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Aerodynamics and Fluid Mechanics

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Articles 121 - 150 of 1219

Full-Text Articles in Aerospace Engineering

Numerical Investigation Of Wind Disturbance Around A Multirotor Uav In Crosswind And Vertical Flight, Garrison Page Jan 2025

Numerical Investigation Of Wind Disturbance Around A Multirotor Uav In Crosswind And Vertical Flight, Garrison Page

Theses and Dissertations--Mechanical and Aerospace Engineering

Uncrewed Aerial Vehicles (UAVs) are being increasingly utilized in a wide range of research applications, especially in meteorology. This is due to such factors as their ease of use, maneuverability compared to other forms of data collection, and for rotor- craft, the ability to hover. However, the rotorwash generated by UAVs can introduce significant disturbances, potentially affecting measurement accuracy from sensors. While several studies have investigated the rotorwash of individual UAVs utilizing Particle Image Velocimetry (PIV) and Computational Fluid Dynamics (CFD), there is limited exploration into how different rotor configurations and external wind conditions influence regions of turbulent flow around …


Development Of An Immersed Boundary Method-Wall Modeled Large Eddy Simulation Approach For Incompressible Flows And Aeroacoustic Predictions, John C. Higgins Jan 2025

Development Of An Immersed Boundary Method-Wall Modeled Large Eddy Simulation Approach For Incompressible Flows And Aeroacoustic Predictions, John C. Higgins

Theses and Dissertations--Mechanical and Aerospace Engineering

The performance capabilities of rotorcraft have improved significantly in the past decade as both manned and unmanned rotorcraft become a larger part of future transportation systems. Private companies as well as various government offices have worked to develop capabilities ranging from transportation/package delivery to intelligence/surveillance to livestock monitoring. Their practicality in both rural and urban areas, however, is questionable due to the significant tonal and broadband noise which is produced by the rotors. Public acceptance of rotorcraft, namely small Unmanned Aerial Vehicles (sUAVs), in transportation systems is an issue largely associated with the noise generation and it's effect on nearby …


Direct Numerical Simulation Of Pulsating Flow In Curved Pipes: Insights Into Aortic Dissection In Humans, Gokul Anugrah Gopakumar Jan 2025

Direct Numerical Simulation Of Pulsating Flow In Curved Pipes: Insights Into Aortic Dissection In Humans, Gokul Anugrah Gopakumar

Theses and Dissertations--Mechanical and Aerospace Engineering

This dissertation investigates the hemodynamics of pulsating blood flow in curved vessels through direct numerical simulations (DNS), with the overarching aim of uncovering fluid dynamic mechanisms linked to the onset and progression of aortic dissection in humans. The work is structured in two parts: (i) fundamental studies in idealized geometries and (ii) preliminary investigations in patient-specific anatomies. In the first part, curved pipe models representing the aortic arch are used to isolate the effects of pulsation frequency, amplitude ratio, and curvature ratio on transitional and turbulent flow dynamics. The simulations reveal that curvature-driven centrifugal forces shift the peak velocity toward …


High-Altitude Balloon-Launched Uncrewed Aircraft System Measurements Of Atmospheric Turbulence And Qualitative Comparison With Infrasound Microphone Response, Anisa Haghighi Jan 2025

High-Altitude Balloon-Launched Uncrewed Aircraft System Measurements Of Atmospheric Turbulence And Qualitative Comparison With Infrasound Microphone Response, Anisa Haghighi

Theses and Dissertations--Mechanical and Aerospace Engineering

This study explores the use of a balloon-launched uncrewed aircraft system (UAS) to measure atmospheric turbulence in the troposphere and lower stratosphere using both wind velocity measurements and infrasonic acoustic energy. The UAS, a glider configured for autonomous descent along a predefined trajectory, had on board, in situ sensors to capture thermodynamic and kinematic atmospheric parameters. Additionally, it carried an infrasonic microphone to evaluate its potential for remotely detecting clear-air turbulence by capturing infrasonic waves. The system’s performance was assessed over the course of three test flights conducted in New Mexico, USA, in 2021. The descent enabled high-resolution profiling, with …


