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Articles 6031 - 6060 of 11135
Full-Text Articles in Engineering
Structural Design Of Liquid Oxygen/Liquid Methane Robotic Lander Janus, Mariana Chaidez
Structural Design Of Liquid Oxygen/Liquid Methane Robotic Lander Janus, Mariana Chaidez
Open Access Theses & Dissertations
As the attempt to send humans to Mars has gained momentum in the last decade, the need to find alternative propellants that are safer, less toxic, and yields a better performance has become apparent [1]. Liquid methane and oxygen have emerged as a suitable alternative. In addition, the incorporation of liquid methane/liquid oxygen into the propulsion system has demonstrated an increase in engine performance, as well as a reduction in the volume, size and complexity of the propulsion system. In an attempt to further understand the technologies that are possible to develop using liquid oxygen (LO2) and liquid methane (LCH4), …
Effects Of Altitude On Monarch Butterfly Aerodynamics, Brittany Greene
Effects Of Altitude On Monarch Butterfly Aerodynamics, Brittany Greene
Summer Community of Scholars Posters (RCEU and HCR Combined Programs)
No abstract provided.
A Usability And Learnability Case Study Of Glass Flight Deck Interfaces And Pilot Interactions Through Scenario-Based Training, Thomas James De Cino
A Usability And Learnability Case Study Of Glass Flight Deck Interfaces And Pilot Interactions Through Scenario-Based Training, Thomas James De Cino
CCAC Theses and Dissertations
In the aviation industry, digitally produced and presented flight, navigation, and aircraft information is commonly referred to as glass flight decks. Glass flight decks are driven by computer-based subsystems and have long been a part of military and commercial aviation sectors. Over the past 15 years, the General Aviation (GA) sector of the aviation industry has become a recent beneficiary of the rapid advancement of computer-based glass flight deck (GFD) systems.
While providing the GA pilot considerable enhancements in the quality of information about the status and operations of the aircraft, training pilots on the use of glass flight decks …
Quantitative Assessment Of Secondary Flows Of Single-Phase Fluid Through Pipe Bends, Z. Kaldy, O. Ayala
Quantitative Assessment Of Secondary Flows Of Single-Phase Fluid Through Pipe Bends, Z. Kaldy, O. Ayala
Engineering Technology Faculty Publications
Single-phase fluid flow was simulated passing through various three dimensional pipe elbows. The simulations varied by Reynolds number, curvature ratios, and sweep angles and were all conducted using the k-e model available in COMSOL Multiphysics 5.1. The intent of this research was to qualitatively assess the flow characteristics under several different conditions. Many similarities were seen especially when comparing curvature ratios, the vorticity location for the turbulent cases show near identical behavior at the elbow midsection. One of the variables quantified in this paper is the maximum secondary velocity module which shows increasing values until the midsection of the elbow.
Integrating Cobots In Engineering Technology Education, Ana M. Djuric, Vukica Jovanovic, Tatiana V. Goris, Otilia Popescu
Integrating Cobots In Engineering Technology Education, Ana M. Djuric, Vukica Jovanovic, Tatiana V. Goris, Otilia Popescu
Engineering Technology Faculty Publications
Collaborative robots or CoBots, unlike traditional robots, are safe and flexible enough to work harmoniously with humans. Exploiting the efficiency of automated operations and the flexibility of manual operations in one process can improve productivity and worker job satisfaction. CoBots technology has been experiencing strong growth in different areas such as ground transportation, food-processing industry, car manufacturing, and naval or aeronautical engineering. Current CoBots education and training opportunities are rare or non-existent in university environments. In response to this need, we developed several CoBots modules which will be integrated in the current robotics and mechatronics courses. In this paper we …
Modeling Of Reliability And Performance Assessment Of A Dissimilar Redundancy Actuation System With Failure Monitoring, Wang Shaoping, Cui Xiaoyu, Shi Jian, Mileta M. Tomovic, Jiao Zongxia
Modeling Of Reliability And Performance Assessment Of A Dissimilar Redundancy Actuation System With Failure Monitoring, Wang Shaoping, Cui Xiaoyu, Shi Jian, Mileta M. Tomovic, Jiao Zongxia
Engineering Technology Faculty Publications
Actuation system is a vital system in an aircraft, providing the force necessary to move flight control surfaces. The system has a significant influence on the overall aircraft performance and its safety. In order to further increase already high reliability and safety, Airbus has implemented a dissimilar redundancy actuation system (DRAS) in its aircraft. The DRAS consists of a hydraulic actuation system (HAS) and an electro-hydrostatic actuation system (EHAS), in which the HAS utilizes a hydraulic source (HS) to move the control surface and the EHAS utilizes an electrical supply (ES) to provide the motion force. This paper focuses on …
