Aerodynamics and Fluid Mechanics Commons^™

Numerical Modeling Of Badminton Shuttlecock Trajectories, Lola G. Torres, Cassandra Pumphrey, Jadyn Peterson, Domenic Barsotti

Discovery Day - Daytona Beach

The Trajectory of a badminton Shuttlecock can vary significantly when compared to a classic projectile motion, primarily due to aerodynamic drag. This project aims to model the flight of the shuttlecock using Newton's second law for gravitational and drag related forces, resulting in a nonlinear system of a first order differential equation. The given parameters include the shuttlecock mass, cross-sectional area, air density, as well as the drag coefficient, determining the overall magnitude of the drag force. The resulting initial value problem is solved numerically using a multitude of Runge_Kutta methods to compare the accuracy and stability across different computational …

Motion With Air Resistance, Gauge Mccain, Jacob Bealefeld, Francesca Wise

Discovery Day - Daytona Beach

The motion of objects moving through air is influenced not only by gravity but also by air resistance, which affects the speed and acceleration of the object over time. This project examines the motion of a falling object by modeling it with an ordinary differential equation that accounts for both gravitational force and a resistive drag force proportional to velocity. Using Newton’s Second Law, a first-order differential equation is derived to describe how the velocity of the object changes as it falls. The solution of this equation demonstrates how the velocity increases initially and gradually approaches a constant value known …

Numerical Method For Strongly Variable-Density Flows At Low Mach Number: Flame-Sheet Regularisation And A Mass-Flux Immersed Boundary Method, Matheus P. Severino, Fernando F. Fachini, Elmer M. Gennaro, Daniel Rodríguez, Leandro F. Souza

Mathematical Modelling and Numerical Simulation with Applications

A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the disparity between the flow and acoustic speed. Therefore, low-Mach-number flows impose mathematical and computational challenges in their description. Standard numerical methods for compressible flows, which are typically designed for problems with a single dominant spatial and temporal scale, require alternative approaches, such as preconditioning techniques or solvers tailored for low-Mach-number equations. The present work introduces a simplified fluid dynamics model for flows …

Advancements In Elliptic Mesh Redistribution And Automated Overset Grid Generation For Computational Fluid Dynamics, Chase Ashby

Theses and Dissertations--Mathematics

Automated and robust structured curvilinear overset grid generation remains a significant challenge for the application of computational fluid dynamics. This thesis intro- duces a specialized anisotropic Mach cone aligned adaptation algorithm for low-boom simulations and an automated procedure for generating structured curvilinear overset grids for immersed boundary simulations. Results demonstrate that anisotropic mesh adaptation can reduce computational resource usage by over 50% while maintaining sonic boom prediction accuracy across the entire sonic boom domain compared to user-constructed Mach cone aligned grids. The proposed immersed overset grid gen- eration procedure eliminates the need for complex surface generation algorithms, producing grids suitable …

Mathematical Modeling: Finite Element Analysis And Computations Arising In Fluid Dynamics And Biological Applications, Jorge Reyes

UNLV Theses, Dissertations, Professional Papers, and Capstones

It is often the case when attempting to capture real word phenomena that the resulting mathematical model is too difficult and even not feasible to be solved analytically. As a result, a computational approach is required and there exists many different methods to numerically solve models described by systems of partial differential equations. The Finite Element Method is one of them and it was pursued herein.This dissertation focuses on the finite element analysis and corresponding numerical computations of several different models. The first part consists of a study on two different fluid flow models: the main governing model of fluid …

Impact Of Spallation And Internal Radiation On Fibrous Ablative Materials, Raghava Sai Chaitanya Davuluri

Theses and Dissertations--Mechanical and Aerospace Engineering

Space vehicles are equipped with Thermal Protection Systems (TPS) that encounter high heat rates and protect the payload while entering a planetary atmosphere. For most missions that interest NASA, ablative materials are used as TPS. These materials undergo several mass and energy transfer mechanisms to absorb intense heat. The size and construction of the TPS are based on the composition of the planetary atmosphere and the impact of various ablative mechanisms on the flow field and the material. Therefore, it is essential to quantify the rates of different ablative phenomena to model TPS accurately. In this work, the impact of …

A Data Driven Modeling Approach For Store Distributed Load And Trajectory Prediction, Nicholas Peters

Doctoral Dissertations and Master's Theses

The task of achieving successful store separation from aircraft and spacecraft has historically been and continues to be, a critical issue for the aerospace industry. Whether it be from store-on-store wake interactions, store-parent body interactions or free stream turbulence, a failed case of store separation poses a serious risk to aircraft operators. Cases of failed store separation do not simply imply missing an intended target, but also bring the risk of collision with, and destruction of, the parent body vehicle. Given this risk, numerous well-tested procedures have been developed to help analyze store separation within the safe confines of wind …

