Fluid Dynamics Commons^™

Numerical Modeling Of Thermo-Poroelasticity Using Finite Element Method, Maya Mckean

Discovery Day - Daytona Beach

We propose a numerical method for solving and modeling thermo-poroelasticity problems using a finite element formulation. Thermo-poroelasticity models describe the coupled interaction between mechanical deformation, fluid flow, and heat transfer in specific materials or environments over time. These models demonstrate the evolution of displacement, pressure, and temperature; we compute these fields in this work using backward Euler time discretization and Enriched Galerkin finite element spatial discretization. For these computations we used FreeFEM, a partial differential equation solver that uses the finite element method, which produced our numerical results. We then compared these values with the expected analytical solution. This was …

From Code To Cube: Interactive Fluid Simulation With Real Time Motion Control, Dominic Ziccardi, Carter Groezinger

Discovery Day - Daytona Beach

This research project explores the use of FluidX3D, an open-source lattice Boltzmann method (LBM) solver, to simulate fluid behavior within a three-dimensional cube container. The system supports both standard water models and rheoscopic fluid visualization, allowing detailed observation of complex flow dynamics in real time. The simulation accurately represents fluid motion, gravity-driven behavior, and rotational response within a bounded cubic domain. The longterm objective is to extend this digital simulation into a physical installation consisting of six synchronized square displays arranged to form a cube. This configuration will create a volumetric illusion of fluid occupying a tangible, handheld structure. An …

The Motion Of A Falling Object Under Linear Drag And How Differential Equations Can Be Used To Find It, Lukas Estrella

Discovery Day - Daytona Beach

This project, "The Motion of a Falling Object Under Linear Drag and How Differential Equations Can Be Used To Find It," investigates the motion of a falling object subject to air resistance through a combination of mathematical modeling and fundamental physical principles. The analysis is grounded in Newton’s second law, which yields a differential equation describing the forces acting on the object. Assuming a linear drag model, in which the resistive force is proportional to velocity, the governing equation reduces to a first-order ordinary differential equation for velocity. This equation is solved using the integrating factor method, yielding an explicit …

Extending The Essentially Entropic Lattice Boltzmann Method To Three-Dimensional Turbulent Flows, Michael Derderian

Discovery Day - Daytona Beach

The Entropic Lattice Boltzmann Method (EELBM) has demonstrated strong numerical stability and accuracy for two-dimensional simulations, particularly at higher resolutions where the entropic formulation introduces only minimal stabilizing turbulent viscosity and eventually converges to the Lattice Bhatnagar–Gross–Krook (LBGK) formulation. This built-in stabilization can be interpreted as an implicit large-eddy simulation (LES) model, allowing EELBM to capture complex turbulent behavior without requiring explicit subgrid-scale closures. While these advantages have been thoroughly validated in 2D, understanding how the entropic constraint regulates dissipation in three dimensions is essential for assessing EELBM’s suitability for practical, turbulence-dominated applications. This work focuses on the development and …

Navier Stokes Pressure Drop Derivation, Brayden Benedetti, Gedaliah Dimbert, Jaden Turobiner

Discovery Day - Daytona Beach

Accurate prediction of pressure losses in propellant and fluid feed systems is essential for reliable design and operation of aerospace and industrial flow networks. This project presents a systematic derivation of a practical pressure drop calculator for a feed system using isopropyl alcohol, beginning from the fundamental conservation laws and culminating in an engineering-level computational model. Starting with the differential form of the Navier–Stokes equations for incompressible flow, the governing equations are simplified through a series of physically justified assumptions, including steady-state flow, negligible body forces, and fully developed internal flow within circular piping. The resulting momentum balance is reduced …

Application Of Navier Stokes In Cfd, Hayden Kerkhoff, Gavin Palmer, Garret Seckinger

