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At least 1,495 records · Page 83

Computational Study of the Side-By-Side Urban Air Taxi Concept

High-fidelity computational fluid dynamics simulations of NASA’s Side-by-side air taxi concept have been carried out. The three-dimensional unsteady Navier-Stokes equations are solved on overset grids using high-order accurate schemes, dual-time stepping, and a hybrid turbulence model. The flow solver has been loosely coupled with a helicopter comprehensive analysis code in order to get the trimmed flight solution. The vehicle simulated is a six-passenger side-by-side intermeshing rotor helicopter with hybrid propulsion for air taxi operations, also known as urban air mobility applications. This concept vehicle is intended to focus and guide NASA research activities in support of aircraft development for emerging aviation markets, in particular vertical take-off and landing air taxi operations.

Ventura Diaz, Patricia↗

Advanced Solar Electric Propulsion for Planetary Defense

Once the current survey to identify all near-Earth objects larger than 140-m diameter is complete, the major hazard from asteroid impacts may be from asteroids in the 50- to 100-m diameter size range. High-power solar electric propulsion systems employed in “slow-push” techniques may be the best way to deflect asteroids in this size range if deflection is warranted. The relative performance of three slow-push techniques—gravity tractor (GT), enhanced gravity tractor (EGT), and ion beam deflection (IBD)—are compared, assuming solar electric propulsion vehicles derived from NASA’s Asteroid Redirect Robotic Mission concept vehicle. Both the enhanced gravity tractor and ion beam deflection concepts are shown to be significantly better than the standard gravity tractor concept. The Hall-thruster based enhanced gravity tractor systems and ion beam deflection systems (based on the use of high-power gridded ion thrusters) are shown to provide comparable performance, i.e., similar deflection times and propellant required. Enhanced gravity tractor systems require the acquisition of material from the surface of the hazardous object in order to achieve the required “enhancement” of the gravitational coupling force. This makes EGT systems sensitive to the rotational state and surface properties of the unknown object, and potentially severely limits its applicability. Ion beam deflection is completely independent of the characteristics of the threat object. In fact, it is the only asteroid deflection technique, slow-push or otherwise, that can make this claim, thus potentially greatly increasing its applicability relative to other deflection techniques. Finally, high-power IBD systems are shown to be capable of deflecting the fictitious asteroid 2015 PDC used in the hypothetical asteroid impact exercise conducted at the 2015 Planetary Defense Conference.

Brophy, John↗

CFD applications in pump flows

The objective of the proposed paper is to develop a computational procedure that solves incompressible Navier-Stokes equations for pump flows. The solution method is based on the pseudo-compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. As a benchmark problem, the flow through the Rocketdyne inducer is numerically simulated. A coarse grid solution is obtained with a single zone by using an algebraic turbulence model. In multi-zone fine grid computation, a one-equation Baldwin-Barth turbulence model is utilized. Numerical results are compared with experimental measurements and a good agreement is found between the two. The resulting computer code is then applied to the flow analysis inside a two-stage fuel pump impeller operating at 80 percent, 100 percent, and 120 percent of design flow.

Kiris, Cetin↗

Further advances in silicon solar cell technology for space application

Recent improvements relating to the design of high efficiency cells are presented. A conceptual design using passivation techniques is discussed, which potentially increases the open circuit voltage to approximately 650 mV. This concept is supported by experimental data using only silicon passivation beneath contacts. The use of thin thermal oxides of silicon for passivation between contacts is also discussed. A number of novel structures have also been fabricated to investigate reduction in the thermal alpha of planar and sculptured cells. It is shown that this may be as low as 0.63 on glassed gridded back cells, and that the IR rejection beyond 1.1 microns may approach 100 percent if the backside is AR coated. Finally, experimental data is given to support the existence of free electron absorption in heavily doped emitters on sculptured cells.

Lillington, D. R.↗

Phased array antenna matching: Simulation and optimization of a planar phased array of circular waveguide elements

A computerized simulation of a planar phased array of circular waveguide elements is reported using mutual coupling and wide angle impedance matching in phased arrays. Special emphasis is given to circular polarization. The aforementioned computer program has as variable inputs: frequency, polarization, grid geometry, element size, dielectric waveguide fill, dielectric plugs in the waveguide for impedance matching, and dielectric sheets covering the array surface for the purpose of wide angle impedance matching. Parameter combinations are found which produce reflection peaks interior to grating lobes, while dielectric cover sheets are successfully employed to extend the usable scan range of a phased array. The most exciting results came from the application of computer aided optimization techniques to the design of this type of array.

