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Cryogenic Spray Quenching of A Simulated Propellant Storage Tank Wall With Heat Transfer Enhancement By A Thin-Film Coating and Flow Pulsing in Microgravity

Human space exploration to the Moon, Mars, and possibly asteroids is NASA’s biggest challenge for the new millennium. One of the critical elements to this mission is the effective, sufficient, and reliable supply of cryogenic propellant fluids. Future lower-earth-orbiting (LEO) propellant fuel depots and human-carrying orbital transfer spacecraft flying to the moon and Mars will have to utilize the high thrust and high efficiency of liquid cryogenic chemical propulsion or nuclear thermal propulsion. Efficient in-space tank-to-tank propellant transfer (propellant fuel depot to orbital transfer spacecraft) of cryogenic propellants is an enabling technology for the planned Crewed Mars Surface Mission. The transfer of cryogenic propellants in space, however, has yet to be accomplished, solely due to the unavailability of cryogenic quenching heat transfer data during chilldown (quenching) and filling of the propellant receiver tank in reduced gravity and microgravity as liquid propellant cannot be stored in a required liquid state until the tank is quenched down to the liquid temperature. Therefore, highly energy efficient thermal-fluid management breakthrough concepts to conserve and minimize the cryogen consumption during propellant transfer have become the focus of research and engineering development, especially for the deep-space mission to Mars. In this paper, we introduce such concepts and demonstrate their feasibility for cryogenic storage tank chilldown in parabolic flights under a simulated space microgravity condition. In order to maximize the storage tank chilldown efficiency for the least amount of cryogen consumption, the technology adopted included cryogenic spray cooling, Teflon thin-film coating of the simulated tank surface, and spray flow pulsing. The completed flight experiments successfully demonstrated that spray cooling is the most efficient cooling method for the tank chilldown in microgravity. In microgravity, Teflon coating alone can improve the efficiency up to 72% and the efficiency can be improved up to 59% by flow pulsing alone. However, Teflon coating together with flow pulsing was found to substantially enhance the chilldown efficiency in microgravity for up to 113%.

spray

A GPU-based Approach for Turbomachinery Application

Accurate modeling of coolant airflows, which form protective films over turbine blades, is essential for designing fuel-efficient and environmentally sustainable gas turbine engines. Excessive coolant reduces thermal efficiency, while insufficient coolant leads to blade overheating and causes damage. Therefore, precise prediction of flow field interactions with cooling air is critical for optimizing turbine performance. This study numerically investigates the cooling effectiveness of purge and film cooling flows within a high-pressure turbine (HPT) rotor using Large Eddy Simulation (LES). The study utilizes NASA Glenn Research Center’s Glenn-HT solver. The simulation models ethe conditions of the Penn State University START rotating rig. A high-fidelity structured mesh comprising up to 800 million cells is employed to resolve high-Reynolds number flow (Re ≈ 350,000) and to capture intricate secondary flow structures, including tip leakage and purge-induced vortices. Film cooling effectiveness computations are highly sensitive to boundary conditions at the cooling holes and to grid resolution. Even with well-resolved grids and included plena, strong mixing challenges traditional eddy viscosity models. To address this, a simplified configuration is simulated: a truncated row of shaped holes on the suction side near the leading edge and a row on the pressure side, both fed from internal plena while the purge slot and tip clearance are also modeled. Two isothermal LES cases are conducted at two distinct wall temperatures, which yield the adiabatic wall temperature and the heat transfer coefficient. The definition and means of computation of the effectiveness is discussed in this paper. The simulations reveal detailed three-dimensional unsteady flow features, including coherent vortical structures and secondary flows originating from the purge cavity. Film cooling effectiveness and Nusselt number distributions are presented for both the blade surface and tip, highlighting regions of elevated heat transfer and complex thermal behavior. These findings underscore the importance of high-resolution LES and realistic boundary conditions in capturing the dynamics of purge and film cooling, offering valuable insights for improving turbine blade design and thermal management strategies.

