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Full-Text Articles in Physics

Direct Simulation And Reduced-Order Modeling Of Premixed Flame Response To Acoustic Modulation, Zheng Qiao May 2022

Direct Simulation And Reduced-Order Modeling Of Premixed Flame Response To Acoustic Modulation, Zheng Qiao

Theses and Dissertations

This dissertation introduces a general, predictive and cost-efficient reduced-order modeling (ROM) technique for characterization of flame response under acoustic modulation. The model is built upon the kinematic flame model–G-equation to describe the flame topology and dynamics, and the novelties of the ROM lie in i) a procedure to create the compatible base flow that can reproduce the correct flame geometry and ii) the use of a physically-consistent acoustic modulation field for the characterization of flame response. This ROM addresses the significant limitations of the classical kinematic model, which is only applicable to simple flame configurations and relies on ad-hoc models …


One Dimensional Study Of Magnetoplasmadynamic Thrusters For A Potential New Class Of Heavy Ion Drivers For Plasma Jet Driven Magnetoinertial Fusion, Patrick M. Brown Jun 2021

One Dimensional Study Of Magnetoplasmadynamic Thrusters For A Potential New Class Of Heavy Ion Drivers For Plasma Jet Driven Magnetoinertial Fusion, Patrick M. Brown

Theses and Dissertations

Plasma Jet Driven Magnetoinertial Fusion (PJMIF) requires high velocity heavy ion drivers in order to compress a magnetized target to fusion conditions. Previous work with heavy ion drivers has revealed sub-par accelerations due to plasma instabilities; thus, it is necessary to investigate new methods of heavy ion plasma acceleration. One such method is Magnetoplasmadynamic (MPD) thrusters. Past studies of these thrusters have been conducted at an initial temperature at or below the energy of full ionization. Here MPD thrusters are investigated using a Godunov type MHD solver with a Harten-Lax van Leer-D (HLLD) flux solving scheme assuming the plasma is …


Impendance Probe Payload Development For Space-Based Joint Service Collaboration, Brian T. Kay Mar 2021

Impendance Probe Payload Development For Space-Based Joint Service Collaboration, Brian T. Kay

Theses and Dissertations

Collaborations utilizing small spacecraft in near earth orbit between the U. S. Coast Guard Academy (CGA), Naval Research Lab (NRL), the U. S. Naval Academy (USNA), and the Air Force Institute of Technology (AFIT) have initiated scientific and engineering space-based experiments. Sourced opportunities like the VaSpace ThinSat missions have provided a platform for payload, sensor, and experiment development that would have otherwise been resource prohibitive. We have constructed an impedance probe payload derived from the existing ‘Space PlasmA Diagnostic suitE’ (SPADE) mission operating from NASA’s International Space Station. Currently both space and laboratory plasmas are investigated with AC impedance measurements …


Nebulizer-Based Systems To Improve Pharmaceutical Aerosol Delivery To The Lungs, Benjamin M. Spence Jan 2021

Nebulizer-Based Systems To Improve Pharmaceutical Aerosol Delivery To The Lungs, Benjamin M. Spence

Theses and Dissertations

Combining vibrating mesh nebulizers with additional new technologies leads to substantial improvements in pharmaceutical aerosol delivery to the lungs across therapeutic administration methods. In this dissertation, streamlined components, aerosol administration synchronization, and/or Excipient Enhanced Growth (EEG) technologies were utilized to develop and test several novel devices and aerosol delivery systems. The first focus of this work was to improve the poor delivery efficiency, e.g., 3.6% of nominal dose (Dugernier et al. 2017), of aerosolized medication administration to adult human subjects concurrent with high flow nasal cannula (HFNC) therapy, a form of continuous-flow non-invasive ventilation (NIV). The developed Low-Volume Mixer-Heater (LVMH) …


Laser Shock Peening Pressure Impulse Determination Via Empirical Data-Matching With Optimization Software, Colin C. Engebretsen Mar 2020

Laser Shock Peening Pressure Impulse Determination Via Empirical Data-Matching With Optimization Software, Colin C. Engebretsen