Dudgeon, J. E.↗

Eleventh Workshop for Computational Fluid Dynamic Applications in Rocket Propulsion

Conference publication includes 79 abstracts and presentations and 3 invited presentations given at the Eleventh Workshop for Computational Fluid Dynamic Applications in Rocket Propulsion held at George C. Marshall Space Flight Center, April 20-22, 1993. The purpose of the workshop is to discuss experimental and computational fluid dynamic activities in rocket propulsion. The workshop is an open meeting for government, industry, and academia. A broad number of topics are discussed including computational fluid dynamic methodology, liquid and solid rocket propulsion, turbomachinery, combustion, heat transfer, and grid generation.

Williams, R. W.↗

Numerical Simulation of Non-Rotating and Rotating Coolant Channel Flow Fields

Future generations of ultra high bypass-ratio jet engines will require far higher pressure ratios and operating temperatures than those of current engines. For the foreseeable future, engine materials will not be able to withstand the high temperatures without some form of cooling. In particular the turbine blades, which are under high thermal as well as mechanical loads, must be cooled. Cooling of turbine blades is achieved by bleeding air from the compressor stage of the engine through complicated internal passages in the turbine blades (internal cooling, including jet-impingement cooling) and by bleeding small amounts of air into the boundary layer of the external flow through small discrete holes on the surface of the blade (film cooling and transpiration cooling). The cooling must be done using a minimum amount of air or any increases in efficiency gained through higher operating temperature will be lost due to added load on the compressor stage. Turbine cooling schemes have traditionally been based on extensive empirical data bases, quasi-one-dimensional computational fluid dynamics (CFD) analysis, and trial and error. With improved capabilities of CFD, these traditional methods can be augmented by full three-dimensional simulations of the coolant flow to predict in detail the heat transfer and metal temperatures. Several aspects of turbine coolant flows make such application of CFD difficult, thus a highly effective CFD methodology must be used. First, high resolution of the flow field is required to attain the needed accuracy for heat transfer predictions, making highly efficient flow solvers essential for such computations. Second, the geometries of the flow passages are complicated but must be modeled accurately in order to capture all important details of the flow. This makes grid generation and grid quality important issues. Finally, since coolant flows are turbulent and separated the effects of turbulence must be modeled with a low Reynolds number turbulence model to accurately predict details of heat transfer.

Rigby, David L.↗

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Yee, H. C.↗

Characterizing diurnal and seasonal cycles in monsoon systems from TRMM and CEOP observations

The CEOP Inter-Monsoon Study (CIMS) is one of the two main science drivers of CEOP that aims to (a) provide better understanding of fundamental physical processes in monsoon regions around the world, and (b) demonstrate the synergy and utility of CEOP data in providing a pathway for model physics evaluation and improvement. As the data collection phase for EOP-3 and EOP-4 is being completed, two full annual cycles (2003-2004) of research-quality data sets from satellites, reference sites, and model output location time series (MOLTS) have been processed and made available for data analyses and model validation studies. This article presents preliminary results of a CIMS study aimed at the characterization and intercomparison of all major monsoon systems. The CEOP reference site data proved its value in such exercises by being a powerful tool to cross-validate the TRMM data, and to intercompare with multi-model results in ongoing work. We use 6 years (1998-2003) of pentad CEOP/TRMM data with 2deg x 2.5deg latitude-longitude grid, over the domain of interests to define the monsoon climatological diurnal and annual cycles for the East Asian Monsoon (EAM), the South Asian Monsoon (SAM), the West Africa Monsoon (WAM), the North America/Mexican Monsoon (NAM), the South American Summer Monsoon (SASM) and the Australian Monsoon (AUM). As noted, the TRMM data used in the study were cross-validated using CEOP reference site data, where applicable. Results show that the observed diurnal cycle of rain peaked around late afternoon over monsoon land, and early morning over the oceans. The diurnal cycles in models tend to peak 2-3 hours earlier than observed. The seasonal cycles of the EAM and SAM show the strongest continentality, i.e, strong control by continental processes away from the ITCZ. The WAM, and the AUM shows the less continentality, i.e, strong control by the oceanic ITCZ.

