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NASA NTRS2003

Finite Volume Methods: Foundation and Analysis

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Barth, Timothy↗

NASA NTRS1996

Spray Combustion Modeling with VOF and Finite-Rate Chemistry

A spray atomization and combustion model is developed based on the volume-of-fluid (VOF) transport equation with finite-rate chemistry model. The gas-liquid interface mass, momentum and energy conservation laws are modeled by continuum surface force mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed range flows. The objectives of the present study are: (1) to develop and verify the fractional volume-of-fluid (VOF) cell partitioning approach into a predictor-corrector algorithm to deal with multiphase (gas-liquid) free surface flow problems; (2) to implement the developed unified algorithm in a general purpose computational fluid dynamics (CFD) code, Finite Difference Navier-Stokes (FDNS), with droplet dynamics and finite-rate chemistry models; and (3) to demonstrate the effectiveness of the present approach by simulating benchmark problems of jet breakup/spray atomization and combustion. Modeling multiphase fluid flows poses a significant challenge because a required boundary must be applied to a transient, irregular surface that is discontinuous, and the flow regimes considered can range from incompressible to highspeed compressible flows. The flow-process modeling is further complicated by surface tension, interfacial heat and mass transfer, spray formation and turbulence, and their interactions. The major contribution of the present method is to combine the novel feature of the Volume of Fluid (VOF) method and the Eulerian/Lagrangian method into a unified algorithm for efficient noniterative, time-accurate calculations of multiphase free surface flows valid at all speeds. The proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and gas), and tracks droplets on a Lagrangian frame when spray model is required, using a unified predictor-corrector technique to account for the non-linear linkages through the convective contributions of VOF. The discontinuities within the sharp interface will be modeled as a volume force to avoid stiffness. Formations of droplets, tracking of droplet dynamics and modeling of the droplet breakup/evaporation, are handled through the same unified predictor-corrector procedure. Thus the new algorithm is non-iterative and is flexible for general geometries with arbitrarily complex topology in free surfaces. The FDNS finite-difference Navier-Stokes code is employed as the baseline of the current development. Benchmark test cases of shear coaxial LOX/H2 liquid jet with atomization/combustion and impinging jet test cases are investigated in the present work. Preliminary data comparisons show good qualitative agreement between data and the present analysis. It is indicative from these results that the present method has great potential to become a general engineering design analysis and diagnostics tool for problems involving spray combustion.

Chen, Yen-Sen↗

NASA NTRS2003

Quantitative Studies on the Propagation and Extinction of Near-Limit Premixed Flames Under Normal and Microgravity

The main objective of this research is to introduce accurate fluid mechanics measurements diagnostics in the 2.2-s drop tower for the determination of the detailed flow-field at the states of extinction. These results are important as they can then be compared with confidence with detailed numerical simulations so that important insight is provided into near-limit phenomena that are controlled by not well-understood kinetics and thermal radiation processes. Past qualitative studies did enhance our general understanding on the subject. However, quantitative studies are essential for the validation of existing models that subsequently be used to describe near-limit phenomena that can initiate catastrophic events in micro- and/or reduced gravity environments.

Dong, Y.↗

NASA NTRS1971

On some problems in a theory of thermally and mechanically interacting continuous media

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

Lee, Y. M.↗

NASA NTRS1991

NASA-UVA Light Aerospace Alloy and Structures Technology Program (LA2ST)

The general objective of the Light Aerospace Alloy and Structures Technology (LA2ST) Program is to conduct interdisciplinary graduate student research on the performance of next generation, light weight aerospace alloys, composites, and associated thermal gradient structures in close collaboration with Langley researchers. Specific technical objectives are established for each research project. Relevant data and basic understanding of material behavior and microstructure, new monolithic and composite alloys, advanced processing methods, new solid and fluid mechanic analyses, measurement advances, and a pool of educated graduate students are sought.

