A contribution to the finite element analysis of high-speed compressible flows and aerodynamics shape optimization

This work covers a contribution to two most interesting research elds in aerodynamics, the fi nite element analysis of high-speed compressible flows (Part I) and aerodynamic shape optimization (Part II). The fi rst part of this study aims at the development of a new stabilization formulation based on the Finite Increment Calculus (FIC) scheme for the Euler and Navier-Stokes equations in the context of the Galerkin nite element method (FEM). The FIC method is based on expressing the balance of fluxes in a spacetime domain of nite size. It is tried to prevent the creation of instabilities normally presented in the numerical solutions due to the high convective term and sharp gradients. In order to overcome the typical instabilities happening in the numerical solution of the high-speed compressible flows, two stabilization terms, called streamline term and transverse term, are added through the FIC formulation in space-time domain to the original conservative equations of mass, momentum and energy. Generally, the streamline term holding the direction of the velocity is responsible for stabilizing the spurious solutions produced from the convective term while the transverse term smooths the solution in the high gradient zones. An explicit fourth order Runge-Kutta scheme is implemented to advance the solution in time. In order to investigate the capability of the proposed formulation, some numerical test examples corresponding to subsonic, transonic and supersonic regimes for inviscid and viscous flows are presented. The behavior of the proposed stabilization technique in providing appropriate solutions has been studied especially near the zones where the solution has some complexities such as shock waves, boundary layer, stagnation point, etc. Although the derived methodology delivers precise results with a nearly coarse mesh, the mesh refinement technique is coupled in the solution to create a suitable mesh particularly in the high gradient zones. The comparison of the numerical results obtained from the FIC formulation with the reference ones demonstrates the robustness of the proposed method for stabilization of the Euler and Navier-Stokes equations. It is observed that the usual oscillations occur in the Galerkin FEM, especially near the high gradient zones, are cured by implementing the proposed stabilization terms. Furthermore, allowing the adaptation framework to modify the mesh, the quality of the results improves signi cantly. The second part of this thesis proposes a procedure for aerodynamic shape optimization combining Genetic Algorithm (GA) and mesh re nement technique. In particular, it is investigated the e ect of mesh re nement on the computational cost and solution accuracy during the process of aerodynamic shape optimization. Therefore, an adaptive remeshing technique is joined to the CFD solver for the analysis of each design candidate to guarantee the production of more realistic solutions during the optimum design process in the presence of shock waves. In this study, some practical transonic airfoil design problems using adap- tive mesh techniques coupled to Multi-Objective Genetic Algorithms (MOGAs) and Euler flow analyzer are addressed. The methodology is implemented to solve three practical design problems; the fi rst test case considers a reconstruction design optimization that minimizes the pressure error between a prede ned pressure curve and candidate pressure distribution. The second test considers the total drag minimization by designing airfoil shape operating at transonic speeds. For the final test case, a multi-objective design optimization is conducted to maximize both the lift to drag ratio (L/D) and lift coe cient (Cl). The solutions obtained with and without adaptive mesh re nement are compared in terms of solution accuracy and computational cost. These design problems under transonic speeds need to be solved with a ne mesh, particularly near the object, to capture the shock waves that will cost high computational time and require solution accuracy. By comparison of the the numerical results obtained with both optimization problems, the obtainment of direct bene ts in the reduction of the total computational cost through a better convergence to the final solution is evaluated. Indeed, the improvement of the solution quality when an adaptive remeshing technique is coupled with the optimum design strategy can be judged.El presente trabajo pretende contribuir a dos de los campos de investigaci on m as interesantes en la aerodin amica, el an alisis num erico de flujos compresibles a alta velocidad (Parte I) y la optimizaci on de la forma aerodin amica (Parte II). La primera parte de este estudio se centra en la soluci on num erica de las ecuaciones de Navier-Stokes, que modelan el comportamiento de flujos compresibles a alta velocidad. La discretizaci on espacial se lleva a cabo mediante el m etodo de elementos nitos (FEM) y se pone especial enfasis en el desarrollo de una nueva formulaci on estabilizada basada en la t ecnica de c alculo de Incremento fi nitos (FIC). En este ultima, los t erminos de estabilizaci on convectiva se obtienen de manera natural de las ecuaciones de gobierno a trav es de postulados de conservaci on y equilibrio de flujos en un dominio espacio-tiempo de tamaño nito. Ello lleva a la obtenci on de dos t erminos de estabilizaci on que funcionan de manera complementaria. Uno act ua en direcci on de las lineas de corriente proporcionando la estabilizaci on necesaria para contrarestrar las inestabilidades propias de la forma discreta de Galerkin y el otro t ermino, de tipo shock capturing, act ua de manera transversal a las l neas de corriente y permite mejorar la soluci on num erica alrededor de discontinuidades y otro tipos de fen omenos localizados en el campo de soluci on de problema. La forma discreta de las ecuaciones de gobierno se completa mediante un esquema de integraci on temporal expl icito de tipo de Runge-Kutta de 4to orden. El esquema de soluci on b asico propuesto se complementa con una t ecnica de re namiento adaptativo de malla que permite mejorar autom aticamente la soluci on num erica en zonas localizadas del dominio en que, dadas las caracter sticas del flujo, se necesita una mayor resoluci on espacial. Con el prop osito de investigar el comportamiento de la formulaci on num erica se estudian diferentes casos de an alisis que implican flujos viscosos y no viscosos en r egimen subs onico, trans onico y supers onico y se estudia con especial detalle el funcionamiento de la t ecnica de estabilizaci on propuesta. Los resultados obtenidos demuestran una exactitud satisfactoria y una buena correlaci on con resultados presentes en la literatura, incluso cuando se trabaja con discretizaciones espaciales relativamente gruesas. Adicionalmente, los estudios num ericos realizados demuestran que el empleo del esquema adaptativo de malla es e ficaz para incrementar la exactitud de la soluci on numerica manteniendo un bajo coste computacional. En la segunda parte de este estudio se propone un m etodo para la optimizaci on de formas aerodin amicas que combina algoritmos gen eticos multiobjetivo (MOGAs) y remallado adaptativo con el objetivo de asegurar, con un coste computacional m nimo, la calidad de la soluci on numerica empleada en el proceso de b usqueda de un determinado diseño objetivo, particularmente cuando el flujo presenta discontinuidades y gradientes muy localizados, ti picos de flujos a alta velocidad. La metodolog a se aplica a resolver tres problemas pr acticos de diseño de per les aerodin amicos en flujo trans onico que implican la optimizaci on de la distribuci on de presiones, minimizaci on de la resistencia de onda y maximizaci on conjunta de la sustentaci on y la relaci on sustentaci on/resistencia. Para cada uno de ellos se estudia el efecto del re namiento en la calidad de la soluci on num erica as como tambi en en el coste computacional y la convergencia del problema. Los estudios realizados demuestran la e cacia de la metodolog a propuesta