Constant Velocity Combustion Scramjet Analysis, Lakshmi Srikanth Tiruveedula
Constant Velocity Combustion Scramjet Analysis, Lakshmi Srikanth Tiruveedula
Electronic Theses and Dissertations
The supersonic combustion ramjet or scramjet, is the most suitable engine cycle for sustained hypersonic flight in the atmosphere. The present work deals with the performance of a scramjet engine by parametrically analyzing the performance of the ideal scramjet using the engine parameters: specific thrust, fuel-to-air ratio, thrust specific fuel consumption, thermal efficiency, propulsive efficiency, overall efficiency and thrust flux. The objective of the work is to determine the desirable performance terms of the ideal scramjet, by varying three different candidate fuels and three different candidate materials for the combustion chamber. The engine parameters are related by the lower heating …
Guided Wave Inspection Of Cracks In The Rivet Hole Of An Aerospace Lap Joint Using Analytical-Fem Approach, Md Yeasin Bhuiyan
Guided Wave Inspection Of Cracks In The Rivet Hole Of An Aerospace Lap Joint Using Analytical-Fem Approach, Md Yeasin Bhuiyan
Theses and Dissertations
Ultrasonic guided waves are very attractive for the inspection of large structures using nondestructive evaluation (NDE) and structural health monitoring (SHM) technique. Combined analytical and finite element analysis (CAFA) has been introduced for the detection of butterfly cracks in the rivet hole of the aerospace lap joint. Finite element analyses have been performed on the local damage area in spite of the whole large structure. Fundamental Lamb wave modes (S0 and A0) have been strike on the local damage from multiple directions to analyze the cracks of multiple-rivet-hole lap joint. The rivet hole cracks (damage) in the plate structure gives …
Development And Testing Of A Fracture Energy-Based Model Of Explosive Asteroid Deflection, James A. Veerkamp
Development And Testing Of A Fracture Energy-Based Model Of Explosive Asteroid Deflection, James A. Veerkamp
Masters Theses
"While asteroid deflection has been studied for the past half century, efforts have generally been directed towards methods that attempt to minimize disruption of the rock body. In order to widen the base of research, a fracture energy-based model of asteroid fragmentation was developed and applied to both asteroid scale and lab testable scale cases. Modeling of the orbital case suggests the capability to deflect a 100 meter diameter asteroid on a 10 year timescale. The model's predicted energy transfer is then compared to laboratory testing using a ballistic pendulum. The results of this testing suggest that the model as …
Strategic Deconfliction Of 4d Trajectory And Perturbation Analysis For Air Traffic Control And Automation System, Xinmin Tang, Yu Zhang, Ping Chen, Bo Li, Songchen Han
Strategic Deconfliction Of 4d Trajectory And Perturbation Analysis For Air Traffic Control And Automation System, Xinmin Tang, Yu Zhang, Ping Chen, Bo Li, Songchen Han
Civil and Environmental Engineering Faculty Publications
Strategic 4D trajectory conflict-free planning is recognized as one of the core technologies of next-generation air traffic control and automation systems. To resolve potential conflicts during strategic 4D conflict-free trajectory planning, a protection-zone conflict-control model based on air traffic control separation constraints was proposed, in which relationships between expected arrival time and adjusted arrival time at conflicting waypoints for aircraft queues were built and transformed into dynamic linear equations under the definition of max-plus algebra. A method for strategic deconfliction of 4D trajectory was then proposed using two strategies: arrival time adjustment and departure time adjustment. In addition, departure time …
Direct Position Control Of Dielectric Barrier Discharge Filaments, Matthew C. Paliwoda, Joshua L. Rovey, Mitchell Wainwright
Direct Position Control Of Dielectric Barrier Discharge Filaments, Matthew C. Paliwoda, Joshua L. Rovey, Mitchell Wainwright
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Controllable patterns of plasma filaments are being explored for reconfigurable metamaterial applications. When operated in a filamentary mode, volume dielectric barrier discharges are known to produce patterns of self-organizing plasma filaments. In this work the presence and intensity of a single filament at a fixed location is controlled by an isolated and independently electrically adjusted needle electrode. Time-averaged normalized light intensity, current, and voltage are measured while varying the voltage of the needle through a self-biasing resistance. For a 7.5 kV, 3.2 kHz DBD, the needle-controlled filament discharges similar to adjacent filaments at low potentials but stops discharging at a …