Theses and Dissertations

Laser shock peening (LSP) is a form of work hardening by means of laser induced pressure impulse. LSP imparts compressive residual stresses which can improve fatigue life of metallic alloys for structural use. The finite element modeling (FEM) of LSP is typically done by applying an assumed pressure impulse, as useful experimental measurement of this pressure impulse has not been adequately accomplished. This shortfall in the field is a current limitation to the accuracy of FE modeling, and was addressed in the current work. A novel method was tested to determine the pressure impulse shape in time and space by …


Direct Numerical Simulation Of Roughness Induced Hypersonic Boundary Layer Transition On A 7° Half-Angle Cone, Tara E. Crouch Mar 2019

Direct Numerical Simulation Of Roughness Induced Hypersonic Boundary Layer Transition On A 7° Half-Angle Cone, Tara E. Crouch

Theses and Dissertations

Direct numerical simulation (DNS) computational fluid dynamic (CFD) calculations were performed on a 30° slice of 7° half-angle cones with increasing nose radii bluntness at Mach 10 while simulating a distributed roughness pattern on the cone surface. These DNS computations were designed to determine if the non-modal transition behavior observed in testing performed at the Arnold Engineering Development Center (AEDC) Hypervelocity Wind Tunnel 9 was induced via distributed surface roughness. When boundary layer transition is dominated by second mode instabilities, an increase in nose radius delays the transition location downstream. However, blunt nose experiments indicated that as the nose radius …


Initial Stage Of Fluid-Structure Interaction Of A Celestial Icosahedron Shaped Vacuum Lighter Than Air Vehicle, Dustin P. Graves Mar 2019

Initial Stage Of Fluid-Structure Interaction Of A Celestial Icosahedron Shaped Vacuum Lighter Than Air Vehicle, Dustin P. Graves

Theses and Dissertations

The analysis of a celestial icosahedron geometry is considered as a potential design for a Vacuum Lighter than Air Vehicle (VLTAV). The goal of the analysis is ultimately to understand the initial fluid-structure interaction of the VLTAV and the surrounding airflow. Up to this point, previous research analyzed the celestial icosahedron VLTAV in relation to withstanding a symmetric sea-level pressure applied to the membrane of the structure. This scenario simulates an internal vacuum being applied in the worst-case atmospheric environmental condition. The next step in analysis is to determine the aerodynamic effects of the geometry. The experimental setup for obtaining …


Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson Mar 2019

Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson

Theses and Dissertations

The modeling focus on serpentine inlet ducts (S-duct), as with any inlet, is to quantify the total pressure recovery and ow distortion after the inlet, which directly impacts the performance of a turbine engine fed by the inlet. Accurate prediction of S-duct ow has yet to be achieved amongst the computational fluid dynamics (CFD) community to improve the reliance on modeling reducing costly testing. While direct numerical simulation of the turbulent ow in an S-duct is too cost prohibitive due to grid scaling with Reynolds number, wall-modeled large eddy simulation (WM-LES) serves as a tractable alternative. US3D, a hypersonic research …


Investigation Of Endwall Vortex Manipulation In High Lift Turbines Caused By Active Endwall Forcing, Horatio J. Babcock Mar 2019

Investigation Of Endwall Vortex Manipulation In High Lift Turbines Caused By Active Endwall Forcing, Horatio J. Babcock

Theses and Dissertations

With the increased demand for lighter, more fuel efficient and smaller gas turbine engines, the impetus to reduce the weight and size of the turbine has become apparent. One approach to reduce this weight is to reduce the number of blades in the turbine. However, to maintain power output, each blade must be capable of supporting a greater amount of lift. While several high-lift turbine profiles have been detailed in literature, most of these profiles have increased endwall losses, despite their desirable mid-span characteristics. To mitigate this endwall loss, a number of active and passive flow approaches have been studied …


Schlieren Imaging And Flow Analysis On A Cone/Flare Model In The Afrl Mach 6 Ludwieg Tube Facility, David A. Labuda Mar 2019

Schlieren Imaging And Flow Analysis On A Cone/Flare Model In The Afrl Mach 6 Ludwieg Tube Facility, David A. Labuda

Theses and Dissertations

High-speed Schlieren photography was utilized to visualize flow in the Air Force Research Laboratory Mach 6 Ludwieg tube facility. A 7° half-angle cone/flare model with variable nosetip radius and flare angle options was used in the study. Testing was performed at two driver tube pressures, generating freestream Reynolds numbers of 10.0x106 and 19.8x106 per meter. The variable-angle flare portion of the model provided a method for adjusting the intensity of the adverse pressure gradient at the cone/flare junction. As expected from existing literature, boundary layer separation along the cone frustum occurred further upstream as the magnitude of the …


