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NASA NTRS2026

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↗
NASA NTRS2003

Effect Of Gravity On Porous Tricalcium Phosphate And Nonstoichiometric Titanium Carbide Produced Via Combustion Synthesis

Novel processing techniques, such as self-propagating high temperature synthesis (SHS), have the capability to rapidly produce advanced porous materials that are difficult to fabricate by other methods. This processing technique is also capable of near net shape synthesis, while variable gravity allows the manipulation of the structure and composition of the material. The creation of porous tricalcium phosphate (TCP) is advantageous in the biomaterials field, since it is both a biocompatible material and an osteoconductive material. Porous tricalcium phosphate produced via SHS is an excellent candidate for bone scaffold material in the bone regeneration process. The porosity allows for great vascularization and ingrowth of tissue. Titanium Carbide is a nonstoichiometric biocompatible material that can be incorporated into a TiC-Ti composite system using combustion synthesis. The TiC-Ti composite exhibits a wide range of mechanical and chemical properties. Both of these material systems (TCP and TiC-Ti) can be used to advantage in designing novel bone replacement materials. Gravity plays an important role in both the pore structure and the chemical uniformity of these composite systems and offers considerable potential in advanced bone engineering.

Castillo, M.↗
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 NTRS2005

Permeability of Candidate Stirling Heater Head Materials Measured

Researchers at the NASA Glenn Research Center are evaluating high-temperature materials for Stirling heater heads for second- and third-generation Stirling radioisotope power systems that would help to increase the system efficiency to 30 to 35 percent and the system specific power to 8 to 10+ W/kg. Ceramic materials could make it possible for the convertor hot-end temperature to be increased to 1050 to 1200 C, in comparison to the current 650 C with an Inconel 718 heater head. A hermetically sealed Stirling heater head must retain a constant internal pressure of nearly 400-psi helium (He) throughout its useful life (120,000 hr) at the design operating temperature. Therefore, He permeability was measured for eight potential materials and compared with the permeability of the current heater head material, Inconel 718. The eight materials included silicon nitride (Si3N4), silicon dioxide (SiO2), both sintered and chemical vapor deposited (CVD) silicon carbide (SiC), alumina (Al2O3), two types of melt-infiltrated (MI) SiC/SiC composites, and a carbon/SiC composite (C/SiC). Glenn submitted samples of each material to Porous Materials, Inc., Ithaca, New York, for permeability analysis. At room temperature and 30-psi He, four materials--Si3N4, Al2O3, SiO2, and sintered SiC--demonstrated lower permeability than Inconel 718. The CVD SiC and all the composite materials were significantly more permeable to He than the baseline material.

Freedman, Marc R.↗
NASA NTRS1991

Mechanical properties of a porous mullite material

Modulus of rupture specimens were used to determine crack growth parameters of a porous mullite material. Strength testing was performed in ambient and moist environments. The power law crack growth rate parameters n and 1n B in 50 percent relative humidity were found to be 44.98 and 0.94, respectively. The inert strength, fracture toughness, and elastic modulus were also determined and found to be 19 MPa, 055 MPa(m) exp 1/2, and 11.6 GPa, respectively.

Viens, Michael J.↗
NASA NTRS1994

An Experimental Study of the Flow Emerging from Porous Walls

The fluid mechanics of air flow exiting from porous materials is investigated. Porous walls with filter ratings differing by about three orders of magnitude are studied. The flow behavior is investigated for its spatial and temporal stability. The measurements show that coalescence effects cause jet development which gives rise to a stable, spatial velocity non-uniformity termed pseudo-turbulence. Beyond a critical mean velocity, the pseudo-turbulence shows a leveling trend and the flow exhibits jets whose dimensions are independent of wall porosity and provide a unique length scale for this type of flow field (approx. 1 mm). A correlation is developed to predict the onset of fully developed jets. The impact of using porous wall materials in cold flow solid rocket motor testing is addressed.