Numerical Investigation On The Effect Of Spectral Radiative Heat Transfer Within An Ablative Material, Raghava S. C. Davuluri, Rui Fu, Kaveh A. Tagavi, Alexandre Martin

Mechanical Engineering Faculty Publications

The spectral radiative heat flux could impact the material response. In order to evaluate it, a coupling scheme between KATS - MR and P1 approximation model of radiation transfer equation (RTE) is constructed and used. A Band model is developed that divides the spectral domain into small bands of unequal widths. Two verification studies are conducted: one by comparing the simulation computed by the Band model with pure conduction results and the other by comparing with similar models of RTE. The comparative results from the verification studies indicate that the Band model is computationally efficient and can be used to …

Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire

Dissertations

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently …

Modeling And Design Optimization For Membrane Filters, Yixuan Sun

Dissertations

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for: (1) pleated membrane …

Fully Coupled Internal Radiative Heat Transfer For The 3d Material Response Of Heat Shield, Raghava S. C. Davuluri, Rui Fu, Kaveh A. Tagavi, Alexandre Martin

Mechanical Engineering Faculty Publications

The radiative transfer equation (RTE) is strongly coupled to the material response code KATS. A P-1 approximation model of RTE is used to account for radiation heat transfer within the material. First, the verification of the RTE model is performed by comparing the numerical and analytical solutions. Next, the coupling scheme is validated by comparing the temperature profiles of pure conduction and conduction coupled with radiative emission. The validation study is conducted on Marschall et al. cases (radiant heating, arc-jet heating, and space shuttle entry), 3D Block, 2D IsoQ sample, and Stardust Return Capsule. The validation results agree well for …

Numerical Reconstruction Of Spalled Particle Trajectories In An Arc-Jet Environment, Raghava S. C. Davuluri, Sean C. C. Bailey, Kaveh A. Tagavi, Alexandre Martin

Mechanical Engineering Faculty Publications

To evaluate the effects of spallation on ablative material, it is necessary to evaluate the mass loss. To do so, a Lagrangian particle trajectory code is used to reconstruct trajectories that match the experimental data for all kinematic parameters. The results from spallation experiments conducted at the NASA HYMETS facility over a wedge sample were used. A data-driven adaptive methodology was used to adapts the ejection parameters until the numerical trajectory matches the experimental data. The preliminary reconstruction results show that the size of the particles seemed to be correlated with the location of the ejection event. The size of …

Dances And Escape Of The Vortex Quartet, Brandon Behring

Dissertations

This dissertation considers the linear stability of a one-parameter family of periodic solutions of the four-vortex problem known as 'leapfrogging' orbits. These solutions, which consist of two pairs of identical yet oppositely-signed vortices, were known to W. Gröbli (1877) and A. E. H. Love (1883) and can be parameterized by a dimensionless parameter related to the geometry of the initial configuration. Simulations by Acheson and numerical Floquet analysis by Tophøj and Aref both indicate, to many digits, that the bifurcation occurs at a value related to the inverse square of the golen ratio. Acheson observed that, after an initial period …

Studies Of Two-Phase Flow With Soluble Surfactant, Ryan Peter Atwater

Dissertations

Numerical methods are developed for accurate solution of two-phase flow in the zero Reynolds number limit of Stokes flow, when surfactant is present on a drop interface and in its bulk phase interior. The methods are designed to achieve high accuracy when the bulk Péclet number is large, or equivalently when the bulk phase surfactant has small diffusivity

In the limit of infinite bulk Péclet number the advection-diffusion equation that governs evolution of surfactant concentration in the bulk is singularly perturbed, indicating a separation of spatial scales. A hybrid numerical method based on a leading order asymptotic reduction in this …

A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu

Master's Theses

A numerical study was conducted to determine the effect of changing the camber of a winglet on the efficiency of a wing in two distinct flight conditions. Camber was altered via a simple plain flap deflection in the winglet, which produced a constant camber change over the winglet span. Hinge points were located at 20%, 50% and 80% of the chord and the trailing edge was deflected between -5° and +5°. Analysis was performed using a combination of three-dimensional vortex lattice method and two-dimensional panel method to obtain aerodynamic forces for the entire wing, based on different winglet camber configurations. …

High Order Explicit Semi-Lagrangian Method For The Solution Of Lagrangian Transport And Stochastic Differential Equations, Hareshram Natarajan

