A quasi-three-dimensional time-linearized Euler method has been developed to compute unsteady flows around oscillating blades. In the baseline method, unsteady flow is decomposed into a steady flow plus a linear harmonically varying unsteady flow. Both the steady flow equations and the unsteady perturbation equations are solved using a pseudo-time-marching method. Based upon this method, a novel nonlinear harmonic Euler method has been developed. Due to the nonlinearity of the aerodynamic governing equations, time-averaging generates extra “unsteady stress” terms. These nonlinear effects are included by a strongly coupled approach between the perturbation equations and the time-averaged equations. Numerical results demonstrate that nonlinear effects are very effectively modeled by the nonlinear harmonic method.

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