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University of Central Florida

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Articles 91 - 120 of 213

Full-Text Articles in Aerospace Engineering

A Finite Difference Model For Induced Hypothermia During Shock, Dylan S. Lyon Jan 2021

A Finite Difference Model For Induced Hypothermia During Shock, Dylan S. Lyon

Honors Undergraduate Theses

The modified Fiala model from Westin was implemented with conditions for circulatory shock and hypothermia. The purpose is to model Emergency Preservation and Resuscitation (EPR), a procedure for inducing hypothermia in patients. Cold tissue temperatures reduce metabolism exponentially, greatly extending the window of anaerobic metabolic activity before permanent deoxygenation damage. EPR in patients undergoing hypovolemic shock can preserve the patient until primary surgical care and blood transfusions are attainable., thereby increasing survival rates. The main applications of EPR are military in-situ stabilization for transit to clinical care and extending the survivability of patients requiring prolonged surgery before blood transfusion. The …


Computational Studies For Extending Understanding Of Complex Droplet Breakup Mechanisms, Caroline Anderson Jan 2021

Computational Studies For Extending Understanding Of Complex Droplet Breakup Mechanisms, Caroline Anderson

Electronic Theses and Dissertations, 2020-2023

Conventional methods of classifying droplet breakup are evaluated in the context of unique variation in environmental and droplet fluid conditions. Most characterization is developed for subsonic speeds and Newtonian fluids, so this study extends understanding on how these forms change to a span of applications outside these conditions. Presented examples include the impact effects on hypersonic vehicles travelling through precipitation, where even smallest of rain drops at such speeds can cause damage. Before the droplet even reaches the vehicle, it interacts with the detached bow shock that leads it. Another example of exceptional recent concern is risk of viral transmission …


Experimental Study Of A Liquid Fuel Bluff Body Flame At Elevated Pressures, Karam Paul Jan 2021

Experimental Study Of A Liquid Fuel Bluff Body Flame At Elevated Pressures, Karam Paul

Honors Undergraduate Theses

The purpose of this research was to operate a bluff body flame holder with the objective of stabilizing a flame at elevated pressures over a range of equivalence ratios. The ability to have a ground-based test rig capable of maintaining stable flames at high pressures and temperatures is critical in understanding flames present in modern jet engines and gas turbine technologies. The facility was reconfigured multiple times and the resultant flame was imaged within the optical test section. A converging nozzle was utilized to choke the flow and vary the operating pressures up to 5 atm. By regulating mass flow …


Motor Control System For Near-Resonance High-Cycle Fatigue Testing, Samer K. Armaly Jan 2021

Motor Control System For Near-Resonance High-Cycle Fatigue Testing, Samer K. Armaly

Honors Undergraduate Theses

This research project develops a low-cost high-cycle fatigue (HCF) testing system comprised of an AC motor, variable frequency drive (VFD), eccentric cam, and feedback controller. The system acts as a forced harmonic oscillator leveraging mechanical resonance to vibrate a specimen at a frequency required to induce the testing's strain amplitudes.

This system depends highly on the material being tested. As such, the controller incorporates material characteristics. A frequency sweep measures the strain amplitude to characterize the specimen. Additionally, other measurements such as acceleration can be used as a proxy control variables for strain. A function converts the control variable to …


Optimization Of A Wing Supporting A Coaxial Rotor For Multiple Flight Conditions, Tadd Yeager Jan 2021

Optimization Of A Wing Supporting A Coaxial Rotor For Multiple Flight Conditions, Tadd Yeager

Electronic Theses and Dissertations, 2020-2023

Rotor-powered drones continue to grow in popularity in private and government sectors. The use of these drones in challenging environments and in high stakes applications calls for a certain level of robustness and redundancy. Often, these drones are equipped with sets of paired coaxial rotors, which not only improve the performance of the vehicle, but also ensure that a failure of one motor does not constitute the failure of the whole vehicle. Some applications such as extraterrestrial exploration, which use these coaxial rotors, can benefit from a wing shaped rotor arm to reduce drag and increase lift, extending mission lifetime. …


Development Of Multi-Scale Characterization Techniques For Stress Corrosion Cracking Of Aerospace Alloys, Nicholas Reed Jan 2021

Development Of Multi-Scale Characterization Techniques For Stress Corrosion Cracking Of Aerospace Alloys, Nicholas Reed

