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NASA NTRS2017

Multi-Group Maximum Entropy Model for Translational Non-Equilibrium

The aim of the current work is to describe a new model for flows in translational non- equilibrium. Starting from the statistical description of a gas proposed by Boltzmann, the model relies on a domain decomposition technique in velocity space. Using the maximum entropy principle, the logarithm of the distribution function in each velocity sub-domain (group) is expressed with a power series in molecular velocity. New governing equations are obtained using the method of weighted residuals by taking the velocity moments of the Boltzmann equation. The model is applied to a spatially homogeneous Boltzmann equation with a Bhatnagar-Gross-Krook1(BGK) model collision operator and the relaxation of an initial non-equilibrium distribution to a Maxwellian is studied using the model. In addition, numerical results obtained using the model for a 1D shock tube problem are also reported.

Entropy↗
NASA NTRS1989

Euler and Navier-Stokes solutions for hypersonic flows

An upwind finite-element technique that uses cell-centered quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive unstructured grids in two and three dimensions. A perfect gas model as well as an equilibrium air model is implemented for solving high-speed flows. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been used to predict 'Type III and IV' shock interactions on a cylinder in two dimensions and a swept cylinder in three dimensions, with a view to determine the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are very distinctly captured with a sequence of adaptively-generated grids. Three-dimensional corner flow, typically encountered in engine inlets due to compression of the flow by ramps in the walls, is also modeled. This procedure is the first step in developing an integrated fluid, thermal, structural analysis capability for hypersonic flight vehicles like the National Aero-Space Plane.

Thareja, Rajiv R.↗
NASA NTRSDate not supplied

Wall-modeled LES of the NASA Juncture Flow Experiment

We perform wall-modeled large eddy simulation (WMLES) of the NASA Juncture Flow experiment (Kegerise & Neuhart, NASA/TM–2019–20286) using an equilibrium wall model and unstructured finite volume solver, to assess its predictive ability for complex geometries. The flow condition simulated corresponds to 5 degrees angle of attack with a freestream Mach number of 0.189, and a Reynolds number based on the mean crank chord of 2.4 million. All simulations neglect the effects of wind tunnel walls, sting and mast present in the experiment. To assess the performance of WMLES on simpler flows with very coarse grids, we simulate flow in a turbulent channel at a friction Reynolds number, Reτ≈2000, and flow through a square duct at anReτ≈1000. The duct flow results using the equilibrium wall model indicate that the skin friction is inaccurate near the corner for grid topologies and resolutions typically used in WMLES, having implications for more complicated flows such as the juncture flow. For the juncture flow simulation, two different approaches are investigated. The first approach consists of a truncated-domain simulation wherein the inflow plane of the computational domain is placed at≈0.2chord length of the wing, and we prescribe the mean flow from a separate Reynolds-averaged Navier-Stokes (RANS) solution along with synthetic turbulence to initiate realistic unsteadiness in the domain. The second approach involves simulating the entire geometry with trips to trigger transition to turbulence. The truncated- and full-domain simulations contain about 62 and 90 million cells, respectively; with 8-10 points per boundary layer thickness in the wall-parallel directions, 14-20 points in the wall-normal direction and a near-wall viscous spacing (∆n+1) of≈100. Preliminary results are encouraging overall in terms of the prediction of wall pressure, wall skin friction, velocity and stresses; but indicate that further work is required to improve the predictions in the separation bubble and wing-fuselage corner regions. The grid resolution used in this study is still fairly coarse, and the results should be interpreted as work in progress.

Prahladh S Iyer↗
NASA NTRS2001

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Zhao, C. Y.↗
NASA NTRS1985

Oxidation states of iron in the terrestrial planets: Evidence and implications for accretion models

Analyses of Mars spectra reveal that primary minerals may be more iron rich than average basalts on Earth, and the oxidation state of iron in the pyroxines suggests equally high or higher oxygen fugacities on Mars than Earth. Analysis of Mercury spectra reveal that silicate iron contents are substantially lower than those on Mars. Mercury, however, probably has a substantial iron core. This is consistent with a lower oxidation state of iron on Mercury than on Mars. These findings are consistent with predictions of models of equilibrium condensation and homogeneous accretion. Those models predict that Mercury would have negligible Fe(2+) in silicates (Fe/Fe+Mg approx. 0.5). For Mercury iron should be virtually all metallic, while for Mars the iron would be all oxidized as FeS and silicate. Surface measurements of Fe/Fe+Mg on Venus, Earth, and Mars further support the predicted relative increase in Fe/Fe+Mg ratio (increased oxidation state) with distance from the Sun. The implied high oxygen fugacities on Mars (Fe(3+) in silicates) provide additional consistence with the model predictions.

Huguenin, R. L.↗
NASA NTRS1972

Equilibrium configurations of Vlasov plasmas carrying a current component along an external magnetic field.

