Optimization of multiphysics problems: transient vibroacoustic and thermal-fluid systems

The aim of this Thesis is to present efficient methods for advanced topology and shape optimization frameworks considering multiphysics systems. The Thesis is conducted in two parts: first part deals with the transient shape optimization of coupled acoustic mechanical interaction problems and the second part deals with the optimization of turbulent flow heat transfer systems.

Part I of the Thesis aims to develop a generalized shape optimization framework for transient vibroacoustic problems. Throughout the work, the geometry is implicitly defined using a level function as the interface between acoustic and structural domains is obtained from the zero iso-level of the level set function. The crisp representation of the geometry contained in the level set is then captured utilizing an immersed boundary method called the cut element method which operates on fixed background meshes. This way, accurate solutions to the strongly coupled vibroacoustic equations are obtained. Moreover, the utilized design parameterization allows the usage of gradient based optimizers for which the work employs a fully discrete adjoint approach for calculating the gradients of objective and constraint functions. The calculated gradients with the developed transient optimization framework is validated and compared against the commonly utilized semi-discrete approach. The study highlights the importance of having consistent sensitivities obtained via the fully discrete adjoint method. Following this, the transient design formulation is also validated on a benchmark case, a simple acoustic partitioner design. The developed framework is further applied to the design of vibroacoustic pulse shaping devices. The framework is extended to demonstrate a transient problem formulation that allows to optimize and control the wideband frequency response. To this end, the objective is defined in frequency domain and a fast Fourier transform (FFT) algorithm is applied on the transient response of the coupled system to obtain the frequency response. The capabilities of the proposed design method is then demonstrated on various vibroacoustic filter designs.

Part II of the Thesis aims to develop an efficient topology optimization framework for large-scale complex turbulent flow systems. The proposed methodology makes use of automatic differentiation (AD) in the derivation of discrete adjoints to calculate exact sensitivities without resorting to any simplifying assumptions. The work utilizes finite volume discretization for Reynolds-averaged Navier–Stokes equations which is also coupled to a two-equation turbulence closure model. The developed framework is demonstrated on the optimization of several 2D and 3D flow systems. The study also highlights the importance of including turbulence modeling in the proposed design method. Furthermore, the developed flow framework is then coupled to heat transfer
in order to demonstrate the topology optimization of heat sinks with turbulent forced convection. Large-scale 3D heat sink design problems are demonstrated and the benefits of full 3D optimization are highlighted via the carried out comparisons.