Mass Spectrometry Of Selected Ionic Liquids In Capillary Electrospray At Nanoliter Volumetric Flow Rates, Shawn W. Miller, Benjamin D. Prince, Raymond J. Bemish, Joshua L. Rovey
Mass Spectrometry Of Selected Ionic Liquids In Capillary Electrospray At Nanoliter Volumetric Flow Rates, Shawn W. Miller, Benjamin D. Prince, Raymond J. Bemish, Joshua L. Rovey
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Capillary-based electrospray thrusters allow user-enabled control of the volumetric flow rate of the propellant. This control, coupled with mass spectrometry techniques spanning a large mass-to-charge range, enables elucidation of the composition of the electrospray beam and through further analyses, a better understanding of the physics occurring at the liquid/vacuum interface. In this work, mass spectra of selected ionic liquids electro sprayed from a capillary emitter are measured, using time-of-flight mass spectrometry, over a wide range of volumetric flow rates. The time-of-flight mass spectrometer enables simultaneous acquisition over a mass-to-charge range of 20 amu/q to ~500,000 amu/q in a single pulse …
Constructal Alkaline Membrane Fuel Cell (Amfc) Design, E. M. Sommer, J. V. C. Vargas, Lauber De Souza Martins, J. C. Ordonez
Constructal Alkaline Membrane Fuel Cell (Amfc) Design, E. M. Sommer, J. V. C. Vargas, Lauber De Souza Martins, J. C. Ordonez
Faculty Publications
This paper introduces a structured procedure to optimize the internal structure (relative sizes, spacing) and external shape (aspect ratios) of a single alkaline membrane fuel cell so that net power is maximized. The optimization of flow geometry is conducted for the smallest (elemental) level of a fuel cell stack, i.e., the single alkaline membrane fuel cell, which is modeled as a unidirectional flow system. The polarization curve, total and net power, and efficiency are obtained as functions of temperature, pressure, electrolyte solution concentration (KOH), geometry and operating parameters. The optimization is subjected to fixed total volume. There are two levels …
Decomposition Of A Double Salt Ionic Liquid Monopropellant On Heated Metallic Surfaces, Steven P. Berg, Joshua L. Rovey
Decomposition Of A Double Salt Ionic Liquid Monopropellant On Heated Metallic Surfaces, Steven P. Berg, Joshua L. Rovey
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A monopropellant consisting of 59% hydroxylammonium nitrate and 41% 1-ethyl-3-methylimidazolium ethyl sulfate by mass is tested for decomposition on heated platinum, rhenium, and titanium surfaces. It was found that the propellant decomposes at 165 °C on titanium, which is the decomposition temperature of HAN. The onset temperature for decomposition on platinum was 85 °C and on rhenium it was 125 °C. This suggests that platinum and rhenium act as catalysts for the decomposition of the monopropellant. From the experimental data, Arrhenius-type reaction rate parameters were calculated. The activation energy for platinum was 3 times less than that of titanium suggesting …
Geometric Consideration Of Nanostructures For Energy Storage Systems, Jonghyun Park, Jie Li, Wei Lu, Ann Marie Sastry
Geometric Consideration Of Nanostructures For Energy Storage Systems, Jonghyun Park, Jie Li, Wei Lu, Ann Marie Sastry
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Battery performance and its fade are determined by various aspects such as the transport of ions and electrons through heterogeneous internal structures; kinetic reactions at the interfaces; and the corresponding interplay between mechanical, chemical, and thermal responses. The fundamental factor determining this complex multiscale and multiphysical nature of a battery is the geometry of active materials. In this work, we systematically consider the tradeoffs among a selection of limiting geometries of media designed to store ions or other species via a diffusion process. Specifically, we begin the investigation by considering diffusion in spheres, rods, and plates at the particle level, …
Structural Health Monitoring Of Composite Overwrapped Pressure Vessels, Luca Letizia
Structural Health Monitoring Of Composite Overwrapped Pressure Vessels, Luca Letizia
Honors Undergraduate Theses
This work is focusing to study the structural behavior of Composite Overwrapped Pressure Vessels (COPVs). These COPVs are found in many engineering applications. In the aerospace field, they are installed onto spaceships and aid the reorientation of the spacecraft in very far and airless, therefore frictionless, orbits to save energy and fuel. The intent of this research is to analyze the difference in performance of both perfectly intact and purposely damaged tanks. Understanding both the source and location of a structural fault will help NASA engineers predict the performance of COPVs subject to similar conditions, which could prevent failures of …