CGU Theses & Dissertations

A semi-Lagrangian method is developed for the solution of Lagrangian transport equations and stochastic differential equations that is consistent with Discontinuous Spectral Element Method (DSEM) approximations of Eulerian conservation laws. The method extends the favorable properties of DSEM that include its high-order accuracy, its local and boundary fitted properties and its high performance on parallel platforms for the concurrent semi-Lagrangian and Eulerian solution of a class of time-dependent problems that can be described by coupled Eulerian-Lagrangian formulations. Such formulations include the probabilistic models used for the simulation of chemically reacting turbulent flows or particle-laden flows. Motivated by the high-fidelity simulation …

Numerical Analysis And Fluid Flow Modeling Of Incompressible Navier-Stokes Equations, Tahj Hill

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Navier-Stokes equations (NSE) are an essential set of partial differential equations for governing the motion of fluids. In this paper, we will study the NSE for an incompressible flow, one which density ρ = ρ0 is constant.

First, we will present the derivation of the NSE and discuss solutions and boundary conditions for the equations. We will then discuss the Reynolds number, a dimensionless number that is important in the observations of fluid flow patterns. We will study the NSE at various Reynolds numbers, and use the Reynolds number to write the NSE in a nondimensional form.

We will …

Estimation Of Performance Airspeeds For High-Bypass Turbofans Equipped Transport-Category Airplanes, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model …

Effect Of Spalled Particles Thermal Degradation On A Hypersonic Flow Field Environment, Raghava S. C. Davuluri, Huaibao Zhang, Alexandre Martin

Mechanical Engineering Faculty Publications

Two-way coupling is performed between a spallation code and a hypersonic aerothermodynamics CFD solver to evaluate the effect of spalled particles on the flow field. Time accurate solutions are computed in argon and air flow fields. A single particle simulations and multiple particles simulations are performed and studied. The results show that the carbon vapor released by spalled particles tend to change the composition of the flow field, particularly the upstream region of the shock.

On The Selection Of A Good Shape Parameter For Rbf Approximation And Its Application For Solving Pdes, Lei-Hsin Kuo

Dissertations

Meshless methods utilizing Radial Basis Functions~(RBFs) are a numerical method that require no mesh connections within the computational domain. They are useful for solving numerous real-world engineering problems. Over the past decades, after the 1970s, several RBFs have been developed and successfully applied to recover unknown functions and to solve Partial Differential Equations (PDEs).
However, some RBFs, such as Multiquadratic (MQ), Gaussian (GA), and Matern functions, contain a free variable, the shape parameter, c. Because c exerts a strong influence on the accuracy of numerical solutions, much effort has been devoted to developing methods for determining shape parameters which provide …

Efficient General Computational Method For Estimation Of Standard Atmosphere Parameters, Nihad E. Daidzic Ph.D., Sc.D.

International Journal of Aviation, Aeronautics, and Aerospace

Knowledge of standard air temperature, pressure, density, speed of sound, and viscosity as a function of altitude is essential information in aircraft design, performance testing, pressure altimeter calibration, and several other aeronautical engineering and aviation science applications. A new efficient computational method for rapid calculations of standard atmospheric parameters up to 86 orthometric km is presented. Additionally, mass and weight of each standard atmospheric layer were calculated using a numerical integration method. The sum of all fractional masses and weights represents the total mass and weight of Earth’s atmosphere. The results obtained here agree well with measurements and models of …

A Contribution Toward Better Understanding Of Overbanking Tendency In Fixed-Wing Aircraft, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

The phenomenon of overbanking tendency for a rigid-body, fixed-wing aircraft is investigated. Overbanking tendency is defined as a spontaneous, unbalanced rolling moment that keeps increasing an airplane’s bank angle in steep turns and must be arrested by opposite aileron action. As stated by the Federal Aviation Administration, the overbanking tendency may lead to a loss of control, especially in instrument meteorological conditions. It was found in this study that the speed differential over wing halves in horizontal turns indeed creates a rolling moment that achieves maximum values for bank angles between 45 and 55 degrees. However, this induced rolling moment …

Evolution Of Perturbations In Flow Field Mechanics, Samantha R. Bell, David Forliti, Nils Sedano, Kriss Vanderhyde

STAR Program Research Presentations

This project explores the stability analysis of a given flow field. Specifically, where the peak disturbance occurs in a flow as this is the disturbance that is most likely to occur. In rocket combustion, it is important to understand where the maximum disturbance occurs so that the mixing of fuel can be stabilized. The instabilities are the results of frequencies in the area surrounding the flow field. The linear stability governing equations are employed to better understand the disturbance. The governing equations for continuity and momentum in the x and y directions are used to form an equation for the …

