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At least 1,081 records · Page 60

Acoustic propagation in curved ducts with extended reacting wall treatment

A finite-element Galerkin formulation was employed to study the attenuation of acoustic waves propagating in two-dimensional S-curved ducts with absorbing walls without a mean flow. The reflection and transmission at the entrance and the exit of a curved duct were determined by coupling the finite-element solutions in the curved duct to the eigenfunctions of an infinite, uniform, hard wall duct. In the frequency range where the duct height and acoustic wave length are nearly equal, the effects of duct length, curvature (duct offset) and absorber thickness were examined. For a given offset in the curved duct, the length of the S-duct was found to significantly affect both the absorptive and reflective characteristics of the duct. A means of reducing the number of elements in the absorber region was also presented. In addition, for a curved duct, power attenuation contours were examined to determine conditions for maximum acoustic power absorption. Again, wall curvature was found to significantly effect the optimization process.

Baumeister, Kenneth J.↗

Ammonia Permeation Through Inorganic Membranes

Moisture probes are used in the tritium facility to measure the moisture content of the gas stream. When tritium reacts with nitrogen to form ammonia, the ammonia gas damages the sensitive moisture probe. The gas stream tested during this experiment for moisture probe protection is composed of nitrogen and argon gas in conjunction with ammonia and water vapor. The gas stream is filtered through an inorganic membrane due to the high reactivity of tritium and a residual gas analyzer (RGA) is used to measure the ammonia and water vapor in the gas stream, as well as the permeability of nitrogen and argon through the inorganic membranes. The membranes tested were boron nitride and silver. The permeability was compared for each membrane at different pressures and flow rates. Fourier-transformed infrared spectroscopy (FT-IR) was used to compare the membranes before and after ammonia permeation. Ammonia gas is a byproduct formed from tritium gas reacting with nitrogen in the gas stream, similar to the Haber Process which occurs when hydrogen reacts with nitrogen [2]. The corrosive nature of ammonia damages metals and sensitive instruments such as moisture probes. Moisture probes are essential in various gas and liquid processes for measuring the moisture content of a gas. Membrane research has found that graphene oxide membranes successfully uptake ammonia from the gas stream at a humidity of approximately 30% at which point the pores pin closed, preventing gas permeation. Further research is being conducted to find an inorganic membrane that will prevent ammonia permeation thus circumventing damage to the sensitive moisture probe. The permeation measurements for argon and nitrogen gas and water and ammonia vapor were measured at various pressures of 800, 1000, 1200, 1500, 1800, and 2000 torr. The permeability average (PA) was calculated for each filter using a Barrer calculation. The average permeations for each filter were then compared. The gas composition was measured using the RGA Nitrogen was permeated through the membranes after ammonia permeation and a FT-IR spectrum was obtained. Boron Nitride: As the nitrogen pressure increased, the permeability of the membrane decreased from 800-1200 torr and remained relatively unchanged from 1200-2000 torr. The membrane exhibited a slight decrease in argon permeability from 800-1200 torr and a slight increase from 1500-2000 torr. The boron nitride membrane when permeated with ammonia and nitrogen prevented less ammonia permeation compared to the blank filter. The boron nitride filter demonstrated a decrease in permeability after ammonia permeation. Silver Membrane: When permeated with nitrogen alone, the membrane permeability decreased from 800 torr to 1200 torr. The permeability of the membrane showed little difference as pressure increased from 1200 torr. When permeated with argon, the same phenomenon occurred but on a much smaller scale. When compared to the blank and the boron nitride membranes the silver membrane exhibited significantly lower permeability. This may be in part due to the coating on the silver membrane and differences in pore size of the membranes. During permeation with ammonium hydroxide vapor and nitrogen, the partial pressure of the ammonia increased as compared to the blank membrane. The permeability before and after permeation with ammonia and nitrogen were compared. Permeability values suggested that after being permeated with the ammonia that the permeability for lower pressures increased slightly. There was no significant change in the FT-IR spectrums before and after permeation. Future work: Continue testing various inorganic membranes for ammonia permeation. Further research chemical separation of ammonia from the gas stream, which may prove difficult due to the high reactivity of tritium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Implementation of a High-Fidelity Interface Resolving Method in Nek5000

