Comparison of shape parametrization techniques for fluid-structure interaction problems

This master thesis describes the development in the framework of Fluid- Structure Interaction (FSI) problems of an efficient and flexible technique treating the fluid-structure interface and mesh motion problems. The main idea is to build, through a new hierarchical approach, a tool with accurate identication capabilities for both the structural rigid movement (translation/rotation) and the elastic deformation (displacement), with the possibility of facing arbitrary structural and fluid discretization schemes. Starting from a review of the state of the art methods, used for these applications, the different shape representation techniques applied, like Free Form Deformation (FFD), Radial Basis Function (RBF) and Inverse Distance Weighting (IDW) are introduced and then compared to test their performances in terms of computational costs and achievable mesh quality. Then, in order to reduce the complexity of the geometrical model and its description, ad hoc innovative optimization techniques, like a selective approach of the RBF interpolation sites as well as a domain-decomposition approach for FFD, are presented showing clear reductions in term of computational costs. Some applications and test-cases, solved by using an open-source Finite Element library (LifeV), dealing with unsteady viscous (internal and external) flows, characterized by different Reynolds number, are shown to highlight the quality and the accuracy of the methods and their stability. For the implementation of the schemes developed, an efficient C++ object oriented code language was used, relying also on Trilinos packages

Reduced order modelling in nuclear reaction thermal hydraulics

The context of the present thesis is to assess the potential of Reduced Order Models (ROMs) for nuclear reactor thermal hydraulics applications. ROMs constitute advanced modelling techniques aiming at fast high fidelity simulations. For the purposes of this research, two approaches have been selected and are investigated in depth: the Proper Orthogonal Decomposition (POD) with Galerkin projection (POD-Galerkin) and the hybrid method of Proper Orthogonal Decomposition with Interpolation using Radial Basis Functions, PODI - Galerkin, in the context of parametric model order reduction. Additionally, in terms of the POD method, two sampling techniques are presented and compared: the standard and the nested POD. The aforementioned methods are applied to a parametric case of non-isothermal mixing in a T-junction pipe for laminar and turbulent flow regimes. The flow is governed by the 3D, unsteady Navier - Stokes equations coupled with the energy equation. Furthermore, a ROM for modelling buoyancy driven flows with the Boussinesq approximation is discussed. Two cases are considered: a closed flow, where the method is applied to a benchmark case of a differentially heated square cavity, and an open flow, where a case of a "cold-trap" formation in a U-bend pipe is investigated. The suitability of the above techniques is assessed based on a comparison between the reduced order results and those obtained using high fidelity OpenFOAM solvers.Open Acces

Constrained deformation for evolutionary optimization

Sieger D. Constrained deformation for evolutionary optimization. Bielefeld: Universität Bielefeld; 2017.This thesis investigates shape deformation techniques for their use in design optimization tasks. In the first part, we introduce state-of-the-art deformation methods and evaluate them in a set of representative benchmarks. Based on these benchmarking results, we derive essential criteria and features a deformation technique should satisfy in order to be successfully applicable within design optimization. In the second part, we concentrate on the application and improvement of deformation techniques based on radial basis functions. We present and evaluate a unified framework for surface and volume mesh deformation and investigate questions of performance and scalability. In the final third part, we concentrate on the integration of additional constraints into the deformation, thereby improving the overall effectiveness of the design optimization process and fostering the creation of more feasible and producible design variations. We present a novel shape deformation technique that effectively maintains different types of geometric constraints such as planarity, circularity, or characteristic feature lines during deformation. At the same time, our method provides a unique level of modeling flexibility, quality, robustness, and scalability. Finally, we integrate techniques for automatic constraint detection directly into our deformation framework, thereby making our method more easily applicable within complex design optimization scenarios

Reduced order methods for laminar and turbulent flows in a finite volume setting: projection-based methods and data-driven techniques

This dissertation presents a family of Reduced Order Models (ROMs) which is specifically designed to deal with both laminar and turbulent flows in a finite volume full order setting. Several aspects associated with the reduction of the incompressible Navier\u2013Stokes equations have been investigated. The first of them is related to the need of an accurate reduced pressure reconstruction. This issue has been studied with the help of two main approaches which consist in the use of the Pressure Poisson Equation (PPE) at the reduced order level and also the employment of the supremizer stabilization method. A second aspect is connected with the enforcement of non-homogeneous Dirichlet boundary conditions at the inlet boundary at the reduced order level. The solutions to address this aspect include two methods, namely, the lifting function method and the penalty method. Different solutions for the treatment of turbulence at the reduced order level have been proposed. We have developed a unified reduction approach which is capable of dealing with turbulent flows based on the Reynolds Averaged Navier\u2013Stokes (RANS) equations complemented by any Eddy Viscosity Model (EVM). The turbulent ROM developed is versatile in the sense that it may be applied on the FOM solutions obtained by different turbulent closure models or EVMs. This is made possible thanks to the formulation of the ROM which merges projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields. The newly proposed turbulent ROM has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to Re 10 to 5

Model order reduction for compressible turbulent flows: hybrid approaches in physics and geometry parametrization

