Session: 04-45 Combustion dynamics - modeling III

Paper Number: 125711

125711 - Adjoint Based Shape Optimization for Thermoacoustic Stability of Combustors Using Free Form Deformation 

Modern gas turbine combustors face the challenge of oscillations caused by the interaction between acoustic pressure waves and the flame. If these acoustic pressure waves are sufficiently in phase with the heat release rate, the oscillations can intensify, leading to a extra heat transfer, excessive noise, or even engine failure. We use the thermoacoustic Helmholtz equation to model thermoacoustic instability within a geometrically-complex annular combustor that can be deformed using Free Form Deformation (FFD). In this method, the initial combustor geometry is supplied within some initial volume including all the components; plenum, heatshield, combustion chamber, injector and dilution holes. A chosen set of control points is then defined through this spatial combustor volume and the positions of these points can be deformed arbitrarily using trivariate Berstein polynomials.

We use the FFD combustor geometry, define the system parameters and impose the acoustic boundary conditions to calculate the eigenvalue and eigenvector of the problem using a finite element method with open-source software FEniCSx. We then use adjoint methods to calculate the shape derivatives of any eigenvalue with respect to the FFD control points. We then calculate modifications to the control points that will reduce the growth rates of the eigenvalues and deform the combustor accordingly. To illustrate the efficacy of this approach, we present a case study involving the first axial mode of an industrial combustor. These findings highlight the potential of this method for reducing combustion instability in annular combustors through small geometric modifications.

Presenting Author: Ekrem Ekici University of Cambridge

Presenting Author Biography: Ekrem Ekici is a 4th year PhD student in University of Cambridge under the supervision of Matthew Juniper. He has completed his undergraduate degree in Yildiz Technical University in Istanbul, Turkiye. He is working on shape optimization of annular combustors to eliminate/reduce thermoacoustic instabilities.

Authors:

Ekrem Ekici University of Cambridge
Matthew P. Juniper Department of Engineering