screech tones reveal in flapping and helical states, respectively. But the long time average mean flow field is still almost axisymmetric. A proper orthogonal decomposition analysis is applied to the three dimensional flow fields for seeking the relationship between the screech tones modes and the large scale structures. The interaction position of the large scale structures with the shock cells is located through the variation of the eigenvalues for the streamwise velocity with the axial positions.