Lau, William K. M.↗

Characterizing Diurnal and Seasonal Cycles in Monsoon Systems from TRMM and CEOP Observations

The CEOP Inter-Monsoon Study (CIMS) is one of the two main science drivers of CEOP that aims to (a) provide better understanding of fundamental physical processes in monsoon regions around the world, and (b) demonstrate the synergy and utility of CEOP data in providing a pathway for model physics evaluation and improvement. As the data collection phase for EOP-3 and EOP-4 is being completed, two full annual cycles (2003-2004) of research-quality data sets from satellites, reference sites, and model output location time series (MOLTS) have been processed and made available for data analyses and model validation studies. This article presents preliminary results of a CIMS study aimed at the characterization and intercomparison of all major monsoon systems. The CEOP reference site data proved its value in such exercises by being a powerful tool to cross-validate the TRMM data, and to intercompare with multi-model results in ongoing work. We use 6 years (1998-2003) of pentad CEOP/TRMM data with 2 deg x 2.5 deg. latitude-longitude grid, over the domain of interests to define the monsoon climatological diurnal and annual cycles for the East Asian Monsoon (EAM), the South Asian Monsoon (SAM), the West Africa Monsoon (WAM), the North America/Mexican Monsoon (NAM), the South American Summer Monsoon (SASM) and the Australian Monsoon (AUM). As noted, the TRMM data used in the study were cross-validated using CEOP reference site data, where applicable. Results show that the observed diurnal cycle of rain peaked around late afternoon over monsoon land, and early morning over the oceans. The diurnal cycles in models tend to peak 2-3 hours earlier than observed. The seasonal cycles of the EAM and SAM show the strongest continentality, i.e, strong control by continental processes away from the ITCZ. The WAM, and the AUM shows the less continentality, i.e, strong control by the oceanic ITCZ.

Lau, William K. M.↗

Classification of Small Negative Lightning Reports at the KSC-ER

The NASA Kennedy Space Center (KSC) and Air Force Eastern Range (ER) operate an extensive suite of lightning sensors because Florida experiences the highest area density of ground strikes in the United States, with area densities approaching 16 fl/sq km/yr when accumulated in 10x10 km (100 sq km) grids. The KSC-ER use data derived from two cloud-to-ground (CG) lightning detection networks, the "Cloud-to-Ground Lightning Surveillance System" (CGLSS) and the U.S. National Lightning Detection Network (TradeMark) (NLDN) plus a 3-dimensional lightning mapping system, the Lightning Detection and Ranging (LDAR) system, to provide warnings for ground operations and to insure mission safety during space launches. For operational applications at the KSC-ER it is important to understand the performance of each lightning detection system in considerable detail. In this work we examine a specific subset of the CGLSS stroke reports that have low values of the negative inferred peak current, Ip, i.e. values between 0 and -7 kA, and were thought to produce a new ground contact (NGC). When possible, the NLDN and LDAR systems were used to validate the CGLSS classification and to determine how many of these reported strokes were first strokes, subsequent strokes in a pre-existing channel (PEC), or cloud pulses that the CGLSS misclassified as CG strokes. It is scientifically important to determine the smallest current that can reach the ground either in the form of a first stroke or by way of a subsequent stroke that creates a new ground contact. In Biagi et al (2007), 52 low amplitude, negative return strokes ([Ip] < or = 10 kA) were evaluated in southern Arizona, northern Texas, and southern Oklahoma. The authors found that 50-87% of the small NLDN reports could be classified as CG (either first or subsequent strokes) on the basis of video and waveform recordings. Low amplitude return strokes are interesting because they are usually difficult to detect, and they are thought to bypass conventional lightning protection that relies on a sufficient attractive radius to prevent "shielding failure" (Golde, 1977). They also have larger location errors compared to the larger current events. In this study, we use the estimated peak current provided by the CGLSS and the results of our classification to determine the minimum Ip for each category of CG stroke and its probability of occurrence. Where possible, these results are compared to the findings in the literature.

