# Adjoint shape optimization of components of the air conditioning systems of aircraft

Adjoint shape optimization computes sensitivities for every cell of a surface mesh generated for CFD of a ducted flow, where the sensitivities describe the impact of the deformation of a grid for satisfying given target functions. Those surface sensitivities can be interpreted as the movement in the wall normal direction of the respective cell. Based on target functions, the adjoint shape optimization considers every cell of the surface mesh as design variable regarding the Reynolds-averaged Navier-Stokes (RANS) equations and their adjoint counterparts.

This technique is applied to components of air-conditioning systems of aircraft, where the main target functions are the dissipated energy in the system and flow homogeneity at the air outlet. The geometry is improved stepwise by using the optimization in a process chain.

As an example, the cabin outlet of the Do 728 (DoKLA) is used. The target function is the flow homogeneity at the air outlet, defined as

J=∫½ (ϑ - ϑ^{d})^{2} dA_{outlet},

where v^{d} is the desired velocity at the outlet. For the optimization, an RANS simulation is performed first. Afterwards, the adjoint equations are solved and the sensitivities are computed. After morphing the mesh, the first optimization step is completed. With the new geometry, the next optimization step can be started. Figure 1 shows the resulting geometries after the first and the 16th iteration step. The associated velocities are shown in Figure 2.

One can see, that the flow at the air outlet becomes more homogeneous through the optimization.

To use the adjoint shape optimization in an automated process chain, the deformation of the mesh is very important. Actually, there are two methods two deform the mesh according to the sensitivities. The first method is the proprietary software package ANSA. Although this is a very stable and robust option, it requires user interaction during the mesh deformation. The second method is an in-house development of DLR Göttingen, which can be automated easily. To use the tool effectively, one has to analyze the relevant case prior to the first mesh deformation. Afterwards, no further user interaction is needed.

# Contact:

Prof. Dr. Claus Wagner

German Aerospace Center (DLR)

Institute of Aerodynamics and Flow Technology, Department Ground Vehicles

Göttingen

Phone: +49 551 709-2261