Efficient optimisation of nonlinear time-periodic aeroelastic problems

Optimisation of unsteady fluid-structure interaction problems is of increasing importance in aeronautical design and other fields of engineering.
In order to apply gradient-based optimisation methods, the gradients of objective functions with respect to design parameters have to be evaluated.
Depending on the required level of modelling fidelity, such calculations can become very computationally expensive or even impractical.
Therefore, lower-fidelity aerodynamic modelling methods are usually used, especially in earlier phases of the design process.

This thesis introduces a new adjoint harmonic balance approach for the optimisation of nonlinear, time-periodic fluid-structure interaction problems.
The harmonic balance technique reduces the computational cost of the simulations, allowing the use of higher-fidelity methods.
The adjoint equations for this approach are then derived to efficiently obtain the gradients of few objective functions with respect to many design parameters.

The harmonic balance method, including a novel frequency iteration technique, is applied to a test case of a pitch-plunge aerofoil undergoing limit cycle oscillations in transonic flight conditions.
For this test case, the harmonic balance is $11$ times faster compared to a time-marching approach.

The accuracy of the adjoint harmonic balance equations is verified by comparing the gradients of $2$ objective functions with respect to $31$ design variables in the limit-cycle oscillation test case.
The calculation of gradients using the adjoint approach is approximately $30$ times faster than finite differences.

Finally, the adjoint harmonic balance technique is used to optimise four aeroelastic test cases.
Two cases are unconstrained, one uses a steady constraint and another an unsteady constraint.
At the end of all four optimisation processes the objective function significantly improves, which shows that the proposed method can be used to reduce the computational cost of high-fidelity aeroelastic optimisation, paving the way for its practical use in early design phases.