Supersonic Turbine Cascade Studies Using Computational Fluid Dynamics And Water Table Experiments, Shelby E. Nelson

Honors College Theses

Design engineers use a variety of tools to perform calculations and to aid in the design process. For example, engineers designing gas turbines, specifically the aerodynamicists, use a combination of hand calculations, experimental data, and complex numerical codes to simulate air flow around each blade. Aerodynamicists designing gas turbines must predict the locations of the shocks to locate inefficiencies in the flow. In this thesis, three methods of calculating the shock angles are compared: analytical, experimental, and computational. Three different airfoil shapes are tested: a rectangular flat plate, a supersonic diamond, and a turbine airfoil. Cascade tests of the airfoil …

Analytic Treatment Of Vortex States In Cylindrical Superconductors In Applied Axial Magnetic Field, Andrei Ludu, J. Van Deun, M. V, Milosevic, A. Cuyt, F. M. Peeters

Publications

We solve the linear Ginzburg–Landau GL equation in the presence of a uniform magnetic field with cylindrical symmetry and we find analytic expressions for the eigenfunctions in terms of the confluent hypergeometric functions. The discrete spectrum results from an implicit equation associated to the boundary conditions and it is resolved in analytic form using the continued fractions formalism. We study the dependence of the spectrum and the eigenfunctions on the sample size and the surface conditions for solid and hollow cylindrical superconductors. Finally, the solutions of the nonlinear GL formalism are constructed as expansions in the linear GL eigenfunction basis …

High Order Finite Elements For Lagrangian Computational Fluid Dynamics, Truman Everett Ellis

Master's Theses

A general finite element method is presented to solve the Euler equations in a Lagrangian reference frame. This FEM framework allows for separate arbitrarily high order representation of kinematic and thermodynamic variables. An accompanying hydrodynamics code written in Matlab is presented as a test-bed to experiment with various basis function choices. A wide range of basis function pairs are postulated and a few choices are developed further, including the bi-quadratic Q2-Q1d and Q2-Q2d elements. These are compared with a corresponding pair of low order bi-linear elements, traditional Q1-Q0 and sub-zonal pressure Q1-Q1d. Several test problems are considered including static convergence …

Spatial Instability Of Electrically Driven Jets With Finite Conductivity And Under Constant Or Variable Applied Field, Saulo Orizaga, Daniel N. Riahi

Applications and Applied Mathematics: An International Journal (AAM)

We investigate the problem of spatial instability of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton’s method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One of these modes is enhanced by the strength Ω of …

Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda

Undergraduate Research Opportunities Program (UROP)

We are computationally investigating fluid flow models for physically correct predictions of flow structures. Models based on the idea of filtering the small scales/structures and also the Navier-Stokes equations which are the fundamental equations of fluid flow, are numerically solved via the continuous finite element method. Crank-Nicolson and fractional-step theta scheme are used for the discretization of the time derivative, while the Taylor-Hood and Mini elements are used for the discretization is space. The effectiveness of these numerical discretizations in time and space are examined by studying the accuracy of fluid characteristics, such as drag, lift and pressure drop.

Modeling Redox-Based Magnetohydrodynamics In Three-Dimensional Microfluidic Channels, Hussameddine S. Kabbani, Aihua Wang, Xiaobing Luo, Shizhi Qian

Mechanical Engineering Faculty Research

RedOx-based magnetohydrodynamic MHD[1] flows in three-dimensional microfluidic channels are investigated theoretically with a coupled mathematical model consisting of the Nernst-Planck equations for the concentrations of ionic species, the local electroneutrality condition for the electric potential, and the Navier-Stokes equations for the flow field. A potential difference is externally applied across two planar electrodes positioned along the opposing walls of a microchannel that is filled with a dilute RedOx electrolyte solution, and a Faradaic current transmitted through the solution results. The entire device is positioned under a magnetic field which can be provided by either a permanent magnet or an electromagnet. …

Development And Application Of Adaptive Dynamic Grids For Wake Vortex/Ground Interaction, Ilker Emin Türkgeldi

Mechanical & Aerospace Engineering Theses & Dissertations

An adaptive and dynamic grid approach is developed for the numerical computations of wake vortex flow problems with ground interaction. The unnecessary grid points at the far field of the original, large, single zone grid are removed for computational efficiency. Next, the grid is modified into an adaptive one, where the fine core region keeps track of the vortices and can be split into two regions when the vortex separation distance exceeds a specified limit length. In the final step a multi zonal feature is added to this grid by means of two embedded grids placed at the vortex centers …