Predicting the onset of flow unsteadiness based on global instability

Global-stability theory is used to predict the onset of flow unsteadiness based on steady solutions of the Reynolds Averaged Navier–Stokes equations. The stability problem is formulated for compressible flow at moderately-high Reynolds numbers, using a turbulence model to provide closure for the averaged Reynolds stresses. The approach provides an efficient method for predicting the occurrence of flow unsteadiness for problems of practical interests, and provides a useful indicator for the legitimate range of application of the steady-flow equations. Numerical solutions are presented based on a finite-difference approximation. The steady baseflow solution and the unsteady disturbance equations are solved using the same grid. Results are presented for the onset of vortex shedding about a circular cylinder at low Reynolds numbers, and for shock-induced transonic-buffet onset at high Reynolds numbers. The results for the onset of flow unsteadiness are in very good agreement with experiments and unsteady calculations.