Gas Turbine

Development of an Additively Manufactured Subscale Secondary Sealed Container for the NASA FROSTE Project

This presentation details the development of an additively manufactured (AM) subscale test article for the secondary sealed container (SSC) as part of the NASA FROSTE project. FROSTE is focused on the collection of regolith samples from shadowed regions of the Moon and the preservation of those samples at cryogenic temperatures for return to Earth. Our team was integrated into the FROSTE program to leverage innovative design approaches and additive manufacturing capabilities in support of a scalable development strategy, where the subscale configuration serves as the development path toward a full-scale SSC. Scalmalloy was selected as the primary material for all AM components due to its favorable strength-to-weight ratio, thermal conductivity, and demonstrated performance in aerospace applications. Its aluminum-based composition supports robust mechanical behavior at cryogenic temperatures while enabling efficient heat transfer and control of thermal gradients within the containment system. The SSC architecture consists of an outer container assembly that houses a phase change material (PCM) tank, which in turn contains primary containers holding the regolith. Thermal management relies on controlled conductive and radiative heat transfer, including a thermal connection assembly that interfaces the PCM tank to an external cryocooler via a thermal strap, and IMLI surrounding the PCM tank to inhibit radiative heat transfer. The outer container assembly incorporates sealing interfaces, thermal connection ports, and I/O feedthroughs, with PTFE spring seals used at critical interfaces to maintain containment integrity. The PCM tank is manufactured as a single monolithic Scalmalloy component and incorporates an integral lattice structure to minimize thermal gradients, internal channels for thermocouple routing, and interface features for thermal connection assembly integration. The tank is centrally suspended within the outer container using support rings, with G10 insulating components employed to inhibit thermal leaks. This work describes the design methodology, AM approach, and key considerations used to inform the design.

regolith

xEMU Spacesuit Boot Lunar South Pole Thermal Vacuum Testing

The Exploration Extravehicular Mobility Unit (xEMU) spacesuit lunar boot was evaluated in the Jet Propulsion Lab (JPL) CITADEL thermal vacuum chamber at lunar South Pole conditions. The JPL CITADEL chamber provides a radiation environment and contact plate temperature of 48K, simulating the temperature of a lunar Permanently Shadowed Region (PSR) at the South Pole of the Moon. The main objectives of the test series are: to evaluate the risk lunar PSRs pose to advanced spacesuit boots, validate the xEMU lunar boot thermal model, and to develop a test methodology to evaluate lunar spacesuit boots. To simulate the thermal effects of a crewmember’s foot inside the boot, a thermal manikin foot was developed to inject heat into the spacesuit boot. Thermal data was collected through a variety of sensors including thermocouples, thermistors, heat flux sensors, and infrared cameras. A test matrix was developed to investigate the variables of foot contact force, simulated skin temperature, external contact plate temperature, and ventilation flowrate. The JPL CITADEL chamber includes a loadlock (airlock) that afforded the ability to simulate the transition of the boot from a thermally neutral IVA condition to a cold EVA condition within seconds. This paper will document the test design, test objectives, success criteria, test support equipment, spacesuit boot to chamber interfaces, and configuration of the test article. Additionally, this paper will document the high-level results of the testing. More detailed test results will be presented in a different paper.

Ben Swartout

Simulations of Yarn Micro-Mechanics of Woven Heat Shield Materials

Carbon and phenolic fibers are commonly used in ablative thermal protection materials, such as 3-dimensional Mid-Density Carbon Phenolic (3MDCP), a 3D-woven composite comprised of mixed-fiber yarn bundles. Predicting the micro-mechanical response and fracture of twisted yarns composed of brittle and ductile fibers requires a modeling approach that captures per-fiber yielding, fiber fracture, and inter-fiber friction and contact. This work presents an extended bonded particle model (BPM) for discrete element method (DEM) simulation of fiber and yarn mechanics, implemented in LAMMPS. The model builds on the incremental bond formulation of Guo et al. and introduces a piecewise elasto-plastic constitutive law for axial extension, enabling representation of fibers that yield before failure. 3MDCP yarns were constructed using measured fiber radius distributions and helical twist geometry. Tensile simulations of single-ply 3MDCP yarns show good agreement with vender stress–strain results. Fiber breakage models also show details on yarn breakage propagration, centered radially in the yarn. Yarn breakage of multi-ply 3MDCP also matched experimental observations in per-ply breakage; however, predicted yarn breakage strength were found higher than experimental observations.

