Predicting the onset of flow unsteadiness based on global instability.

*(English)*Zbl 1123.76018Summary: 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.

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\textit{J. D. Crouch} et al., J. Comput. Phys. 224, No. 2, 924--940 (2007; Zbl 1123.76018)

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