Kentucky Re-Entry Universal Payload System (Krups): Second Atmospheric Re-Entry Flight, Kirsten F. Ford Jan 2025

Kentucky Re-Entry Universal Payload System (Krups): Second Atmospheric Re-Entry Flight, Kirsten F. Ford

Theses and Dissertations--Mechanical and Aerospace Engineering

Kentucky Re-entry Universal Payload System (KRUPS) is a small-scale re-entry capsule developed at the University of Kentucky. The KRUPS project began in 2013 with the aspiration of providing an affordable and repeatable method of collecting data on the re-entry environment. Numerically-based methods used to model re-entry require experimental data to validate their predictions. However, re-entry data is not easily obtained. Flight tests of re-entry vehicles require extensive time and resources, including a substantial financial burden. Alternatively, ground testing is not able to accurately and completely replicate the complex re-entry environment. Thus, there is a need for an inexpensive and accessible …


Damping Modulation Of Dampened Kapton Surfaces, Sebastian Esteban Jan 2025

Damping Modulation Of Dampened Kapton Surfaces, Sebastian Esteban

Honors Undergraduate Theses

When droplets are vibrated or disturbed, they can exhibit a complex sloshing motion, an understudied behavior in drop physics. Droplet sloshing involves a complex combination of transverse and longitudinal motion that changes the droplet's effective weight on the surface the droplet is on. Our current understanding stems from preliminary work focusing on a cantilever beam of fixed thickness and variable viscosity of the liquid being sloshed. This investigation will focus on how variable cantilever thickness and constant viscosity for a liquid being sloshed affects the beam's deflection under consistent vibration. It will also investigate how the natural frequency of a …


The Aerodynamics Of Bird Perching: Understanding Wing And Body Interactions In Pigeon Flight, Anirudh Sriram Jan 2025

The Aerodynamics Of Bird Perching: Understanding Wing And Body Interactions In Pigeon Flight, Anirudh Sriram

Honors Undergraduate Theses

During landing, birds often execute a perching maneuver. The perching maneuver refers to the complex series of actions that birds, and pigeons in particular, will perform when landing. They will typically decelerate by pitching their body to a high angle of attack and spreading their wings. It is believed to help achieve better control and reach optimal lift and drag coefficients. This study seeks to better understand the vortex interactions between the main and tail wings during this maneuver. However, it is still an unexplored phenomenon. Thus, two bird models were conceived to analyze it, one with and one without …


Utilizing Pneumatic Artificial Muscles To Simulate Wingbeat Kinematics For Morphing Uav Wings, Vireli S. Anbarasu Jan 2025

Utilizing Pneumatic Artificial Muscles To Simulate Wingbeat Kinematics For Morphing Uav Wings, Vireli S. Anbarasu

Honors Undergraduate Theses

The controlling muscles of a bird wing change stiffness and length to provide high efficiency when executing a flight maneuver. This variable stiffness allows the muscles to cycle between increasing energy, transmitting it, and restoring it, allowing an overall increase in mechanical and aerodynamic efficiency. Inspired by this, we have developed a system that uses pneumatic artificial muscles (PAMs) to actuate a morphing wing. The stiffness in the PAMS can be controlled to mimic the changes bird flight muscles undergo when executing a forward flapping maneuver. We will evaluate the performance of the PAMs in actuating a morphing wing through …


Drag Reduction In Ground Vehicles Using A Model Porous Medium, Abdullah Ikram Nabi Jan 2025

Drag Reduction In Ground Vehicles Using A Model Porous Medium, Abdullah Ikram Nabi

Master’s Theses

This research investigates aerodynamic drag reduction on a 25° Slanted Ahmed Body (SAB) by integrating porous media model rods through combined experimental and computational methods at a Reynolds number of 1.16×10⁴. Two porous media configurations: short rods (6.75% of the model height) and long rods (20.0% of the model height), both featuring cylindrical rods with 80% porosity, were systematically compared against a baseline SAB. In-depth analyses were performed to investigate the wake flow topology, recirculation region characteristics, pressure coefficient distribution, Reynolds stress distributions and drag coefficient. Experimental investigations employed particle image velocimetry for precise flow visualization, while Reynold Averaged Navier-Stokes …