Ward, Jennifer G.↗

Biomaterials Out of Thin Air: in Situ, On-Demand Printing of Advanced Biocomposites

Upmass is the single most significant limitation of our current space mission capability. Although biomaterials and biocomposites have mass, strength, flexibility, and self-healing properties that could significantly reduce upmass, their use is limited by the following drawbacks: Expensive, specific production. Many biomaterials can only be produced as part of significant support ecosystem; Inaccessible functional customization. The grain of wood, the porosity of bone, and so on are an integral part of the materials' desired mechanical properties, but are not deterministic when the material is naturally grown; Limited compositions. Most biomaterials (unlike metal, plastic, etc.) cannot be easily combined or modified to produce new materials. This project builds on recent advances in: Synthetic biology. Libraries of standardized genetic parts which can be used for controlled cellular material production, delivery, and binding; 3D printing. Commercial off-the-shelf components which can be used to make of a pico- to nanoliter cell deposition system; Tissue engineering. Proven cell-compatible support hydrogels and scaffolds can be modified to bind the deposited biomaterials of interest. Objectives: Feasibility and benefit analysis. Two mission contexts span the concept's scope (see below); Proof-of-concept demonstration. A simple grid of two proteins, fluorescent for easy detection, to validate the core technology concept; Proposed implementations for follow-on work. Avenues for future work on each core component (host cell, production control, material delivery, material binding, etc.); Complementary studies exploration. A survey of other emerging areas (in situ resource utilization, protein engineering, etc.) with the potential to multiply our technology's impact. Potential Impacts: This application could dramatically expand manufacturing capabilities on Earth and in space: In situ resource utilization. A far greater range of materials and products will be available from the limited palette offered by in situ resource extraction techniques; Reduced equipment and material upmass for off-Earth habitats. Ready- to-use highly specialized construction materials (radiation hardened, compressive/tensile, light or dense) from an extremely low starting mass; Structured biomaterial production. New ready-to-use macro, micro, and molecular manufacturing techniques for traditional biomaterials such as wood, bone and shell; New and novel biocomposite creation. The ability to create completely novel material composites from any base material that cells can be engineered to produce. Suggested Mission Contexts: ISS part manufacturing. A 'minimal working example' making a finished biomaterial part aboard the International Space Station; A long-term Mars habitat. 'Cradle-to-grave' use at a hypothetical Mars habitat, covering everything from tools to construction materials. Alternate Abstract: Imagine being able to print anything from tools and composite building materials to food and human tissues. Imagine being on Mars with the ability to replace any broken part, whether it's a part of your spacesuit, your habitat, or your own body. We propose a technique that would allow just that. By printing 3D arrays of cells engineered to secrete the necessary materials, the abundant in situ resources of atmosphere and regolith become organic, inorganic, or organic-inorganic composite materials. Such materials include novel, biologically derived materials not previously possible to fabricate.

habitats↗

Biomaterials Out of Thin Air: in Situ, On-demand Printing of Advanced Biocomposites