Discovery Day - Daytona Beach

This project investigates the use of 2-Dimensional Computational Fluid Dynamics (CFD) to analyze aerodynamic behavior, then compare data with the numerical solution of the Navier–Stokes equations run by MATLAB. By leveraging open‑source and possible industry CFD platforms—including OpenFOAM and commercial solvers such as ANSYS Fluent and Inventor Professional—the study evaluates how computational methods simulate, optimize, and predict key aerodynamic quantities such as lift, drag, stall angle, and Reynolds number.   The project focuses on modeling an airflow over specific parameters, such as different angles of attacks and ISA Atmospheric Conditions. Parametric variations in density, angle of attack, chord length, and temperature …

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 …

Global Time-Resolved Measurements Of Inlet/Isolator Unstart Induced By Mass Injection, Andrew N. Bustard, Benjamin L. Bemis, Aaron Marques, Matthew J. Zahr, Thomas J. Juliano

Publications

The inner surface pressure of an axisymmetric inlet/isolator model was measured using anodized-aluminum pressure-sensitive paint (PSP) viewing through cast acrylic. Temperaturesensitive paint was utilized to correct for the PSP’s temperature sensitivity. The model was tested under Mach 5.7 flow at 𝑹𝒆 = 7.1 ×106 /m under conventional noise conditions. Transverse jet injection with jet-to-inlet mass-flow ratios up to 0.8 was used to induce unstart in the inlet/isolator. Background-oriented schlieren visualization of the inlet shocks was collected simultaneously with the PSP to determine when the inlet unstarted. Computational fluid dynamics results were used to determine off-wall flow structures and quantify approach …

Numerical Study Of Nutrient Mixing In Trabecular Bone In Microgravity, Disuse And Normogravity, Sagar Gharti

Doctoral Dissertations and Master's Theses

Mechanical loading is known to regulate bone remodeling by driving interstitial fluid flow which stimulates cells and drives nutrient transport within the trabecular network. In microgravity, the absence of mechanical stimulation or loading suppresses convective flow processes, causing diffusion-driven nutrient mixing and renewal, and accelerated bone loss. This thesis investigates how oscillation frequency and trabecular bone density jointly control nutrient mixing and wall shear stress within trabecular cavities.

A computational fluid dynamics (CFD) framework is developed in STAR-CCM+ using a soft-cap oscillation model that mimics cyclic compression. Three idealized trabecular morphologies are simulated across different frequencies to represent microgravity or …

Meshless Discrete Velocity Boltzmann Model For Porous Media Flow, Amandine Maidenberg

Doctoral Dissertations and Master's Theses

This dissertation explores the combination of two sophisticated techniques for addressing computational fluid dynamics: the discrete velocity Boltzmann equation (DVBE) and the localized collocation meshless model with upwinding (U-LCMM). The DVBE is a high-level model that describes the foundations of transport phenomena by addressing the microscale motions of particles themselves and the effect of their aggregate behaviors on continuum principles. This equation integrates multiple scales of phenomena; while it can be used for fluid flow at Navier-Stokes scales, it can also resolve fine features that can only be described at the molecular level. This type of model is necessary for …

Acoustic-Gravity Wave Propagation Based On Solutions To The Generalized Multi-Component Transport Equations, Benedict PiñEyro

Doctoral Dissertations and Master's Theses

Nonlinear atmospheric models have provided important insight into acoustic waves generated by natural and man-made hazards, which may steepen into shocks or N-waves while also dissipating when propagating in the thermosphere. Although models have yielded results that agree with observations of ionospheric perturbations, dynamical models for the diffusive and stratified lower thermosphere often use single gas approximations with height-dependent physical properties that omit the dynamics of the major and minor constituents. Thus, the inter-species diffusion associated with these flows (e.g. variations of mean molecular weight, and specific heat) are not accounted for. This approximation is simpler and less computationally expensive …

Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal

Doctoral Dissertations and Master's Theses

Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …

Investigation Of A Busemann Intake At Negative Angle Of Attack, Mark E. Noftz, Andrew N. Bustard, Nicholas J. Bisek, Thomas J. Juliano, Joseph S. Jewell