Discrete Element Method

Simulations of Yarn Micro-Mechanics of Woven Heat Shield Materials (3MDCP)

Carbon and phenolic fibers are commonly used in ablative thermal protection materials, such as 3-dimensional Mid-Density Carbon Phenolic (3MDCP), a 3D-woven composite comprised of mixed-fiber yarn bundles. Predicting the micro-mechanical response and fracture of twisted yarns composed of brittle and ductile fibers requires a modeling approach that captures per-fiber yielding, fiber fracture, and inter-fiber friction and contact. This work presents an extended bonded particle model (BPM) for discrete element method (DEM) simulation of fiber and yarn mechanics, implemented in LAMMPS. The model builds on the incremental bond formulation of Guo et al. and introduces a piecewise elasto-plastic constitutive law for axial extension, enabling representation of fibers that yield before failure. 3MDCP yarns were constructed using measured fiber radius distributions and helical twist geometry. Tensile simulations of single-ply 3MDCP yarns show good agreement with vender stress–strain results. Fiber breakage models also show details on yarn breakage propagration, centered radially in the yarn. Yarn breakage of multi-ply 3MDCP also matched experimental observations in per-ply breakage; however, predicted yarn breakage strength were found higher than experimental observations.

Woven

LES-Based Analysis of Film Cooling in a High-Pressure Turbine Rotor Including Effects of Purge and Tip Flow

Accurate modeling of coolant airflows, which form protective films over turbine blades, is essential for designing fuel-efficient and environmentally sustainable gas turbine engines. Excessive coolant reduces thermal efficiency, while insufficient coolant leads to blade overheating and causes damage. Therefore, precise prediction of flow field interactions with cooling air is critical for optimizing turbine performance. This study numerically investigates the cooling effectiveness of purge and film cooling flows within a high-pressure turbine (HPT) rotor using Large Eddy Simulation (LES). The study utilizes NASA Glenn Research Center’s Glenn-HT solver. The simulation models ethe conditions of the Penn State University START rotating rig. A high-fidelity structured mesh comprising up to 800 million cells is employed to resolve high-Reynolds number flow (Re ≈ 350,000) and to capture intricate secondary flow structures, including tip leakage and purge-induced vortices. Film cooling effectiveness computations are highly sensitive to boundary conditions at the cooling holes and to grid resolution. Even with well-resolved grids and included plena, strong mixing challenges traditional eddy viscosity models. To address this, a simplified configuration is simulated: a truncated row of shaped holes on the suction side near the leading edge and a row on the pressure side, both fed from internal plena while the purge slot and tip clearance are also modeled. Two isothermal LES cases are conducted at two distinct wall temperatures, which yield the adiabatic wall temperature and the heat transfer coefficient. The definition and means of computation of the effectiveness is discussed in this paper. The simulations reveal detailed three-dimensional unsteady flow features, including coherent vortical structures and secondary flows originating from the purge cavity. Film cooling effectiveness and Nusselt number distributions are presented for both the blade surface and tip, highlighting regions of elevated heat transfer and complex thermal behavior. These findings underscore the importance of high-resolution LES and realistic boundary conditions in capturing the dynamics of purge and film cooling, offering valuable insights for improving turbine blade design and thermal management strategies.

