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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation

Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces. In this work, we propose a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. Combined with the monotonic sound speed property of the five-equation formulation, the proposed pressure-equilibrium preserving scheme significantly improves robustness in the presence of strong multiphase interactions, including shock–interface interactions and advection of material interfaces.

ESG

Discrete Rotational Energy for Polyatomic Molecules in Direct Simulation Monte Carlo

The environments experienced by vehicles upon entry into planetary atmospheres generally result in severe aerothermodynamic loading. These flows are characterized by the formation of strong shock waves, behind which high temperatures and non-equilibrium environments are generated, and the accurate prediction of internal energy relaxation and chemical kinetics becomes important. This manuscript focuses on the internal relaxation of the rotational energy of polyatomic molecules. Previous work has described the implementation of a discrete rotational energy model for diatomic molecules (linear rotators). Later, Gimelshein et. al extended this model to include polyatomic molecular internal energies. However, they did not include details on how to generate the particles at equilibrium conditions and centrifugal distortion was not included in their model. The purpose of the present study is to extend the afore-mentioned models to the treatment of discrete rotational energy in polyatomic molecules with the addition of centrifugal distortion. An overview of the background theory needed for the implementation of the model will be given followed by the model itself and verification of the model. For example, sampled versus Boltzmann distributions are compared in Figure 1 for CH3 (oblate rotator – two quantum numbers) and examples of thermal relaxation behavior for linear and non-linear rotators are presented in Figure 2. In addition, comparisons of thermophysical properties will be presented, as well as examples of adiabatic relaxation and application to hypersonic flow.

Rarefied Gas Dynamics

Thermochemically-Closed Sonic-Flow Inversion for Enthalpy and Temperature in Multispecies Arc-Jet Flows

A thermochemically-closed sonic-flow inversion framework (TSIF) is developed to infer bulk enthalpy and total temperature upstream of a choked nozzle in arc-jet flows. The formulation recasts a pressure-rise total enthalpy quantification technique as an inverse problem in characteristic-velocity c * space using measured mass flow rate, upstream total pressure, gas composition, and nozzle throat geometry as inputs. Unlike calorimetric energy-balance approaches or optical diagnostics, the method relies primarily on routinely measured facility quantities combined with explicit thermochemical closure. Thermochemical states are obtained using NASA’s open-source Chemical Equilibrium with Applications (CEA) code, enabling construction of a chemistry-consistent relation between characteristic velocity, total enthalpy, and total temperature under equilibrium or frozen assumptions. A discharge coefficient is self-calibrated using cold-flow (arc-off) operation data and applied to hot-flow (arc-on) measurements, enabling upstream losses to be accounted for without empirical correlations. The framework is applied to air, N 2 , and CO 2 –N 2 arc-jet flows and demonstrates expected trends for the inferred thermochemical states as function of arc power, specific energy input, mass-flow, heater configuration, and test gas. In the air limit, under equilibrium assumptions, the method recovers the classical high-enthalpy asymptotic correlation of Winovich with a mean residual of 4.4%, demonstrating compatibility with established sonic-flow scaling, while extending applicability to arbitrary multi-species mixtures and non-equilibrium chemistry. The framework provides a mixture-flexible methodology for determining bulk thermochemical states in modern arc-jet environments using routine facility pressure, mass-flow, gas-composition, and nozzle-geometry information together with a cold-flow calibration.

stagnation heat flux

Thermochemically-Closed Sonic-Flow Inversion for Enthalpy and Temperature in Multispecies Arc-Jet Flows