Publications

A high-speed, shape-transitioned, inward-turning intake was tested in Purdue’s Boeing/AFOSR Mach 6 Quiet Tunnel. The inlet model, called the Indiana Inlet (INlet), had a total contraction ratio of 4.68:1 and a design point of Mach 6 at 0° angle of attack. The model was outfitted with a suite of high-frequency pressure transducers, and the external flowfield was imaged with high-speed schlieren photography. The INlet was tested under low freestream disturbance levels for a variety of freestream unit Reynolds numbers and at-4° angle of attack. An unsteady shockwave near the leading edge of the inlet forebody, indicative of boundary layer separation, …

Development Of On-The-Fly Quasi-Steady State Approximation For Chemical Kinetics In Cfd, Abhinav Balamurugan

Doctoral Dissertations and Master's Theses

This study analyzes the feasibility of On-The-Fly Quasi-Steady-State Approximation (OTF-QSSA) application for solving chemical kinetics within Computational Fluid Dynamics (CFD) simulations, aiming to reduce the computational demand of detailed mechanisms. An algorithm that dynamically identifies and designates Quasi-Steady-State (QSS) species at specific grid locations and instances during the simulation was developed. With this information, our method pseudo-delays the advancement of concentrations for these QSS species—effectively setting their rate of concentration change to zero for a set number iteration before updating using the detailed mechanism and thereby omitting the computationally intensive processes typically required for their calculation during those skipped iteration. …

Dynamics Of A 3-D Inlet/Isolator Measured With Fast Pressure-Sensitive Paint, Andrew N. Bustard, Mark E. Noftz, Mitsugu Hasegawa, Hirotaka Sakaue, Joseph S. Jewell, Nicholas J. Bisek, Thomas J. Juliano

Publications

Fast pressure-sensitive paint (PSP) was applied to an inlet/isolator designed using the Osculating Internal Waverider Inlet with Parallel Streamlines (OIWPS) method. The dorsal isolator surface pressure was measured using anodized-aluminum PSP through transparent cast acrylic that makes up the ventral portion of the isolator. Temperature-sensitive paint was utilized to correct for the PSP’s temperature sensitivity. The model was tested under Mach 5.7 flow at Re = 8.5 ×106 /m and 10.2 ×106 /m in the AFOSR–Notre Dame Large Mach-6 Quiet Tunnel (ANDLM6QT) under conventional noise conditions. Flow phenomena, such as shocks originating in the inlet and flow separation at the …

Design Of An Internal Osculating Waverider Intake, Mark E. Noftz, Andrew J. Shuck, Joseph S. Jewell, Jonathan Poggie, Andrew N. Bustard, Thomas J. Juliano, Nicholas J. Bisek

Publications

The design of an inward-turning, high-speed, three-dimensional streamline traced intake is presented from osculating axisymmetric theory. To satisfy the osculating intake design criteria, a stitched Busemann diffuser and Internal Conical Flow-A solution is used as the basic isentropic compressive streamline. This new contour provides efficient compression, high flow uniformity, and straight leading edge shocks of equal strength. Additionally, a novel method for constructing the inlet cowl is presented. The combined process leads to a new method of high-speed intake design. A generic shape-transitioned intake is constructed and named the Indiana Inlet for the Indiana universities that contributed to the project. …

Hydrodynamics, Andrei Ludu

Publications

The mathematical description of the states of a fluid is based on the study of three fields defined on the domain occupied by the fluid: the velocity field V, the density ρ, and the pressure field P. These three “unknowns” are determined by integrating other five scalar equations, namely the mass conservation (continuity equation), the three components of the equation of momentum balance (Euler or Navier–Stokes), and the energy balance. This last equation needs in addition information about the thermodynamics of the fluid, so it may need to be supplied with some equation of state. In addition to these five …

Kinematics Of Fluids, Andrei Ludu

Publications

The goal of this chapter is to discuss the general frame of hydrodynamics, like particle trajectories (path lines), streamlines, streak lines, free surfaces, and fluid surfaces, and to compare their behavior in the Eulerian and Lagrangian frames. The following sections and chapters proceed on the assumption that the fluid is practically continuous and homogeneous in structure. Of course, the concept of continuum is an abstraction that does not take into account the molecular and nuclear structure of matter. In that, we assume that the properties of the fluid do not change if we consider smaller and smaller amounts of matter …