Tracking Shock Movement On The Surface Of An Oscillating, Straked Semispan Delta Wing, Justin A. Pung Mar 2019

Tracking Shock Movement On The Surface Of An Oscillating, Straked Semispan Delta Wing, Justin A. Pung

Theses and Dissertations

A recent research effort, sponsored by the Air Force Office of Scientific Research, numerically investigated the unsteady aerodynamic flow field around an oscillating, straked, delta wing. The study was centered on determining the importance of the unsteady aerodynamic forces acting as a driver for a nonlinear motion known as limit cycle oscillations. The current effort focused on creating a computational model to compare to the results of previous tests and modeling efforts and discover new information regarding the onset of LCO. The computational model was constructed using the Cartesian overset capabilities of the CREATE-AV™ fixed wing fluid dynamics solver Kestrel. …


Analytical Models And Control Design Approaches For A 6 Dof Motion Test Apparatus, Kyra L. Schmidt Mar 2019

Analytical Models And Control Design Approaches For A 6 Dof Motion Test Apparatus, Kyra L. Schmidt

Theses and Dissertations

Wind tunnels play an indispensable role in the process of aircraft design, providing a test bed to produce valuable, accurate data that can be extrapolated to actual flight conditions. Historically, time-averaged data has made up the bulk of wind tunnel research, but modern flight design necessitates the use of dynamic wind tunnel testing to provide time-accurate data for high frequency motion. This research explores the use of a 6 degree of freedom (DOF) motion test apparatus (MTA) in the form of a robotic arm to allow models inside a subsonic wind tunnel to track prescribed trajectories to obtain time-accurate force …


Computational Aerothermodynamic Analysis Of Satellite Trans-Atmospheric Skip Entry Survivability, John J. Runco Mar 2019

Computational Aerothermodynamic Analysis Of Satellite Trans-Atmospheric Skip Entry Survivability, John J. Runco

Theses and Dissertations

Computational aerothermodynamic analysis is presented for a spacecraft in low Earth orbit performing an atmospheric skip entry maneuver. Typically, atmospheric reentry is a terminal operation signaling mission end-of-life and, in some instances, executed for spacecraft disposal. A variation on reentry – skip entry – is an aeroassisted trans-atmospheric maneuver in which a spacecraft utilizes the effects of aerodynamic drag in order to reduce energy prior to a terminal entry, pinpoint a targeted entry, or change orbital elements such as inclination. Spacecraft performing a skip entry enable new modes of maneuver to enhance operations in nominal or possibly contested mission environments. …


Reconstruction Of The 3d Temperature And Species Concentration Spatial Distribution Of A Jet Engine Exhaust Plume Using An Infrared Fourier Transform Spectrometer Hyperspectral Imager, Mason D. Paulec Sep 2018

Reconstruction Of The 3d Temperature And Species Concentration Spatial Distribution Of A Jet Engine Exhaust Plume Using An Infrared Fourier Transform Spectrometer Hyperspectral Imager, Mason D. Paulec

Theses and Dissertations

The measurement of combustion byproducts is useful for determining pollution of any fuel burning application, efficiency of combustion, and determining detectability of aircraft exhausts. Both intrusive and non-intrusive techniques have been utilized to measure these quantities. For the majority of the non-intrusive techniques, the absorption and emission spectra of the gases are utilized for measurements. For this research, the use of the Telops Infrared Fourier Transform Spectrometer (IFTS) Hyperspectral Imager (HSI) was explored within the scope of combustion diagnostic methods, as an option for remote measurements of a jet turbine to determine concentration of species and temperature of the combustion …


Application Of Spectral Solution And Neural Network Techniques In Plasma Modeling For Electric Propulsion, Joseph R. Whitman Sep 2018

Application Of Spectral Solution And Neural Network Techniques In Plasma Modeling For Electric Propulsion, Joseph R. Whitman