Smart Material Actuation And Morphing For Unmanned Aircraft Systems, Caio H. Da Silva Lima
Smart Material Actuation And Morphing For Unmanned Aircraft Systems, Caio H. Da Silva Lima
Honors Undergraduate Theses
The intent of this thesis is to outline the design, analysis, and characterization of an axially compressed piezocomposite actuator and, in particular, to determine the correlation and accuracy of two models used to predict deflection of an axially compressed piezocomposite bimorph. Restrictions in material properties lead to vehicle inefficiencies caused by the discontinuous geometry of deflected control surfaces in unmanned aircraft systems. This performance disadvantage in discrete control surfaces is caused in part by the sharp edges that are formed when the surface is pivoted. Flow continuity over the body of a vehicle is important in minimizing the effects of …
An Experimental Investigation Of Heat Transfer For Arrays Of Impingement Jets Onto The Featured Surfaces With Cylindrical And Elliptical Raised Surfaces, Marc A. Medina
Honors Undergraduate Theses
This study focuses on multi-jet impingement for gas turbine geometries in which the objective is to understand the influence of the roughness elements on a target surface to the heat transfer. Current work has proven that implementing roughness elements for multi-jet impingement target surfaces has increased heat transfer ranging anywhere from 10-30%. This study has chosen to investigate three different roughness elements, elliptical in cross-section, to compare to smooth surface geometries for multi-jet impingement. An experimental was taken for this study to extend the current knowledge of multi-jet impingement geometries and to further understand the heat transfer performance. A temperature …
Conjugate Heat Transfer Analysis Of Combined Regenerative And Discrete Film Cooling In A Rocket Nozzle, Charlotte M. Pearce
Conjugate Heat Transfer Analysis Of Combined Regenerative And Discrete Film Cooling In A Rocket Nozzle, Charlotte M. Pearce
Honors Undergraduate Theses
Conjugate heat transfer analysis has been carried out on an 89kN thrust chamber in order to evaluate whether combined discrete film cooling and regenerative cooling in a rocket nozzle is feasible. Several cooling configurations were tested against a baseline design of regenerative cooling only. New designs include combined cooling channels with one row of discrete film cooling holes near the throat of the nozzle, and turbulated cooling channels combined with a row of discrete film cooling holes. Blowing ratio and channel mass flow rate were both varied for each design. The effectiveness of each configuration was measured via the maximum …
Characterization Of Dispersion And Residual Stress In Nanoparticle Reinforced Hybrid Carbon Fiber Composites, Alex Selimov
Characterization Of Dispersion And Residual Stress In Nanoparticle Reinforced Hybrid Carbon Fiber Composites, Alex Selimov
Honors Undergraduate Theses
Hybrid carbon fiber reinforced composites are a new breed of materials that are currently being explored and characterized for next generation aerospace applications. Through the introduction of secondary reinforcements, such as alumina nanoparticles, hybrid properties including improved mechanical properties and stress sensing capabilities can be achieved. In order to maximize these properties, it is necessary to achieve a homogeneous dispersion of particulate filler. Utilizing the photoluminescent properties of alumina, it is possible to compare local levels of particle concentration through emission intensities as a way to determine the effectiveness of the tested manufacturing parameters in increasing material homogeneity. Parameters of …
Cryogenic Processing Of Al 7050-T7451 Alloy For Improved Surface Integrity, Bo Huang
Cryogenic Processing Of Al 7050-T7451 Alloy For Improved Surface Integrity, Bo Huang
Theses and Dissertations--Mechanical and Aerospace Engineering
Al 7050-T7451 alloy with good combinations of strength, stress corrosion cracking resistance and toughness, is used broadly in the aerospace/aviation industry for fatigue-critical airframe structural components. However, it is also considered as a highly anisotropic alloy as the crack growth behavior along the short transverse direction is very different from the one in the long transverse direction, due to the inhomogeneous microstructure with the elongated grains distributed in the work material used in the sheet/plate applications. Further processes on these materials are needed to improve its mechanical and material properties and broaden its applications.
