Engineering Commons^™

High-Order Positivity-Preserving L2-Stable Spectral Collocation Schemes For The 3-D Compressible Navier-Stokes Equations, Johnathon Keith Upperman

Mathematics & Statistics Theses & Dissertations

High-order entropy stable schemes are a popular method used in simulations with the compressible Euler and Navier-Stokes equations. The strength of these methods is that they formally satisfy a discrete entropy inequality which can be used to guarantee L₂ stability of the numerical solution. However, a fundamental assumption that is explicitly or implicitly used in all entropy stability proofs available in the literature for the compressible Euler and Navier-Stokes equations is that the thermodynamic variables (e.g., density and temperature) are strictly positive in the entire space{time domain considered. Without this assumption, any entropy stability proof for a numerical scheme …

Pressure-Driven Transport Of Particles Through A Converging-Diverging Microchannel, Ye Ai, Sang W. Joo, Xiangchun Xuan, Shizhi Qian

Mechanical & Aerospace Engineering Faculty Publications

Pressure-driven transport of particles through a symmetric converging-diverging microchannel is studied by solving a coupled nonlinear system, which is composed of the Navier-Stokes and continuity equations using the arbitrary Lagrangian-Eulerian finite-element technique. The predicted particle translation is in good agreement with existing experimental observations. The effects of pressure gradient, particle size, channel geometry, and a particle's initial location on the particle transport are investigated. The pressure gradient has no effect on the ratio of the translational velocity of particles through a converging-diverging channel to that in the upstream straight channel. Particles are generally accelerated in the converging region and then …

Numerical Prediction Of Turbulent Diffusion Flames Formed By Cylindrical Tube Injector, Ali S. Kheireddine

Mechanical & Aerospace Engineering Theses & Dissertations

This work summarizes numerical results for a diffusion flame formed from a cylindrical tube fuel injector, issuing gaseous fuel jet vertically in a quiescent atmosphere. Both pure fuels as well as fuel mixtures are examined. The primary objective is to predict the flame base height as a function of the jet velocity. A finite volume scheme is used to discretize the time-averaged Navier-Stokes equations for the reacting flow, resulting from the turbulent fuel jet motion. The turbulent stresses, and heat and mass fluxes are computed from the Reynolds stress turbulence model. A chemical kinetics model involving a two-step chemical reaction …

Simulation Of Active Control Of Asymmetric Flows Around Slender Pointed Forebodies, Hazem Sharaf El-Din

Mechanical & Aerospace Engineering Theses & Dissertations

At high angles of attack, the flowfield over slender forebodies becomes asymmetric with substantial side force, which may exceed the available control capability. The unsteady compressible Navier-Stokes equations are used to investigate the effectiveness of different active control methods to alleviate and possibly eliminate the flow asymmetry and the subsequent side force. Although the research work focuses on active control methods, a passive control method has been investigated. The implicit, Roe flux-difference splitting, finite volume scheme is used for the numerical computations. Both locally-conical and three-dimensional solutions of the Navier-Stokes equations are obtained.

The asymmetric flow over five-degree semi-apex angle …

Unsteady Flow Simulations About Moving Boundary Configurations Using Dynamic Domain Decomposition Techniques, Guan-Wei Yen

Mechanical & Aerospace Engineering Theses & Dissertations

A computational method is developed to solve the coupled governing equations of an unsteady flowfield and those of rigid-body dynamics in six degrees-of-freedom (6-DOF). This method is capable of simulating the unsteady flowfields around multiple component configurations with at least one of the components in relative motion with respect to the others. Two of the important phenomena that such analyses can help us to understand are the unsteady aerodynamic interference and the boundary-induced component of such a flowfield. By hybridizing two dynamic domain decomposition techniques, the grid generation task is simplified, the computer memory requirement is reduced, and the governing …

Multigrid Acceleration Of Time-Dependent Solutions Of Navier-Stokes Equations, Sarafa Oladele Ibraheem

Mechanical & Aerospace Engineering Theses & Dissertations

Recent progress in Computational Fluid Dynamics is encouraging scientists to look at fine details of flow physics of problems in which natural unsteady phenomena have hitherto been neglected. The acceleration methods that have proven very successful in steady state computations can be explored for time dependent computations. In this work, an efficient multigrid methods is developed to solve the time-dependent Euler and Navier-Stokes equations. The Beam-Warming ADI method is used as the base algorithm for time stepping calculations. Application of the developed algorithm proved very efficient in selected steady and unsteady test problems. For instance, the inherent unsteadiness present in …

Studies On Nonequilibrium Phenomena In Supersonic Chemically Reacting Flows, Rajnish Chandrasekhar

Mechanical & Aerospace Engineering Theses & Dissertations

This study deals with a systematic investigation of nonequilibrium processes in supersonic combustion. The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with nonequilibrium chemistry and thermodynamics, coupled with radiation, for hydrogen-air systems. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved.

