Matthew Juniper short videos: Recent Episodes
Cambridge University
Thermoacoustic oscillations are a persistent problem in rocket and aircraft engines. They can be eliminated with small design changes. The challenge is to find the design changes that will stabilize all thermoacoustic oscillation modes simultaneously. Adjoint methods are ideal for this because they show, in a single calculation for each mode, how to reduce the growth rate of each mode. The top frame shows a diagram of a thermoacoustic system: a flame (red line) in a tube with variable cross-section and open ends (green lines). The bottom frame shows the frequency (horizontal axis) and growth rate (vertical axis) of thermoacoustic modes (circles). At each iteration, the optimization algorithm works out the shape change that will make the modes more stable, and then changes the shape of the thermoacoustic system accordingly. This is repeated until all modes are stable.
An empty pipe is placed around the flame from a camping gas stove, causing thermo-acoustic oscillations.
The top frame is a diagram of the combustion system analysed in Rama Balachandran thesis (2005, University of Cambridge). The flame is the red vertical line. It sits downstream of the fuel/air feed system (to the left of the flame) and upstream of the combustion chamber (to the right of the flame). The bottom frame shows the eigenvalues (black circles) of this thermoacoustic system. Those with a positive growth rate (above the dashed line) are unstable.
Using adjoint methods, we calculate the sensitivity of each unstable eigenvalue to changes in the system geometry. We then shift the geometry slightly in a way that is calculated to optimally stabilize all the eigenvalues. We repeat this process until all the eigenvalues are stable.
This process is very quick with adjoint methods, but prohibitively expensive with standard methods.