Adjoint-based shape optimization applied to multiphase flows

Abstract

The adjoint method in computational fluid dynamics (CFD) offers a computationally affordable optimization by efficiently calculating gradients of objective functions with respect to design parameters. It outperforms other methods in terms of computational cost and is widely used in sensitivity analysis. Traditional methods, such as finite difference, require a large number of simulations as the number of design parameters increases, limiting the scope of optimization. However, the adjoint method in CFD allows for gradient calculation of an objective function at the cost of one flow field computation, making it practically independent of the number of design parameters and providing a more flexible and robust optimization tool. The aim of this thesis is to advance knowledge and expertise in the utilization of the adjoint method, with a specific focus on flows inside pipe bends commonly encountered in problems involving multiphase flows with particle transport. The work encompasses validating implementations, optimizing fluid dynamics systems, addressing problems related to particles in optimized systems, and proposing a novel adjoint-based formulation for shape optimization applied to multiphase flows. The adjoint fluid dynamics equations are derived at the level of partial differential equations using the continuous adjoint approach. The frozen turbulence assumption is adopted, neglecting variations of the turbulence field with respect to the design parameters. Furthermore, a technique for mesh adaptation is employed to adjust the shape of the computational domain as it is optimized. Firstly, the adjoint method is applied in a shape optimization process to minimize the total pressure losses in three different pipe fittings. Secondly, gas-solid flows are simulated in both the original and optimized pipe fittings to compare the erosion wear caused by particle impacts on the walls. This investigation explores how single-phase flow optimization can also affect the particle problem, i.e., mitigate erosion. The results demonstrate substantial reductions in peak erosion as a consequence of minimizing total losses, which can potentially increase the service life of these systems. Finally, new adjoint equations are derived to account for the dispersed phase of multiphase flows, and the corresponding sensitivity derivatives are obtained to maximize the deposition efficiency of particles on bend walls.