Computational methods for internal flows with emphasis on turbomachinery

Current computational methods for analyzing flows in turbomachinery and other related internal propulsion components are presented. The methods are divided into two classes. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler aproaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures. Various grids used in association with these procedures are also discussed

Analysis of fractional step, finite element methods for the incompressible navier-stokes equations

En la presente tesis se han estudiado métodos de paso fraccionado para la resolución numérica de la ecuación de Navier-Stokes incompresible mediante el método de los elementos finitos; dicha ecuación rige el movimiento de un fluido incompresible viscoso. Partiendo del análisis del método de proyección clásico, se desarrolla un método para el problema de Stokes (lineal y estacionario) con iguales propiedades en cuanto a discretizacion espacial que aquel, explicando así sus propiedades de estabilización de la presión. Se da también una extensión del nuevo método a la ecuación de Navier-Stokes incompresible estacionaria (no lineal).En la segunda parte de la tesis, se desarrolla un método de paso fraccionado para el problema de evolución que supera un inconveniente del método de proyección relativo a la imposición de las condiciones de contorno.Para todos los métodos desarrollados, se demuestran teoremas de convergencia y estimaciones de error, se proponen implementaciones eficientes y se proporcionan numerosos resultados numéricos

Unstructured mesh based models for incompressible turbulent flows

A development of high resolution NFT model for simulation of incompressible flows is presented. The model uses finite volume spatial discretisation with edge based data structure and operates on unstructured meshes with arbitrary shaped cells. The key features of the model include non-oscillatory advection scheme Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and non-symmetric Krylov-subspace elliptic solver. The NFT MPDATA model integrates the Reynolds Average Navier Stokes (RANS) equations. The implementation of the Spalart-Allmaras one equations turbulence model extends the development further to turbulent flows. An efficient non-staggered mesh arrangement for pressure and velocity is employed and provides smooth solutions without a need of artificial dissipation. In contrast to commonly used schemes, a collocated arrangement for flow variables is possible as the stabilisation of the NFT MPDATA scheme arises naturally from the design of MPDATA. Other benefits of MPDATA include: second order accuracy, strict sign-preserving and full multidimensionality. The flexibility and robustness of the new approach is studied and validated for laminar and turbulent flows. Theoretical developments are supported by numerical testing. Successful quantitative and qualitative comparisons with the numerical and experimental results available from literature confirm the validity and accuracy of the NFT MPDATA scheme and open the avenue for its exploitation for engineering problems with complex geometries requiring flexible representation using unstructured meshes

Hybrid Neural Network Reduced Order Modelling for Turbulent Flows with Geometric Parameters

Geometrically parametrized Partial Differential Equations are nowadays widely used in many different fields as, for example, shape optimization processes or patient specific surgery studies. The focus of this work is on some advances for this topic, capable of increasing the accuracy with respect to previous approaches while relying on a high cost-benefit ratio performance. The main scope of this paper is the introduction of a new technique mixing up a classical Galerkin-projection approach together with a data-driven method to obtain a versatile and accurate algorithm for the resolution of geometrically parametrized incompressible turbulent Navier-Stokes problems. The effectiveness of this procedure is demonstrated on two different test cases: a classical academic back step problem and a shape deformation Ahmed body application. The results show into details the properties of the architecture we developed while exposing possible future perspectives for this work

Defect correction methods for computational aeroacoustics

The idea of Defect Correction Method (DCM) has been around for a long time. It can be used in a number of different ways and can be applied to solve various linear and non-linear problems. Most defect correction related methods were used in conjunction with discretisation methods and two-level multigrid methods. This thesis examines how various iterative methods, both for linear and nonlinear problems, may be built into a unified framework through the use of defect correction. The framework is extended to the area of Computational Aeroacoustics (CAA) where sound waves generated by the pressure fluctuations are typically several orders of magnitude smaller than the pressure variations in the main flow field that accounts for flow acceleration. A decomposition of variables is used to break down the components of a typical flow variable into (1) the mean flow, (2) flow perturbations or aerodynamic sources of sound, and (3) the acoustic perturbation. The framework as discussed in this thesis would incorporate such variable decomposition. The basic principle of DCM can be applied to recover the propagating acoustic perturbation through a coupling technique. This provides an excellent concept in the re-use of existing commercial CFD software based on the framework and in the retrieval of acoustic pressure. Numerical examples demonstrating the defect correction framework for a typical car sun-roof problem was examined with promising numerical results. To this end the complete process of coupling Reynolds average Navier-Stokes and the Helmholtz equation is also presented using the DCM framework. The DCM framework is also extended to handle higher order numerical methods for the numerical solutions of partial differential equations leading to an easy re-use of existing software approximating derivatives with a lower order discretisation. Numerical experiments were performed to demonstrate the capability of the DCM framework. It is also used to a simplified 2-D problems aiming at the understanding of Large Eddy Simulation (LES) and filtering techniques. To this end the framework of DCM leads to an efficient and robust software implementation for many CFD and aeroacoustic computation in a simple nutshell