A model of equilibrium configurations of Vlasov plasmas is considered which represents a combination of the models of Harris (1962) and Nicholson (1963). These plasma configurations carry a current component along an external magnetic field. The considered slab model contains a diamagnetic current and a field-aligned current for an arbitrary ratio of particle pressure to magnetic pressure of the applied constant field. For a fixed pressure ratio and field-aligned current, the model admits a family of equilibrium solutions in which the diamagnetic currents range from zero to a maximum value. The amount of diamagnetic current flowing in a machine depends on the width of the machine, the field-aligned current and other plasma parameters.

Kan, J. R.↗
NASA NTRS1989

Model formulation of non-equilibrium gas radiation for hypersonic flight vehicles

Several radiation models for low density nonequilibrium hypersonic flow are studied. It is proposed that these models should be tested by the 3-D VRFL code developed at NASA/JSC. A modified and optimized radiation model may be obtained from the testing. Then, the current VRFL code could be expanded to solve hypersonic flow problems with nonequilibrium thermal radiation.

Chang, Ing↗
NASA NTRS2019

Computational Modeling for Non-Equilibrium Shock Tube Flows

Time accurate simulation of non-equilibrium flows inside shock tube facilities presents several challenges from both physical and mathematical aspects. Furthermore, the large computational cost makes it impractical to support a real-time experimental test campaign. In this work, we explore other methods for modeling the shock tube problem with the main focus on the post-shock region and the absolute radiation emanating from it. The proposed alternative approach is several orders of magnitude less computationally expensive while still accurate enough with regards to the quantities of interest. Excellent agreement is found with the established stagnation-line approach. Comparison with time-accurate simulations shows good agreement close to the peak values and disagreement of the temperatures relaxation and radiance profiles toward equilibrium.

Bensassi, Khalil↗
NASA NTRS2019

Computational Modeling for Non-equilibrium Shock Tube Flows

Time accurate simulation of non-equilibrium flows inside shock tube facilities presents several challenges from both physical and mathematical aspects. Furthermore, the drastic computational cost makes it non-practical to support real-time experimental test campaign. In this work, we explore other methods for modeling the shock tube prob- lem with the main focus on the post-shock region and the absolute radiation emanating from it. The proposed alternative approach is several orders of magnitude less computa- tionally expansive while still accurate enough with regards to the quantities of interest. Excellent agreement is found with the well-established stagnation-line approach. Comparison with the time-accurate simulation shows good agreement close to the peak values and disagreement of the temperatures relaxation and radiance profiles toward equilibrium, due to shock speed unsteadiness.

Bensassi, Khalil↗
NASA NTRS1974

Stellar model chromospheres. II - Procyon /F5 IV-V/

Derivation of a model for the chromosphere and upper photosphere of Procyon (F5 IV-V) based on calibrated observations of the K and 8542-A lines of Ca II, the k(2796-A) line of Mg II, and the K-line wings. The feasibility of this model synthesis approach to derive a preliminary model chromosphere is demonstrated despite the lack of spatial and spectral resolution associated with solar chromospheric studies. The proposed upper photosphere model is very similar to the radiative equilibrium Procyon model of Strom and Kurucz (1966), while the proposed chromospheric model is similar to the quiet solar chromosphere temperature distribution of Shine (1973) in the 6000 to 8000 K range.

Ayres, T. R.↗
NASA NTRSDate not supplied

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO). PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Material Response↗
NASA NTRSDate not supplied

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗
NASA NTRS2016

Investigation of Non-Equilibrium Radiation for Earth Entry

For Earth re-entry at velocities between 8 and 11.5 km/s, the accuracy of NASA's computational uid dynamic and radiative simulations of non-equilibrium shock layer radiation is assessed through comparisons with measurements. These measurements were obtained in the NASA Ames Research Center's Electric Arc Shock Tube (EAST) facility. The experiments were aimed at measuring the spatially and spectrally resolved radiance at relevant entry conditions for both an approximate Earth atmosphere (79% N2 : 21% O2 by mole) as well as a more accurate composition featuring the trace species Ar and CO2 (78.08% N2 : 20.95% O2 : 0.04% CO2 : 0.93% Ar by mole). The experiments were configured to target a wide range of conditions, of which shots from 8 to 11.5 km/s at 0.2 Torr (26.7 Pa) are examined in this paper. The non-equilibrium component was chosen to be the focus of this study as it can account for a significant percentage of the emitted radiation for Earth re-entry, and more importantly, non-equilibrium has traditionally been assigned a large uncertainty for vehicle design. The main goals of this study are to present the shock tube data in the form of a non-equilibrium metric, evaluate the level of agreement between the experiment and simulations, identify key discrepancies and to examine critical aspects of modeling non-equilibrium radiating flows. Radiance pro les integrated over discreet wavelength regions, ranging from the Vacuum Ultra Violet (VUV) through to the Near Infra-Red (NIR), were compared in order to maximize both the spectral coverage and the number of experiments that could be used in the analysis. A previously defined non-equilibrium metric has been used to allow comparisons with several shots and reveal trends in the data. Overall, LAURA/HARA is shown to under-predict EAST by as much as 40% and over-predict by as much as 12% depending on the shock speed. DPLR/NEQAIR is shown to under-predict EAST by as much as 50% and over-predict by as much as 20% depending on the shock speed. The one standard deviation scatter in the EAST results was calculated to be 31%. An estimate for the upper bound of the absolute error in wall-directed heat flux was calculated. Below 9 km/s, where the relative difference is large, the absolute error in radiative heat flux due to non-equilibrium models is estimated to be less then 1 W/sq cm. At the highest shock speed of 11 km/s, the error in non-equilibrium is estimated to be less than 20 W/sq cm.