The Replacement Rule For Nonlinear Shallow Water Waves, A. Ludu, Z. Zong

Publications

When a (1 + 1)-dimensional nonlinear PDE in real function η(x, t) admits localized traveling solutions we can consider L to be the average width of the envelope, A the average value of the amplitude of the envelope, and V the group velocity of such a solution. The replacement rule (RR or nonlinear dispersion relation) procedure is able to provide a simple qualitative relation between these three parameters, without actually solve the equation. Examples are provided from KdV, C-H and BBM equations, but the procedure appears to be almost universally valid for such (1 + 1)-dimensional nonlinear PDE and their …

A Numerical Solution Of Water Flow In Unsaturated Soil With Evapotraspiration, Andrei Ludu, Harihar Khanal, Ramesh Chandra Timsina, Kedar Nath Uprety

Publications

Flow movement in unsaturated soil can be expressed by Richards equation. This equation can be obtained by applying the mass conversation law and the Darcy law. In this work, we solve one-dimensional Kirchhoff transformed Richards equation with loss of water due to the evaporation of unsaturated porous media (soils) and transpiration of plants numerically using Crank-Nicolson method. The result has compared with evapotranspiration function and without it in the governing equation. It has found that an additional work in time and flow movement is needs to reach the given boundary condition for the model without evapotranspiration.

Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields, Anu Kossery Jayaprakash, William Mackunis, Vladimir Golubev, Oksana Stalnov

Publications

A robust nonlinear control method is developed for fluid flow velocity tracking, which formally addresses the inherent challenges in practical implementation of closed-loop active flow control systems. A key challenge being addressed here is flow control design to compensate for model parameter variations that can arise from actuator perturbations. The control design is based on a detailed reduced-order model of the actuated flow dynamics, which is rigorously derived to incorporate the inherent time-varying uncertainty in the both the model parameters and the actuator dynamics. To the best of the authors’ knowledge, this is the first robust nonlinear closed-loop active flow …

Nonlinear Schrödinger Equation Solitons On Quantum Droplets, A. Ludu, A.S. Carstea

Publications

Irrotational flow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrödinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic functions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum, and parity for …

Experimental Study Of Breathers And Rogue Waves Generated By Random Waves Over Non-Uniform Bathymetry, A. Ludu, A. Wang, Z. Zong, L. Zou, Y. Pei

Publications

We present experimental evidence of formation and persistence of localized waves, breathers, and solitons, occurring in a random sea state and uniformly traveling over non-uniform bathymetry. Recent studies suggest connections between breather dynamics and irregular sea states and between extreme wave formation and breathers, random sea states, or non-uniform bathymetry individually. In this paper, we investigate the joint connection between these phenomena, and we found that breathers and deep-water solitons can persist in more complex environments. Three different sets of significant heights have been generated within a Joint North Sea Wave Observation Project wave spectrum, and the wave heights were …

Semi-Lagrangian Implicit Bhatnagar-Gross-Krook Collision Model For The Finite-Volume Discrete Boltzmann Method, Leitao Chen, Sauro Succi, Xiaofeng Cai, Laura Schaefer

Publications

In order to increase the accuracy of temporal solutions, reduce the computational cost of time marching, and improve the stability associated with collisions for the finite-volume discrete Boltzmann method, an advanced implicit Bhatnagar-Gross-Krook (BGK) collision model using a semi-Lagrangian approach is proposed in this paper. Unlike existing models, in which the implicit BGK collision is resolved either by a temporal extrapolation or by a variable transformation, the proposed model removes the implicitness by tracing the particle distribution functions (PDFs) back in time along their characteristic paths during the collision process. An interpolation scheme is needed to evaluate the PDFs at …

Studies Of Oval Tube And Fin Heat Exchangers, Phillip Nielsen

Discovery Day - Prescott

Heating Ventilation and air-conditioning (HVAC) is a system which changes the temperature of the surroundings for the purposes of cooling or heating. This system requires energy to maintain a temperature difference from the outside temperature. This is important since minimized power is one of the requirements for the system to achieve a better efficiency. Optimizing the flow over the evaporator coils is one way to increase the cooling efficiency. This will reduce the power required to have a sustainable system. Optimizing the flow to increase the energy transfer between the fins and the incoming air could result in a greater …