Gangloff, Richard P.↗

NASA NTRS2015

Toxicity of Mineral Dusts and a Proposed Mechanism for the Pathogenesis of Particle-Induced Lung Diseases

Humans will set foot on the moon again. The lunar surface has been bombarded for 4 billion years by micrometeoroids and cosmic radiation, creating a layer of fine dust having a potentially reactive particle surface. To investigate the impact of surface reactivity (SR) on the toxicity of particles, and in particular, lunar dust (LD), we ground 2 Apollo 14 LD samples to increase their SR and compare their toxicity with those of unground LD, TiO2 and quartz. Intratracheally instilled at 0, 1, 2.5, or 7.5 mg/rat, all dusts caused dose-dependent increases in pulmonary lesions, and enhancement of biomarkers of toxicity assessed in bronchoalveolar lavage fluids (BALF). The toxicity of LD was greater than that of TiO2 but less than that of quartz. Three LDs differed 14-fold in SR but were equally toxic; quartz had the lowest SR but was most toxic. These results show no correlation between particle SR and toxicity. Often pulmonary toxicity of a dust can be attributed to oxidative stress (OS). We further observed dose-dependent and dustcytotoxicity- dependent increases in neutrophils. The oxidative content per BALF cell was also directly proportional to both the dose and cytotoxicity of the dusts. Because neutrophils are short-lived and release of oxidative contents after they die could initiate and promote a spectrum of lesions, we postulate a general mechanism for the pathogenesis of particle-induced diseases in the lung that involves chiefly neutrophils, the source of persistent endogenous OS. This mechanism explains why one dust (e.g., quartz or nanoparticles) is more toxic than another (e.g., micrometer-sized TiO2), why dust-induced lesions progress with time, and why lung cancer occurs in rats but not in mice and hamsters exposed to the same duration and concentration of dust.

Lam, C.‐W.↗

NASA NTRS1995

Microgravity research opportunities for the 1990s

The Committee on Microgravity Research (CMGR) was made a standing committee of the Space Studies Board (SSB) and charged with developing a long-range research strategy. The scientific disciplines contained within the microgravity program, and covered in this report, include fluid mechanics and transport phenomena, combustion, biological sciences and biotechnology, materials science, and microgravity physics. The purpose of this report is to recommend means to accomplish the goal of advancing science and technology in each of the component disciplines. Microgravity research should be aimed at making significant impacts in each discipline emphasized. The conclusions and recommendations presented in this report fall into five categories: (1) overall goals for the microgravity research program; (2) general priorities among the major scientific disciplines affected by gravity; (3) identification of the more promising experimental challenges and opportunities within each discipline; (4) general scientific recommendations that apply to all microgravity-related disciplines; and (5) recommendations concerning administrative policies and procedures that are essential to the conduct of excellent laboratory science.

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NASA NTRS2000

Analysis of the Radar Reflectivity of Aircraft Vortex Wakes

Radar has been proposed as a way to track wake vortices to reduce aircraft spacing and tests have revealed radar echoes from aircraft wakes in clear air. The results are always interpreted qualitatively using Tatarski's theory of weak scattering by isotropic atmospheric turbulence. The goal of the present work was to predict the value of the radar cross-section (RCS) using simpler models. This is accomplished in two steps. First, the refractive index is obtained. Since the structure of the aircraft wakes is different from atmospheric turbulence, three simple mechanisms specific to vortex wakes are considered: (1) Radial density gradient in a two-dimensional vortex, (2) three-dimensional fluctuations in the vortex cores, and (3) Adiabatic transport of the atmospheric fluid in a two-dimensional oval surrounding the pair of vortices. The index of refraction is obtained more precisely for the two-dimensional mechanisms than for the three-dimensional ones. In the second step, knowing the index of refraction, a scattering analysis is performed. Tatarski's weak scattering approximation is kept but the usual assumptions of a far-field and a uniform incident wave are dropped. Neither assumption is generally valid for a wake that is coherent across the radar beam. For analytical insight, a simpler approximation that invokes, in addition to weak scattering, the far-field and wide cylindrical beam assumptions, is also developed and compared with the more general analysis. The predicted RCS values for the oval surround the vortices (mechanism C) agree with the experiments of Bilson conducted over a wide range of frequencies. However, the predictions have a cut-off away from normal incidence which is not present in the measurements. Estimates suggest that this is due to turbulence in the baroclinic vorticity generated at the boundary of the oval. The reflectivity of a vortex itself (mechanism A) is comparable to that of the oval (mechanism C) but cuts-off at frequencies lower than those considered in all the experiments to date. The RCS of a vortex happens to peak at the frequency (about 49 MHz) where atmospheric radars (known as ST radars) operate and so the present prediction could be verified in the future. Finally , we suggest that hot engine exhaust could increase RCE by 40 db and reveal vortex circulation, provided its mixing with the surroundings is prevented in the laminarising flow of the vortices.