The material with ultra-fine or nano …
Comparisons Of Ablator Experimental Performance To Response Modeling And Effects Of Water Phase Transition In Porous Tps Materials, David L. Smith
Comparisons Of Ablator Experimental Performance To Response Modeling And Effects Of Water Phase Transition In Porous Tps Materials, David L. Smith
Theses and Dissertations--Mechanical and Aerospace Engineering
The Mars Science Laboratory Entry Descent and Landing Instrumentation (MEDLI) project performed extensive arc jet tests for development, qualification, and calibration of instrumented heat shield plugs. These plugs each contained several thermocouples for recording near-surface and in-depth temperature response of the Phenolic Impregnated Carbon Ablator (PICA) heat shield. The arc jet test results are entered into a comprehensive database so that broad trends across the test series can be compared. One method of analysis is to compare with ablator material response calculations and solve the in-depth heat conduction equations. Using the near-surface thermocouple measurements as a boundary condition in numerical …
High Temperature Shock Tube Ignition Studies Of Co2 Diluted Mixtures, Owen Pryor
High Temperature Shock Tube Ignition Studies Of Co2 Diluted Mixtures, Owen Pryor
Electronic Theses and Dissertations
Energy demand is expected to grow by 20% over the next 10 years. In order to account for this increase in energy consumption new and novel combustion techniques are required to mitigate the effects of pollution and fossil fuel dependency. Oxy-fuel combustion in supercritical carbon dioxide (sCO2) cycles can increase plant efficiencies up to 52% and reduce pollutants such as NOX and CO2 by 99%. Supercritical engine cycles have demonstrated electricity costs of $121/MWh, which is competitive in comparison to conventional coal ($95.60/MWh) and natural gas power plants ($128.4/MWe). This increase in efficiency is mainly driven by the near-liquid density …
Approximated Control Affine Dynamics Mode For An Agricultural Field Robot Considering Wheel Terrain Interaction, Pablo Menendez-Aponte
Approximated Control Affine Dynamics Mode For An Agricultural Field Robot Considering Wheel Terrain Interaction, Pablo Menendez-Aponte
Electronic Theses and Dissertations
As populations and the demand for higher crop yields grow, so to does the need for efficient agricultural wheeled mobile robots. To achieve precise navigation through a field it is desirable that the control system is designed based on an accurate dynamic model. In this paper a control affine model for a custom designed skid-steer differential drive wheeled mobile robot is found. The Terramechanic wheel terrain interaction is adopted and modified to consider wheels with a torus geometry. Varying slip ratios and slip angles are considered in the terrain reaction forces, which is curve-fitted using a nonlinear least squares approach …
Kinematical Modelling And Its Analytical Inverse Kinematic Solution For The Handling Mechanism Of An Agricultural Robot, Sinem Gozde Defterli
Kinematical Modelling And Its Analytical Inverse Kinematic Solution For The Handling Mechanism Of An Agricultural Robot, Sinem Gozde Defterli
Electronic Theses and Dissertations
Early detection of the crop diseases helps to prevent failure in the amount and the quality of the production. In agricultural robotics, the idea of a disease detection robot is a fresh and an innovative hot-button topic. The exclusion of the diseased parts from the strawberry plants for further analyses is one of the main tasks of a recently developed strawberry robot. To this purpose, the handling mechanism in the robot needs to achieve an accurate manipulation task to reach the target. Reaching, cutting and storing the diseased leaf are challenging and delicate processes during the procedure of the handling …
Design Optimization Of Sandwich Core, Mohammad Tauhiduzzaman
Design Optimization Of Sandwich Core, Mohammad Tauhiduzzaman
Open Access Theses & Dissertations
Ultralight sandwich structures comprising of low-density core with stiff facings have attracted significant research interest for their considerable weight saving applications. The aircraft industries are focusing on decreasing the structural mass to lower the manufacturing and operating costs. Design analysis of the sandwich cores using finite element analysis has been developed as a promising concept to feature sandwich structures with maximum strength, stiffness, and reduced weight. To obtain multifunctional behavior of sandwich panels, a profound investigation of geometrical and mechanical properties in the transverse plane is required because it is very susceptible to any kind loadings. Structural optimization is one …