Influence Of Actuated Air Brakes On The Apogee Of Sub-Orbital Rockets, Michael L. Farha Jan 2025

Influence Of Actuated Air Brakes On The Apogee Of Sub-Orbital Rockets, Michael L. Farha

Graduate Theses, Dissertations, and Problem Reports (ETD)

Collegiate engineering competitions have played a foundational role in the educational outcomes of university students for as long as they have existed. Among these competitions is the Spaceport America Cup, which challenges students to design, build, and launch high-power rockets with the incentive to fly as close as possible to a pre-established target apogee. Many teams competing in this competition have chosen to approach the challenge by incorporating deployable air brakes into their rocket designs. This approach comes with many uncertainties, both in controls and aerodynamics. For teams just starting out, aerodynamic performance is often one of the most challenging …


Qualitative Analysis Of Surface Modification On Wiffleball Aerodynamics, Cole Lanni Jan 2025

Qualitative Analysis Of Surface Modification On Wiffleball Aerodynamics, Cole Lanni

Williams Honors College, Honors Research Projects

This project investigated how surface modifications to a Wiffleball affect its aerodynamic behavior, particularly its vertical and horizontal movement when thrown. The study tested the hypothesis that altering surface texture through cutting or sanding would influence airflow and pressure differentials, thereby changing the ball's movement. Six ball conditions: including unmodified, sanded, and various cut patterns were tested using a pitching machine in a controlled indoor environment. Each variation was pitched ten times, and movement was analyzed through measurements of contact points on posterboards and performing statistical testing, specifically ANOVA with Post Hoc analysis. Results indicated that surface modifications significantly increased …


Design Of An Active-Control Pressure Regulator For A Rocket, Seth Arkwright Jan 2025

Design Of An Active-Control Pressure Regulator For A Rocket, Seth Arkwright

Williams Honors College, Honors Research Projects

An electronically actuated pressure-regulation valve and controller are necessary for maintaining pressure levels in a pressure-fed liquid-fueled rocket engine. Mechanical regulators are too heavy and have unacceptably high-pressure variation throughout the operation of a dynamic system like a rocket. Developing an electronic pressure regulator using a PID controller is a method by which a reliable, accurate, and lightweight flow regulator can be built for use on a rocket vehicle. This work will outline the development of flow simulations, PID controller, physical valve hardware, and initial testing.


Review: Dielectric Barrier Discharge Plasma Actuators For In-Flight Applications, Sabeel Saleem Mohammed Jan 2025

Review: Dielectric Barrier Discharge Plasma Actuators For In-Flight Applications, Sabeel Saleem Mohammed

Anthós

Dielectric barrier discharge (DBD) is a phenomenon observed when high voltage is passed through a dielectric barrier at high frequencies. Current DBD plasma actuators (PAs) excel at laminar fluid boundary layer control but suffer from limited momentum flux and fluid mechanic inefficiencies. In this article, Mohammed analyzes previous discourse on DBD PAs and offers directions for future research and potential DBD PA applications. Previous work on DBD PAs documented thrust generation at high voltages and frequencies, thrust in varying fluid compositions, and vortex generation. However, certain arrangements hinder flow magnitudes, limiting the use of multiple DBD PAs in close proximity. …


Bio-Inspired Airfoil Design Based On The Aerodynamic Analysis Of A Bird Feather Microstructure, Jack C. Ihm Jan 2025

Bio-Inspired Airfoil Design Based On The Aerodynamic Analysis Of A Bird Feather Microstructure, Jack C. Ihm

College of Graduate Studies: Theses & Dissertations

This study investigates the aerodynamic effects of a bio-inspired airfoil design based on the microstructure of a secondary feather from a female wood duck. The research hypothesized that incorporating barbs and barbules into an airfoil design would modify boundary layer behavior by introducing localized flow disturbances. To test this, a bio-inspired airfoil was developed by integrating the microstructure into a NACA 0012 airfoil and analyzed using computational fluid dynamics (CFD) simulations at angles of attack of 0°, 5°, 10°, and 15°. The results showed that the bio-inspired airfoil influenced boundary layer behavior, producing localized flow disturbances near x/c = 0.7 …


