DIRECT NUMERICAL-SIMULATION OF SUPERSONIC JET FLOW

A numerical method is given for direct numerical simulation of the non linear evolution of instability waves in supersonic round jets, with s patial discretisation based on high-order compact finite differences. The numerical properties of a class of symmetric and asymmetric scheme s are analysed. Implementation for the Navier-Stokes equations in cyli ndrical polar coordinates is discussed with particular attention given to treatment of the origin to ensure stability and efficiency. Valida tion of the schemes is carried out by detailed comparison with linear stability theory. The computer code is applied to study the initial st ages of nonlinear development of unstable modes in a Mach 3 jet. The m odes of instability that are present include strongly unstable axisymm etric acoustic and helical vortical waves, as well as weakly unstable radiating acoustic and vortical modes. Three distinctive wave patterns are observed from the simulations including a cross-hatched internal shock structure. Nonlinear interactions between the vortical and acous tic modes are investigated.