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Development of a One-Domain Volume-Averaged Navier–Stokes Solver

The interaction between a high-enthalpy flow and a thermal protection material is inherently multiscale and multiphysics. In conventional aerothermal analyses, the external flow and material response are generally modeled using separate computational domains coupled through boundary conditions at the material surface. Although this approach has supported many practical applications, it requires assumptions about the location and behavior of the interface and may become difficult to apply when material decomposition, internal reactions, and surface recession substantially alter the porous structure. This report presents the development of a one-domain formulation in which the free-fluid and porous-material regions are represented within a single computational domain. The formulation is based on the volume-averaged Navier–Stokes (VANS) equations, derived from the governing equations for reacting, compressible flow and condensed material. Volume averaging transfers the influence of the unresolved material microstructure to the macroscale equations through effective transport properties, interfacial source terms, and dispersion fluxes. Particular attention is given to regions in which porosity and permeability vary rapidly, including the diffuse transition between a porous material and the surrounding fluid. The resulting equations are implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO). The report describes the pressure–velocity coupling strategy used by the solver, examines spatial filtering techniques for deriving effective properties, and evaluates the influence of a smoothly varying interface permeability. Numerical demonstrations include canonical porous-flow configurations, a flow-tube configuration representative of FiberForm® permeability experiments, and the oxidation of a porous carbon material. The purpose of this work is to establish a mathematical and computational foundation for a unified treatment of flow and thermal protection material response. The present formulation is intended to support the progressive inclusion of additional physical processes, including multicomponent transport, finite-rate gas–surface chemistry, pyrolysis, internal oxidation, and material recession. It also provides a framework for connecting pore-scale simulations and microstructural characterization with macroscale aerothermal-response calculations. This report is intended for researchers and engineers working in computational fluid dynamics, porous-media transport, material response, and thermal protection system modeling. It documents both the theoretical development and the initial numerical assessment of the one-domain approach, while identifying the closure of effective and dispersion terms as an important subject for continued investigation.

Ablation

The Effect of Gravity on the Combustion Synthesis of Porous Ceramics and Metal Matrix Composites

Combustion synthesis (self propagating, high temperature synthesis-SHS) is a novel technique that is capable of producing many advanced materials. The ignition temperature (Tig) of such combustion synthesis reactions is often coincident with that of the lowest melting point reactant. The resultant liquid metal wets and spreads around the other solid reactant particles of higher melting points, thereby improving the reactant contact and kinetics, followed by formation of the required compounds. This ignition initiates a combustion propagating wave whose narrow reaction front rapidly travels through the reactants. Since this process is highly exothermic, the heat released by combustion often melts the reactant particles ahead of the combustion front and ignites the adjacent reactant layer, resulting in a self-sustaining reaction. Whenever a fluid phase (liquid or gas) is generated by the reaction system, gravity-driven phenomena can occur. Such phenomena include convective flows of fluid by conventional or unstable convection and settling of the higher density phases. A combustion process is often associated with various kinds of fluid flow. For instance, if the SHS reaction is carried out under inert or reactive gas atmospheres, or a volatile, e.g., B2O3, is deliberately introduced as a reactant, convective flows of the gas will occur due to a temperature gradient existing in the atmosphere when a combustion wave is initiated. The increased gas flow will produce a porous (or expanded) SHS product. Owing to the highly exothermic nature of many SHS reactions, liquid phase(s) can also form before, at, or after the combustion front. The huge temperature gradient at the combustion front can induce convective flows (conventional or unstable) of the liquid phase. Each of these types of convective fluid flow can change the combustion behavior of the synthesizing reaction, and, therefore, the resultant product microstructure. In addition, when two or more phases of different density are produced at or ahead of the propagating combustion front settling of the higher density phase will occur resulting in a non-uniform product microstructure and properties.