This thesis provides a dissertation about efficient and reliable methods developed to deal with fluid flows problems, discretized by the use of finite volume approaches. In general increasing complexity dynamics are taken into consideration and suited strategies are utilized to overcome arising hurdles. The basic idea behind this work is the construction of reduced order models capable of providing fully consistent solutions with respect to the high fidelity flow fields. Full order solutions are often obtained through the use of segregated solvers, employing slightly modified conservation laws so that they can be decoupled and then solved one at a time. Classical reduction architecture, on the contrary, rely on the Galerkin projection of a complete Navier-Stokes system to be projected all at once, causing a mild discrepancy with the high order solutions. In this thesis three different segregated reduced order algorithms are presented for the resolution of laminar, turbulent and compressible flows respectively. Turbulent flows are frequently approached by the employment of Reynolds averaged Navier-Stokes equations. Since this set of equations is not self closed, an additional modeling is required for some terms related with turbulence. In particular in this thesis we will rely on eddy viscosity models. Since there are a variety of different turbulence models for the approximation of this supplementary viscosity, one of the aims of this work is to provide reduced order models which are independent on this selection. This goal is reached by the application of hybrid methods where Navier-Stokes equations are projected in a standard way while the viscosity field gets approximated by the use of data-driven interpolation methods or by the evaluation of a properly trained neural network. By exploiting the aforementioned expedients it is possible to resolve fluid flow problems characterized by high Reynolds numbers and elevated Mach numbers in a less costly and more general way

Data-driven parameter and model order reduction for industrial optimisation problems with applications in naval engineering

In this work we study data-driven reduced order models with a specific focus on reduction in parameter space to fight the curse of dimensionality, especially for functions with low-intrinsic structure, in the context of digital twins. To this end we proposed two different methods to improve the accuracy of responce surfaces built using the Active Subspaces (AS): a kernel-based approach which maps the inputs onto an higher dimensional space before applying AS, and a local approach in which a clustering induced by the presence of a global active subspace is exploited to construct localized regressors. We also used AS within a multi-fidelity nonlinear autoregressive scheme to reduced the approximation error of high-dimensional scalar function using only high-fidelity data. This multi-fidelity approach has also been integrated within a non-intrusive Proper Oorthogonal Decomposition (POD) based framework in which every modal coefficient is reconstructed with a greater precision. Moving to optimization algorithms we devised an extension of the classical genetic algorithm exploiting AS to accelerate the convergence, especially for highdimensional optimization problems. We applied different combinations of such methods in a diverse range of engineering problems such as structural optimization of cruise ships, shape optimization of a combatant hull and a NACA airfoil profile, and the prediction of hydroacoustic noises. A specific attention has been devoted to the naval engineering applications and many of the methodological advances in this work have been inspired by them. This work has been conducted within the framework of the IRONTH project, an industrial Ph.D. grant financed by Fincantieri S.p.A

A high-performance open-source framework for multiphysics simulation and adjoint-based shape and topology optimization

The first part of this thesis presents the advances made in the Open-Source software SU2, towards transforming it into a high-performance framework for design and optimization of multiphysics problems. Through this work, and in collaboration with other authors, a tenfold performance improvement was achieved for some problems. More importantly, problems that had previously been impossible to solve in SU2, can now be used in numerical optimization with shape or topology variables. Furthermore, it is now exponentially simpler to study new multiphysics applications, and to develop new numerical schemes taking advantage of modern high-performance-computing systems. In the second part of this thesis, these capabilities allowed the application of topology optimiza- tion to medium scale fluid-structure interaction problems, using high-fidelity models (nonlinear elasticity and Reynolds-averaged Navier-Stokes equations), which had not been done before in the literature. This showed that topology optimization can be used to target aerodynamic objectives, by tailoring the interaction between fluid and structure. However, it also made ev- ident the limitations of density-based methods for this type of problem, in particular, reliably converging to discrete solutions. This was overcome with new strategies to both guarantee and accelerate (i.e. reduce the overall computational cost) the convergence to discrete solutions in fluid-structure interaction problems.Open Acces

Non-intrusive reduced order modelling for aerodynamic applications

During the design and optimisation of aerodynamic components, the simulations to be performed involve a large number of parameters related to the geometry and flow conditions. In this scenario, the simulation of all possible configurations is not af-fordable. To overcome this problem, the present work proposes a novel multi-output neural network (NN) for the prediction of aerodynamic coefficients of aerofoils and wings using compressible flow data. Contrary to existing NNs that are designed to predict aerodynamic quantities of interest, the proposed network considers as output the pressure or stresses at a number of selected points on the aerodynamic surface. The proposed approach is compared against the more traditional networks where the aero-dynamic coefficients are directly the outputs of the network. Furthermore, a detailed comparison of the proposed NN against the popular proper orthogonal decomposi-tion (POD) method is presented. The numerical results, involving high dimensional problems with flow and geometric parameters, show the benefits of the proposed ap-proach.The proposed NN is used to accelerate the evaluation of the objective function in an inverse aerodynamic shape design problem. The optimisation algorithm uses the gradient-free modified cuckoo search method. Applications in two and three dimen-sions are shown, demonstrating the potential of the proposed framework in the con-text of both optimisation and inverse design problems. The performance of the pro-posed optimisation framework is also compared against existing frameworks where the more traditional NNs are employed