Error Minimization via Metric-Based Curved-Mesh Adaptation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143100/1/6.2017-3099.pd

Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90641/1/AIAA-53965-537.pd

Unified Lagrangian formulation for fluid and solid mechanics, fluid-structure interaction and coupled thermal problems using the PFEM

The objective of this thesis is the derivation and implementation of a unified Finite Element formulation for the solution of uid and solid mechanics, Fluid-Structure Interaction (FSI) and coupled thermal problems. The unified procedure is based on a stabilized velocity-pressure Lagrangian formulation. Each time step increment is solved using a two-step Gauss-Seidel scheme: first the linear momentum equations are solved for the velocity increments, next the continuity equation is solved for the pressure in the updated configuration. The Particle Finite Element Method (PFEM) is used for the fluid domains, while the Finite Element Method (FEM) is employed for the solid ones. As a consequence, the domain is remeshed only in the parts occupied by the fluid. Linear shape functions are used for both the velocity and the pressure fields. In order to deal with the incompressibility of the materials, the formulation has been stabilized using an updated version of the Finite Calculus (FIC) method. The procedure has been derived for quasi-incompressible Newtonian fluids. In this work, the FIC stabilization procedure has been extended also to the analysis of quasi-incompressible hypoelastic solids. Specific attention has been given to the study of free surface flow problems. In particular, the mass preservation feature of the PFEM-FIC stabilized procedure has been deeply studied with the help of several numerical examples. Furthermore, the conditioning of the problem has been analyzed in detail describing the effect of the bulk modulus on the numerical scheme. A strategy based on the use of a pseudo bulk modulus for improving the conditioning of the linear system is also presented. The unified formulation has been validated by comparing its numerical results to experimental tests and other numerical solutions for fluid and solid mechanics, and FSI problems. The convergence of the scheme has been also analyzed for most of the problems presented. The unified formulation has been coupled with the heat tranfer problem using a staggered scheme. A simple algorithm for simulating phase change problems is also described. The numerical solution of several FSI problems involving the temperature is given. The thermal coupled scheme has been used successfully for the solution of an industrial problem. The objective of study was to analyze the damage of a nuclear power plant pressure vessel induced by a high viscous fluid at high temperature, the corium. The numerical study of this industrial problem has been included in the thesis.El objectivo de la presente tesis es la derivación e implementación de una formulación unificada con elementos finitos para la solución de problemas de mecánica de fluidos y de sólidos, interacción fluido-estructura (Fluid-Structure Interaction (FSI)) y con acoplamiento térmico. El método unificado està basado en una formulación Lagrangiana estabilizada y las variables incognitas son las velocidades y la presión. Cada paso de tiempo se soluciona a través de un esquema de dos pasos de tipo Gauss-Seidel. Primero se resuelven las ecuaciones de momento lineal por los incrementos de velocidad, luego se calculan las presiones en la configuración actualizada usando la ecuación de continuidad. Para los dominios fluidos se utiliza el método de elementos finitos de partículas (Particle Finite Element Method (PFEM)) mientras que los sólidos se solucionan con el método de elementos finitos (Finite Element Method (FEM)). Por lo tanto, se ramalla sólo las partes del dominio ocupadas por el fluido. Los campos de velocidad y presión se interpolan con funciones de forma lineales. Para poder analizar materiales incompresibles, la formulación ha sido estabilizada con una nueva versión del método Finite Calculus (FIC). La técnica de estabilización ha sido derivada para fluidos Newtonianos casi-incompresibles. En este trabajo, la estabilización con FIC se usa también para el análisis de sólidos hipoelásticos casi-incompresibles. En la tesis se dedica particular atención al estudio de flujo con superficie libre. En particular, se analiza en profundidad el tema de las pérdidas de masa y se muestra con varios ejemplos numéricos la capacidad del método de garantizar la conservación de masa en problemas de flujos en supeficie libre. Además se estudia con detalle el condicionamiento del esquema numérico analizando particularmente el efecto del módulo de compresibilidad. Se presenta también una estrategia basada en el uso de un pseudo módulo de compresibilidad para mejorar el condicionamiento del problema. La formulación unificada ha sido validada comparando sus resultados numéricos con pruebas de laboratorio y resultados numéricos de otras formulaciones. En la mayoría de los ejemplos también se ha estudiado la convergencia del método. En la tesis también se describe una estrategia segregada para el acoplamiento de la formulación unificada con el problema de transmisión de calor. Además se presenta una simple estrategia para simular el cambio de fase. El esquema acoplado ha sido utilizado para resolver varios problemas de FSI donde se incluye la temperatura y su efecto. El esquema acoplado con el problema térmico ha sido utilizado con éxito para resolver un problema industrial. El objetivo del estudio era la simulación del daño y la fusión de la vasija de un reactor nuclear provocados por el contacto con un fluido altamente viscoso y a gran temperatura. En la tesis se describe con detalle el estudio numérico realizado para esta aplicación industrialPostprint (published version