Theses and Dissertations

A solver for Poisson's equation was developed using the Radix-2 FFT method first invented by Carl Friedrich Gauss. Its performance was characterized using simulated data and identical boundary conditions to those found in a Hall Effect Thruster. The characterization showed errors below machine-zero with noise-free data, and above 20% noise-to-signal strength, the error increased linearly with the noise. This solver can be implemented into AFRL's plasma simulator, the Thermophysics Universal Research Framework (TURF) and used to quickly and accurately compute the electric field based on charge distributions. The validity of a machine learning approach and data-based complex system modeling approach …


Modeling A Space-Based Quantum Link, Alexander W. Duchane Mar 2018

Modeling A Space-Based Quantum Link, Alexander W. Duchane

Theses and Dissertations

Quantum sources and single photon detectors have improved, allowing quantum algorithms for communication, encryption, computing, and sensing to transition from theory and small-scale laboratory experiments to field experiments. One such quantum algorithm, Quantum Key Distribution, uses optical pulses to generate shared random bit strings between two locations. These shared bit strings can be turned into encryption keys to be used as a one-time-pad or integrated with symmetric encryption techniques such as the Advanced Encryption Standard. This method of key generation and encryption is resistant to future advances in quantum computing which significantly degrade the effectiveness of current asymmetric key sharing …


Wall-Modeled Large Eddy Simulation Of A Three-Dimensional Shock-Boundary Layer Interaction, Nicholas J. Marco Mar 2018

Wall-Modeled Large Eddy Simulation Of A Three-Dimensional Shock-Boundary Layer Interaction, Nicholas J. Marco

Theses and Dissertations

The direct simulation of turbulent flows is prohibitive at high Reynolds numbers; thus, methods such as RANS and LES are used. However, these methods still require a large number of cells near a solid boundary. To circumvent this issue, a Wall-Modeled Large Eddy Simulation (WM-LES) can be used. Of interest is how these wall models perform in comparison to a Wall-Resolved Large Eddy Simulation (WR-LES) and experimental results of a shock turbulent boundary layer interactions (STBLI) and specifically, whether equilibrium wall models are sufficient to resolve the oscillatory and hence non-equilibrium nature of these flows or whether a non-equilibrium model …


Optical Flow-Based Odometry For Underground Tunnel Exploration, Terra Kier Jun 2011

Optical Flow-Based Odometry For Underground Tunnel Exploration, Terra Kier

Theses and Dissertations

As military operations in degraded or GPS-denied environments continue to increase in frequency and importance, there is an increased necessity to be able to determine precision location within these environments. Furthermore, authorities are finding a record number of tunnels along the U.S.-Mexico border; therefore, underground tunnel characterization is becoming a high priority for U.S. Homeland Security as well. This thesis investigates the performance of a new image registration technique based on a two camera optical- flow configuration using phase correlation techniques. These techniques differ from other image based navigation methods but present a viable alternative increasing autonomy and answering the …


Polarimetric Enhancements To Electro-Optical Aided Navigation Techniques, Jeremiah D. Johnson Mar 2011

Polarimetric Enhancements To Electro-Optical Aided Navigation Techniques, Jeremiah D. Johnson

Theses and Dissertations

Navigation in indoor and urban environments by small unmanned systems is a topic of interest for the Air Force. The Advanced Navigation Technology Center at the Air Force Institute of Technology is continually looking for novel approaches to navigation in GPS deprived environments. Inertial sensors have been coupled with image aided concepts, such as feature tracking, with good results. However, feature density in areas with large, flat, smooth surfaces tends to be low. Polarimetric sensors have been used for surface reconstruction, surface characterization and outdoor navigation. This thesis combines aspects of some of these algorithms along with a realistic, micro-facet …


Mission Analysis And Design For Space Based Inter-Satellite Laser Power Beaming, Nicholas M. Keller Mar 2010

Mission Analysis And Design For Space Based Inter-Satellite Laser Power Beaming, Nicholas M. Keller

Theses and Dissertations

This research effort develops an interdisciplinary design tool to optimize an orbit for the purpose of wirelessly beaming power from the International Space Stations (ISS) Japanese Experimental Module Exposed Facility (JEM/EF) to a target satellite. For the purpose of this initiative, the target satellite will be referred to as FalconSAT6, a reference to the proposed follow-on satellite to the U.S. Air Force Academy’s (USAFA) FalconSAT5 program. The USAFA FalconSAT program provides cadets an opportunity to design, analyze, build, test and operate small satellites to conduct Department of Defense (DoD) space missions. The tool developed for this research is designed to …