The development and utilization of computational fluid dynamics (CFD) models for large, high-temperature electric melters in the Waste Treatment and Immobilization Plant (WTP) in eastern Washington State have proven to be valuable for various purposes. These models allow for a better understanding of the physio-chemical processes occurring within the melter vessels and can contribute to improving operational efficiency, throughput, and addressing operational issues related to vitrification. The CFD models employed for these melter vessels incorporate multiphase fluid flow and heat transfer simulations in different regions, including the plenum, cold cap, and molten glass regions. As the tank waste and glass formers are introduced into the melter, a reacting batch layer known as the cold cap forms on top of the molten glass. To enhance the melt rate, forced convection bubblers located at the bottom of the melters generate convection currents that help homogenize the molten glass and provide heat to the cold cap. As the bubbles rise through the highly viscous glass, they adopt a spherical-cap shape [1]. Meanwhile, the conversion of the batch to glass generates significant amounts of gases (such as water vapor, carbon dioxide, sulfur dioxide, and NOx) due to thermal decomposition [2]. These gases become trapped between the cold cap and molten glass, forming a foam layer [3]. For modeling multiphase flow in CFD and heat transfer simulations of waste glass melters at different scales, efforts are underway to augment the capabilities of the Nek5000 [4] and NekRS [5] open-source codes [6]. Nek5000/NekRS is a scalable and efficient spectral element code that has been successfully applied to a wide range of fluid dynamics problems. By leveraging the Nek5000/NekRS software, it becomes possible to model the melter systems more affordably and with lower computational requirements compared to currently utilized commercial CFD software. The specific objectives of this ongoing effort include: 1. Implementation of a level set method in Nek5000/NekRS: The level set method is a numerical technique commonly employed in CFD simulations to track and represent the interface between different phases or materials accurately. By incorporating this method into Nek5000/NekRS, the ability to simulate multiphase flows in waste glass melters at a high level of fidelity can be achieved. 2. Demonstration of capability for air bubbling through molten glass: As part of the development process, a specific case of air bubbling through molten glass will be simulated using the augmented Nek5000/NekRS code. This demonstration aims to showcase the ability of the software to accurately capture and analyze the complex phenomena involved in the multiphase flow within waste glass melters. By achieving these objectives, the improved Nek5000/NekRS code will offer a powerful computational tool for simulating and analyzing waste glass melter systems, enabling better understanding, optimization, and troubleshooting of these vitrification processes. The ability to accurately model and simulate multiphase flows has broad relevance across many industries and scientific domains, and the improved functionality can contribute to advancements in various fields beyond waste glass melter simulations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Study of Plume Impingement Effects in the Lunar Lander Environment

Plume impingement effects from the descent and ascent engine firings of the Lunar Lander were analyzed in support of the Lunar Architecture Team under the Constellation Program. The descent stage analysis was performed to obtain shear and pressure forces on the lunar surface as well as velocity and density profiles in the flow field in an effort to understand lunar soil erosion and ejected soil impact damage which was analyzed as part of a separate study. A CFD/DSMC decoupled methodology was used with the Bird continuum breakdown parameter to distinguish the continuum flow from the rarefied flow. The ascent stage analysis was performed to ascertain the forces and moments acting on the Lunar Lander Ascent Module due to the firing of the main engine on take-off. The Reacting and Multiphase Program (RAMP) method of characteristics (MOC) code was used to model the continuum region of the nozzle plume, and the Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) was used to model the impingement results in the rarefied region. The ascent module (AM) was analyzed for various pitch and yaw rotations and for various heights in relation to the descent module (DM). For the ascent stage analysis, the plume inflow boundary was located near the nozzle exit plane in a region where the flow number density was large enough to make the DSMC solution computationally expensive. Therefore, a scaling coefficient was used to make the DSMC solution more computationally manageable. An analysis of the effectiveness of this scaling technique was performed by investigating various scaling parameters for a single height and rotation of the AM. Because the inflow boundary was near the nozzle exit plane, another analysis was performed investigating three different inflow contours to determine the effects of the flow expansion around the nozzle lip on the final plume impingement results.