An Analysis Of The Atmospheric Propagation Of Underground-Explosion-Generated Infrasonic Waves Based On The Equations Of Fluid Dynamics: Ground Recordings, Roberto Sabatini, Jonathan B. Snively, Michael P. Hickey, J. L. Garrison

Publications

An investigation on the propagation of underground-explosion-generated infrasonic waves is carried out via numerical simulations of the equations of fluid dynamics. More specifically, the continuity, momentum, and energy conservation equations are solved along with the Herzfeld-Rice equations in order to take into account the effects of vibrational relaxation phenomena. The radiation of acoustic energy by the ground motion caused by underground explosions is initiated by enforcing the equality, at ground level, between the component of the air velocity normal to the Earth's surface and the normal velocity of the ground layer. The velocity of the ground layer is defined semi-empirically …

Ice Spiral Patterns On The Ocean Surface, Andrei Ludu, Zhi Zong

Publications

We investigate a new two-dimensional compressible Navier-Stokes hydrodynamic model design to explain and study large scale ice swirls formation at the surface of the ocean. The linearized model generates a basis of Bessel solutions from where various types of spiral patterns can be generated and their evolution and stability in time analyzed. By restricting the nonlinear system of equations to its quadratic terms we obtain swirl solutions emphasizing logarithmic spiral geometry. The resulting solutions are analyzed and validated using three mathematical approaches: one predicting the formation of patterns as Townes solitary modes, another approach mapping the nonlinear system into a …

Meshless Modeling Of Flow Dispersion And Progressive Piping In Poroelastic Levees, Anthony Khoury, Eduardo Divo, Alain J. Kassab, Sai Kakuturu, Lakshmi Reddi

Publications

Performance data on earth dams and levees continue to indicate that piping is one of the major causes of failure. Current criteria for prevention of piping in earth dams and levees have remained largely empirical. This paper aims at developing a mechanistic understanding of the conditions necessary to prevent piping and to enhance the likelihood of self-healing of cracks in levees subjected to hydrodynamic loading from astronomical and meteorological (including hurricane storm surge-induced) forces. Systematic experimental investigations are performed to evaluate erosion in finite-length cracks as a result of transient hydrodynamic loading. Here, a novel application of the localized collocation …

Floating Active Baffles, System And Method Of Slosh Damping Comprising The Same, Dae Won Kim, Rudy L. Baum, Vijay Santhanam, Balaji Sivasubramanian, Sathya Gangadharan

Publications

This disclosure provides a system for damping slosh of a liquid within a tank, a baffle for use in the system, and a method of damping slosh using the system. The system includes a plurality of baffles. Each baffle has a body configured to substantially float upon the liquid. Each baffle also has an activation material received along at least a portion of the body. The activation material is magnetically reactive provided in a quantity sufficient to enable the body to be manipulated in the presence of a magnetic field (M). The system further includes an actuator configured to pro­vide …

Patient-Specific Multiscale Computational Fluid Dynamics Assessment Of Embolization Rates In The Hybrid Norwood: Effects Of Size And Placement Of The Reverse Blalock–Taussig Shunt, Ray Prather, John Seligson, Marcus Ni, Eduardo Divo, Alain J. Kassab, William Decampli

Publications

The hybrid Norwood operation is performed to treat hypoplastic left heart syndrome. Distal arch obstruction may compromise flow to the brain. In a variant of this procedure, a synthetic graft (reverse Blalock–Taussig shunt) is placed between the pulmonary trunk and innominate artery to improve upper torso blood flow. Thrombi originating in the graft may embolize to the brain. In this study, we used computational fluid dynamics and particle tracking to investigate the patterns of particle embolization as a function of the anatomic position of the reverse Blalock–Taussig shunt. The degree of distal arch obstruction and position of particle origin influence …