For a basic understanding of the flow physics, premixed flows undergoing finite rate chemical reactions are investigated. Results obtained for specific conditions indicate that the radiative interactions vary substantially, depending on reactions involving HO$\sb2$ and NO species, and that this can have a noticeable influence on …

Navier-Stokes Simulation Of Quasi-Axisymmetric And Three-Dimensional Supersonic Vortex Breakdown, Hamdy A. Kandil

Mechanical & Aerospace Engineering Theses & Dissertations

Computational simulation of supersonic vortex breakdown is considered for internal and external flow applications. The interaction of a supersonic swirling flow with a shock wave in bounded and unbounded domains is studied. The problem is formulated using the unsteady, compressible, full Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. Solutions are obtained for quasi-axisymmetric and three-dimensional flows. The quasi-axisymmetric solutions are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity to each other. For the flow in a bounded domain, a supersonic swirling flow …

Laminar And Turbulent Natural Convection Heat Transfer In Trombe Wall Channels, Tony D. T. Chen

Mechanical & Aerospace Engineering Theses & Dissertations

The natural convective heat transfer and air movement in a Trombe wall solar passive system has been studied analytically and numerically. Three Trombe wall channel geometries including the parallel channel with axial inlet and exit, parallel channel with side vents and Trombe wall channel coupled to the room have been considered. Several models representing these Trombe wall geometries have been formulated. For the parallel channel with axial inlet and exit geometry, a momentum-integral method has been used to solve parabolic governing equations for two-dimensional laminar flow. This formulation leads to a second order ordinary differential equation for pressure defect in …

Unsteady Euler And Navier-Stokes Computations Around Oscillating Delta Wing Including Dynamics, Ahmed Abd-El-Bar Ahmed Salman

Mechanical & Aerospace Engineering Theses & Dissertations

Unsteady flows around rigid or flexible delta wings with and without oscillating leading-edge flaps are considered. These unsteady flow problems are categorized under two classes of problems. In the first class, the wing motion is prescribed a priori and in the second class, the wing motion is obtained as a part of the solution. The formulation of the first class includes either the unsteady Euler or unsteady Navier-Stokes equations for the fluid dynamics and the unsteady linearized Navier-displacement (ND) equations for the grid deformation.

The problem of unsteady transonic flow past a bicircular-arc airfoil undergoing prescribed thickening-thinning oscillation is studied …

A Computational Aerodynamic Design Optimization Method Using Sensitivity Analysis, Mohamed E. Eleshaky

Mechanical & Aerospace Engineering Theses & Dissertations

A new and efficient procedure for aerodynamic shape optimization is presented. The salient lineaments of this procedure are: (1) using a discrete sensitivity analysis approach to determine analytically the aerodynamic sensitivity coefficients; (2) obtaining the flowfield solution either by a computational fluid dynamics (CFD) analysis or, alternatively, by a flowfield extrapolation method which is based on a truncated Taylor's series; (3) defining the aerodynamic shape in such a way that it is not restricted to any class of surfaces and the optimizer automatically shapes the aerodynamic configuration to any arbitrary geometry; and (4) requiring no expertise other than that needed …

Prediction And Control Of Asymmetric Vortical Flows Around Slender Bodies Using Navier-Stokes Equations, Tin-Chee Wong

Mechanical & Aerospace Engineering Theses & Dissertations

Steady and unsteady vortex-dominated flows around slender bodies at high angles of attack are solved using the unsteady, compressible Navier-Stokes equations. An implicit upwind, finite-volume scheme is used for the numerical computations.

For supersonic flows past pointed bodies, the locally-conical flow assumption has been used. Asymmetric flows past five-degree semiapex cones using the thin-layer Navier-Stokes equations at different angles of attack, freestream Mach numbers, Reynolds numbers, grid fineness, computational domain size, sources of disturbances and cross-section shapes have been studied. The onset of flow asymmetry occurs when the relative incidence of pointed forebodies exceeds certain critical values. At these critical …

Navier-Stokes Simulations Of Flows About Complex Configurations Using Domain Decomposition Techniques, Kamran Fouladi-Semnani