Marichalar, Jeremiah↗

Silicon production in an aerosol reactor

An aerosol reactor for the growth of large silicon particles by silane pyrolysis was shown to demonstrate the following properties: (1) generate seed particles by pyrolysis of a small amount of silane; (2) mix seed aerosol with primary silane flow, limiting number concentration such that the amount of silane is sufficient to grow the desired size of particles from the seed; and (3) react the silane at a rate which is controlled such that the seed particles scavenge the condensible vapors rapidly enough to inhibit further nucleation.

Wu, J. J.↗

Multiphysics Thermal-Fluid Design Analysis of a Non-Nuclear Tester for Hot-Hydrogen Materials and Component Development

The objective of this effort is to perform design analyses for a non-nuclear hot-hydrogen materials tester, as a first step towards developing efficient and accurate multiphysics, thermo-fluid computational methodology to predict environments for hypothetical solid-core, nuclear thermal engine thrust chamber design and analysis. The computational methodology is based on a multidimensional, finite-volume, turbulent, chemically reacting, thermally radiating, unstructured-grid, and pressure-based formulation. The multiphysics invoked in this study include hydrogen dissociation kinetics and thermodynamics, turbulent flow, convective, and thermal radiative heat transfers. The goals of the design analyses are to maintain maximum hot-hydrogen jet impingement energy and to minimize chamber wall heating. The results of analyses on three test fixture configurations and the rationale for final selection are presented. The interrogation of physics revealed that reactions of hydrogen dissociation and recombination are highly correlated with local temperature and are necessary for accurate prediction of the hot-hydrogen jet temperature.

Wang, Ten-See↗

Analysis of Material Sample Heated by Impinging Hot Hydrogen Jet in a Non-Nuclear Tester

A computational conjugate heat transfer methodology was developed and anchored with data obtained from a hot-hydrogen jet heated, non-nuclear materials tester, as a first step towards developing an efficient and accurate multiphysics, thermo-fluid computational methodology to predict environments for hypothetical solid-core, nuclear thermal engine thrust chamber. The computational methodology is based on a multidimensional, finite-volume, turbulent, chemically reacting, thermally radiating, unstructured-grid, and pressure-based formulation. The multiphysics invoked in this study include hydrogen dissociation kinetics and thermodynamics, turbulent flow, convective and thermal radiative, and conjugate heat transfers. Predicted hot hydrogen jet and material surface temperatures were compared with those of measurement. Predicted solid temperatures were compared with those obtained with a standard heat transfer code. The interrogation of physics revealed that reactions of hydrogen dissociation and recombination are highly correlated with local temperature and are necessary for accurate prediction of the hot-hydrogen jet temperature.

Wang, Ten-See↗

Approximate convective heating equations for hypersonic flows

Laminar and turbulent heating-rate equations appropriate for engineering predictions of the convective heating rates about blunt reentry spacecraft at hypersonic conditions are developed. The approximate methods are applicable to both nonreacting and reacting gas mixtures for either constant or variable-entropy edge conditions. A procedure which accounts for variable-entropy effects and is not based on mass balancing is presented. Results of the approximate heating methods are in good agreement with existing experimental results as well as boundary-layer and viscous-shock-layer solutions.

Zoby, E. V.↗

An Integrated Tool for the Coupled Thermal and Mechanical Analysis of Pyrolyzing Heatshield Materials

Materials that pyrolyze at elevated temperature have been commonly used as thermal protection materials in hypersonic flight, and advanced pyrolyzing materials for this purpose continue to be developed. Because of the large temperature gradients that can arise in thermal protection materials, significant thermal stresses can develop. Advanced applications of pyrolytic materials are calling for more complex heatshield configurations, making accurate thermal stress analysis more important, and more challenging. For non-pyrolyzing materials, many finite element codes are available and capable of performing coupled thermal-mechanical analyses. These codes do not, however, have a built-in capability to perform analyses that include pyrolysis effects. When a pyrolyzing material is heated, one or more components of the original virgin material pyrolyze and create a gas. This gas flows away from the pyrolysis zone to the surface, resulting in a reduction in surface heating. A porous residue, referred to as char, remains in place of the virgin material. While the processes involved can be complex, it has been found that a simple physical model in which virgin material reacts to form char and pyrolysis gas, will yield satisfactory analytical results. Specifically, the effects that must be modeled include: (1) Variation of thermal properties (density, specific heat, thermal conductivity) as the material composition changes; (2) Energy released or absorbed by the pyrolysis reactions; (3) Energy convected by the flow of pyrolysis gas from the interior to the surface; (4) The reduction in surface heating due to surface blowing; and (5) Chemical and mass diffusion effects at the surface between the pyrolysis gas and edge gas Computational tools for the one-dimensional thermal analysis these materials exist and have proven to be reliable design tools. The objective of the present work is to extend the analysis capabilities of pyrolyzing materials to axisymmetric configurations, and to couple thermal and mechanical analyses so that thermal stresses may be efficiently and accurately calculated.