Ramachandran, N.↗
NASA NTRS2010

Large-Flow-Area Flow-Selective Liquid/Gas Separator

This liquid/gas separator provides the basis for a first stage of a fuel cell product water/oxygen gas phase separator. It can separate liquid and gas in bulk in multiple gravity environments. The system separates fuel cell product water entrained with circulating oxygen gas from the outlet of a fuel cell stack before allowing the gas to return to the fuel cell stack inlet. Additional makeup oxygen gas is added either before or after the separator to account for the gas consumed in the fuel cell power plant. A large volume is provided upstream of porous material in the separator to allow for the collection of water that does not exit the separator with the outgoing oxygen gas. The water then can be removed as it continues to collect, so that the accumulation of water does not impede the separating action of the device. The system is designed with a series of tubes of the porous material configured into a shell-and-tube heat exchanger configuration. The two-phase fluid stream to be separated enters the shell-side portion of the device. Gas flows to the center passages of the tubes through the porous material and is then routed to a common volume at the end of the tubes by simple pressure difference from a pumping device. Gas flows through the porous material of the tubes with greater ease as a function of the ratio of the dynamic viscosity of the water and gas. By careful selection of the dimensions of the tubes (wall thickness, porosity, diameter, length of the tubes, number of the tubes, and tube-to-tube spacing in the shell volume) a suitable design can be made to match the magnitude of water and gas flow, developed pressures from the oxygen reactant pumping device, and required residual water inventory for the shellside volume.

Vasquez, Arturo↗
NASA NTRSDate not supplied

Predictive Modeling of Carbon Ablators

Efforts to build a Predictive Material Modeling (PMM) framework from the micro-scale to the macro-scale are presented in this abstract. To reduce the need for extensive testing, accelerate the design cycle process, and reduce uncertainty margins applied to final designs, NASA is developing simulation and modeling tools that enable characterization of material properties and response to high-enthalpy environments. The Porous Microstructure Analysis (PuMA) code has been developed for computing macroscale (volume averaged) properties of porous materials using microscale images from micro-computed tomography (micro-CT). Microscale modeling requires a realistic representation of a material microstructure; these are obtained either synthetically during the design of the material or through X-ray micro-CT. Volume averaged properties are then used to inform macroscale material response models, such as those implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO) software, also actively developed by NASA. The computational model in PATO is a generic heat and mass transfer model for porous reactive materials containing several solid phases and a single gas phase. The detailed chemical interactions occurring between the solid phases and the gas phase are modeled at the pore scale assuming local thermal equilibrium. These tools were developed to efficiently interface with other pre-existing codes such as SPARTA (direct simulation Monte Carlo), DPLR (hypersonic CFD), NEQAIR (radiative transport) and DAKOTA (uncertainty quantification and optimization). Detailed flight data (Mars Science Laboratory [MSL] Entry Descent and Landing Instrument [MEDLI]) is critical for validating these computational tools for NASA applications. Examples of modeling ablative material response using these codes will be presented including 3D simulations of the full-scale heatshield of the MSL capsule. The simulations demonstrate the ability of the modern material response code, PATO, to handle the material response of geometrically complex and large domains, through the use of massively parallel computations.

Thermal Protection Systems↗
NASA NTRSDate not supplied

Predictive Modeling of Carbon Ablators Using Micro and Macro-Scale Modeling

Efforts to build a Predictive Material Modeling (PMM) framework from the micro-scale to the macro-scale are presented in this abstract. To reduce the need for extensive testing, accelerate the design cycle process, and reduce uncertainty margins applied to final designs, NASA is developing simulation and modeling tools that enable characterization of material properties and response to high-enthalpy environments. The Porous Microstructure Analysis (PuMA) code has been developed for computing macroscale (volume averaged) properties of porous materials using microscale images from micro-computed tomography (micro-CT). Microscale modeling requires a realistic representation of a material microstructure; these are obtained either synthetically during the design of the material or through X-ray micro-CT. Volume averaged properties are then used to inform macroscale material response models, such as those implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO) software, also actively developed by NASA. The computational model in PATO is a generic heat and mass transfer model for porous reactive materials containing several solid phases and a single gas phase. The detailed chemical interactions occurring between the solid phases and the gas phase are modeled at the pore scale assuming local thermal equilibrium. These tools were developed to efficiently interface with other pre-existing codes such as SPARTA (direct simulation Monte Carlo), DPLR (hypersonic CFD), NEQAIR (radiative transport) and DAKOTA (uncertainty quantification and optimization). Detailed flight data (Mars Science Laboratory [MSL] Entry Descent and Landing Instrument [MEDLI]) is critical for validating these computational tools for NASA applications. Examples of modeling ablative material response using these codes will be presented including 3D simulations of the full-scale heatshield of the MSL capsule. The simulations demonstrate the ability of the modern material response code, PATO, to handle the material response of geometrically complex and large domains, through the use of massively parallel computations.

