Development of shape optimization for internal flows

Sammanfattning: This thesis describes the development of an adjoint based optimizationmethod.The goal is to develop a robust method capable of handling multipledesign variables, whereastraditional methods have shown to be too costly for many design parameters.The main application is for internal flow geometries within theautomotive industry.The advantage of using the adjoint method is that the simulation timebecomes independent of the number of design variables.The continuous adjoint Navier-Stokes equations are presented andsimplified for internal flow applications.Contribution from the goal function enter only boundary conditions ofthe simplified adjoint Navier-Stokes equations. A goal function tominimize total pressure drop is implemented and used in the cases presented.Two different optimization approaches using the adjoint method wereapplied. The first one is based on surface sensitivities. The surfacesensitivities give information about how the objective function isaffected by normal motion of the surface. The sensitivities were coupledto a mesh morphing library in OpenFOAM which diffuses the motion of theboundary nodes to the internalpoints of the mesh. This method was applied to an inlet pipe with aReynolds number of 1.9'10^5 based on the diameter at the inlet. Theresulting geometry gave a 6.5% decrease in the total pressure dropthrough the pipe.In the second approach the sensitivities with respect to motion of thecell center were derived from the Arbitrary-Lagrangian Eulerianformulation of the Navier-Stokes equations. It was shown that the cellsensitivities can be calculated as a post processing step using theresults from the adjoint and the primal flow fields. The cellsensitivities were compared to the surface sensitivities and the resultsshow similar behavior for the cells closest to the surface. A method toconnect the cell sensitivities to the shape of the geometry withdifferent levels of smoothing is presented.Optimization was performed on a laminar internal flow geometry using thecell sensitivities and applying two different smoothing criteria.