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 Jan 2025

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, …


Physics-Informed Neural Network Based Aerodynamic Modeling Framework, Nathaniel E. Michek Jan 2025

Physics-Informed Neural Network Based Aerodynamic Modeling Framework, Nathaniel E. Michek

Graduate Theses, Dissertations, and Problem Reports (ETD)

Significant advances have been made in developing aerodynamic models over the years. While these advances span many modeling techniques and data collection methods, certain aerodynamic regimes still pose significant challenges. These regimes commonly occur when an aerodynamic body is under extreme flight conditions. Many of these conditions occur simultaneously in the rare and poorly understood case of a tumbling aerodynamic body. The flight of a tumbling aerodynamic body goes through the entire range of aerodynamic angles, alpha and beta, causing significant non-linearities and time-dependent effects associated with flow separation. During tumbling, the aerodynamic body simultaneously rotates about all three axes …


Hybrid Rans-Les Analysis Of Turbulent Flame Under Near Blow-Off Condition In A Multi-Stage Swirl Combustor, Brandon O'Brien Jan 2025

Hybrid Rans-Les Analysis Of Turbulent Flame Under Near Blow-Off Condition In A Multi-Stage Swirl Combustor, Brandon O'Brien

College of Graduate Studies: Theses & Dissertations

Advances in computational resources are making computational fluid dynamics (CFD) increasingly accessible for a variety of engineering applications. However, certain complex problems, such as simulating detailed flame kinetics, remain computationally prohibitive for many users. Developing cost-effective methods to simulate these challenges would greatly benefit applications involving flame dynamics, such as turbine engines or industrial burners. This study investigates the effect of main stage swirler intensity on near lean blow-off characteristics in a multi-staged swirl combustor using Ansys Fluent. The hybrid RANS-LES turbulence model, Stress Blended Eddy Simulation (SBES) coupled with Flamelet Generated Manifold (FGM) combustion model was selected to model …


Development Of An Quadcopter Unmanned Aerial Vehicle For Atmospheric Remote Sensing, Omar J. Addasi Jan 2025

Development Of An Quadcopter Unmanned Aerial Vehicle For Atmospheric Remote Sensing, Omar J. Addasi

Dissertations and Theses

This paper explores the development of a quadcopter unmanned aerial vehicle (UAV, a.k.a. drone) for atmospheric remote sensing of temperature, pressure, humidity, and PM2.5 particulate matter quantities. A 3-D printed drone body is designed and flight tuning is performed. An optimal length for an upward extending mast for the drone body is determined. Low cost, lightweight sensors are compared against higher precision sensors in both static and dynamic conditions. In addition, an initial investigation into the design of a pressure sensor based anemometer is performed.


Effects Of Changes In Strouhal And Reynolds Numbers On Beetle Wing Aerodynamics, Keith L. Thiha Jan 2025

Effects Of Changes In Strouhal And Reynolds Numbers On Beetle Wing Aerodynamics, Keith L. Thiha

Honors Undergraduate Theses

Insect flight has long been a subject of interest across the scientific community, largely due to the exceptional aerodynamic performance insects demonstrate relative to their size. Insects tend to have very high aerodynamic performance characteristics like thrust and lift generation compared to their size. This has many potential applications in improving aircraft performance, however the flow phenomena concerning insect wing aerodynamics is still an area of ongoing research. This study aims to investigate how variations in key nondimensional flow parameters—specifically the Reynolds number and Strouhal number—affect the aerodynamic performance of beetle wings. Strouhal numbers ranging from 0.2 to 0.6 were …


Heat Transfer In Tightly Packed Cylinder Arrays, Martin Kovachev Dec 2024

Heat Transfer In Tightly Packed Cylinder Arrays, Martin Kovachev

Doctoral Dissertations and Master's Theses

Cylindrical arrays with a cross flow are commonly used for heat transfer augmentation within an internal channel. In most applications, the cylinders have a spacing of over 2 diameters (2D) between their center points in both the lateral and downstream directions. One option for battery thermal management in hybrid/electric aviation is to use cylindrical batteries packed in arrays with an applied cross flow. In the context of aviation, it is important to maximize space and weight savings. Tightly packing these cylinder arrays with a spacing of under 2D in both directions would save on both of these yet have not …