Pronchick, Stephen W.↗

Numerical simulations of the superdetonative ram accelerator combusting flow field

The effects of projectile canting and fins on the ram accelerator combusting flowfield and the possible cause of the ram accelerator unstart are investigated by performing axisymmetric, two-dimensional, and three-dimensional calculations. Calculations are performed using the INCA code for solving Navier-Stokes equations and a guasi-global combustion model of Westbrook and Dryer (1981, 1984), which includes N2 and nine reacting species (CH4, CO, CO2, H2, H, O2, O, OH, and H2O), which are allowed to undergo a 12-step reaction. It is found that, without canting, interactions between the fins, boundary layers, and combustion fronts are insufficient to unstart the projectile at superdetonative velocities. With canting, the projectile will unstart at flow conditions where it appears to accelerate without canting. Unstart occurs at some critical canting angle. It is also found that three-dimensionality plays an important role in the overall combustion process.

Soetrisno, Moeljo↗

Limitations of cetane number to predict transient combustion phenomena in high-pressure fuel sprays

Fundamental understanding of in-cylinder processes in diesel engines is important to screen emerging biofuels and advanced combustion modes that can reduce greenhouse gas emissions and regulated pollutants including soot. In this study, the role of fuel properties on spray development and combustion is investigated by systematically isolating chemical and thermophysical effects. Three different fuels are considered, two with similar chemical properties and two with similar thermophysical properties with one fuel common to both groups. Experiments are performed in a constant-pressure flow chamber de-signed to provide stable test conditions and facilitate acquisition of at least 150 injections in quick succession for each fuel under reacting conditions at high-pressure, high-temperature ambient conditions using a modified conventional diesel engine injector. Further, high speed optical diagnostics including rainbow schlieren deflectometry, OH* chemiluminescence, and a two-color pyrometry system are employed to simultaneously image the transient spray and reacting jets. Image analysis is performed to determine liquid length, vapor penetration length, timing and location of first stage and main ignition events, lift-off location, total soot mass, and more. Results show that fuels with similar chemical properties or cetane number (CN) exhibit similar delay times for first stage and main ignition events as may be expected, but very different liquid length, first stage and main ignition locations, lift-off length, apparent turbulent flame speed, and soot formation. As such, the ability to characterize candidate biofuels with CN or other parameters derived from simple flame configurations is called into question. In this study, thermo-physical properties controlling the liquid length are identified as the main contributing factor for the observed differences.