Shock Tube↗
NASA NTRS1987

Model for determining vapor equilibrium rates in the hanging drop method for protein crystal growth

An engineering analysis of the rate of evaporation of solvent in the hanging drop method of protein crystal growth is presented. Results are applied to 18 drop and well arrangements commonly encountered in the laboratory. The chemical nature of the salt, drop size and shape, drop concentration, well size, well concentration, and temperature are taken into account. The rate of evaporation increases with temperature, drop size, and the salt concentration difference between the drop and the well. The evaporation in this model possesses no unique half-life. Once the salt in the drop achieves 80 percent of its final concentration, further evaporation suffers from the law of diminishing returns.

Baird, James K.↗
NASA NTRS2005

Nebula Models of Non-Equilibrium Mineralogy: Wark-Lovering Rims

Introduction: The meteorite record contains several examples of minerals that would not persist if allowed to come to equilibrium with a cooling gas of solar composition. This includes all minerals in CAIs and AOAs. Their survival is generally ascribed to physical removal of the object from the gas (isolation into a large parent object, or ejection by a stellar wind), but could also result from outward radial diffusion into cooler regions, which we discuss here. Accretion of CAIs into planetesimals has also been relied on to preserve them against loss into the sun. However, this suggestion faces several objections. Simple outward diffusion in turbulence has recently been modeled in some detail, and can preserve CAIs against loss into the sun [2]. Naturally, outward radial diffusion in turbulence is slower than immediate ejection by a stellar wind, which occurs on an orbital timescale. Here we ask whether these different transport mechanisms can be distinguished by nonequilibrium mineralogy, which provides a sort of clock. Our application here is to one aspect of CAI mineralogy - the Wark-Lovering rims (WLR); even more specifically, to alteration of one layer in the WLR sequence from melilite (Mel) to anorthite (An).

Cuzzi, J. N.↗
NASA NTRS1990

CO fundamental lines - Indicators for inhomogeneous atmospheres in cool stars

Carbon monoxide fundamental lines near 4.7 microns are employed to probe the thermal structure of the atmospheres of cool stars. A new non-LTE radiation transfer code is used to analyze high-resolution infrared CO line spectra and derive observation-based stellar atmosphere models. The main results are: (1) the CO-based models developed here deviate strongly from previously published models based on UV/visible observations; (2) varying degrees of agreement between the CO empirical models and predictions based on theoretical radiative-equilibrium atmosphere models are found; and (3) the parameter used to quantify this agreement is anticorrelated with the magnitude of chromospheric activity in the observed stars. These results suggest thermally bifurcated upper atmospheres as the standard case for cool stars.

Wiedemann, Guenter↗
NASA NTRS2019

Martian Magma Evolution from Olivine-Hosted Melt Inclusions in Shergottites Using MELTS Models

Shergottites, the largest martian meteorite group, come from at least two geochemically different source reservoirs i.e. incompatible trace element (ITE)-depleted and enriched. The depleted shergottites are thought to be derived from an ITE-depleted mantle reservoir, while enriched shergottites are thought to be derived from an ITE-enriched mantle reservoir that represents late stage residual melt from a magma ocean or interaction with martian crust. Moreover, the martian crust is distinct from shergottites, by being highly oxidized, distinctly ITE-enriched, and older. The link between the crust and shergottite compositions is poorly understood. Here we model shergottite differentiation to resolve the origin of enriched shergottites and why the bulk martian crust is compositionally distinct from shergottites. Early formed olivine-hosted melt inclusions can provide primary melt composition from which the parental magma had crystallized and also information at different stages of crystallization during parent magma differentiation that leads to shergottite magma evolution as well as crustal contribution assessment. We analyzed olivine-hosted melt inclusions of two enriched poikilitic shergottites for their major, minor and trace element concentrations using electron microprobe and laser ablation ICP-MS. We corrected the melt inclusion compositions for post-entrapment re-equilibration with their host olivine. To comprehend the crystallization sequence of these rocks and whether the melt entrapment is consistent with the crystallization, we use MELTS models for equilibrium and fractional crystallization. The results of these models suggest that all the melts were trapped in a closed system progressive crystallization at 1150-1210 ⁰C within 1 kbar to 1 bar pressure that is equivalent to <8.5 km, implying melt entrapment without any additional exogenous materials.

Ferdous, J.↗
NASA NTRS2011

Non-Equilibrium Turbulence and Two-Equation Modeling

Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.

Rubinstein, Robert↗