Thermal Protection Systems↗
NASA NTRS1985

Impact Crater Scaling Laws

The effects of the impactor size and velocity, of the material properties of the impactor and impacted body, and of the gravitational field strength were examined. The dependence of the coupling parameter on the Gruniesen parameter and the us/up slope values that characterize a Tillotson material model were tested. Whether a code calculation can recover the scaling exponents that can be derived theoretically for an idealized perfectly-porous material that crushes at zero strength and subsequently is incompressible was investigated. A model that was close to the idealized case was generated in a form suitable for code calculations and utilized for a series of one dimensional calculations. The code calculation demonstrated the theoretical coupling parameter. Calculations of impacts using a physically real porous material model seem to indicate a coupling parameter of the same form applicable to a nonporous material, distinctly different from that expected from other theoretical and experimental results for porous materials. The one dimensional calculations are being extended to two dimensional impacts.

Holsapple, K. A.↗
NASA NTRS1999

Flow Simulation of Solid Rocket Motors: Injection Induced Water-Flow Tests from Porous Media - 1

Prior to selecting a proper porous material for use in simulating the internal port flow of a solid rocket motor (SRM), in cold-flow testing, the flow emerging from porous materials is experimentally investigated. The injection-flow emerging from a porous matrix always exhibits a lumpy velocity profile that is spatially stable and affects the development of the longitudinal port flow. This flow instability, termed pseudoturbulence, is an inherent signature of the porous matrix and is found to generally increase with the wall porosity and with the injection flow rate. Visualization studies further show that the flow from porous walls made from shaving-type material (sintered stainless-steel) exhibits strong recirculation zones that are conspicuously absent in walls made from nodular or spherical material (sintered bronze). Detailed flow visualization observations and hot-film measurements are reported from tests of injection-flow and a coupled cross-flow from different porous wall materials. Based on the experimental data, discussion is provided on the choice of suitable material for SRM model testing while addressing the consequences and shortcomings from such a test.

Ramachandran, N.↗
NASA NTRS2009

Machined Titanium Heat-Pipe Wick Structure

Wick structures fabricated by machining of titanium porous material are essential components of lightweight titanium/ water heat pipes of a type now being developed for operation at temperatures up to 530 K in high-radiation environments. In the fabrication of some prior heat pipes, wicks have been made by extruding axial grooves into aluminum unfortunately, titanium cannot be extruded. In the fabrication of some other prior heat pipes, wicks have been made by in-situ sintering of metal powders shaped by the use of forming mandrels that are subsequently removed, but in the specific application that gave rise to the present fabrication method, the required dimensions and shapes of the heat-pipe structures would make it very difficult if not impossible to remove the mandrels due to the length and the small diameter. In the present method, a wick is made from one or more sections that are fabricated separately and assembled outside the tube that constitutes the outer heat pipe wall. The starting wick material is a slab of porous titanium material. This material is machined in its original flat configuration to form axial grooves. In addition, interlocking features are machined at the mating ends of short wick sections that are to be assembled to make a full-length continuous wick structure. Once the sections have been thus assembled, the resulting full-length flat wick structure is rolled into a cylindrical shape and inserted in the heatpipe tube (see figure). This wick-structure fabrication method is not limited to titanium/water heat pipes: It could be extended to other heat pipe materials and working fluids in which the wicks could be made from materials that could be pre-formed into porous slabs.

