Development of shape optimization for internal flows

Licentiate thesis, 2013

This thesis describes the development of an adjoint based optimization method. The goal is to develop a robust method capable of handling multiple design variables, whereas traditional methods have shown to be too costly for many design parameters. The main application is for internal flow geometries within the automotive industry. The advantage of using the adjoint method is that the simulation time becomes independent of the number of design variables. The continuous adjoint Navier-Stokes equations are presented and simplified for internal flow applications. Contribution from the goal function enter only boundary conditions of the simplified adjoint Navier-Stokes equations. A goal function to minimize total pressure drop is implemented and used in the cases presented. Two different optimization approaches using the adjoint method were applied. The first one is based on surface sensitivities. The surface sensitivities give information about how the objective function is affected by normal motion of the surface. The sensitivities were coupled to a mesh morphing library in OpenFOAM which diffuses the motion of the boundary nodes to the internal points of the mesh. This method was applied to an inlet pipe with a Reynolds number of 1.9*10^5 based on the diameter at the inlet. The resulting geometry gave a 6.5% decrease in the total pressure drop through the pipe. In the second approach the sensitivities with respect to motion of the cell center were derived from the Arbitrary-Lagrangian Eulerian formulation of the Navier-Stokes equations. It was shown that the cell sensitivities can be calculated as a post processing step using the results from the adjoint and the primal flow fields. The cell sensitivities were compared to the surface sensitivities and the results show similar behavior for the cells closest to the surface. A method to connect the cell sensitivities to the shape of the geometry with different levels of smoothing is presented. Optimization was performed on a laminar internal flow geometry using the cell sensitivities and applying two different smoothing criteria.