J J Moore

Highly Porous Polyimide Gel for Use as Battery Separator with Room Temperature Ionic Liquid Electrolytes

Advanced aerospace vehicular concepts require advances in many existing technologies, including space power and energy storage systems. Batteries represent one of the major areas in need of improvement, both in terms of energy density and safety, with growing concerns over the fire safety of commercial lithium-ion batteries. This has prompted efforts to develop nonflammable battery components, namely the electrolyte and separator. Existing commercial lithium-ion batteries utilize polyolefin microporous membranes as separators with an electrolyte consisting of a lithium salt dissolved in a mixture of cyclic carbonate solvents. This separator/electrolyte combination has ionic conductivities in the range of 10 −2 to 10 −3 S/cm. However, the cyclic carbonate solvents are inherently flammable. Room-temperature ionic liquids (RTILs) appear to be a safer alternative. They offer good ionic conductivities and are inherently nonvolatile and nonflammable, giving them a safety advantage. However, many promising RTILs for battery electrolytes are not compatible with commercial polyolefin separator materials. Alternative separator materials, such as polyimides, are non-flammable and are capable of accepting RTILs into their structure. Polyimide gels, with a composition of 4,4′-oxydianiline, 3,3′,4,4′-tetracarboxylic dianhydride and cross-linked with Desmodur N3300A, possess an open-porous, fibrillar network architecture which offers a high degree of porosity (typically greater than 85% porosity) for lithium-ion transport and conduction, as well as good mechanical properties. Furthermore, these polyimide gels are compatible with selected imidazolium-based RTILs. Nonflammable separator/electrolyte systems with room-temperature conductivities in the range of 10 −3 S/cm have been evaluated. It has been demonstrated that 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide was the most promising among six RTILs screened, in terms of both ionic conductivity and constant current cycling.

Polyimide

Composite battery separator

A composite battery separator comprises a support element (10) having an open pore structure such as a ribbed lattice and at least one liquid permeable sheet (20,22) to distribute the compressive force evenly onto the surfaces of the layers (24, 26) of negative active material and positive active material. In a non-flooded battery cell the compressible, porous material (18), such as a glass mat which absorbs the electrolyte, is compressed into a major portion of the pores or openings (16) in the support element. The unfilled pores in the material (18) form a gas diffusion path as the channels (41) formed between adjacent ribs in the lattice element (30,36). Facing two lattice elements (30, 31) with acute angled cross-ribs (34, 38) facing each other prevents the elements from interlocking and distorting a porous, separator (42) disposed between the lattice elements.

Edwards, Dean B.

Computation of three-dimensional mixed convective boundary layer flow

The paper presents the numerical solution of heat and mass transfer during cross-flow (orthogonal) mixed convection. In this class of flow, a buoyancy-driven transport in the vertical direction and a forced convective flow in the horizontal direction results in a three-dimensional boundary layer structure adjacent to the plate. The rates of heat and mass transfer are determined by a combined influence of the two transport processes. The equations for the conservation of mass, momentum, energy, and species concentration were solved along with appropriate boundary conditions to determine the distributions of velocity components, temperature, and concentration across the thickness of the boundary layer at different locations on the plate. Results were expressed in dimensionless form using Reynolds number, Richardson number for heat transfer, Richardson number for mass transfer, Prandtl number, and Schmidt number as parameters. It was found that the transport is dominated by buoyancy at smaller vertical locations and at larger distances away from the forced convection leading edge. Effects of forced convection appeared to be very strong at smaller horizontal distances from the leading edge. The cross stream forced convection enhanced the rate of heat and mass transfer by a very significant amount.

Prashandt Gadepalli

Vapor Transport Crystal Growth of Mercury-Cadmium-Telluride in Microgravity

Two epitaxial growth experiments of Hg 1-x Cd x Te layers on (100) CdTe substrates in closed ampoules using HgI 2 as a transport agent have been performed during the USML-1 mission. The characterization results to date demonstrate a considerable improvement of the space-grown epitaxial layers relative to ground-control specimens in terms of morphology, compositional uniformity, and structural micro homogeneity. These results show the effects of microgravity and fluid dynamic disturbances on-ground on the deposition and growth processes. The continued analysis of this technologically important system is designed to further elucidate the observed crystallographic improvements and their relation to mass flow.