Rosenfeld, John H.↗
NASA NTRS1977

Development of Si3N4 and SiC of improved toughness

The application of energy absorbing surface layers to Si3N4 and SiC was investigated. Among the layers studied were microcracked materials such as iron titanate and a silica-zircon mixture and porous materials such as reaction sintered Si3N4. Energy absorption due to microcrack extension upon impact was found not to be an important mechanism. Instead, the fivefold improvement in Charpy and ballistic impact at elevated temperature (1250 C and 1370 C) found for Fe2TiO5 was due to plastic deformation while similar improvement found for silica-zircon mixtures at RT was due to crushing of the porous material. Due to thermal expansion mismatch, these two materials could not withstand thermal cycling when used as energy absorbing surface layers on Si3N4. Reaction sintered Si3N4 layers on dense Si3N4 were found to give up to a sevenfold increase in ballistic impact resistance due to crushing of the layer upon impact. High porosity (45%), large particle size R.S. Si3N4 layers fabricated from -100, +200 mesh Si powder gave better impact improvement than less porous (30%), small particle size layers fabricated from -325 mesh Si powder.

Brennan, J. J.↗
NASA NTRS1982

Internal heat transfer coefficients of porous metals

The internal heat transfer coefficients of porous metals have been experimentally determined in order to develop correlations between approximately defined Nusselt and Reynolds numbers. Scaled-up models of porous materials, and actual porous metal specimens, were subjected to countercurrent heat and mass transfer boundary conditions. Solid and gas phase temperatures were measured for both the scaled-up models and the actual porous metal specimens. On the basis of these measurements, the average internal heat transfer coefficient was evaluated, and a correlation between the Nusselt and Reynolds numbers was derived.

Kar, K. K.↗
NASA NTRS2016

Experimental Evaluation of Equivalent-Fluid Models for Melamine Foam

Melamine foam is a soft porous material commonly used in noise control applications. Many models exist to represent porous materials at various levels of fidelity. This work focuses on rigid frame equivalent fluid models, which represent the foam as a fluid with a complex speed of sound and density. There are several empirical models available to determine these frequency dependent parameters based on an estimate of the material flow resistivity. Alternatively, these properties can be experimentally educed using an impedance tube setup. Since vibroacoustic models are generally sensitive to these properties, this paper assesses the accuracy of several empirical models relative to impedance tube measurements collected with melamine foam samples. Diffuse field sound absorption measurements collected using large test articles in a laboratory are also compared with absorption predictions determined using model-based and measured foam properties. Melamine foam slabs of various thicknesses are considered.

Allen, Albert R.↗
NASA NTRSDate not supplied

Modeling instrumented test articles for Plasmatron X aerothermal environment

This work discusses the ablative response of thermal protection system materials when exposed to aerothermal environments. It focuses on modeling instrumented test article assemblies tested in the Plasmatron X inductively coupled plasma wind tunnel. For this purpose, as the samples are mounted to a water-cooled arm using numerous assembly components and are embedded with thermocouples for in-depth temperature measurements, the variation in ablative response of the samples as a result of these components is studied. The aerothermal boundary conditions for Plasmatron X are obtained for hypersonic flight-relevant conditions using the multi-physics aerothermal framework built at the University of Illinois at Urbana-Champaign. For simulating the material response, a material response code, Porous Material Analysis Toolbox based on OpenFOAM (PATO) is used. In PATO, numerous configurations and materials of thermocouples were studied. The optimal configuration for obtaining temperature measurements with minimal error using embedded thermocouples was found to be the U-shaped Type S, 30 American wire gauge thermocouple configuration.

Thermal Protection Systems↗
NASA NTRSDate not supplied

Modeling instrumented test articles for Plasmatron X aerothermal environment

This work discusses the ablative response of thermal protection system materials when exposed to aerothermal environments. It focuses on modeling instrumented test article assemblies tested in the Plasmatron X inductively coupled plasma wind tunnel. For this purpose, as the samples are mounted to a water-cooled arm using numerous assembly components and are embedded with thermocouples for in-depth temperature measurements, the variation in ablative response of the samples as a result of these components is studied. The aerothermal boundary conditions for Plasmatron X are obtained for hypersonic flight-relevant conditions using the multi-physics aerothermal framework built at the University of Illinois at Urbana-Champaign. For simulating the material response, a material response code, Porous Material Analysis Toolbox based on OpenFOAM (PATO) is used. In PATO, numerous configurations and materials of thermocouples were studied. The optimal configuration for obtaining temperature measurements with minimal error using embedded thermocouples was found to be the U-shaped Type S, 30 American wire gauge thermocouple configuration.

Thermal Protection Systems↗