Development of shape optimization for internal flows
This thesis describes the development of an adjoint based optimization
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
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.
computational fluid dynamics
continuous adjoint method.