Adjoint-based shape optimization of a laboratory combustor, changing areas only

The top figure shows a 3D rendering of a laboratory combustor. Air enters on the left into a plenum. Air then flows through a narrow feed tube into a combustion chamber on the right. A flame sits at the left end of the combustion chamber. The bottom figure shows the acoustic natural frequencies (eigenmodes) of this system. These are calculated with an acoustic network model. Frequency is on the horizontal axis and growth rate is on the vertical axis. The eigenmodes with positive growth rate (marked in red) are unstable. In this case there are seven unstable modes. The sensitivity of the eigenmodes to changes in the area of the tube is calculated with an adjoint network model. This information is used to stabilize all seven modes by making relatively small changes to the areas.