33 ADVANCED PROPULSION SYSTEMS↗

Catalytic Microtube Rocket Igniter

Devices that generate both high energy and high temperature are required to ignite reliably the propellant mixtures in combustion chambers like those present in rockets and other combustion systems. This catalytic microtube rocket igniter generates these conditions with a small, catalysis-based torch. While traditional spark plug systems can require anywhere from 50 W to multiple kW of power in different applications, this system has demonstrated ignition at less than 25 W. Reactants are fed to the igniter from the same tanks that feed the reactants to the rest of the rocket or combustion system. While this specific igniter was originally designed for liquid methane and liquid oxygen rockets, it can be easily operated with gaseous propellants or modified for hydrogen use in commercial combustion devices. For the present cryogenic propellant rocket case, the main propellant tanks liquid oxygen and liquid methane, respectively are regulated and split into different systems for the individual stages of the rocket and igniter. As the catalyst requires a gas phase for reaction, either the stored boil-off of the tanks can be used directly or one stream each of fuel and oxidizer can go through a heat exchanger/vaporizer that turns the liquid propellants into a gaseous form. For commercial applications, where the reactants are stored as gases, the system is simplified. The resulting gas-phase streams of fuel and oxidizer are then further divided for the individual components of the igniter. One stream each of the fuel and oxidizer is introduced to a mixing bottle/apparatus where they are mixed to a fuel-rich composition with an O/F mass-based mixture ratio of under 1.0. This premixed flow then feeds into the catalytic microtube device. The total flow is on the order of 0.01 g/s. The microtube device is composed of a pair of sub-millimeter diameter platinum tubes connected only at the outlet so that the two outlet flows are parallel to each other. The tubes are each approximately 10 cm long and are heated via direct electric resistive heating. This heating brings the gasses to their minimum required ignition temperature, which is lower than the auto-thermal ignition temperature, and causes the onset of both surface and gas phase ignition producing hot temperatures and a highly reacting flame. The combustion products from the catalytic tubes, which are below the melting point of platinum, are injected into the center of another combustion stage, called the primary augmenter. The reactants for this combustion stage come from the same source but the flows of non-premixed methane and oxygen gas are split off to a secondary mixing apparatus and can be mixed in a near-stoichiometric to highly lean mixture ratio. The primary augmenter is a component that has channels venting this mixed gas to impinge on each other in the center of the augmenter, perpendicular to the flow from the catalyst. The total crosssectional area of these channels is on a similar order as that of the catalyst. The augmenter has internal channels that act as a manifold to distribute equally the gas to the inward-venting channels. This stage creates a stable flame kernel as its flows, which are on the order of 0.01 g/s, are ignited by the combustion products of the catalyst. This stage is designed to produce combustion products in the flame kernel that exceed the autothermal ignition temperature of oxygen and methane.

Schneider, Steven J.↗

Computational Assessment of Inlet Backflow Effects on Rotating Detonation Engine Performance and Operability

The performance impact of flow reversal at the inlet of an airbreathing rotating detonation engine (RDE) is investigated using 2 and 3-dimensional computational fluid dynamic (CFD) simulations. Flow reversal, or backflow, occurs in RDE inlets in the high-pressure region directly behind the rotating detonation front. This is also where most of the engine thrust or pressure gain is produced. The amount of backflow relative to throughflow depends on the inlet design. For the present work, a simple annular ‘slit’ design is used. The simulations are idealized in several ways, including that fuel and air are premixed, but prevented from reacting when within the inlet region. The results indicate that even with idealizations, the impact of inlet backflow on pressure gain can be substantial. The simulations also reveal an intriguing instability that develops in certain configurations. The mass flow rate into the RDE begins to oscillate at a regular frequency that is substantially less than the detonation rotational frequency. This is accompanied by oscillations in the detonation height. The oscillation amplitude grows over time until the detonation ultimately fails. Both the performance and instability results emphasize the need for carefully designed RDE inlets that provide low loss when flow is in the forward direction, but high resistance when the flow is reversed. Development of such high-diodicity inlets is critical to achieving pressure gain in airbreathing RDE’s.

Detonation↗

Computational Assessment of Inlet Backflow Effects on Rotating Detonation Engine Performance and Operability

The performance impact of flow reversal at the inlet of an airbreathing rotating detonation engine (RDE) is investigated using 2 and 3-dimensional computational fluid dynamic (CFD) simulations. Flow reversal, or backflow, occurs in RDE inlets in the high-pressure region directly behind the rotating detonation front. This is also where most of the engine thrust or pressure gain is produced. The amount of backflow relative to throughflow depends on the inlet design. For the present work, a simple annular ‘slit’ design is used. The simulations are idealized in several ways, including that fuel and air are premixed, but prevented from reacting when within the inlet region. The results indicate that even with idealizations, the impact of inlet backflow on pressure gain can be substantial. The simulations also reveal an intriguing instability that develops in certain configurations. The mass flow rate into the RDE begins to oscillate at a regular frequency that is substantially less than the detonation rotational frequency. This is accompanied by oscillations in the detonation height. The oscillation amplitude grows over time until the detonation ultimately fails. Both the performance and instability results emphasize the need for carefully designed RDE inlets that provide low loss when flow is in the forward direction, but high resistance when the flow is reversed. Development of such high-diodicity inlets is critical to achieving pressure gain in airbreathing RDE’s.