Electronic Theses and Dissertations, 2020-2023

Corrosion presents an inherent challenge in the safe and effective use of metallic aerospace structures for extended periods of time. Progress in the fundamental understanding of corrosion initiation and propagation under stress requires a multi-scale approach that leverages experiments to develop predictive models. Although there exists a large amount of research results tracking the corrosive processes of anodic dissolution and hydrogen embrittlement, the amount of available data and modeling of the micro-scale initiation of corrosion is sparse. This work leverages a suite of characterization techniques to systematically analyze an aerospace grade aluminum alloy AA7075-T6, providing important multi-scale data for correlation …


Bicycle Wheel Aerodynamics Predictions Using Cfd: Efficiency Using Blade Element Method, Drew Vigne Jan 2021

Bicycle Wheel Aerodynamics Predictions Using Cfd: Efficiency Using Blade Element Method, Drew Vigne

Honors Undergraduate Theses

The cycling industry has long relied on expensive wind tunnel testing when designing aerodynamic products, particularly in the context of wheels which account for 10 to 15 percent of a cyclist's total aerodynamic drag. With the recent advent of Computational Fluid Dynamics (CFD), the industry now has an economical tool to supplement the wheel design process; however, the complex nature of rotating spoked wheels requires high resolution meshes to model at acceptable fidelity. This research investigates an alternative CFD method that lowers the computational cost of modeling aerodynamic bicycle wheels by modeling spokes using Blade Element Method (BEM). Two CFD …


Development Of Lifting Line Theory For The Fanwing Propulsion System, Christopher Kaminski Jan 2021

Development Of Lifting Line Theory For The Fanwing Propulsion System, Christopher Kaminski

Honors Undergraduate Theses

The FanWing propulsion system is a novel propulsion system which aerodynamically behaves as a hybrid between a helicopter and a fixed wing aircraft, and if the knowledge base with regards to this novel concept can be fully explored, there could be a new class of aircraft developed. In the current research, only 2D CFD studies have been done for the FanWing, hence the 3D lift characteristics of the FanWing have been unknown thus far, at least in the theoretical domain. Therefore, it was proposed to develop a modified Prandtl's Lifting Line Theory numerical solution and a CFD solution, comparing the …


Solid Materia And Multiphase Detonations Wave Dynamics In A Rotating Detonation Engine, Ian Dunn Jan 2021

Solid Materia And Multiphase Detonations Wave Dynamics In A Rotating Detonation Engine, Ian Dunn

Electronic Theses and Dissertations, 2020-2023

Coal dust explosions can be hazardous; however, they can also generate a significant rise in stagnation pressure if adequately harnessed. Rotating detonation engine combustors seek to take advantage of the stagnation pressure rise phenomenon in a more sustained and controlled manner via confinement to a physical annulus, leading to increased overall thermodynamic efficiency. This investigation presents an analysis of detonations fueled by Carbon Black, a solid particulate consisting of virtually pure carbon molecules and lean Hydrogen-Air mixtures. As was previously realized with the addition of Carbon Black, an increase of operability limits and detonation velocities over that of a pure …


Numerical Modeling Of Shockwave Initiated Combustion Of A Hydrogen-Oxygen Mixture Within A Shock Tube, Reed Forehand Jan 2021

Numerical Modeling Of Shockwave Initiated Combustion Of A Hydrogen-Oxygen Mixture Within A Shock Tube, Reed Forehand

Electronic Theses and Dissertations, 2020-2023

Shock tubes are as close to an ideal reactor as most modern experiments can attain to examine chemical kinetics. As reaction temperatures drop, homogeneous combustion within a shock tube begins to exhibit inhomogeneous modes, which in a typical Hydrogen-Oxygen system are ex- pressed as deflagration to detonation transition. Experimental results of such a system in the Uni- versity of Central Florida's low-pressure shock tube have been collected through end and side-wall imaging to analyze flame structure and chemical kinetics. The purpose of this work is to con- duct a baselining of these results using both chemical and computational fluid dynamics …


Simulating Ejecta Blown Off The Lunar Surface Due To Landing Spacecraft Using The Mercury N-Body Integrator, Isabel Rivera Jan 2021

Simulating Ejecta Blown Off The Lunar Surface Due To Landing Spacecraft Using The Mercury N-Body Integrator, Isabel Rivera

