A Hybrid Adjoint Network Model for Thermoacoustic Optimization

A method is proposed that allows the computation of the continuous adjoint of a thermoacoustic network model based on the discretized direct equations. This hybrid approach exploits the self-adjoint character of the duct element, which allows all jump conditions to be derived from the direct scattering matrix. In this way, the need to derive the adjoin: equations for every element of the network model is eliminated. This methodology combines the advantages of the discrete and continuous adjoint, as the accuracy of the continuous adjoint is achieved while maintaining the flexibility of the discrete adjoint. It is demonstrated how the obtained adjoint system may be utilized to optimize a thermoacoustic configuration by determining the optimal damper setting for an annular combustor.

Automated summary

A method is proposed to compute the continuous adjoint of a thermoacoustic network model using the discretized direct equations. It exploits the self-adjoint character of the duct element and derives all jump conditions from the direct scattering matrix, eliminating the need to derive adjoint equations for each network element. This method combines the advantages of discrete and continuous adjoints, achieving the accuracy of the continuous adjoint while maintaining the flexibility of the discrete adjoint. It demonstrates how the obtained adjoint system can be used to optimize a thermoacoustic configuration by determining the optimal damper setting for an annular combustor.