Assessment of Upwind/Symmetric WENO Schemes for Direct Numerical Simulation of Screech Tone in Supersonic Jet

Screech tones are the high intensity shock-associated noise with discrete frequency in imperfectly supersonic jet. Accuracte numerical simulation of shock-associated noise requires numerical scheme with high order accuracy, low dissipation and low dispersion as well as robust shock-capturing ability. The applicability of eight kinds of upwind/symmetric WENO schemes for the direct numerical simulation of screech tone is evaluated through comparison study on the spectral characteristics and direct numerical simulations of underexpanded supersonic cold jet issuing from circular sonic nozzle. The spectral characteristics based on the approximate dispersion relation shows that the adaptive central-upwind (WENO-SYMCU-6) scheme has the best resolution and the minimum value of point-per-wavelength. However, the comparison of nonlinear response indicates that the improved upwind WENO-ZM-5 (\(p=1\)) scheme has almost the weakest nonlinear response for the single Fourier mode. And the performances in the direct numerical simulations also show that the WENO-ZM-5 (\(p=1\)) scheme is the best. With this method, not only the screech tones of the high amplitude axisymmetric mode are obtained, but also a variety of high-frequency coupling modes with the highest amplitudes can be distinguished in a wider spectrum range. And there is no nonphysical high-frequency wave induced by the nonlinear implementation of WENO schemes at the near region of the nozzle exit lip.