Electronic Theses and Dissertations, 2020-2023

The experiences of the Apollo lunar landings revealed the danger lunar dust can pose to surrounding hardware, outposts, and orbiting spacecraft. Future lunar missions such as the Artemis program will require more information about the trajectories of ejecta blown by landers to protect orbiting spacecraft such as the Lunar Gateway. In this paper, we simulate lunar lander ejecta trajectories using the Mercury N-body integrator. We placed cones of test particles on the Moon at the North Pole, South Pole, and Equator with various ejection speeds and angles. The results show that particles ejected at speeds near the Moon's escape velocity …


Mimicking Blood Rheology For More Accurate Modeling In Benchtop Research, Lindsey Webb Aug 2020

Mimicking Blood Rheology For More Accurate Modeling In Benchtop Research, Lindsey Webb

The Pegasus Review: UCF Undergraduate Research Journal

Because blood is challenging to use as a working fluid in a laboratory setting due to health and safety concerns, a blood analogue would be useful to perform benchtop experiments. Viscosity is an important fluid property for modeling and experiments, especially because blood is a shear thinning fluid; therefore, it has a decreasing viscosity with higher shear rates. This project seeks to create a blood-mimicking fluid for benchtop laboratory use. Numerous fluids with different combinations of water, glycerin, salt, and xanthan gum (XG) were created to mimic blood viscosity at different hematocrit levels. Four additional solutions were also created from …


A Generalized Low Order Model For Vortex Shedding From A Tandem Cylinder Arrangement Using Delay Coupled Van Der Pol Oscillators, Michael Soroka Jan 2020

A Generalized Low Order Model For Vortex Shedding From A Tandem Cylinder Arrangement Using Delay Coupled Van Der Pol Oscillators, Michael Soroka

Honors Undergraduate Theses

A generalized low order model (LOM) for the fluctuating lift coefficient caused by vortex shedding from a tandem cylinder pair is proposed to expand upon models from previous authors. This model could provide a reduced computational time method for collecting qualitative and quantitive data from a tandem shedding pair. A delay coupled system with sufficient bifurcation characteristics is developed to account for the different flow regimes (extended-body, reattachment, and co-shedding) which occur as cylinder spacing is varied. Coefficient and parameter fitting is performed to fit experimental data. Finally, results and physical interpretations of the interactions in the model are discussed. …


Inertial Orbit Estimation Using Multiple Space Based Observers: A New Measurement Model, James Hippelheuser Jan 2020

Inertial Orbit Estimation Using Multiple Space Based Observers: A New Measurement Model, James Hippelheuser

Electronic Theses and Dissertations, 2020-2023

Presented within this work is a new method for inertial orbit estimation of an object, either known or unknown, adaptable to a network of low-cost observation satellites. The observation satellites would only require a monocular camera for line of sight measurements. Using the line of sight measurements of each observer, a pair of orthogonal geometric planes that intersect both the observation satellite and the target are created. The intersection of the two planes in the inertial frame defines the new measurement model that is implemented with multiple observation nodes. Total system observability is analyzed and the instantaneous (per node) observability …


Operability And Wave Characterization Of Hydrogen And Oxygen Fed Rotating Detonation Rocket Engine, Robert Burke Jan 2020

Operability And Wave Characterization Of Hydrogen And Oxygen Fed Rotating Detonation Rocket Engine, Robert Burke

Electronic Theses and Dissertations, 2020-2023

Recently, novel experimental evidence of continuous rotating detonations for gaseous H2/O2 propellants with a rotating detonation rocket engine (RDRE) was attained on the 3-inch Air Force Research Laboratory (AFRL) Distribution A RDRE, with the fuel and oxidizer injectors modified for H2/O2 gas propellants. Evident in previous experiments, detonation instabilities arising from upstream deflagration, from recirculation zones, and from insufficient gas mixing challenged resolution of detonation wave behavior from back-end imaging with the available optical equipment. Images were often over-illuminated from both the high amount of deflagration in the plume and the higher density of detonation waves in the annulus coupled …


Piezospectroscopic Sensing Systems - Multi-Scale And In-Situ Sensing Technology For Structural Integrity, Remelisa Esteves Jan 2020