A Biomimetic, Energy-Harvesting, Obstacle-Avoiding, Path-Planning Algorithm For Uavs, Snorri Gudmundsson
A Biomimetic, Energy-Harvesting, Obstacle-Avoiding, Path-Planning Algorithm For Uavs, Snorri Gudmundsson
Doctoral Dissertations and Master's Theses
This dissertation presents two new approaches to energy harvesting for Unmanned Aerial Vehicles (UAV). One method is based on the Potential Flow Method (PFM); the other method seeds a wind-field map based on updraft peak analysis and then applies a variant of the Bellman-Ford algorithm to find the minimum-cost path. Both methods are enhanced by taking into account the performance characteristics of the aircraft using advanced performance theory. The combined approach yields five possible trajectories from which the one with the minimum energy cost is selected. The dissertation concludes by using the developed theory and modeling tools to simulate the …
Machine Vision Identification Of Airport Runways With Visible And Infrared Videos, Andrew J. Moore, Matthew Schubert, Chester Dolph, Glenn Woodell
Machine Vision Identification Of Airport Runways With Visible And Infrared Videos, Andrew J. Moore, Matthew Schubert, Chester Dolph, Glenn Woodell
Electrical & Computer Engineering Faculty Publications
A widely used machine vision pipeline based on the Speeded-Up Robust Features feature detector was applied to the problem of identifying a runway from a universe of known runways, which was constructed using video records of 19 straight-in glidepath approaches to nine runways. The recordings studied included visible, short-wave infrared, and long-wave infrared videos in clear conditions, rain, and fog. Both daytime and nighttime runway approaches were used. High detection specificity (identification of the runway approached and rejection of the other runways in the universe) was observed in all conditions (greater than 90% Bayesian posterior probability). In the visible band, …
First-Year Project Experience In Aerospace: Apogee Determination Of Model Rockets With Explicit Consideration Of Drag Effect, Hüseyin Sarper, Drew Landman, Linda Vahala
First-Year Project Experience In Aerospace: Apogee Determination Of Model Rockets With Explicit Consideration Of Drag Effect, Hüseyin Sarper, Drew Landman, Linda Vahala
Electrical & Computer Engineering Faculty Publications
This paper describes a student team project using model rockets and engines to learn engineering solution methods for determining the apogee of model rocket when the drag effect is considered explicitly instead of estimating its effect later. Model rocketry is a powerful tool for instructors who wish to incorporate science, engineering, and mathematics into a fun, engaging, and challenging activity for the students. The apogee can be determined using a number of distinct methods: trigonometry, onboard altimeters, analytical calculations, and simulation. This paper emphasizes numerical analytical solution using spreadsheet programming instead of a full analytical solution that requires higher mathematics. …
An Investigation Of Inital Shock Cell Formation In Turbulent Coanda Wall Jets, Caroline P. Lubert, Christian R. Schwantes, Richard J. Shafer
An Investigation Of Inital Shock Cell Formation In Turbulent Coanda Wall Jets, Caroline P. Lubert, Christian R. Schwantes, Richard J. Shafer
Department of Mathematics and Statistics - Faculty Scholarship
Turbulent Coanda wall jets are present in a multitude of natural and man-made applications. Their obvious advantages in terms of flow deflection are often outweighed by disadvantages related to the increased noise levels associated with these jets. Primary high-frequency noise sources are turbulent mixing noise (TMN) and shock-associated noise (SAN). Clearly, accurate modeling of these noise sources will facilitate better predictions of the behavior of such jet noise with physical characteristics. This paper, which focuses on SAN, shows how the Method of Characteristics can be applied to a steady two-dimensional axisymmetric supersonic flow to rewrite the three governing partial differential …