Predicting Solar Protons: A Statistical Approach, Jonathan C. Spaulding Mar 2009

Predicting Solar Protons: A Statistical Approach, Jonathan C. Spaulding

Theses and Dissertations

A small fraction of solar flares are accompanied by high energy (>10 MeV) protons. These events can cause degradation or failure of satellite systems and can be harmful to humans in space or in high altitude flight. For risk management purposes, the Air Force is interested in predicting these events. Several algorithms exist to do this operationally, but none predict when these events will occur with much accuracy. Here, we analyzed 3610 M1 and greater flares including 106 with proton events from the GOES sensors from 1 Jan 1986 to 31 Dec 2004 to produce new results, including a …


Hyperspectral Imaging Of A Turbine Engine Exhaust Plume To Determine Radiance, Temperature, And Concentration Spatial Distributions, Spencer J. Bowen Mar 2009

Hyperspectral Imaging Of A Turbine Engine Exhaust Plume To Determine Radiance, Temperature, And Concentration Spatial Distributions, Spencer J. Bowen

Theses and Dissertations

The usefulness of imaging Fourier transform spectroscopy (IFTS) when looking at a rapidly varying turbine engine exhaust scene was explored by characterizing the scene change artifacts (SCAs) present in the plume and the effect they have on the calibrated spectra using the Telops, Inc.-manufactured Field-portable Imaging Radiometric Spectrometer Technology, Midwave Extended (FIRST-MWE). It was determined that IFTS technology can be applied to the problem of a rapidly varying turbine engine exhaust plume due to the zero mean, stochastic nature of the SCAs, through the use of temporal averaging. The FIRST-MWE produced radiometrically calibrated hyperspectral datacubes, with calibration uncertainty of 35% …


Tightly Integrating Optical And Inertial Sensors For Navigation Using The Ukf, Sedat Ebcin Mar 2008

Tightly Integrating Optical And Inertial Sensors For Navigation Using The Ukf, Sedat Ebcin

Theses and Dissertations

The motivation of this research is to address the benefits of tightly integrating optical and inertial sensors where GNSS signals are not available. The research begins with describing the navigation problem. Then, error and measurement models are presented. Given a set of features, a feature detection and projection algorithm is developed which utilizes inertial measurements to predict vectors in the feature space between images. The unscented Kalman filter is applied to the navigation system using the inertial measurements and feature matches to estimate the navigation trajectory. Finally, the image-aided navigation algorithm is tested using a simulation and an experiment. As …


Characterizing A Co-Flow Nozzle For Use In A Filtered Rayleigh Scattering System, David S. Miceli Jun 2006

Characterizing A Co-Flow Nozzle For Use In A Filtered Rayleigh Scattering System, David S. Miceli

Theses and Dissertations

Research was conducted on the flow field exiting a co-annular flow nozzle for use in filtered Rayleigh scattering flow visualizations. More specifically, the flow visualizations were of the flow field exiting a coflow nozzle and illuminated by a tunable, nominal 4.2 watt narrow line width Argon laser operating at 514.5nm. ND:YAG lasers are typically used in this application, but some of the properties of a tunable Argon laser make it an attractive alternative. Before generating flow visualizations, the coflow nozzle was characterized both experimentally and computationally. Due to a flow asymmetry in the outer annulus flow field, the nozzle was …


An Experimental Study Of A Pulsed Dc Plasma Flow Control Actuator, Jennifer D. Wall Jun 2006

An Experimental Study Of A Pulsed Dc Plasma Flow Control Actuator, Jennifer D. Wall

Theses and Dissertations

An experiment on the effects of a pulsed DC plasma actuator on a separated flow in a low speed wind tunnel was conducted. The actuator consisted of two asymmetric copper electrodes oriented normal to the flow separated by a dielectric barrier and mounted on a flat plate in the center of the tunnel. A contoured insert was constructed and used to create an adverse pressure gradient in the test section comparable to a Pak-B low pressure turbine blade distribution. Suction was applied from the upper wall to induce separation along the flat plate over the electrodes. The DC power supply …


Assessing The Potential For Improved Scramjet Performance Through Application Of Electromagnetic Flow Control, Martin F. Lindsey Mar 2006

