Shape optimization typically involves geometries characterized by several dozen design variables set with no prior knowledge of the design domain topology. A surrogate model can replace the numerous geometry-based design variables with a much more compact set of design variables that have a built-in global understanding of the geometry, thus reducing the size of the optimization problem. In this paper, we present a grid parametrization approach for the design domain geometry based on the method of Proper Orthogonal Decomposition using the method of snapshots, and replace the geometry-based design variables with the smallest possible set of POD coefficients. We demonstrate this method in the well-known problem of designing the section of an air-conditioning duct to maximize the permeability evaluated using CFD with an incompressible 2D model implemented in OpenFOAM.