Adjoint-based computation of shape sensitivity in a Rijke-Tube
* Presenting author
Geometrical shape is the most important parameter defining acoustic spectra. While adjoint-based sensitivity analysis of shape alterations is a well established technique in other engineering disciplines such as airfoil design, it is less common in acoustic and especially thermo-acoustic contexts. Only recently the thermo-acoustic community has begun to deploy such methods for stability assessment. The present paper aims at continuing this effort by discussing (i) the challenges of domain shape deformations to adjoint-based gradient calclulations, (ii) potential extensions of the theory to higher orders, and (iii) a parameter-free implementation into a state-of the art thermo-acoustic Helmholtz solver. Deformations of a simple thermoacoustic system -- a Rijke-Tube -- will be studied as an example case to validate the method. Despite this practical focus on thermo-acoustics, the results of the paper are fruitful to other acoustic topics involving stability analyses as the underlying concepts readily apply to any eigenvalue problem linear or non-linear in its eigenvalue. Indeed, the gradient information calculated from first-order theory is the first building block for efficient algorithms to optimize the shape of acoustic devices.