Direct numerical simulation of supersonic jet flow

A numerical method is given for direct numerical simulation of the nonlinear evolution of instability waves in supersonic round jets, with spatial discretisation based on high-order compact finite differences. The numerical properties of a class of symmetric and asymmetric schemes are analysed. Implementation for the Navier-Stokes equations in cylindrical polar coordinates is discussed with particular attention given to treatment of the origin to ensure stability and efficiency. Validation of the schemes is carried out by detailed comparison with linear stability theory. The computer code is applied to study the initial stages of nonlinear development of unstable modes in a Mach 3 jet. The modes of instability that are present include strongly unstable axisymmetric 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 acoustic modes are investigated.