The Integration And Validation Of A Class 3b Laser For Stereo Particle Imaging Velocimetry, Jensen Lam Dec 2024

The Integration And Validation Of A Class 3b Laser For Stereo Particle Imaging Velocimetry, Jensen Lam

Master's Theses

Particle Imaging Velocimetry (PIV) is a laser flow diagnostic measurement technique used to measure spatial and temporal velocity fields. In an effort to promote experimental aerodynamic research, specifically an entry point for students to learn Particle Imaging Velocimetry, an in-house Class 3B laser PIV system was developed and its experimental results were verified with a Class 4 laser. Both systems were integrated on the Cal Poly Water Tunnel Laboratory. The work emphasizes the application of lasers controlled by a micro-controller to perform microsecond-based pulses and integrating a newly-developed device with an old system consisting of software, cameras, and synchronizers. The …


Equivalent-Area Studies For Sonic Boom Loudness Mitigation On A Commercial Supersonic Aircraft Configuration, Zachary N. Foster Dec 2024

Equivalent-Area Studies For Sonic Boom Loudness Mitigation On A Commercial Supersonic Aircraft Configuration, Zachary N. Foster

All Graduate Reports and Creative Projects, Fall 2023 to Present

Since the early 1970s, the FAA has banned commercial supersonic flight over populated areas. This ban has limited aerospace manufacturers’ and commercial aircraft companies’ ability to design and operate subsonic aircraft in their fleets. Since then, research has been conducted to understand the sonic boom and learn how to minimize its loudness. The work presented in this project report aims to use a 1D low-fidelity analysis to study the effect of perturbations to the outer mold line (OML) of a representative model of the N+2 Quiet Commercial Supersonic Concept Aircraft. Using a 1D analysis that employs an equivalent area method, …


Impact Of Weather Systems On Uav Parameters Using Computational Fluid Dynamics, Saif Aljuhaishi, Yaseen K. Al-Timimi, Basim I. Wahab Nov 2024

Impact Of Weather Systems On Uav Parameters Using Computational Fluid Dynamics, Saif Aljuhaishi, Yaseen K. Al-Timimi, Basim I. Wahab

Karbala International Journal of Modern Science

Since drones cannot fly in any kind of weather, they are not safe for time-sensitive activities. The study examines how the passage of weather systems in Iraq leads to the ban on drone flights, and how these weather conditions impact the aerodynamic forces of the drone. Hourly climate data for the study area were obtained from ECMWF ERA5 and CAMS in NetCDF format for four climate stations (Erbil, Baghdad, Rutbah, and Basrah). A ScanEagle drone was chosen for this study. The Python programming language was used to perform mathematical operations to calculate the ban on drone flights. ArcGIS 10.8 was …


Spacecraft Attitude Control Simulator, Bricen S. Rigby Oct 2024

Spacecraft Attitude Control Simulator, Bricen S. Rigby

College of Engineering Summer Undergraduate Research Program

The Spacecraft Attitude Control Simulator is a single-axis attitude control platform which is intended to recreate the frictionless space environment in order to test cold-gas thruster control schemes. The overall goal of this research project was to observe settling data from the platform and compare it to simulated data. In practice, the predicted settling time was only 7% larger than observed settling time.


Dynamic Estimation Of Large-Scale Flow Events In Open Cavity Flows, Alexandre Mota Oct 2024

Dynamic Estimation Of Large-Scale Flow Events In Open Cavity Flows, Alexandre Mota

Doctoral Dissertations and Master's Theses

Flow over an open cavity has a dynamically complex flowfield, generating pressure fluctuations that can amplify shear stress and cause structural damage to the stores within it and the aircraft as a whole. These pressure loads are linked to large-scale resonant shear layer phenomena. Consequently, it is crucial to establish this link by characterizing the large-scale flow events conditional upon pressure measurements to improve the prediction and control of the detrimental pressure fluctuations. In this study, a link between the pressure measurements (to control) and large-scale shear layer events (to actuate) will be established using a combination of two data-driven …


Computer Based Modeling For Small E-Vtol Propeller Performance, Ege Konuk Oct 2024

Computer Based Modeling For Small E-Vtol Propeller Performance, Ege Konuk

Mechanical & Aerospace Engineering Theses & Dissertations

The emerging field of urban air mobility (UAM) offers a novel transportation method for civil, commercial, and military applications. Vertical take-off and landing (VTOL) configurations present challenges for performance prediction during crucial flight operations. An advanced computational framework for predicting propeller performance in electric vertical takeoff and landing (eVTOL) aircraft during transition flight is essential for future concept designs. This research extends the Blade Element Momentum Theory (BEMT) to model propeller behavior at high incidence angles, crucial for eVTOL operation.