Piezospectroscopic Sensing Systems - Multi-Scale And In-Situ Sensing Technology For Structural Integrity, Remelisa Esteves

Electronic Theses and Dissertations, 2020-2023

The aerospace industry relies on nondestructive evaluation (NDE) to ensure aircraft safety and will benefit from methods that allow for early damage detection. Photoluminescence piezospectroscopy (PS) has demonstrated stress and damage sensing of substrates when coupled with alpha-alumina nanoparticles in a polymer matrix applied as a sensor coating. Alpha phase alumina exhibits photoluminescent spectral emission lines (R-lines) that shift due to changes in the stress state of the alumina. The coatings' capability for sensing early subsurface damage suggests the potential for implementing stress sensing paint for integrity monitoring of aircraft structures. To achieve a viable stress sensing coating that can …


Dynamic Modeling And Simulation Of A Power Plant Steam Condenser On The Siemens Sppa-T3000 Platform, Mohammad Odeh Jan 2020

Dynamic Modeling And Simulation Of A Power Plant Steam Condenser On The Siemens Sppa-T3000 Platform, Mohammad Odeh

Electronic Theses and Dissertations, 2020-2023

With rapidly increasing computational power, modeling and simulation of complex systems is gradually becoming the norm for evaluating and predicting performance. This research focuses on modeling and simulating thermodynamic behavior of condensers within Combined Cycle Power Plants. This is particularly useful for power generation companies as this allows a wide range of operating conditions to be simulated and characterized without risking damage or the need to shut down the power plant, all of which results in losing revenue in the process. Moreover, being able to observe the thermodynamic evolution of the system provides useful insight into efficiency and response to …


A Study Into Validating A Coupled Method Of Characteristics And Direct Simulation Monte Carlo Method Against Empirical Data, Andrew Brown Jan 2020

A Study Into Validating A Coupled Method Of Characteristics And Direct Simulation Monte Carlo Method Against Empirical Data, Andrew Brown

Electronic Theses and Dissertations, 2020-2023

The following will outline the methodology and results of validating a coupled Method of Characteristics (MOC) and Direct Simulation Monte Carlo (DSMC) method. This research focused specifically on modeling plume impingement, induced by Reaction Control System (RCS) thrusters that flew on the National Aeronautics and Space Administration's (NASA's) space shuttle Discovery. For each simulation, the continuum portion of the RCS thruster was simulated using MOC for solving hyperbolic Partial Differential Equations (PDEs) and computed with the NASA code, Reacting and Multi-phase Program (RAMP). The solution was then implemented as a starting condition into the NASA DSMC code, Direct Simulation and …


Thermal-Hydraulic Optimization Of The Heat Exchange Between A Molten Salt Small Modular Reactor And A Super-Critical Carbon Dioxide Power Cycle, James Sherwood Jan 2020

Thermal-Hydraulic Optimization Of The Heat Exchange Between A Molten Salt Small Modular Reactor And A Super-Critical Carbon Dioxide Power Cycle, James Sherwood

Honors Undergraduate Theses

The next generation of nuclear power sources, Gen. IV, will include an emphasis on small, modular reactor (SMR) designs, which will allow for standardized, factory-based manufacturing and flexibility in the design of power plants by utilizing one or several modular reactor units in parallel. One of the reactor concepts being investigated is the Molten Salt Reactor concept (MSR), which utilizes a molten salt flow loop to cool the reactor and transfer heat to the power conversion cycle (PCS).Here, the use of a supercritical carbon dioxide (S-CO2) Brayton cycle is assumed for that PCS. The purpose of this thesis is to …


Design And Visual Servo Control Of A Mechanical Gripper For Autonomous Strawberry Harvesting, Jonah Mapes Jan 2020

Design And Visual Servo Control Of A Mechanical Gripper For Autonomous Strawberry Harvesting, Jonah Mapes

Electronic Theses and Dissertations, 2020-2023

With rising labor costs and high consumer demand, economic conditions are becoming increasingly favorable for mechanization in the strawberry industry. However, virtually all strawberry crops are still picked by hand because the harvesting process is very challenging to automate, and strawberries are susceptible to bruising. For these reasons, the development of a harvester which can avoid damaging the fruit is of interest. Conventional designs for robotic grippers are less than ideal, as precise positioning or force feedback capabilities are required to reduce the risk of bruising. As an alternative, a novel "camera-in-hand" gripper design is presented which effectively avoids bruising …