A thermochemically-closed sonic-flow inversion framework (TSIF) is developed to infer bulk enthalpy and total temperature upstream of a choked nozzle in arc-jet flows. The formulation recasts a pressure-rise total enthalpy quantification technique as an inverse problem in characteristic-velocity c * space using measured mass flow rate, upstream total pressure, gas composition, and nozzle throat geometry as inputs. Unlike calorimetric energy-balance approaches or optical diagnostics, the method relies primarily on routinely measured facility quantities combined with explicit thermochemical closure. Thermochemical states are obtained using NASA’s open-source Chemical Equilibrium with Applications (CEA) code, enabling construction of a chemistry-consistent relation between characteristic velocity, total enthalpy, and total temperature under equilibrium or frozen assumptions. A discharge coefficient is self-calibrated using cold-flow (arc-off) operation data and applied to hot-flow (arc-on) measurements, enabling upstream losses to be accounted for without empirical correlations. The framework is applied to air, N 2 , and CO 2 –N 2 arc-jet flows and demonstrates expected trends for the inferred thermochemical states as function of arc power, specific energy input, mass-flow, heater configuration, and test gas. In the air limit, under equilibrium assumptions, the method recovers the classical high-enthalpy asymptotic correlation of Winovich with a mean residual of 4.4%, demonstrating compatibility with established sonic-flow scaling, while extending applicability to arbitrary multi-species mixtures and non-equilibrium chemistry. The framework provides a mixture-flexible methodology for determining bulk thermochemical states in modern arc-jet environments using routine facility pressure, mass-flow, gas-composition, and nozzle-geometry information together with a cold-flow calibration.

inviscid theory

Discrete Rotational Energy for Polyatomic Molecules in Direct Simulation Monte Carlo

Accurate prediction of aerothermodynamic loads in thermal non-equilibrium flows requires precise modeling of internal energy exchange. While previous direct simulation Monte Carlo frameworks have successfully implemented discrete rotational energy models for diatomic species, the treatment of polyatomic molecules has traditionally relied on continuous energy assumptions that break down at low temperatures and neglect critical high-temperature corrections. This study extends the discrete rotational energy models of Boyd and Gimelshein to fully encompass polyatomic molecules. The proposed framework implements quantized rotational energy level sampling for linear, spherical, and symmetric/asymmetric top rotors. Crucially, the model incorporates centrifugal distortion to address the limitations of the rigid-rotor assumption at hypersonic temperatures, and accounts for nuclear spin parity, which dictates the permissible rotational states and macroscopic specific heats at low temperatures. The model is verified through equilibrium sampling procedures, demonstrating agreement with theoretical quantum Boltzmann distributions and accurately reproducing thermophysical properties across a wide range of temperatures.

DSMC

Updates and Modernization of NASA’s Chemical Equilibrium with Applications (CEA) Code

NASA’s Chemical Equilibrium with Applications (CEA) code is a foundational tool for propulsion system analysis. It provides equilibrium chemistry, rocket performance, shock, and detonation calculations used across NASA and the broader aerospace community. NASA Engineering and Safety Center (NESC) Activity TI-22-01730 modernized the legacy CEA2 Fortran code into CEA v3, a Fortran 2008, object-oriented software package with expanded interface support, updated thermochemical data, improved maintainability, and substantially improved workflow integration. The modernized code preserves backward compatibility with legacy CEA input workflows while enabling direct use from modern analysis environments, including Python, C, MATLAB, and automated design studies.

Mark K Leader

Updates and Modernization of the Chemical Equilibrium with Applications (CEA) Code

NASA’s Chemical Equilibrium with Applications (CEA) code is a foundational tool for propulsion system analysis. It provides equilibrium chemistry, rocket performance, shock, and detonation calculations used across NASA and the broader aerospace community. NASA Engineering and Safety Center (NESC) Activity TI-22-01730 modernized the legacy CEA2 Fortran code into CEA v3, a Fortran 2008, object-oriented software package with expanded interface support, updated thermochemical data, improved maintainability, and substantially improved workflow integration. The modernized code preserves backward compatibility with legacy CEA input workflows while enabling direct use from modern analysis environments, including Python, C, MATLAB, and automated design studies.