Assessing The Potential For Improved Scramjet Performance Through Application Of Electromagnetic Flow Control, Martin F. Lindsey

Theses and Dissertations

Hypersonic flight using scramjet propulsion bridges the gap between turbojets and rockets. Recent efforts focus on magnetogasdynamic (MGD) flow control to mitigate the problems of high thermomechanical loads and low efficiencies associated with scramjets. This research is the first flight-scale, three-dimensional computational analysis of a realistic scramjet to assess how MGD flow control improves scramjet performance. Developing a quasi-one dimensional design tool culminated in the first open source scramjet geometry. This geometry was tested with the Air Force Research Laboratory's electromagnetic computational code. To increase fidelity, an algorithm was developed to incorporate thermochemistry, resulting in the only open-source model of …


Spatially-Resolved Temperature Diagnostic For Supersonic Flow Using Cross-Beam Doppler-Limited Laser Saturation Spectroscopy, Grady T. Phillips Mar 2006

Spatially-Resolved Temperature Diagnostic For Supersonic Flow Using Cross-Beam Doppler-Limited Laser Saturation Spectroscopy, Grady T. Phillips

Theses and Dissertations

Optical techniques for measuring the temperature in three-dimensional supersonic reactive flows have typically depended on lineshape measurements using single-beam laser absorption spectroscopy. However, absorption over extended path lengths in flows with symmetric, turbulent eddies can lead to systematically high extracted temperatures due to Doppler shifts resulting from flow along the absorption path. To eliminate these problems, Cross-Beam Saturation Absorption Spectroscopy (CBSAS) and Cross-Beam Inter-Modulated Fluorescence (CBIMF) have been developed which utilize two crossed and nearly copropogating laser beams.to record the spectral signal of an I2 ro-vibrational line in a small three-dimensional volume using a tunable CW dye laser. Temperature …


Control Demonstration Of A Thin Deformable In-Plane Actuated Mirror, Gina A. Peterson Mar 2006

Control Demonstration Of A Thin Deformable In-Plane Actuated Mirror, Gina A. Peterson

Theses and Dissertations

Current imaging satellites are limited in resolution and coverage area by the aperture size of their primary optical mirror. To get a large optical mirror into space, current launch weight and size restrictions must be overcome. Membrane-like optical mirrors can overcome these restrictions with their very lightweight and flexible properties. However, thin, deformable membrane mirrors are very susceptible to the space environment and require active control for surface stabilization and shaping. The primary goal of this research is to demonstrate that an in-plane actuated membrane-like deformable optical mirror can be controlled to optical wavelength tolerances in a closed-loop system. Fabrication …


Macroscopic Computational Model Of Dielectric Barrier Discharge Plasma Actuators, Timothy R. Klein Feb 2006

Macroscopic Computational Model Of Dielectric Barrier Discharge Plasma Actuators, Timothy R. Klein

Theses and Dissertations

Recent progress in the generation and sustainment of gas discharges at atmospheric pressure has energized research in the field of plasma-aerodynamics. Plasma actuators are promising devices that achieve flow control with no moving parts, do not alter the airfoil shape and place no parts in the flow. The operation of a plasma actuator is examined using a macroscopic (force and power addition) computational fluid dynamic model of a dielectric barrier discharge, DBD, in Fluent. A parametric approach is adopted to survey the range of requisite magnitudes of momentum and energy delivered to the flow field and to identify the effects …


Adaptive Harmonic Balance Method For Unsteady, Nonlinear, One-Dimensional Periodic Flows, Raymond C. Maple Sep 2002

Adaptive Harmonic Balance Method For Unsteady, Nonlinear, One-Dimensional Periodic Flows, Raymond C. Maple

Theses and Dissertations

A new adaptive split-domain harmonic balance computational fluid dynamics (CFD) method is developed to solve highly nonlinear time-periodic flows such as those found in turbomachinery. The basic harmonic balance CFD method transforms an unsteady time-periodic problem into a steady-state problem by assuming a solution in the form of a Fourier series in time. The new method employs a unique multi-domain split-operator solution technique to remove a large-series stability restriction present in previous harmonic balance CFD approaches. In addition, the new method adapts the frequency content to the flow, starting with a small number of Fourier frequencies and augmenting the frequency …