Numerical modelling of entropy production in mixed convection heat transfer

Energy losses in fluids engineering systems occur due to thermal and viscous irreversibilities. These irreversibilities can be tracked to identify regions of design modification for efficiency improvement in thermofluid systems. The rate of entropy production in numerical heat transfer is an important parameter that characterizes the degree of these irreversibilities. This can lead to improved designs with higher system efficiency levels for energy savings in various engineering applications. Previous conventional techniques have generally detected energy losses on a global scale or end-to-end basis. This thesis focuses on two-dimensional numerical modeling of entropy generation and the Second Law of Thermodynamics in mixed convection heat transfer. A Control-Volume Based Finite Element Method (CVFEM) is used to discretize and solve the governing conservation equations. An entropy-based algorithm is developed by post-processing of the velocity and temperature fields to obtain numerical predictions of the rate of entropy production. The new model is used to analyze heat transfer and entropy production for both natural and mixed convection in enclosures filled with different fluids, including nanofluids. The optimal conditions for which viscous and thermal irreversibilities are minimized is analyzed. The results from Computational Fluid Dynamics (CFD) are validated using available benchmark data. A new approach for minimizing the rate of entropy production in different flow configurations with nanofluids is also obtained. In addition, the local entropy production rates are obtained from two forms of the discretized Second Law – namely, transport and positive-definite forms of the entropy transport equation. The computed local entropy generation rates from both methods are compared and related to expected numerical errors from available benchmark solutions. An entropy-based error indicator is determined to assess the solution accuracy of fluid flow simulations with heat transfer using the Second Law of Thermodynamics. The formulation presents a new approach for the characterization of numerical error using a parameter called the “apparent entropy production difference.” Furthermore, a corrective mechanism on the numerical algorithm is developed. The transport entropy is used to calculate an artificial viscosity (named as an entropy-based artificial viscosity) to reduce the numerical error and ensure closer compliance with the Second Law

ICASE semiannual report, April 1 - September 30, 1989

The Institute conducts unclassified basic research in applied mathematics, numerical analysis, and computer science in order to extend and improve problem-solving capabilities in science and engineering, particularly in aeronautics and space. The major categories of the current Institute for Computer Applications in Science and Engineering (ICASE) research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification problems, with emphasis on effective numerical methods; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers. ICASE reports are considered to be primarily preprints of manuscripts that have been submitted to appropriate research journals or that are to appear in conference proceedings

The NASTRAN theoretical manual (level 16.0)

The manual is a commentary on the NASTRAN computer program, introducing the program to all interested persons. The manual's most important function is to present the developments of the analytical and numerical procedures that underlie the program. This manual is one of the four manuals which document the NASTRAN computer program

The simulation of single phase, compressible fluid flow in fractured petroleum reservoirs using finite elements

Summary in English.Bibliography: leaves 181-193.In this thesis, commonly used equations governing the flow of fluids are reviewed, from first principles where appropriate. The assumptions that are made in the process are critically assessed and their limitations are discussed. The equations deal with flow through a porous and permeable medium, a single fracture, a network of fractures, and with the coupling of the fracture network and blocks of matrix material