A Double-Passage Shape Correction Method for Predictions of Unsteady Flow and Aeroelasticity in Turbomachinery (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, a double-passage shape correction (DPSC) method is presentedfor simulation of unsteady flows around vibrating blades and aeroelastic prediction.Based on the idea of phase-lagged boundary conditions, the shape correctionmethod was proposed aimed at efficiently dealing with unsteady flow problems inturbomachinery. However, the original single-passage shape correction (SPSC) mayshow the disadvantage of slow convergence of unsteady solutions and even producenonphysical oscillation. The reason is found to be related with the disturbances onthe circumferential boundaries that can not be damped by numerical schemes. Toovercome these difficulties, the DPSC method is adopted here, in which the Fouriercoefficients are computed from flow variables at implicit boundaries instead of circumferentialboundaries in the SPSC method. This treatment actually reduces the interactionbetween the calculation of Fourier coefficients and the update of flow variables.Therefore a faster convergence speed could be achieved and also the solutionstability is improved. The present method is developed to be suitable for viscous andturbulent flows. And for real three-dimensional (3D) problems, the rotating effects arealso considered. For validation, a 2D oscillating turbine cascade, a 3D oscillating flatplate cascade and a 3D practical transonic fan rotor are investigated. Comparisonswith experimental data or other solutions and relevant discussions are presented indetail. Numerical results show that the solution accuracy of DPSC method is favorableand at least comparable to the SPSC method. However, fewer iteration cycles areneeded to get a converged and stable unsteady solution, which greatly improves thecomputational efficiency.