Combustion

Turbo-Design: Open-Source Radial Equilibrium Turbomachinery Solver: Part I - Turbines

Advances in 3D Geometrical Designs and Cooling have played a significant role in improving the efficiency of turbomachinery. However, these advancements must be effectively translated back to the modeler. Machine learning can facilitate this transition. Specifically, machine learning–based loss models can bridge the gap between 3D and 1D designs, enabling modelers not only to predict velocity triangles but also to extract additional geometric features. Currently, the design tools used at NASA have not been updated to support such integration—until now. TurboDesign is an open-source, Python-based framework that replaces TD2 (LEW-11029-1) and AXOD2 (LEW-16323-1), both of which are radial equilibrium solvers for axial turbines. The goal of this update is to enable the integration of machine learning loss models into radial equilibrium equations. Additionally, TurboDesign is designed to support radial machines. This paper presents the governing equations, the assumptions underlying the code, the integration of legacy loss models, an example of machine learning model integration, and a validation comparison with CFD. All code, tutorials, and documentation are available at: https://www.github.com/nasa/turbo-design

Radial Equilibrium

RTE: A Computer Code for Rocket Thermal Evaluation

The numerical model for a rocket thermal analysis code (RTE) is discussed. RTE is a comprehensive thermal analysis code for thermal analysis of regeneratively cooled rocket engines. The input to the code consists of the composition of fuel/oxidant mixture and flow rates, chamber pressure, coolant temperature and pressure. dimensions of the engine, materials and the number of nodes in different parts of the engine. The code allows for temperature variation in axial, radial and circumferential directions. By implementing an iterative scheme, it provides nodal temperature distribution, rates of heat transfer, hot gas and coolant thermal and transport properties. The fuel/oxidant mixture ratio can be varied along the thrust chamber. This feature allows the user to incorporate a non-equilibrium model or an energy release model for the hot-gas-side. The user has the option of bypassing the hot-gas-side calculations and directly inputting the gas-side fluxes. This feature is used to link RTE to a boundary layer module for the hot-gas-side heat flux calculations.

Mohammad H N Naraghi

A Machine Learning Framework for Error Compensation in Radiative Transfer Calculations

Radiative heat transfer influences the amount of heat flux transferred to the surface of the hypersonic vehicle, which is essential to evaluate the performance of thermal protection systems. The radiative heat flux is found to be computationally prohibitive while accounting for the variation in spatial, angular, and spectral domains. A new methodology has been recently developed to alleviate the cost of computation in the spectral domain by constructing flow-agnostic reduced-order models (ROMs). The developed spectral ROM databases provide grouping strategies that account for non-equilibrium absorption and emission as well as interaction between disparate species due to spectral overlap in associated radiative processes. However, the developed ROMs need to be optimized for a specific combination of interacting gas species and would need to re-calibrated in case individual species are added/omitted. In this work, we use various machine learning (ML) techniques to approximate the radiative intensities determined by a ROM optimized for a specific gas mixture. The ML model relies on the ROM databases developed for a single species which ignores any spectral overlap. Thus, radiation evaluation starts with a simple summation of radiative intensities predicted using these non-calibrated ROMs for the contributing species. The ML framework then provides a correction to account for the interplay in the frequency, i.e., emission of photons by one species and absorption by another, and yields mixture-specific radiation fields. Once trained on the individual ROM databases, the ML framework offers instantaneous corrections that serves as a time/cost effective alternative to the optimization of ROMs for a specific gas mixture. The ML framework is trained on both the high fidelity and ROM evaluated line of sight (LOS) data from Orion, Stardust, and FIRE II cases to obtain a general purpose correction model for earth re-entry scenarios when radiation contributions from both atomic nitrogen and atomic oxygen are considered. A geometric length scale parameter is used in the training process to account for errors introduced in the ROM databases as a consequence of high optical thickness. The efficacy of the ML framework is underscored through extensive analysis of train and test errors with respect to all the re-entry scenarios. The applicability of such an ML framework was further corroborated by embedding it in a state-of-the-art US3D - NERO system for determining the radiative heat flux transferred to the hypersonic vehicle surface.

Radiation

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λc, that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λc-based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

Amanda Stricklan

Chalcogenide-Based Non-Volatile Memory Technology

Chalcogenide is a proven phase change material used in re-writeable CDs and DVDs. This material changes phases, reversibly and quickly, between an amorphous state that is dull in appearance and electrically high in resistance, and a polycrystalline state that is highly reflective and low in resistance. The application of this commercially proven technology to create dense, high-speed, non-volatile semiconductor memories is discussed.

