Mathematical Architecture for Models of Fluid Flow Phenomena

This thesis is a study of several high accuracy numerical methods for fluid flow problems and turbulence modeling.First we consider a stabilized finite element method for the Navier-Stokes equations which has second order temporal accuracy. The method requires only the solution of one linear system (arising from an Oseen problem) per time step. We proceed by introducing a family of defect correction methods for the time dependent Navier-Stokes equations, aiming at higher Reynolds' number. The method presented is unconditionally stable, computationally cheap and gives an accurate approximation to the quantities sought. Next, we present a defect correction method with increased time accuracy. The method is applied to the evolutionary transport problem, it is proven to be unconditionally stable, and the desired time accuracy is attained with no extra computational cost. We then turn to the turbulence modeling in coupled Navier-Stokes systems - namely, MagnetoHydroDynamics. Magnetically conducting fluids arise in important applications including plasma physics, geophysics and astronomy. In many of these, turbulent MHD (magnetohydrodynamic) flows are typical. The difficulties of accurately modeling and simulating turbulent flows are magnified many times over in the MHD case. We consider the mathematical properties of a model for the simulation of the large eddies in turbulent viscous, incompressible, electrically conducting flows. We prove existence, uniqueness and convergence of solutions for the simplest closed MHD model. Furthermore, we show that the model preserves the properties of the 3D MHD equations. Lastly, we consider the family of approximate deconvolution models (ADM) for turbulent MHD flows. We prove existence, uniqueness and convergence of solutions, and derive a bound on the modeling error. We verify the physical properties of the models and provide the results of the computational tests

HIGHER ACCURACY METHODS FOR FLUID FLOWS IN VARIOUS APPLICATIONS: THEORY AND IMPLEMENTATION

This dissertation contains research on several topics related to Defect-deferred correction (DDC) method applying to CFD problems. First, we want to improve the error due to temporal discretization for the problem of two convection dominated convection-diffusion problems, coupled across a joint interface. This serves as a step towards investigating an atmosphere-ocean coupling problem with the interface condition that allows for the exchange of energies between the domains. The main diffuculty is to decouple the problem in an unconditionally stable way for using legacy code for subdomains. To overcome the issue, we apply the Deferred Correction (DC) method. The DC method computes two successive approximations and we will exploit this extra flexibility by also introducing the artificial viscosity to resolve the low viscosity issue. The low viscosity issue is to lose an accuracy and a way of finding a approximate solution as a diffusion coeffiscient gets low. Even though that reduces the accuracy of the first approximation, we recover the second order accuracy in the correction step. Overall, we construct a defect and deferred correction (DDC) method. So that not only the second order accuracy in time and space is obtained but the method is also applicable to flows with low viscosity. Upon successfully completing the project in Chapter 1, we move on to implementing similar ideas for a fluid-fluid interaction problem with nonlinear interface condition; the results of this endeavor are reported in Chapter 2. In the third chapter, we represent a way of using an algorithm of an existing penalty-projection for MagnetoHydroDynamics, which allows for the usage of the less sophisticated and more computationally attractive Taylor-Hood pair of finite element spaces. We numerically show that the new modification of the method allows to get first order accuracy in time on the Taylor-Hood finite elements while the existing method would fail on it. In the fourth chapter, we apply the DC method to the magnetohydrodynamic (MHD) system written in Elsásser variables to get second order accuracy in time. We propose and analyze an algorithm based on the penalty projection with graddiv stabilized Taylor Hood solutions of Elsásser formulations

HIGH ACCURACY METHODS AND REGULARIZATION TECHNIQUES FOR FLUID FLOWS AND FLUID-FLUID INTERACTION

This dissertation contains several approaches to resolve irregularity issues of CFD problems, including a decoupling of non-linearly coupled fluid-fluid interaction, due to high Reynolds number. New models present not only regularize the linear systems but also produce high accurate solutions both in space and time. To achieve this goal, methods solve a computationally attractive artificial viscosity approximation of the target problem, and then utilize a correction approach to make it high order accurate. This way, they all allow the usage of legacy code | a frequent requirement in the simulation of fluid flows in complex geometries. In addition, they all pave the way for parallelization of the correction step, which roughly halves the computational time for each method, i.e. solves at about the same time that is required for DNS with artificial viscosity. Also, methods present do not requires all over function evaluations as one can store them, and reuse for the correction steps. All of the chapters in this dissertation are self-contained, and introduce model first, and then present both theoretical and computational findings of the corresponding method

Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143090/1/1.J055595.pd

Direct numerical simulation of multi-phase flow in complex media

Tesi en modalitat de compendi de publicacionsIn numerous applications, two-phase liquid-gas transport at sub-millimeter length scales plays a substantial role in the determination of the behavior of the system at hand. As its main application, the present work focuses on the polymer electrolyte membrane (PEM) fuel cells. Desirable performance and operational life-time of this class of high-throughput energy conversion devices requires an effective water management, which per se relies on proper prediction of the water-air transport mechanisms. Such two-phase flow involves interfacial forces and phenomena, like hysteresis, that are associated with the physicochemical properties the liquid, gas, and if present, the solid substrate. In this context, numerical modeling is a viable means to obtain valuable predictive understanding of the transport mechanisms, specially for cases that experimental analyses are complicated and/or prohibitively expensive. In this work, an efficient finite element/level-set framework is developed for three-dimensional simulation of two-phase flow. In order to achieve a robust solver for practical applications, the physical complexities are consistently included and the involved numerical issues are properly tackled; the pressure discontinuity at the liquid-gas interface is consistently captured by utilizing an enriched finite element space. The method is stabilized within the framework of variational multiscale stabilization technique. A novel treatment is further proposed for the small-cut instability problem. It is shown that the proposed model can provide accurate results minimizing the spurious currents. A robust technique is also developed in order to filter out the possible noises in the level-set field. It is shown that it is a key to prevent irregularities caused by the persistent remnant of the spurious currents. It is shown how the well-established contact-line models can be incorporated into the variational formulation. The importance of the inclusion of the sub-elemental hydrodynamics is also elaborated. The results presented in the present work rely on the combination of the linearized molecular kinetic and the hydrodynamic theories. Recalling the realistic behavior of liquids in contact with solid substrates, the contact--angle hysteresis phenomenon is taken into account by imposing a consistent pinning/unpinning mechanism developed within the framework of the level-set method. Aside from the main developments, a novel technique is also proposed to significantly improve the accuracy and minimize the the loss in the geometrical features of the interface during the level-set convection based on the back and forth error compensation correction (BFECC) algorithm. Within the context of this thesis, the numerical model is validated for various cases of gas bubble in a liquid and liquid droplets in a gas. For the latter scenario, besides free droplets, the accuracy of the proposed numerical method is assessed for capturing the dynamics droplets spreading on solid substrates. The performance of the model is then analyzed for the capturing the configuration of a water droplet on an inclined substrate in the presence the contact--angle hysteresis. The proposed method is finally employed to simulate the dynamics of a water droplet confined in a gas channel and exposed to air-flow.Existen numerosas aplicaciones industriales en las que transporte bifásico (líquido-gas) a escalas submilimétricas resulta crucial para la determinación del comportamiento del sistema en cuestión. Entre todas ellas, el presente trabajo se centra en las pilas de combustible con membrana de electrolito polimérico (PEMFC). El rendimiento deseable y la vida útil operativa de esta clase de dispositivos de conversión de energía de alto rendimiento requieren una gestión eficaz del agua (conocida como “water management”), que per se depende de la predicción adecuada de los mecanismos de transporte de agua y aire. Así pues, el análisis del flujo microfluídico de dos fases obliga considerar fuerzas y fenómenos interfaciales, tales como la histéresis, que están asociados con las propiedades fisicoquímicas del líquido, el gas y, si está presente, el sustrato sólido. En este contexto, la modelización numérica es una alternativa viable para obtener una predicción precisa de los mecanismos de transporte, especialmente en aquellos casos en los que los análisis experimentales son prohibitivos, ya sea por su complejidad o coste económico. En este trabajo, se desarrolla un marco eficiente, basado en la combinación del método de elementos finitos y el método de “level-set”, para la simulación tridimensional de flujos bifásicos. Con el fin de lograr una herramienta numérica robusta para aplicaciones prácticas, las complejidades físicas se incluyen consistentemente y los problemas numéricos involucrados se abordan adecuadamente. Concretamente, la discontinuidad de la presión en la interfaz líquido-gas se captura consistentemente utilizando un espacio de elementos finitos enriquecido. La estabilización del método se consigue mediante la introducción de la técnica de multiescalas variacionales. Asimismo, se propone también un tratamiento novedoso para el problema de la inestabilidad de tipo “small-cut”. Se muestra que el modelo propuesto puede proporcionar resultados precisos minimizando las corrientes espurias en la interfaz liquido-gas. Complementariamente, se presenta una nueva metodología para filtrar el ruido en el campo de “level-set”. Esta metodología resulta ser crucial para prevenir las irregularidades provocadas por el remanente persistente de las corrientes espurias. El comportamiento de la línea de contacto es considerado a través de la inclusión los modelos correspondientes en la formulación variacional. A este respecto, el presente trabajo aborda la importancia de la inclusión de la hidrodinámica subelemental. Los resultados presentados se basan en la combinación de la cinética molecular linealizada y las teorías hidrodinámicas. Para representación del comportamiento realista de los líquidos en contacto con sustratos sólidos, el fenómeno de histéresis del ángulo de contacto se tiene en cuenta imponiendo un mecanismo de anclado / desanclado consistente desarrollado en el marco del método de level-set. Aparte de los desarrollos principales, también se propone una técnica novedosa para la convección de la función ”level-set”. Ésta permite mejorar significativamente la precisión, minimizando a su vez la pérdida en las características geométricas de la interfaz asociadas al transporte. Esta nueva metodología está basada en el algoritmo de corrección de compensación de errores (BFECC). La herramienta numérica desarrollada en esta tesis es validada para varios casos que involucran burbujas de gas en un líquido y pequeñas gotas de líquido en un gas. Para el último escenario, además de las gotas libres, se evalúa la precisión de la herramienta propuesta para capturar la dinámica de las gotas sobre sustratos sólidos. A continuación, se analiza el rendimiento del modelo para capturar la configuración de una gota de agua sobre un sustrato inclinado en presencia de la histéresis del ángulo de contacto. El método propuesto finalmente se aplicaPostprint (published version