Mechanical Properties Of Boron Carbide (B4c), Ruslan Kuliiev Jan 2020

Mechanical Properties Of Boron Carbide (B4c), Ruslan Kuliiev

Electronic Theses and Dissertations, 2020-2023

Boron carbide (B4C) is one of the most important opaque boride ceramics that has high hardness and Young's modulus that along with low density lead to a significant resistance to ballistic impact and, thus, B4C is broadly used as a protective material. B4C has also high neutron capturing cross section; therefore, it is used as control rods and neutron absorption shielding in nuclear reactors. In this work thermal, electrical and mechanical properties of dense B4C ceramics (99%) sintered using Spark Plasma Sintering (SPS) were investigated. The Young's modulus of B4C measured by three different techniques – IE, RUS, and nanoindentation …


Experimentation And Simulation Of Pulsed Eddy Current Thermography Of Subsurface Aircraft Corrosive Defects, Johnathan Hernandez Jan 2020

Experimentation And Simulation Of Pulsed Eddy Current Thermography Of Subsurface Aircraft Corrosive Defects, Johnathan Hernandez

Electronic Theses and Dissertations, 2020-2023

During the life cycle of aircraft, external structures are under constant attack from environmental degradation in the form of corrosion. Corrosive defects consist of multiple types of surface and subsurface damage that are often undetectable due to surface coatings or insulation leading to loss in structural integrity. Non-destructive techniques for corrosion detection typically require the removal of paint. Detection of corrosion under insulation (CUI) is highly valuable for cost and time effectiveness. Although techniques have been developed for detection of CUI, not many of these satisfy the criteria for portability and hangar operation. To address this, multiple techniques were investigated …


Ensuring Positive Definiteness In Linear Viscoelastic Material Functions Based On Prony Series, Christopher D. Rehberg Jan 2020

Ensuring Positive Definiteness In Linear Viscoelastic Material Functions Based On Prony Series, Christopher D. Rehberg

Honors Undergraduate Theses

This thesis presents a method to correct for non-positive-definiteness in linear viscoelastic material functions. Viscoelastic material functions for anisotropic materials need to be interconverted in a matrix coefficient prony series form, with a requirement of positive definiteness. Fitting is usually done as a uniaxial prony series, resulting in scalar coefficients. When these uniaxial coefficients are placed in a coefficient matrix, the required positive definiteness cannot be guaranteed. For those matrices that do not meet this requirement, finding the nearest symmetric semi-positive definite form of the matrix results in a viable prony series matrix coefficient with the required positive definiteness. These …


Degradation From Cmas Infiltration In 7ysz Eb-Pvd Thermal Barrier Coatings, Zachary Stein Jan 2020

Degradation From Cmas Infiltration In 7ysz Eb-Pvd Thermal Barrier Coatings, Zachary Stein

Honors Undergraduate Theses

The lifetime of the high temperature ceramic coating 7 wt.% yttria-stabilized zirconia (7YSZ) is reduced when calcium-magnesium-alumino-silicate (CMAS) particulates enters aero-engines during operation in a sandy or dusty environment, melts, and infiltrates into the coating. 7YSZ undergo both chemical and mechanical degradation from CMAS infiltration during cycling. Characterization methods with synchrotron X-ray diffraction (XRD) provides a non-destructive means to measure the impact of time and temperature on coating degradation with high spatial resolution of 7YSZ coatings infiltrated and annealed by CMAS for 1 hour and 10 hours as well as at 1225 °C and 1250 °C. Additionally, qualitative results of …


Development Of A Computationally Inexpensive Method Of Simulating Primary Droplet Breakup, Brendon A. Cavainolo Jan 2020

Development Of A Computationally Inexpensive Method Of Simulating Primary Droplet Breakup, Brendon A. Cavainolo

Honors Undergraduate Theses

Liquid droplet impingement on aircraft can be problematic as it leads to ice accretion. There have been many incidents of aircraft disasters involving ice accretion, such as American Eagle Flight 4184. Understanding liquid droplet impingement is critical in designing aircraft that can mitigate the damages caused by icing. However, the FAA's regulations are only specified for "Appendix C" droplets; thus, aircraft designs may not be safe when accounting for droplets such as Supercooled Large Droplets. The assumptions of many models, such as the Taylor-Analogy Breakup (TAB) model, are no longer accurate for Supercooled Large Droplets, and the physics of those …