Heribert Wiedemeier

A Predictive Bubble Point Pressure Model for Porous Liquid Acquisition Device Screens

This article presents a simplified model for porous screen channel liquid acquisition devices based on a maximum bubble point pressure method from Adamson and Gast (1997). To validate the model, three 304 stainless steel (325 × 2300, 450 × 2750, and 510 × 3600) mesh samples were tested in methanol, acetone, isopropyl alcohol, and water. Screen pores are estimated based on analysis from scanning electron microscopy, historical data, and current test data. Results show that the bubble point pressure is proportional to the surface tension of the fluid only when accounting for nonzero contact angles. The previous assumption that bubble point pressure scales inversely with effective pore diameter is shown to be invalid, as the second finest 450 × 2750 produced the highest bubble point of the three screens. The simplified bubble point model can be used to make predictions for any pure fluid when pore diameters are based on bubble point tests and not SEM analysis.

Liquid Acquisition Device

A Probabilistic Model of a Porous Heat Exchanger

This paper presents a probabilistic one-dimensional finite element model for heat transfer processes in porous heat exchangers. The Galerkin approach is used to develop the finite element matrices. Some of the submatrices are asymmetric due to the presence of the flow term. The Neumann expansion is used to write the temperature distribution as a series of random variables, and the expectation operator is applied to obtain the mean and deviation statistics. To demonstrate the feasibility of the formulation, a one-dimensional model of heat transfer phenomenon in superfluid flow through a porous media is considered. Results of this formulation agree well with the Monte-Carlo simulations and the analytical solutions. Although the numerical experiments are confined to parametric random variables, a formulation is presented to account for the random spatial variations.

O P Agrawal

Analytical Model for Steady Flow through a Finite Channel with One Porous Wall with Arbitrary Variable Suction or Injection

This paper presents an exact solution of two-dimensional laminar flow through a finite length channel with one porous wall. It improves upon previous solutions by (1) satisfying the no-slip boundary condition at the channel dead end, (2) adding a turbulent term to the porous wall boundary condition, (3) allowing for arbitrary variable suction or injection across the porous wall, and (4) model validation against new cryogenic liquid hydrogen and oxygen experimental data. Of particular interest in the current work is the modeling of cryogenic propellant flow through a porous liquid acquisition device (LAD) screen and channel inside a propellant tank. First, a detailed review of the literature is presented for previously attempted solutions to channel flow with one porous wall. Next, the governing equations, boundary conditions, and model assumptions are used to derive the analytical flow solution and present general model results for pressure and velocity fields within the channel. Then, the model solution is compared with horizontal LAD channel flow data in liquid oxygen as well as vertical LAD channel flow data in an inverted outflow configuration in liquid hydrogen. Model results are used to update the static cryogenic bubble point pressure model with a dynamic bubble point term which factors in enhanced convection and cooling at the screen during propellant outflow. Convective heat transfer at the LAD screen during outflow is also quantified by comparing model and data. The new analytical flow solution with the dynamic bubble point model is shown to compare well with available cryogenic experimental data

Navier Stokes Equations

An Improved Theoretical Ni-Cd Battery Performance Model

Previous reports have shown how a battery model was developed using porous electrode theory. Since then the model has been upgraded and expanded. These upgrades include oxygen reation and positive electrode intercalation and proton diffusion. The effects of additional details of the solid state physics of the nickel electrode will be reported here.

battery

Mitigating Grazing Flow Impedance Eduction Errors in Additively Manufactured Porous Liners

Additively manufactured porous metamaterials, including triply periodic minimal surface (TPMS) cores, are promising candidates for aeroengine liners but often behave as extended-reacting treatments under grazing flow. Standard impedance eduction procedures assume locally-reacting behavior and can yield physically inconsistent results for such materials. This study evaluates internal partitions (thin solid walls inserted at regular intervals along the liner’s streamwise extent) as a means of suppressing internal streamwise propagation to improve eduction consistency. Six TPMS configurations were tested in the NASA Langley Grazing Flow Impedance Tube (GFIT) at partition spacings of 4′′, 2′′, and 1′′, as well as unpartitioned, and at Mach numbers up to 0.3. For most geometries, 2′′ partition spacing eliminated impedance discontinuities and substantially improved Prony correlation, though effectiveness varied with core topology. Partitions also altered the acoustic response of the liners: resistance increased, resonance frequencies shifted downward, and peak attenuation decreased while bandwidth broadened in some cases. Because partitions modify the liner itself, the educed impedance characterizes the partitioned system rather than the original unpartitioned core. These results establish partitioning as a practical pathway toward liners that are more compatible with standard eduction methods, while demonstrating that the intervention is itself an acoustic design change.

