Tobias Kattmann

• Shape optimization using gradients computed via the adjoint method has become a common feature and also, practically, a requirement among the major computational fluid dynamics (CFD) and multi-physics solvers. Accurate sensitivities are widespread available for single-zone steady-state problems, with unsteady or multi-physics adjoint solvers being less common. Yet, gradient availability is a desirable feature for all primal simulation capabilities. Many practical flows of industrial interest are unsteady in nature, and for the simulation of heating/cooling devices the coupling between a fluid and solid domain is essential to accurately capture the system's behavior. Combining these two general observations of the demand for sensitivities and unsteady conjugate heat transfer applications, is the objective of the present work. Consequently, this dissertation presents the development and application of an unsteady discrete adjoint solver for conjugate heat transfer (CHT). Based on the framework available in the open-source multi-physics and design solver SU2, an efficient method to compute shape sensitivities via the discrete adjoint method for transient CHT problems is presented. The handling of the algorithmic differentiation (AD) tool together with the orchestration of the numerous time-steps and various involved zones is crucial, to retain a code that is efficient with respect to memory and compute time. Therefore, a modular approach for the evaluation of the various derivative terms (diagonal, cross, dual-time-step) is used. Beyond design for time-accurate simulations, capabilities for steady state optimization of repeating heat exchanger geometries, as pin-fin arrays, are developed. For both tested CHT configurations (one unsteady and one steady), the gradient validation shows excellent accuracy against finite differences and successful constrained optimization highlights the practical applicability in a design chain. The current development is not presented in isolation, but as a part of the SU2-project, for which detailed information is provided in the appropriate context.