The study begins with a review of tilt-wing/rotor configurations for eVTOLs and tackles the complex aerodynamic phenomena associated with rotors …


Contributions To The Understanding Of Turbulent Boundary Layers Over Curved Walls, Nicholas Zhu Aug 2024

Contributions To The Understanding Of Turbulent Boundary Layers Over Curved Walls, Nicholas Zhu

Doctoral Dissertations and Master's Theses

A wind tunnel campaign was conducted to investigate the DARPA Suboff boundary layer. To emphasize the axisymmetric boundary layer, the generic submarine model's sail, appendages, and propeller were omitted. The study focused on the afterbody from 70–95% of the model length to examine the concurrent pressure gradient and wall curvature effects, which are commonplace in engineering. Three particle image velocimetry (PIV) configurations were employed to measure the boundary layer in detail: one spanned the entire afterbody, another had narrow strips sampled at 16 kHz, and the third used two simultaneous orthogonal measurement planes. Considerable effort was made to reduce the …


Heat Transfer To Arrays Of Oscillating Impingement Jets, Alex Q. Clay Aug 2024

Heat Transfer To Arrays Of Oscillating Impingement Jets, Alex Q. Clay

Doctoral Dissertations and Master's Theses

In gas turbine engines, the desire to increase turbine entry temperatures has become more relevant in order to increase engine efficiency. However, materials used in these engines can only withstand temperatures that are so high. Because of this, the ability to cool hot section components will always limit operating temperatures. Impingement cooling jets have become a common way of cooling due to the high rates of heat transfer that can be achieved. However, previous research has shown that the interaction of impingement jets with cylinder wake can improve the intensity and uniformity of heat transfer. The goal of this study …


Enhancing Crossflow Dynamics Through The Gas Injection From Multiple Cylinders, Sahrish B. Naqvi, Sadia Siddiqa, Maciej Matyka, Rama S. R. Gorla, Md. Mamum Molla Aug 2024

Enhancing Crossflow Dynamics Through The Gas Injection From Multiple Cylinders, Sahrish B. Naqvi, Sadia Siddiqa, Maciej Matyka, Rama S. R. Gorla, Md. Mamum Molla

Faculty Publications

We investigate unsteady, two-dimensional laminar fluid flow around cylinders, focusing on understanding the impact of injecting methane gas through two diametrically opposite arcs on the cylinder in the crossflow of the second fluid. This study encompasses applications in mixing and dispersion, which are crucial in various technological and natural processes. Our analysis addresses velocity field’s contribution to the spatiotemporal distribution of transported quantities. We observed that mixing induces a transition from laminar to turbulent flow. Depending on the injected-to-crossflow velocity ratios, the wake vortices downstream of cylinder arrays separate from or connect to the injected gas. This phenomenon significantly impacts …


Bi-Modal Excitation Of A Supersonic Rectangular Jet, Benjamin Malczewski Aug 2024

Bi-Modal Excitation Of A Supersonic Rectangular Jet, Benjamin Malczewski

Doctoral Dissertations and Master's Theses

This work addresses the issue of supersonic rectangular jet noise via bi-modal excitation. A Mach 1.5 heated rectangular jet with a 2:1 aspect ratio is considered. Theoretical work is presented in which a Reduced-Order Model (ROM) is used in conjunction with the Linearized Euler Equations to predict the nonlinear growth and decay of various frequencies due to the interaction between harmonically related modes and the mean flow. Scope is limited to a symmetric disturbance. The case of no interaction is used to help identify a dominant coherent structure, referred to as “f”. For the symmetric disturbance, a Strouhal number of …