J Maimon

Optimization of a 10–Step Reduced CH₄/O₂ Combustion Mechanism for RDRE Applications

A 10-step, 9-species reduced mechanism for methane/oxygen combustion is evaluated and optimized for use in rotating detonation rocket engine (RDRE) simulations at an operating pressure of 10 bar. The mechanism is assessed against GRI-Mech 3.0 for ignition delay times, adiabatic equilibrium temperature and species, Chapman-Jouguet (CJ) detonation parameters, and laminar flame speed. A sequential Nelder–Mead optimization procedure is applied to the rate constants of reactions R1, R4, and R5, targeting ignition delay agreement over the equivalence ratio range φ = 1.0–1.4 and temperature range T = 1400–2000 K. The optimized mechanism achieves ignition delay agreement within 28% of GRI-Mech 3.0 for the temperature range relevant to RDRE operation (τ ≥ 5 μs). Adiabatic equilibrium temperatures and CJ detonation parameters are reproduced within 0.15% of GRI-Mech 3.0 values, confirming thermodynamic consistency of the mechanism. Laminar flame speed predictions deviate significantly from GRI-Mech 3.0, which is attributed to the absence of HO₂ chemistry in the reduced mechanism; this limitation does not affect RDRE simulation fidelity since laminar flame propagation is of secondary importance in RDREs.

Computational Fluid Dynamics

Atmospheric, Non-Combusting Droplet Sizing and Spray Imaging Results From a Non-Proprietary Aero Gas Turbine Engine Pressure Swirl Atomizer using Shadowgraphy and Planar Laser Scatter

Members from industry and federal agencies of the United States have developed a collaborating group focused on improving the understanding of the atomization processes common to gas turbine engines. The group is aimed on providing high quality data using x-ray diagnostics in the internal geometry and the near-field dense spray as well as optical diagnostics in the visible spectrum, downstream of the nozzle. This paper reports results from one of the two non-proprietary injectors designs from the group: the primary-secondary injector. In particular, we characterize the spray from only the primary, pressure-swirl atomizing circuit using water through the nozzle. We observed Sauter mean diameter decreased with increased water pressure drop across the nozzle. SMD was also collected at three axial distances and showed decreased size with distance from the nozzle. Planar laser sheet droplet scattering provided qualitative assessment of the spray. Higher water pressure drops provided better atomization than lower pressure drops. The addition of swirling air flow through the injector alleviates and improves the atomization quality, particularly at the lower water pressure drops.

optical diagnostics

The Effect of Temperature and Pressure on the Distribution of Iron Group Elements Between Metal and Olivine Phases in the Process of Differentiation of Protoplanetary Material

The distribution patterns of Ni, Co, Mn, and Cr were studied in olivines of various origins: from meteorites (chondrites, achondrites, pallasites), which are likely analogs of the protoplanetary material, to peridotite inclusions in kimberlite pipes, which are analogs of mantle material. According to X-ray microanalysis data, each genetic group of olivines is characterized by a specific concentration of these elements. Nickel is concentrated (up to 0.34 percent) in peridotite olivines, while manganese is concentrated in meteoritic olivines. The maximum chromium content (0.2 percent) was found in ureilites, which were formed under reducing conditions. Experiments at pressures of 20 to 70 kbar and temperatures of 1100 to 2000°C have shown that in a mixture of olivine and Ni metal or NiO nickel enters the silicate phase (up to 4 percent), displacing Fe into the metallic phase. Equilibrium temperatures were estimated from the Fe, Ni distribution coefficients between the metal and olivine: 1500 K for pallasites, 1600 K for olivine-bronzite H6 chondrites, 1200 K for olivine-hypersthene L6, 900 K for LL6, and 1900 K for ureilites (at P = 1 atm). The equilibrium conditions of peridotites are close to T = 1800 K and P over 100 kbar. The distribution patterns of the transition elements are explained on the basis of physical-chemical properties. It is concluded that there is a sharp difference between the conditions of differentiation of the protoplanetary material at the time meteorites were formed and the conditions of differentiation of the planets into concentric layers.

A P Vinogradov

Non-Metallic Materials

Nonmetallic materials development - cryogenic insulation, adhesives research, and membrane diffusion theory

Materials Science