Deforming grid variational principle for unsteady small disturbance flows in cascades

A variational method for computing unsteady subsonic flows in turbomachinery blade rows is presented. A variational principle that describes the harmonic small disturbance behavior of the full potential equations about a nonlinear mean flow is developed. Included in this variational principle is the effect of a deforming computational grid that conforms to the motion of vibrating airfoils. Bilinear isoparametric finite elements are used to discretize the variational principle, and the resulting discretized equations are solved efficiently using lower-upper decomposition. The use of a deforming computational grid dramatically improves the accuracy of the method since no error-producing extrapolation is required to apply the upwash boundary conditions or to evaluate the unsteady pressure on the airfoil surfaces