liners

Boundary Layer Analysis of Shock Tube Flows

Shock tubes offer a controlled environment to reproduce kinetic and radiative phenomena characteristic of atmospheric entry flows under ground-test conditions. The boundary layer developing behind the incident shock wave determines the available test time, influences particle residence times important for similarity scaling, and can affect radiative energy transport. In this study, we couple a quasi-1D space marcher with the compressible boundary-layer equations to numerically compute the post-shock flow in a shock frame of reference for various test gas mixtures representative of different planetary atmospheres. The solvers are individually verified against CFD simulations and analytical correlations available in the literature. Coupled solutions are computed for a finite-rate chemistry in the boundary layer and a non-catalytic isothermal wall. Results yield refined estimates of the maximum separation distance, as well as insights into concentration profiles of relevant species within the boundary layer.

Andrea Fagnani

Material Properties and Modeling of Room Temperature Vulcanizing Silicone

Room Temperature Vulcanizing silicone (RTV) is a high-temperature adhesive that has successfully been used as a gap-filler between Thermal Protection System (TPS) tiles for heatshields on numerous missions. It is also used to bond instrumentation plugs such as temperature and pressure sensors into the heatshields. While RTV has been traditionally assumed to be a non-porous and non-ablating material, numerous experiments have shown that RTV pyrolyzes and becomes highly porous as it is heated. Heating RTV has also shown swelling, or intumescence, which can pose unique problems that lead to roughness induced boundary-layer transition, surface oxide formation and contamination of heat shield sensors. Therefore, it is crucial to understand and model the intumescence phenomenon of RTV. As data for RTV material properties is limited, the first step in modeling RTV is to collect material properties such as pyrolysis mass-loss, microstructure change, virgin and char porosity, etc. which was performed in our initial study. Additionally, thermomechanical properties such as Young’s modulus and Poisson ratio are required for modeling the intumescence of RTV, which were taken from literature and the coefficient of thermal expansion was collected using in-situ heating and Micro Computed Tomography (µ-CT) in previous studies. Finally, numerous other properties such as pyrolysis gas properties, virgin and char thermal conductivity and specific heat were compiled from previous experiments and literature into a material database that can be used for simulations. In Porous Material Analysis Toolbox based on OpenFOAM (PATO) [4], structural mechanics coupled with material response was used for simulating the intumescence of RTV as it is heated. However, since the permeability of the material is very low, the pyrolysis gas creates an internal pressure build-up as the material is being heated, significantly contributing to the deformation of the material. To correctly characterize this phenomenon, additional physics models were implemented into PATO's stress analysis solver, and results were compared with RTV dilatometry test data as a preliminary verification case. Future work will include experiments of RTV at the Plasmatron X facility and the in-situ heating cell with µ-CT, and improvement of simulation tools to more accurately model RTV intumescence.

PATO

Influential Factors for Liquid Acquisition Device Screen Selection for Cryogenic Propulsion Systems

This paper presents the influential factors which govern screen selection for liquid acquisition devices (LADs) operating in microgravity conditions for future in-space cryogenic propulsion engines and cryogenic propellant depots. Space flight requirements, which include mass flow rate, acceleration level and direction, and thermal environment, dictate screen selection for a particular mission. The five influential factors include bubble point pressure, flow-through-screen pressure drop, wicking rate, screen compliance, and material compatibility. Governing equations and analytical models for these parameters are developed from first principles. A comprehensive survey of the historical data on coarser LAD meshes over four decades of work is conducted, and liquid hydrogen data for finer Dutch Twill meshes (325 x 2300, 450 x 2750, 510 x 3600) from recently concluded experiments is also presented to validate analytical models. Each of these parameters is measurable from ground based tests, making it facile to predict flight system performance. Therefore analytical models in this paper will be valuable for future LAD designs for both cryogenic and storable propulsion systems. Additionally, analysis will be given on the impact of the factors on liquid hydrogen systems.