Secondary Flows

Thermo-Poro-Mechanical Modeling of RTV Intumescence

Room temperature vulcanizing (RTV) silicone is a high-temperature adhesive used as a gap-filler between heatshield tiles in numerous entry missions. Its propensity to intumesce, or swell upon exposure to heat, is a well-known effect that needs to be carefully quantified during design. At tile interfaces of charring ablators, intumescence, combined with differential recession, could cause the gap filler to protrude past the ablator outer mold line, forming a “fence”. Fencing can in turn cause transition to turbulence of the flow wetting the heat shield, leading to augmented surface heating. Recent experiments conducted at the Plasmatron X facility, the high enthalpy wind tunnel of the Center for Hypersonics and Entry Systems Studies, have shown prominent fencing of RTV gap fillers in PICA, under both nitrogen and air plasmas. Similar observations are well known in the arcjet literature. Further experiments under controlled environment, performed using in situ X-ray micro-computed tomography (micro-CT) at the Advanced Light Source (ALS), have shown heating rate-dependent swelling and shrinkage of RTV during pyrolysis. To simulate RTV intumescence, a novel model was introduced in the Porous Materials Analysis Toolbox based on OpenFOAM, PATO, to account for pore-pressure buildup within both closed- and open-pores. The governing equation for the thermo-poro-mechanical response were developed, assuming linear elasticity for the charring silicone. A new multi-pyrolysis model that tracks non-monotonic advancement of material properties with pyrolysis was proposed. This model addresses the limitations of state-of-the-art ablator models to capture the different stages of thermal degradation and coupled thermomechanics. Swelling of RTV was simulated using the new thermo-poro-mechanical model and compared against in situ micro-CT data. Results showed good agreement in intumescence height and temperature profiles at all heating rates, indicating that the key factor contributing to RTV swelling is the internal pressure build-up within closed- and open-pores. As RTV is cured into a soft (rubbery) compound with low-porosity and permeability, initial temperature increase and pyrolysis gas production cause a significant increase of internal pressure, causing a pronounced volume growth. As thermal degradation progresses, rigidization of the silicone occurs due to char hardening which counteract volume shrinkage after gas pressure relief. Overall, our model shows that accounting for changes in properties such porosity, permeability and key thermomechanical coefficients is crucial for capturing the RTV volume change during ablation and enable a predictive capability for heatshield tile interface response. A plan for future calibration of thermomechanical properties evolution during degradation is discussed, as a key next step to close the new model.

RTV

Thermo-Poro-Mechanical Modeling of RTV Intumescence

Room temperature vulcanizing (RTV) silicone is a high-temperature adhesive used as a gap-filler between heatshield tiles in numerous entry missions. Its propensity to intumesce, or swell upon exposure to heat, is a well-known effect that needs to be carefully quantified during design. At tile interfaces of charring ablators, intumescence, combined with differential recession, could cause the gap filler to protrude past the ablator outer mold line, forming a “fence”. Fencing can in turn cause transition to turbulence of the flow wetting the heat shield, leading to augmented surface heating. Recent experiments conducted at the Plasmatron X facility, the high enthalpy wind tunnel of the Center for Hypersonics and Entry Systems Studies, have shown prominent fencing of RTV gap fillers in PICA, under both nitrogen and air plasmas. Similar observations are well known in the arcjet literature. Further experiments under controlled environment, performed using in situ X-ray micro-computed tomography (micro-CT) at the Advanced Light Source (ALS), have shown heating rate-dependent swelling and shrinkage of RTV during pyrolysis. To simulate RTV intumescence, a novel model was introduced in the Porous Materials Analysis Toolbox based on OpenFOAM, PATO, to account for pore-pressure buildup within both closed- and open-pores. The governing equation for the thermo-poro-mechanical response were developed, assuming linear elasticity for the charring silicone. A new multi-pyrolysis model that tracks non-monotonic advancement of material properties with pyrolysis was proposed. This model addresses the limitations of state-of-the-art ablator models to capture the different stages of thermal degradation and coupled thermomechanics. Swelling of RTV was simulated using the new thermo-poro-mechanical model and compared against in situ micro-CT data. Results showed good agreement in intumescence height and temperature profiles at all heating rates, indicating that the key factor contributing to RTV swelling is the internal pressure build-up within closed- and open-pores. As RTV is cured into a soft (rubbery) compound with low-porosity and permeability, initial temperature increase and pyrolysis gas production cause a significant increase of internal pressure, causing a pronounced volume growth. As thermal degradation progresses, rigidization of the silicone occurs due to char hardening which counteract volume shrinkage after gas pressure relief. Overall, our model shows that accounting for changes in properties such porosity, permeability and key thermomechanical coefficients is crucial for capturing the RTV volume change during ablation and enable a predictive capability for heatshield tile interface response. A plan for future calibration of thermomechanical properties evolution during degradation is discussed, as a key next step to close the new model.

silicone intumescence

The Use of Immersion Rigs for High Temperature Hydrogen Exposure Testing within the Nuclear Thermal Rocket Element Environmental Simulator (NTREES): Thermal Soak Rig (TSR)