Mechanical & Aerospace Engineering Theses & Dissertations

An algorithm is developed to obtain numerical simulations of flows about complex configurations composed of multiple and nonsimilar components with arbitrary geometries. The algorithm uses a hybridization of the domain decomposition techniques for grid generation and to reduce the computer memory requirement. Three dimensional, Reynolds-averaged, unsteady, compressible, and complete Navier-Stokes equations are solved on each of the subdomains by a fully-vectorized, finite-volume, upwind-biased, approximately-factored, and multigrid method. The effect of Reynolds stresses is incorporated through an algebraic turbulence model with several modifications for interference flows. The present algorithm combines the advantages of an efficient, geometrically conservative, minimally and automatically dissipative …

Effects Of Nose Bluntness And Shock-Shock Interactions On Blunt Bodies In Viscous Hypersonic Flows, Dal J. Singh

Mechanical & Aerospace Engineering Theses & Dissertations

A numerical study has been conducted to investigate the effects of blunt leading edges on the viscous flow field around a hypersonic vehicle such as the proposed National Aero-Space Plane. Attention is focused on two specific regions of the flow field. Analysis of these flow regions is required to accurately predict the overall flow field as well as to get necessary information on localized zones of high pressure and intense heating.

The forebody is modeled by slender cones and ogives with spherically blunted nose. A combination of Navier-Stokes and parabolized Navier-Stokes equations is used to compute the flow field. The …

Numerical Simulation Of Turbulent Flows Past Three-Dimensional Cavities, Shivakumar Srinivasan

Mechanical & Aerospace Engineering Theses & Dissertations

Computations have been performed to simulate turbulent supersonic, transonic, and subsonic flows past three-dimensional deep, transitional, and shallow cavities. Simulation of these self sustained oscillatory flows has been generated through time accurate solutions of Reynolds averaged full Navier-Stokes equations using the explicit MacCormack scheme. The Reynolds stresses have been modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses have been performed for the instantaneous pressure values on the cavity floor. Comparison with experimental data is made in terms of the mean …

Investigation Of Supersonic Chemically Reacting And Radiating Channel Flow, Mortaza Mani

Mechanical & Aerospace Engineering Theses & Dissertations

The two-dimensional time dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multi-stage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multi-dimensional radiative transfer equations for a nongray model are provided for a general configuration, and then reduced for a planer geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the …

A Study Of Flow Separation In Transonic Flow Using Inviscid And Viscous Cfd Schemes, James Andrew Rhodes

Mechanical & Aerospace Engineering Theses & Dissertations

A comparison of flow separation in transonic flows is made using various computational schemes which solve the Euler and the Navier-Stokes equations of fluid mechanics. The flows examined are computed using several simple two-dimensional configurations including a backward facing step and a bump in a channel. Comparison of the results obtained using shock fitting and flux vector splitting methods are presented and the results obtained using the Euler codes are compared to results on the same configurations using a code which solves the Navier-Stokes equations.

Topology And Grid Adaption For High-Speed Flow Computations, Jamshid Samareh Abolhassani

Mechanical & Aerospace Engineering Theses & Dissertations

This study investigates the effects of grid topology and grid adaption on numerical solutions of the Navier-Stokes equations. In the first part of this study, a general procedure is presented for computation of high-speed flow over complex three-dimensional configurations. This includes the grid generation and solution algorithm for Navier-Stokes equations in a general three-dimensional curvilinear coordinate system. The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and a Reynolds number of 2,000,000. The O-type and H-type grids have been used for this study, and the results …

A Numerical Study Of Three-Dimensional Vortex Breakdown, Robert Edward Spall

Mechanical & Aerospace Engineering Theses & Dissertations

A numerical simulation of vortex breakdown using the time-dependent Navier-Stokes equations was performed. Unlike previous studies, the numerical algorithm, formulated in terms of the velocity and vorticity, was not restricted to axisymmetric flows. Prototype vortices were parameterized in terms of their Reynolds number and Rossby number. Two cases were studied extensively. In one case, a vortex was imbedded in a uniform free stream. In the other case, the axial velocity of the free stream was decelerated in the streamwise direction. For both cases breakdown occurred when the Rossby number was below a critical value. Vortex lines, particle traces and velocity …

Implementation And Performance Analysis Of Numerical Algorithms On The Mpp, Flex/32, And Cray/2, Raad A. Fatoohi

Electrical & Computer Engineering Theses & Dissertations

This dissertation presents the results of the implementation of a number of numerical algorithms on three parallel/vector computers. The object of this research is to determine how well, or poorly, a number of numerical algorithms would map onto three different architectures and to analyze the performance of these architectures using these algorithms. These algorithms are: a relaxation scheme for the solution of the Cauchy-Riemann equations, an ADI method for the solution of the diffusion equation, and a compact difference scheme for the solution of two-dimensional Navier-Stokes equations. The computers were chosen so as to encompass a variety of architectures. They …