Shariff, Karim↗

NASA NTRS1972

The fluid mechanics of thrombus formation

Experimental data are presented for the growth of thrombi (blood clots) in a stagnation point flow of fresh blood. Thrombus shape, size and structure are shown to depend on local flow conditions. The evolution of a thrombus is described in terms of a physical model that includes platelet diffusion, a platelet aggregation mechanism, and diffusion and convection of the chemical species responsible for aggregation. Diffusion-controlled and convection-controlled regimes are defined by flow parameters and thrombus location, and the characteristic growth pattern in each regime is explained. Quantitative comparisons with an approximate theoretical model are presented, and a more general model is formulated.

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NASA NTRS2000

Mechanisms for the Crystallization of ZBLAN

A number of research teams have observed that glass forming melts that are solidified in low-g exhibit enhanced glass formation. This project will examine one of these glasses, the heavy metal fluoride glass ZBLAN. A four year ground based research program has been approved to examine the crystallization of ZBLAN glasses with the purpose of testing a theory for the crystallization of ZBLAN glass. The theory could explain the general observations of enhanced glass formation of other glasses melted and solidified in low-g. Fluid flow in 1-g results from buoyancy forces and surface tension driven convection. This fluid flow can introduce shear in undercooled liquids in 1-g. In low-g it is known that fluid flows are greatly reduced so that the shear rate in fluids in low-g are extremely low. It is believed that fluids may have some weak structure in the absence of flow. Even very small shear rates could cause this structure to collapse in response to the shear. A general result would be shear thinning of the fluid. The hypothesis of this research is that: Shear thinning in undercooled liquids increases the rate of nucleation and crystallization of glass forming melts. Shear of the melt can be reduced in low-g enhancing undercooling and glass formation. Samples will be melted and quenched in 1-g under quiescent conditions at a number of controlled cooling rates to determine times and temperatures of crystallization and heated at controlled heating rates to determine kinetic crystallization parameters. Experiments will also be performed on the materials while under controlled vibration conditions and compared with the quiescent experiments in order to evaluate the effect of shear in the liquid on crystallization kinetics. After the experimental parameters are well known, experiments will be repeated under low-g (and 2-g) conditions on the KC-135 aircraft during low-g parabolic maneuvers. The results will determine the effects of shear on crystallization. Our experimental setups will be designed with low-g experiments in mind and will be tested as breadboard low-g experiments. It is very likely that the thermal analysis instrumentation can be adapted to be run in the microgravity glovebox facilities. Critical space experiments may result to test the theory at longer low-g time experiments in space.

Ethridge, Edwin C.↗

NASA NTRS1998

Summer Work Experience: Determining Methane Combustion Mechanisms and Sub-Scale Diffuser Properties for Space Transporation System Engine Testing

To assess engine performance during the testing of Space Shuttle Main Engines (SSMEs), the design of an optimal altitude diffuser is studied for future Space Transportation Systems (STS). For other Space Transportation Systems, rocket propellant using kerosene is also studied. Methane and dodecane have similar reaction schemes as kerosene, and are used to simulate kerosene combustion processes at various temperatures. The equations for the methane combustion mechanism at high temperature are given, and engine combustion is simulated on the General Aerodynamic Simulation Program (GASP). The successful design of an altitude diffuser depends on the study of a sub-scaled diffuser model tested through two-dimensional (2-D) flow-techniques. Subroutines given calculate the static temperature and pressure at each Mach number within the diffuser flow. Implementing these subroutines into program code for the properties of 2-D compressible fluid flow determines all fluid characteristics, and will be used in the development of an optimal diffuser design.