The Nuclear Thermal Rocket Element Environmental Simulator (NTREES) facility was purpose constructed to perform non-nuclear evaluations of nuclear thermal propulsion (NTP) system fuel materials and structures within prototypic thermochemical environments. This system has been utilized steadily in its ability to subject test specimens to thermochemical and thermohydraulic environments simulating that of an operating nuclear rocket engine. Fission heat is simulated by induction power and experiments are conducted within a ~1000 psi pressure vessel. Hydrogen is conventionally passed through the heated fuel surrogate test specimen while pressure, temperature, and gas species data are collected at various points along the experiment. In order to test fuel and material coupon samples, a class of test apparatus named “immersion rigs” are being developed and employed to more rapidly test these smaller and more technically challenging test specimen. One example of a promising potential fuel structure, Tristructural-isotropic (TRISO) particles, presents unique challenges for testing of this type. TRISO fuel micro-particles are spheroids typically on the order of 500 – 1000 μm in diameter, and exposing a batch sample to hot hydrogen requires purpose-built special test equipment. Thusly, an immersion rig was developed and successfully demonstrated to expose ~1 g of micro-particles to hydrogen gas at temperatures and pressures relevant to NTP systems for the purpose of fuel evaluation. The rig, comprised primarily of graphite and pure tungsten, houses in its core a batch of micro-particles between pucks of porous silicon carbide (SiC). This approach permits gas flow while simultaneously retaining the particles in place. Herein is a discussion of the design, analysis, fabrication, and testing of the NTREES Thermal Soak Rig (TSR).

Space Nuclear Propulsion

Development of a High Force Thermal Latch

This paper describes the preliminary development of a high force thermal latch (HFTL). The HFTL has one moving part which is restrained in the latched position by a low melting temperature or fusible metal alloy. When heated the fusible alloy flows to a receiving chamber and in so doing at first releases the tension load in the latch bolt and later releases the bolt itself. The HFTL can be used in place of pyrotechnically activated spacecraft release devices in those instances where the elimination of both pyrotechnic shock-loading and rapid strain-energy release take precedence over the near instantaneous release offered by ordnance initiated devices.

William D Nygren

Advanced Space Power PEM Fuel Cell Systems

A model showing mass and heat transfer in proton exchange membrane (PEM) single cells is presented. For space applications, stack operation requiring combined water and thermal management is needed. Advanced hardware designs able to combine these two techniques are available. Test results are shown for membrane materials which can operate with sufficiently fast diffusive water transport to sustain current densities of 300 ma per square centimeter. Higher power density levels are predicted to require active water removal.

PEM

Riddles About the Origin and Thermal History of the Moon

Analyses of lunar rocks have confirmed that the interior of the Moon has been subjected to magmatic differentiation, as has been determined by calculation of the thermal history of the Moon. However, it appears that differentiation occurred so early that it could not have been related to heating by long-lived radioactive elements, but rather indicates a high initial temperature of the Moon. The reasons for the high initial temperature remain unknown. The presence of a central, partially melted area revealed by seismic observations forces us to reject convective models of the Moon, while the dimensions of this area, together with the measured heat fluxes from the interior, serve as "boundary conditions" for any new calculations of the thermal history for a two-layered differentiated model of the Moon operative over the past 3.5 billion years. If we start with the early differentiation of the Moon and the high content of long-lived radioactive elements in it, explanation of its current thermal properties represents no difficulty. But these prerequisites themselves remain unexplained. Due to the continuing controversy concerning the true nature of the process of magmatic differentiation of the Moon, estimation of the composition of the entire Moon on the basis of analyses of surface rock remains unreliable, and use of these estimates to clarify the origin of the Moon is premature. Existing hypotheses concerning the origin of the Moon encounter dynamic difficulties, as well as difficulties with explanation of the high initial temperature, to say nothing of the difficulty involved in explaining the proposed differences in the composition of the Earth and Moon.

B Yu Levin

Thermal Considerations for 2039 Opposition Class Nuclear Electric Propulsion/Chemical Propulsion Crewed Mars Mission