Viscoelastic Analysis Of High Strain Composites For Deployable Structures In Space Applications, Andrew Gomez-Delrio Jan 2020

Viscoelastic Analysis Of High Strain Composites For Deployable Structures In Space Applications, Andrew Gomez-Delrio

Electronic Theses and Dissertations, 2020-2023

Thin-ply composite laminates capable of enduring high strains are currently under investigation for compliant deployable spacecraft structures. Deployable structures such as booms fabricated from these materials can be flattened and coiled to high curvatures, achieving a compact configuration for stowage. Once in orbit, they are released with minimal actuation for deployment, allowing the operational geometry to be recovered. Previous studies have shown that the viscoelastic properties of the composite epoxy matrix can negatively impact final shape accuracy due to stress relaxation during stowage. In addition, since the strain energy stored is relied upon for deployment, considerable relaxation can potentially result …


Evaluation Of Convective Heat Transfer Numerical Methods On Rough Surfaces From Additive Manufacturing, Jose Urcia Jan 2020

Evaluation Of Convective Heat Transfer Numerical Methods On Rough Surfaces From Additive Manufacturing, Jose Urcia

Electronic Theses and Dissertations, 2020-2023

The high versatility of additive manufacturing has led to an increase in use in a number of different fields. Surface roughness then comes as a natural consequence of additive manufacturing which interferes with a smooth wall assumption such as those found in gas turbine blades. The Discrete Element Roughness Method (DERM) has been used to improve convective heat transfer predictions on surface roughness. This work aims to validate the core momentum and heat transfer correlation of DERM through an evaluation of Computational fluid dynamics (CFD)-based solution of the flow around individual roughness elements with the goal of improving the correlations. …


Rapid Orbital Motion Emulator (Rome): Kinematics Modeling And Control, Ahmed Elsadek Ahmed Seleit Jan 2020

Rapid Orbital Motion Emulator (Rome): Kinematics Modeling And Control, Ahmed Elsadek Ahmed Seleit

Electronic Theses and Dissertations, 2020-2023

Space missions design requires already tested and trusted control algorithms for spacecraft motion. Rapidly testing control algorithms at a low cost is essential. A novel robotic system that emulates orbital motion in a laboratory environment is presented. The system is composed of a six degree of freedom robotic manipulator fixed on top of an omnidirectional ground vehicle accompanied with onboard computer and sensors. The integrated mobile manipulator is used as a testbed to emulate and realize orbital motion and control algorithms. The kinematic relations of the ground vehicle, robotic manipulator and the coupled kinematics are derived. The system is used …


Efforts In Numerical Modeling Of Undulating Propulsion, George Loubimov Jan 2020

Efforts In Numerical Modeling Of Undulating Propulsion, George Loubimov

Electronic Theses and Dissertations, 2020-2023

Naval propulsion is a critical component for every vessel, and it is the subject of this thesis, specifically bio-inspired propulsion. Numerical modeling is used as a tool to understand the relationship between mechanical undulation and the hydrodynamic response. Through three stages, the research presented here examines and refines tools for understanding fundamentals of undulating propulsion. Those three objectives are: to verify and validate the proposed numerical models against existing experiments, establishing a baseline of fidelity; to examine the causal linkage between fluid-boundary interactions and undulating propulsion; and to create a moment based method for characterizing generalized undulating propulsive mechanisms. First, …


Study Of Non-Ideal Effects On Shock Wave Propagation, Cory Kinney Jan 2020

Study Of Non-Ideal Effects On Shock Wave Propagation, Cory Kinney

Electronic Theses and Dissertations, 2020-2023

Shock tube experiments provide insightful data on combustion, emissions, and ablation characterization for a wide variety of defense and energy sector research topics. Accurate characterization of shock tube facilities is essential to verifying the accuracy of research data. Non-ideal effects, such as boundary layer growth, introduce uncertainty into pressure and temperature conditions, the primary independent variables of interest for shock tube research results. The effect of boundary layer growth on shock tube experiments was investigated by conducting simulations for University of Central Florida's two geometrically different shock tube using StanShock, a quasi-one-dimensional, reacting, compressible flow solver. The characteristic quantities considered …