Williams, Powtawche N.↗

NASA NTRS2020

Mars Ascent Vehicle Solid Propulsion Configuration

As part of a Mars Sample Return (MSR) campaign, two Mars Ascent Vehicle (MAV) configurations have been designed in parallel. Each ascent vehicle configuration has a different propulsion system, which ultimately leads to two unique vehicle designs. As part of a Preliminary Architecture Assessment (PAA), these vehicle designs were developed to the same level of maturity in order to inform the selection of one of the vehicles as the point of departure design for the campaign. The selection will be made in November 2019. Although the initial MSR architecture called for a hybrid-based propulsion MAV featuring solid wax fuel with liquid oxidizer, a configuration using more traditional solid propulsion was developed as an additional risk mitigation option. Though lacking in the single stage to orbit (SSTO) and throttle flexibility of a hybrid configuration, a solid configuration vehicle allows a simpler design with significantly longer flight heritage and higher Technology Readiness Level (TRL). This paper describes the design of the solid propulsion configuration. An additional paper will be published describing the design of the hybrid propulsion configuration. The solid propulsion configuration MAV was developed in 2019 by NASA Marshall Space Flight Center (MSFC) in association with NASA Jet Propulsion Laboratory (JPL). It features two stages with a modified STAR-17 motor for the second stage and a traditional electromechanical actuator Thrust Vector Controller (TVC). The vehicle was designed to deliver approximately 0.47kg of Martian geological samples to a circular orbit at Mars of 343km at a 25° inclination. Although solid motor designs in general are at a relatively high TRL, the integrated vehicle subsystems that operate in conjunction with these propulsion elements do not typically operate in a Martian environment, which in this application can get as cold as -40°C. The PAA advanced the maturity of these subsystems by performing detailed design and analysis on the vehicle with respect to structures and mechanisms, Guidance/Navigation/Control (GNC) systems, avionics, Reaction Control System (RCS), TVC, thermal environments, and advanced Computational Fluid Dynamics (CFD). This paper will summarize the results of these studies.

Yaghoubi, Darius↗

NASA NTRS2020

Mars Ascent Vehicle Solid Propulsion Configuration

Yaghoubi, Darius↗

NASA NTRS2010

Fast-Response-Time Shape-Memory-Effect Foam Actuators

Bulk shape memory alloys, such as Nitinol or CuAlZn, display strong recovery forces undergoing a phase transformation after being strained in their martensitic state. These recovery forces are used for actuation. As the phase transformation is thermally driven, the response time of the actuation can be slow, as the heat must be passively inserted or removed from the alloy. Shape memory alloy TiNi torque tubes have been investigated for at least 20 years and have demonstrated high actuation forces [3,000 in.-lb (approximately equal to 340 N-m) torques] and are very lightweight. However, they are not easy to attach to existing structures. Adhesives will fail in shear at low-torque loads and the TiNi is not weldable, so that mechanical crimp fits have been generally used. These are not reliable, especially in vibratory environments. The TiNi is also slow to heat up, as it can only be heated indirectly using heater and cooling must be done passively. This has restricted their use to on-off actuators where cycle times of approximately one minute is acceptable. Self-propagating high-temperature synthesis (SHS) has been used in the past to make porous TiNi metal foams. Shape Change Technologies has been able to train SHS derived TiNi to exhibit the shape memory effect. As it is an open-celled material, fast response times were observed when the material was heated using hot and cold fluids. A methodology was developed to make the open-celled porous TiNi foams as a tube with integrated hexagonal ends, which then becomes a torsional actuator with fast response times. Under processing developed independently, researchers were able to verify torques of 84 in.-lb (approximately equal to 9.5 Nm) using an actuator weighing 1.3 oz (approximately equal to 37 g) with very fast (less than 1/16th of a second) initial response times when hot and cold fluids were used to facilitate heat transfer. Integrated structural connections were added as part of the net shape process, eliminating the need for welding, adhesives, or mechanical crimping. Inexpensive net-shape processing was used, which reduces the cost of the actuator by over a factor of 10 over nonporous TiNi made by hot drawing of tube or electrical discharge machining. By forming the alloy as an open-celled foam, the surface area for heat transfer is dramatically increased, allowing for much faster response times. The technology also allows for netshape fabrication of the actuator, which allows for structural connections to be integrated into the actuator material, making these actuators significantly less expensive. Commercial applications include actuators for concepts such as the variable area chevron and nozzle in jet aircraft. Lightweight tube or rod components can be supplied to interested parties.

Jardine, Peter↗

NASA NTRS1992

NASA-UVA light aerospace alloy and structures technology program (LA(sup 2)ST)

The general objective of the Light Aerospace Alloy and Structures Technology (LA(sup 2)ST) Program is to conduct interdisciplinary graduate student research on the performance of next generation, light weight aerospace alloys, composites, and thermal gradient structures in collaboration with Langley researchers. Specific technical objectives are established for each research project. We aim to produce relevant data and basic understanding of material behavior and microstructure, new monolithic and composite alloys, advanced processing methods, new solid and fluid mechanics analyses, measurement advances, and critically, a pool of educated graduate students for aerospace technologies. Four research areas are being actively investigated, including: (1) Mechanical and Environmental Degradation Mechanisms in Advanced Light Metals and Composites; (2) Aerospace Materials Science; (3) Mechanics of Materials and Composites for Aerospace Structures; and (4) Thermal Gradient Structures.