The high specific impulse (Isp) of Nuclear Electric Propulsion (NEP) technology offers the potential for advanced space mission capabilities. However, the five critical technology elements of NEP vehicles have yet to prove technical maturity levels for consideration into mission design. In response to the critical reviews by the NASA Engineering and Safety Center (NESC) and the National Academies of Sciences, Engineering, and Medicine (NASEM), NASA’s Space Nuclear Propulsion (SNP) project created an NEP Technology Maturation Plan (TMP) for focused development of NEP technology. The TMP called for a coordinated set of technology development efforts to meet this objective. The Modular Assembled Radiators for NEP VehicLes (MARVL) Early Career Initiative (ECI) project was initiated to develop a portion of the fifth Critical Technology Element (CTE) of the NEP vehicle: the Primary Heat Rejection Subsystem (PHRS). A target application of a 2039 human-rated Mars mission was outlined in the TMP. For the outlined mission, a NEP vehicle will experience several thermal environments which will impact the design and operation of the PHRS. To maintain radiator temperatures within the required effective temperature range, the effect of natural, induced, and NEP internally generated heat loads on the radiator panel must be well understood. Furthermore, this analysis is critical for analyzing the influence of various orientations and positions of the NEP vehicle relative to nearby celestial bodies throughout the mission. This study conducted a complete enveloping analysis of the thermal environments influencing the NEP vehicle throughout the mission. Thermal analysis was conducted for the radiator panels based on the defined mission environments. This thermal analysis concludes with the selection of ideal radiator orientations for the NEP vehicle, and the identification of worst case hot and cold environmental sink temperatures throughout the mission. For the target application, the environmental sink temperature while the reactor is powered OFF or powered ON ranges from 30 K to 353 K and 2.7 K to 243 K respectively. When considering interplanetary space, the minimum environmental sink temperature when the reactor is powered OFF and the radiators are oriented “edge to Sun” is 2.7 K. The environmental thermal models generated in this study will be used for future studies with the full vehicle system model. The environmental sink temperature curves generated will be used for future radiator and component analysis to predict transient performance in the space environment. The environmental sink temperature and heat rejection capability curves will inform the trade between commissioning orbits that are in consideration. The model may also serve as a useful tool as reference for future crewed space missions, missions involving radiators or temperature sensitive equipment, or other missions requiring analysis of natural orbital thermal environments.

Nuclear Electric Propulsion

SR-1 Freedom Thermal Architecture Challenges

The SR-1 Freedom mission aims to demonstrate nuclear electric propulsion (NEP) and deliver the Skyfall helicopter payload to Mars. Repurposing the existing Gateway Power and Propulsion Element (PPE) spacecraft and combining it with a 20 kWe-class nuclear power module (NPM) presents a variety of thermal architecture challenges. These include unprecedented waste heat rejection requirements, integration with a spacecraft bus originally designed for a different mission profile, and novel packaging constraints. This presentation will describe the simplified concept of operations as it relates to on-orbit thermal environments, early-phase architecture trades and supporting analyses, and planned forward work. We will also discuss our strategy for integrated thermal modeling of the complete spacecraft and examples of interface challenges necessitated by this ambitious effort.

Thermal

Safe, High Power / Voltage Battery Design Challenges

NASA seeks safe, high performing battery module designs that can deliver 3C discharge rates continuously, achieve 160 Wh/kg, and is passively propagation resistant to a single cell thermal runaway event. One solution is presented that uses a patented oscillating heat pipe technology for thermal management. Combined with light weight packaging and a new commercially available gas permeable vent port, all 5 preliminary safety tests results performed to date are showing ample margins.

High power

Thermomechanical Modeling of Woven Materials With Particle-Based, Explicit-Fiber Simulations

Fiber-based materials are extensively used to protect spacecraft during entry. Insulative fibers, often in a fiber network or woven, provide rigidity, strength, and control of material anisotropy and density. Woven thermal protection materials, such as ADEPT (Adaptable, Deployable Entry and Placement Technology), 3D-MAT (3-Dimensional Multifunctional Ablative Thermal Protection), and 3MDCP (3D Woven Mid-Density Carbon Phenolic), enable missions with stronger and denser materials for entry profiles with high shear and heat flux. Vulnerabilities to woven thermal protection materials include manufacturing-induced material property variation, and impact from micrometeoroids. Simulating woven materials under these conditions require models that can resolve hierarchal structures, thermomechanical behavior, and failure. To address this, we simulate weave thermal conduction and mechanical deformation. We simulate the full weave with a coarse-grained yarn model is presented. The model combines a validated, high-resolution single 3MDCP yarn model and phenolic resin model. Instead of modeling every fiber, each yarn ply with order 10, instead of order 1000, fibers. The discrete element bonded particle model (DEM-BPM) of fibers captures the thermal and mechanical behavior within and between fibers. We study the proportion of heat transfer and stress via the contact network, fiber bonds, and overall weave geometry.

bonded particle

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