Fuel Depot

Advances in Entry Systems Modeling: Modeling Summer Visit 2025 Technical Reports

This NASA Technical Memorandum presents the collective work carried out during the Modeling Summer Visit (MSV) 2025, a collaborative research program between NASA Ames Research Center and three leading European research institutions: the University of Bordeaux, the von Karman Institute (VKI), and Ecole Polytechnique. Held from July 7th to August 1st, 2025, the NASA ARC MSV program brought together 42 researchers from Europe to work alongside NASA staff on 22 projects in entry systems modeling. The program was organized by Bruno Dias, Sergio Fraile-Izquierdo, and Jeremie Meurisse from Analytical Mechanics Associates, Inc., in collaboration with Marc Massot (Ecole Polytechnique), Jean Lachaud (University of Bordeaux), and Thierry Magin (VKI). The MSV program traces its origins to an initiative started by Nagi N. Mansour in 2018, with this 2025 edition representing a consolidation and expansion of that original vision. The projects were organized into six thematic groups: Porous Media, Numerical Methods, Plasma/Rarefied Methods, Experimental Reconstruction, Flow and Material Coupling Methods, and Transition and High-Speed Flows. Throughout the four-week program, participants presented their work in three public presentations (July 7th, July 21st, and August 1st), allowing for continuous feedback and discussion of their evolving research.

Plasmas

Experimental Characterization of Additively Manufactured Nickel-Titanium Shape Memory Alloy Heat Pipes

Shape memory alloys (SMA) have been identified for use in spacecraft components as replacement for conventional deployment mechanisms. They may be used in thermal management components such as radiators to create self-deploying radiators. One SMA, NiTi, has also been developed for additive manufacturing processes. Heat pipes are a common way to create highly effective and lightweight spaceflight radiators, and heat pipes can also be made from NiTi and related alloys. The wick is the critical element of a functioning heat pipe, and recent progress over the past years has led to the development of additively manufactured heat pipe wicks in various materials. The combination of these efforts is the focus of this project: creating an additively manufactured, shape memory alloy self-deploying heat pipe radiator. This paper will focus on the experimental characterization of these additively manufactured NiTi heat pipes. The heat pipe coupons were additively manufactured by direct metal laser sintering (DMLS), with an integral liquid cooled condenser. Heat is input to the heat pipe via a thin film heater. Thermocouples were spot welded to the heat pipes to measure temperature at several axial locations. The heat pipes were tested with two working fluids: water and ethanol. Ethanol is not an ideal working fluid for heat pipes but is useful in characterizing them because it wets well to a wide variety of surfaces. Water is in general a superior working fluid for heat pipes, but its contact angle and therefore wicking performance strongly depends on the surface chemistry of the surface it is in contact with. A particular measurement of interest in this test is the evaporator to condenser thermal conductance, which will be compared in the full paper to recently published correlations for additively manufactured heat pipes. Experimental results for two straight geometry and one bellows geometry heat pipe will be presented. The bellows geometry is of interest for condenser of the self-deploying radiator design.

Additive manufacturing

Mechanisms of Protonic Nonvolatile Memory Device

A nonvolatile memory device based on protonic transport in oxides has been proposed. The mobile H+ ions are introduced into the SiO2 layer by annealing Si/SiO2/Si structures in H2 at temperatures greater than 500 deg C. This effect has only been observed for confined oxides that have been annealed at greater than or equal to 1100 C prior to the hydrogenation anneal. This includes buried oxides such as Unibond and SIMOX as well as thermal oxides annealed with a polysilicon cap. An applied field moves the charge within the oxide and the charge stops moving when the field is removed. In a memory device, the hydrogen-annealed oxide is the gate oxide and the position of the mobile charge is sensed by the shift of the I-V curve. Much is still not understood about the motion of the charge across the buried oxide. Previous work has assumed that H+ transport and the time it takes to traverse the oxide is governed by interactions within the bulk of the oxide. Based on parameters that affect the transport time, we conclude that H+ trapping and detrapping at the Si/SiO2 interface are more important than H+ interactions within the oxide bulk. These parameters include the applied field, the H+ concentration and the oxide thickness. One consequence is that projections of device write-time based on the previous assumptions of H+ transport mechanisms may be overly optimistic.

P J Macfarlane