Gangloff, Richard P.↗

NASA NTRS1992

Reactive collision terms for fluid transport theory

A modified Bhatnagar-Gross-Krook (BGK) collision method is used for the derivation of reactive collision terms to allow for complete higher-moment approximations in fluid transport theory. The general reactive collision terms for the 8-, 10- and 13-moment approximation for binary reactions are derived. Then, reactive collision terms for specific chemistry are derived with the assumptions: (1) all reactants and products have 13-moment distribution functions; (2) simple, classical assumptions provide sufficient models for reaction dynamics; and (3) the reaction rate is energy-independent. The derived specific formulas reflect two extremes in reactive collision dynamics: direct and indirect reaction mechanisms. Finally, considerations for correct use of the reactive collision terms are discussed in the context of space plasma environments.

Eccles, J. V.↗

NASA NTRS2000

Thermophysics Characterization of Kerosene Combustion

A one-formula surrogate fuel formulation and its quasi-global combustion kinetics model are developed to support the design of injectors and thrust chambers of kerosene-fueled rocket engines. This surrogate fuel model depicts a fuel blend that properly represents the general physical and chemical properties of kerosene. The accompanying gaseous-phase thermodynamics of the surrogate fuel is anchored with the heat of formation of kerosene and verified by comparing a series of one-dimensional rocket thrust chamber calculations. The quasi-global combustion kinetics model consists of several global steps for parent fuel decomposition, soot formation, and soot oxidation, and a detailed wet-CO mechanism. The final thermophysics formulations are incorporated with a computational fluid dynamics model for prediction of the combustor efficiency of an uni-element, tri-propellant combustor and the radiation of a kerosene-fueled thruster plume. The model predictions agreed reasonably well with those of the tests.

Wang, Ten-See↗

NASA NTRS2011

CO2 Insulation for Thermal Control of the Mars Science Laboratory

The National Aeronautics and Space Administration (NASA) is sending a large (>850 kg) rover as part of the Mars Science Laboratory (MSL) mission to Mars in 2011. The rover's primary power source is a Multi-Mission Radioisotope Thermoelectric Generator (MMRTG) that generates roughly 2000 W of heat, which is converted to approximately 110 W of electrical power for use by the rover electronics, science instruments, and mechanism-actuators. The large rover size and extreme thermal environments (cold and hot) for which the rover is designed for led to a sophisticated thermal control system to keep it within allowable temperature limits. The pre-existing Martian atmosphere of low thermal conductivity CO2 gas (8 Torr) is used to thermally protect the rover and its components from the extremely cold Martian environment (temperatures as low as -130 deg C). Conventional vacuum based insulation like Multi Layer Insulation (MLI) is not effective in a gaseous atmosphere, so engineered gaps between the warm rover internal components and the cold rover external structure were employed to implement this thermal isolation. Large gaps would lead to more thermal isolation, but would also require more of the precious volume available within the rover. Therefore, a balance of the degree of thermal isolation achieved vs. the volume of rover utilized is required to reach an acceptable design. The temperature differences between the controlled components and the rover structure vary from location to location so each gap has to be evaluated on a case-by-case basis to arrive at an optimal thickness. For every configuration and temperature difference, there is a critical thickness below which the heat transfer mechanism is dominated by simple gaseous thermal conduction. For larger gaps, the mechanism is dominated by natural convection. In general, convection leads to a poorer level of thermal isolation as compared to conduction. All these considerations play important roles in the optimization process. A three-step process was utilized to design this insulation. The first step is to come up with a simple, textbook based, closed-form equation assessment of gap thickness vs. resultant thermal isolation achieved. The second step is a more sophisticated numerical assessment using Computational Fluid Dynamics (CFD) software to investigate the effect of complicated geometries and temperature contours along them to arrive at the effective thermal isolation in a CO2 atmosphere. The third step is to test samples of representative geometries in a CO2 filled chamber to measure the thermal isolation achieved. The results of these assessments along with the consistency checks across these methods leads to the formulation of design-guidelines for gap implementation within the rover geometry. Finally, based on the geometric and functional constraints within the real rover system, a detailed design that accommodates all these factors is arrived at. This paper will describe in detail this entire process, the results of these assessments and the final design that was implemented.

CO2↗