Efficient approach for analysis of unsteady viscous flows in turbomachines

A nonlinear harmonic methodology has been developed to calculate unsteady viscous flows through turbomachinery blades. Flow variables are decomposed into time-averaged variables and unsteady perturbations, resulting in the time-averaged equations with extra nonlinear stress terms depending on the unsteady perturbations. An efficient evaluation of an unsteady flowfield is obtained by solving the first-order harmonic equations. The nonlinear interactions between the time-averaged flowfield and the unsteady perturbations were included by a strong coupling approach. The basic computational methodology was applied to the two-dimensional Navier-Stokes equations, and the method was validated against several test cases. Computational results show that this method is much more efficient than the nonlinear time-marching methods while still modeling dominant nonlinear effects.