Upmass is the single most significant limitation of our current space mission capability. Although biomaterials and biocomposites have mass, strength, flexibility, and self-healing properties that could significantly reduce upmass, their use is limited by the following drawbacks: Expensive, specific production. Many biomaterials can only be produced as part of significant support ecosystem; Inaccessible functional customization. The grain of wood, the porosity of bone, and so on are an integral part of the materials' desired mechanical properties, but are not deterministic when the material is naturally grown; Limited compositions. Most biomaterials (unlike metal, plastic, etc.) cannot be easily combined or modified to produce new materials. This project builds on recent advances in: Synthetic biology. Libraries of standardized genetic parts which can be used for controlled cellular material production, delivery, and binding; 3D printing. Commercial off-the-shelf components which can be used to make of a pico- to nanoliter cell deposition system; Tissue engineering. Proven cell-compatible support hydrogels and scaffolds can be modified to bind the deposited biomaterials of interest. Objectives: Feasibility and benefit analysis. Two mission contexts span the concept's scope (see below); Proof-of-concept demonstration. A simple grid of two proteins, fluorescent for easy detection, to validate the core technology concept; Proposed implementations for follow-on work. Avenues for future work on each core component (host cell, production control, material delivery, material binding, etc.); Complementary studies exploration. A survey of other emerging areas (in situ resource utilization, protein engineering, etc.) with the potential to multiply our technology's impact. Potential Impacts: This application could dramatically expand manufacturing capabilities on Earth and in space: In situ resource utilization. A far greater range of materials and products will be available from the limited palette offered by in situ resource extraction techniques; Reduced equipment and material upmass for off-Earth habitats. Ready- to-use highly specialized construction materials (radiation hardened, compressive/tensile, light or dense) from an extremely low starting mass; Structured biomaterial production. New ready-to-use macro, micro, and molecular manufacturing techniques for traditional biomaterials such as wood, bone and shell; New and novel biocomposite creation. The ability to create completely novel material composites from any base material that cells can be engineered to produce. Suggested Mission Contexts: ISS part manufacturing. A 'minimal working example' making a finished biomaterial part aboard the International Space Station; A long-term Mars habitat. 'Cradle-to-grave' use at a hypothetical Mars habitat, covering everything from tools to construction materials. Alternate Abstract: Imagine being able to print anything from tools and composite building materials to food and human tissues. Imagine being on Mars with the ability to replace any broken part, whether it's a part of your spacesuit, your habitat, or your own body. We propose a technique that would allow just that. By printing 3D arrays of cells engineered to secrete the necessary materials, the abundant in situ resources of atmosphere and regolith become organic, inorganic, or organic-inorganic composite materials. Such materials include novel, biologically derived materials not previously possible to fabricate.

habitats↗

Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass- Or Time-Optimal Solutions

This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood-allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.

Hughes, Kyle M.↗

Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass-or Time-Optimal Solutions

This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood---allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.

Hughes, Kyle M.↗

Application of FUN3D and CFL3D to the Third Workshop on CFD Uncertainty Analysis

Two Reynolds-averaged Navier-Stokes computer codes - one unstructured and one structured - are applied to two workshop cases (for the 3rd Workshop on CFD Uncertainty Analysis, held at Instituto Superior Tecnico, Lisbon, in October 2008) for the purpose of uncertainty analysis. The Spalart-Allmaras turbulence model is employed. The first case uses the method of manufactured solution and is intended as a verification case. In other words, the CFD solution is expected to approach the exact solution as the grid is refined. The second case is a validation case (comparison against experiment), for which modeling errors inherent in the turbulence model and errors/uncertainty in the experiment may prevent close agreement. The results from the two computer codes are also compared. This exercise verifies that the codes are consistent both with the exact manufactured solution and with each other. In terms of order property, both codes behave as expected for the manufactured solution. For the backward facing step, CFD uncertainty on the finest grid is computed and is generally very low for both codes (whose results are nearly identical). Agreement with experiment is good at some locations for particular variables, but there are also many areas where the CFD and experimental uncertainties do not overlap.

Rumsey, C. L.↗

InP concentrator solar cells

The design, fabrication, and characterization of high-performance, n(+)/p InP shallow-homojunction (SHJ) concentrator solar cells are described. The InP device structures were grown by atmospheric-pressure metalorganic vapor phase epitaxy. A preliminary assessment of the effects of grid-collection distance and emitter-sheet resistance on cell performance is presented. At concentration ratios of around 100, cells with efficiencies of 21.4 percent AM0 (24.3 percent direct) at 25 C are fabricated. These are the highest efficiencies yet reported for single-junction InP solar cells. The performance of these cells as a function of temperature is discussed, and areas for future improvement are outlined. Application of these results to other InP-based photovoltaic devices is discussed.

Ward, J. S.↗

Eleventh Workshop for Computational Fluid Dynamic Applications in Rocket Propulsion, Part 1

Conference publication includes 79 abstracts and presentations given at the Eleventh Workshop for Computational Fluid Dynamic Applications in Rocket Propulsion held at the George C. Marshall Space Flight Center, April 20-22, 1993. The purpose of this workshop is to discuss experimental and computational fluid dynamic activities in rocket propulsion. The workshop is an open meeting for government, industry, and academia. A broad number of topics are discussed including computational fluid dynamic methodology, liquid and solid rocket propulsion, turbomachinery, combustion, heat transfer, and grid generation.

Williams, Robert W.↗