detonation↗

Superior performance biodiesel from biomass-derived fusel alcohols and low grade oils: Fatty acid fusel esters (FAFE)

We demonstrated production of a superior performance biodiesel referred to here as fatty acid fusel alcohol esters (FAFE) – by reacting fusel alcohols (isobutanol, 3-methyl-1-butanol, and (S)-(-)-2-methyl-1-butanol) with oil (glyceryl trioleate) using lipase from Aspergillus oryzae. Reaction conditions corresponding to a molar ratio of 5:1 (fusel alcohols to oil), enzyme loading of 2% w/w, reaction temperature of 35 °C, shaking speed of 250 rpm, and reaction time of 24 h achieved >97% conversion to FAFE. Further, FAFE obtained from reacting a fusel alcohol mixture with corn oil were evaluated for use as a fuel for diesel engines. FAFE mixtures showed superior combustion and cold-flow properties, with the derived cetane numbers up to 4.8 points higher, cloud points up to -6 °C lower, and the heat of combustion up to 2.1% higher than the corresponding FAME samples, depending on the fusel mixture used. This represents a significant improvement for all three metrics, which are typically anti-correlated. Finally, FAFE provides a new opportunity for expanded usage of biodiesel by addressing feedstock limitations, fuel performance, and low temperature tolerance.

09 BIOMASS FUELS↗

Direct numerical simulations for hybrid rocket boundary layers: Performance modeling and scaling

This paper presents a comprehensive performance and scaling analysis of direct numerical simulations for reacting boundary layers, focusing on slab burner configurations. Using a PETSc-based finite volume CFD framework, the study evaluates the scalability and computational cost of flow, chemistry, and radiation evaluations across 2D and 3D simulations. Polymethyl methacrylate (PMMA) is the fuel with pure O 2 as the oxidizer, modeled using a detailed chemical kinetics mechanism with 113 species and 660 reactions. A ray-tracing-based radiation solver, designed for distributed memory applications, is implemented to model radiation heat transfer. Parallel scalability is analyzed for the coupled flow, chemistry, and radiation heat transfer processes. Weak and strong scaling studies are conducted on up to 15,000 computational ranks, revealing robust performance when flow cells exceed 200 per rank. Chemistry evaluations dominate the computational cost in large 3D simulations, accounting for approximately 40% of the total runtime, while flow processes contribute around 35%, and radiation solver contributions remain below 10% due to reduced evaluation frequencies. GPU accelerated chemistry evaluation, implemented with Zero-RK, demonstrates significant promise, achieving up to a 4x speedup for workloads exceeding 30,000 cells per GPU. However, diminishing returns are observed for smaller workloads due to CPU-GPU communication overhead. This study identifies key challenges, including memory bottlenecks and the effects of domain partitioning on flow scalability, while highlighting the potential of GPU-accelerated chemistry to reduce computational costs. In conclusion, these findings provide realizable run configurations for 2D, 3D, and GPU-accelerated cases, offering insights for optimizing reactive flow solvers.

CFD Scalability↗

Comprehensive uncertainty quantification (UQ) for full engineering models by solving probability density function (PDF) equation

This report details a new method for propagating parameter uncertainty (forward uncertainty quantification) in partial differential equations (PDE) based computational mechanics applications. The method provides full-field quantities of interest by solving for the joint probability density function (PDF) equations which are implied by the PDEs with uncertain parameters. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known apriori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the driving (dynamics) term of the PDEs based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the dynamics term of the governing PDEs. The efficacy of the method is demonstrated by applying it to two target problems: solid mechanics explicit dynamics with uncertain material model parameters, and reacting hypersonic fluid mechanics with uncertain chemical kinetic rate parameters. A minimally invasive implementation of the method for representative codes SPARC (reacting hypersonics) and NimbleSM (finite- element solid mechanics) and associated software details are described. For solid mechanics demonstration problems the method shows order of magnitudes improvement in accuracy over traditional stochastic collocation. For the reacting hypersonics problem, the method is implemented as a streamline integration and results show very good accuracy for the approximate sample solutions of re-entry flow past the Apollo capsule geometry at Mach 30.

42 ENGINEERING↗