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Navier-Stokes Solutions with Moving Overset Grids

A simple, robust numerical method to localize intergrid boundary points and to interpolate unsteady flow variables across 2-D, overset grids is presented. The overset grids are allowed to move relative to each other. The intergrid boundary points are localized in terms of three grid points on the donor grid by a directional search algorithm. The parameters of the search algorithm give the interpolation weights at the interpolation point. No interpolation data needs to be stored. The method is independent of numerical solution algorithms and it may easily be implemented on any 2-D, single block flow solver to make it a multi-block, zonal solver with arbitrarily overset/overlapping computational grids.

The method was first applied to a flapping/stationary airfoil combination in tandem with an overlapping grid topology. C-grids around each airfoil are overlapped in the region between the trailing edge of the leading airfoil and the leading edge of the trailing airfoil. As the periodic flapping motion in the cross-flow direction is imposed on the upstream airfoil, the upstream grid moves with respect to the downstream grid in the inertial frame of reference. The overlapping boundary points on each grid are then localized on the donor grid. The unsteady flowfield is computed at areduced frequency of 1.5, M = 0.30 and Re = 3 million. The instantaneous flowfield as the leading airfoil passes through its mean position, the continuity of the contour lines across the overlapping boundaries indicates that the overlapping boundary conditions are applied successfully. The computed aerodynamic loads compare well with the unsteady potential flow solution.

Next, steady and unsteady flowfields around a single NACA0012 airfoil is computed. In the overset C-grid system, the outer boundary points of the overset C--grid, which are denoted by the "+" sign, are first localized sequentially on the base grid. This process defines the boundary points of the hole cut in the base grid. The boundary points of the hole on the base grid are then localized on the overset C--grid. In a steady-state flowfield computed at 5 degree incidence the contour lines of the flow variables are again continuous across the grid boundaries and in excellent agreement with the single grid solution. Surface pressures also compare quite well. The same overset C grid is also employed for an unsteady solution as the airfoil undergoes a periodic flapping motion. As seen in the instantaneous flowfield as the airfoil passes the neutral position with the maximum velocity, the computed flowfields are again in excellent agreement with the single grid solution. The comparison of the time history of the unsteady aerodynamic loads also agree well.

Good agreement between single and overset grid solutions is also abtained for a cascade flow. A C-grid around a blade is overset onto cartesian base grid and intergrid boundary points are similarly localized. The computed flowfield and the blade surface pressure distribution compare well against single grid solutions.

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