Unsteady Viscous Flow Simulations by a Fully Implicit Method with Deforming Grid

Abstract

A deforming grid technique that is intentionally placed into the multi-block framework is applied to the grid displacements in this paper. This method is mainly based on a modified TFI algorithm. A fully implicit solver is used for the unsteady viscous flow simulations on deforming grids. Some test cases for airfoils are made to demonstrate the effect of grid perturbations. Finally, the grid regeneration for airfoil icing problems is accomplished by the grid deformation technique. Nomenclature c = chord length of airfoil Cp = pressure coefficient t ∆ = time step m α = mean model incidence 0 α = oscillation amplitude k = reduced frequency of pitching motion M = Mach number Re = Reynolds number I. Introduction he unsteady flows associated with the moving boundaries have been of long interest to aerodynamic researches. For unsteady problems, the grid has to conform to the instantaneous shape of a moving body. Here, grid movement becomes an important issue (Refs. 1). In most cases, rotating the grid system rigidly with the airfoil can easily treat rigid body motions. However, this approach is no longer applicable if the body deforms, if the block boundaries must be fixed for multi-block grid system or if the relative motion of a multi-component configuration is to be taken into account (e.g. an oscillating flap). To tackle such problems, efficient grid movement technique is required. The present work is to develop an unsteady viscous simulating method for the moving boundary problems with deforming grid. The transfinite interpolation (TFI) algorithm is a very popular algebraic grid generation technique that can effectively interpolates grid points in the computational domain from prescribed points along the block boundaries. This method can be seen as a perturbation method, which is flexible and is independent of the initial grid generation. By using TFI of displacements, the grid deformation process becomes completely independent of the generation of the initial grid, for which any suitable technique can be used (Ref. 2). In this paper, the TFI technique is employed to regenerate the grid at each time step for oscillating pitching airfoils. The same strategy is also employed in the case of the icing problems for a single airfoil. The deforming grid technique is intentionally placed into the multi-block framework. The flow solver developed in Reference 3 has been modified to solve the moving boundary problems by deforming grid. The algorithm is a fully implicit, cell-centered scheme. The dynamic grid algorithm that is coupled with the flow solver moves the computational grid to conform to the instantaneous position of the moving boundary.