Modeling, Discretization, Optimization, and Simulation of Multiphysics Problems (IIT Indore)

The goal of this winter school is to give an introduction to numerical modeling of multiphysics problems. These are nonstationary, nonlinear, coupled partial differential equations. The philosophy of this school is to provide a mixture of very basic techniques that are immediately applied to `complicated' practical and/or current research problems

Turbulent boundary layer with strong favorable pressure gradient and curvature effects: Streamline coordinate and scaling analysis

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favorable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterized and compared to a lower Reynolds number flow over the same geometry. The momentum budgets are analyzed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral analysis-based scalings for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. These proposed scalings exhibit a better collapse of Reynolds stress profiles compared to friction velocity scaling and Zagarola-Smits scaling in the strong favorable pressure gradient region and in the mild adverse pressure region that precedes it in this flow

Adding Semi-Structured Automated Grid Generation and the Menter-Shear Stress Turbulence Transport Model for Internal Combustion Engine Simulations to Novel FEM LANL Combustion Codes

The addition of GridPro semi-structured, automated generation of grids for complex moving boundaries for combustion engine applications and the Menter Shear Stress Turbulent Transfer (SST) model are being developed by Los Alamos National Laboratory. The software is called Fast, Easy, Accurate, and Robust Continuum Engineering (FEARCE). In addition to improving the time and effort required to build complex grid geometry for turbulent reactive multi-phase flow in internal combustion engines, the SST turbulence model has been programmed into the Predictor Corrector Fractional-Step (PCS) Finite Element Method (FEM) for reactive flow and turbulent incompressible flow regime validation is performed. The Reynolds-Averaged Navier-Stokes finite-element solver without h-adaption is used for validation of the SST turbulence model on two benchmark problems in the subsonic flow regime: (1) 2D duct channel flow, and (2) a 2-D backward-facing step with an applied constant heat flux on the bottom surface downstream of the single-sided sudden expansion of the step. The 2D BFS using the newly installed SST FEARCE code yielded a corresponding X_re = 6.655H vs. that as experimentally determined by Vogel and Eaton 85\u27 of X_re_vogel =6.66667H

Aeronautical engineering: A continuing bibliography with indexes (supplement 242)

This bibliography lists 466 reports, articles, and other documents introduced into the NASA scientific and technical information system in July, 1989. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics