Numerical optimization methods have made significant progress over the last decades and play an important role in modern industrial design processes. In most cases, gradient-free algorithms are used, which only require the value of the objective function in each optimization step. These methods are robust and can be integrated into a standard design process at low implementation effort. However, in aerodynamic design problems using high-fidelity Computational Fluid Dynamics (CFD), the computational cost is high, especially when a large number of design parameters are used. Gradient-based methods, on the other hand, are particularly suited for problems involving large design spaces and generally converge to a local optimum in a few design cycles. However, the computational efficiency of these methods is mainly determined by the gradient calculation.This thesis presents the development of an efficient gradient-based optimization framework for the aerodynamic design of turbomachinery applications. In particular, the adjoint approach is used to evaluate the gradients of the objective function with respect to all design parameters at low computational cost. The present work covers the various components of the optimization framework, including the solution of the flow governing equations, adjoint-based sensitivity analysis, geometry parameterization, and mesh generation. A substantial part of the thesis describes the implementation and validation of those components. The flow solver is a Reynolds-Averaged Navier-Stokes code applicable to multiblock structured grids. The spatial discretization is realized with a Roe-type upwind scheme with a MUSCL extrapolation for second order spatial accuracy. Viscous fluxes are centrally discretized, and for the turbulence closure problem the Spalart-Allmaras and the Shear-Stress Transport (SST) models are used. The code uses an implicit multistage Runge-Kutta time-stepping scheme, accelerated by local time-stepping and geometric multigrid. The corresponding discrete adjoint solver uses the same time marching scheme as the flow solver and features similar performance characteristics in terms of runtime and memory footprint. The adjoint solver has been implemented primarily by hand with selective use of algorithmic differentiation (AD) to simplify the development. The geometry parameterization is based on B-Spline representations which has two main advantages: (a) the simple integration of geometric constraints for structural requirements, and (b) the connection to Computer-Aided Design (CAD) software for manufacturing. The whole optimization framework is driven by a Sequential Quadratic Programming (SQP) algorithm. The proposed framework has been successfully applied to optimize axial and radial turbines on multiple operating points subject to aerodynamic and geometric constraints. The different studies show the effectiveness of the developed method in terms of improved performances and computational cost. In particular, a comparative study shows that the proposed method is able to find optimized blade shapes at a computational time which is about one order of magnitude lower compared to a gradient-free optimization algorithm. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Data assimilation arises in a vast array of different topics: traditionally in meteorological and oceanographic modelling, wind tunnel or water tunnel experiments and recently from biomedical engineering. Data assimilation is a process for combine measured or observed data with a mathematical model, to obtain estimates of the expected data. The measured data usually contains inaccuracies and is given with low spatial and/or temporal resolution. In this thesis data assimilation for time dependent fluid flow is considered. The flow is assumed to satisfy a given partial differential equation, representing the mathematical model. The problem is to determine the initial state which leads to a flow field which satisfies the flow equation and is close to the given data. In the first part we consider one-dimensional flow governed by Burgers’ equation. We analyze two iterative methods for data assimilation problem for this equation. One of them so called adjoint optimization method, is based on minimization in L2-norm. We show that this minimization problem is ill-posed but the adjoint optimization iterative method is regularizing, and represents the well-known Landweber method in inverse problems. The second method is based on L2-minimization of the gradient. We prove that this problem always has a solution. We present numerical comparisons of these two methods. In the second part three-dimensional inviscid compressible flow represented by the Euler equations is considered. Adjoint technique is used to obtain an explicit formula for the gradient to the optimization problem. The gradient is used in combination with a quasi-Newton method to obtain a solution. The main focus regards the derivation of the adjoint equations with boundary conditions. An existing flow solver EDGE has been modified to solve the adjoint Euler equations and the gradient computations are validated numerically. The proposed iteration method are applied to a test problem where the initial pressure state is reconstructed, for exact data as well as when disturbances in data are present. The numerical convergence and the result are satisfying.