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NASA NTRS1987

Finite difference solution for a generalized Reynolds equation with homogeneous two-phase flow

An attempt is made to relate elements of two-phase flow and kinetic theory to the modified generalized Reynolds equation and to the energy equation, in order to arrive at a unified model simulating the pressure and flows in journal bearings, hydrostatic journal bearings, or squeeze film dampers when a two-phase situation occurs due to sudden fluid depressurization and heat generation. The numerical examples presented furnish a test of the algorithm for constant properties, and give insight into the effect of the shaft fluid heat transfer coefficient on the temperature profiles. The different level of pressures achievable for a given angular velocity depends on whether the bearing is thermal or nonisothermal; upwind differencing is noted to be essential for the derivation of a realistic profile.

Braun, M. J.↗

NASA NTRS1999

Gravitational Acceleration Effects on Macrosegregation: Experiment and Computational Modeling

Experiments were performed under terrestrial gravity (1g) and during parabolic flights (10-2 g) to study the solidification and macrosegregation patterns of Al-Cu alloys. Alloys having 2% and 5% Cu were solidified against a chill at two different cooling rates. Microscopic and Electron Microprobe characterization was used to produce microstructural and macrosegregation maps. In all cases positive segregation occurred next to the chill because shrinkage flow, as expected. This positive segregation was higher in the low-g samples, apparently because of the higher heat transfer coefficient. A 2-D computational model was used to explain the experimental results. The continuum formulation was employed to describe the macroscopic transports of mass, energy, and momentum, associated with the solidification phenomena, for a two-phase system. The model considers that liquid flow is driven by thermal and solutal buoyancy, and by solidification shrinkage. The solidification event was divided into two stages. In the first one, the liquid containing freely moving equiaxed grains was described through the relative viscosity concept. In the second stage, when a fixed dendritic network was formed after dendritic coherency, the mushy zone was treated as a porous medium. The macrosegregation maps and the cooling curves obtained during experiments were used for validation of the solidification and segregation model. The model can explain the solidification and macrosegregation patterns and the differences between low- and high-gravity results.

Leon-Torres, J.↗

DOE OSTI2025

Quench process modeling & simulation in the heat-treatment of critical aerospace components

To manufacture light-weight, advanced metal alloy components for gas turbine engines, quench heat-treatment processes are typically used. By quenching the component from elevated temperatures, the alloy sometimes undergoes a solid-state phase transformation which produces special microstructures with the required, enhanced mechanical properties. However, the quenching can also lead to cracks forming in the component. Addressing the quench cracking problems adds a significant burden to the cost, schedule, and energy demand of manufacture. Currently, optimizing the quench process to mitigate or avoid the cracking is performed largely by trial-and-error, relying heavily on costly experimental (thermocouple)trials to understand the local thermal gradients which cause the cracks to form. In this first part (Phase 1) of the work, high-performance computing is employed to establish the ability of modern CFD (computational fluid dynamics) to alleviate or wholly replace the experimental quenching trials by virtual testing. A Baseline CFD model is defined and its accuracy established to be comparable to(and which usually exceeds) the accuracy of existing HTC (heat-transfer coefficient) based simulation methods of quenching. As a first-principles based approach, “calibration” of the Baseline CFD model is independent of the quench process itself, but instead relies on the accuracy of the underlying (modeled),generic two-phase fluid processes which cannot be currently resolved by CFD for large, industrial-scale cases. A novel, high-fidelity DNS capability has been developed and verified to examine and further improve upon the mean-field closure submodels on which the Baseline CFD approach is based.1

99 GENERAL AND MISCELLANEOUS↗

NASA NTRS1977

Applicability of empirical data currently used in predicting solid propellant exhaust plumes

Theoretical and experimental approaches to exhaust plume analysis are compared. A two-phase model is extended to include treatment of reacting gas chemistry, and thermodynamical modeling of the gaseous phase of the flow field is considered. The applicability of empirical data currently available to define particle drag coefficients, heat transfer coefficients, mean particle size, and particle size distributions is investigated. Experimental and analytical comparisons are presented for subscale solid rocket motors operating at three altitudes with attention to pitot total pressure and stagnation point heating rate measurements. The mathematical treatment input requirements are explained. The two-phase flow field solution adequately predicts gasdynamic properties in the inviscid portion of two-phase exhaust plumes. It is found that prediction of exhaust plume gas pressures requires an adequate model of flow field dynamics.

Tevepaugh, J. A.↗

NASA NTRS1971

Review of Orbital Propellant Transfer Techniques and the Feasibility of a Thermal Bootstrap Propellant Transfer Concepts

This study was performed in support of the NASA Task B-2 Study Plan for Space Basing. The nature of space-based operations implies that orbital transfer of propellant is a prime consideration. The intent of this report is (1) to report on the findings and recommendations of existing literature on space-based propellant transfer techniques, and (2) to determine possible alternatives to the recommended methods. The reviewed literature recommends, in general, the use of conventional liquid transfer techniques (i.e., pumping) in conjunction with an artificially induced gravitational field. An alternate concept that was studied, the Thermal Bootstrap Transfer Process, is based on the compression of a two-phase fluid with subsequent condensation to a liquid (vapor compression/condensation). This concept utilizes the intrinsic energy capacities of the tanks and propellant by exploiting temperature differentials and available energy differences. The results indicate the thermodynamic feasibility of the Thermal Bootstrap Transfer Process for a specific range of tank sizes, temperatures, fill-factors and receiver tank heat transfer coefficients.

Yoshikawa, H. H.↗

DOE OSTI2025

Pool boiling heat transfer evaluation of next-generation dielectric fluid: Opteon™ 2P50

The growing use of artificial intelligence has led to heavy thermal loads and high heat dissipation rates in data centers. Conventional air-cooled technologies are not able to fulfill these requirements. To overcome these challenges, two-phase immersion cooling (2PIC) has emerged as one of the leading technologies for high power-density chips. 2PIC increases the heat dissipation rate and efficiency of the system while reducing the footprint of the cooling equipment. A fluid with adequate dielectric properties, a suitable normal boiling temperature to maintain chip temperatures, and good material compatibility, is desired for 2PIC system. In this study, the pool boiling heat transfer of a new developmental dielectric fluid, Opteon™ 2P50, was experimentally investigated. The heat transfer coefficients at various heat fluxes (20–150 kW/m 2 ) and the critical heat flux were measured using a smooth aluminum surface. Compared with HFE-7100, Opteon™ 2P50 shows higher heat transfer coefficient (up to 59% higher) and a slightly lower value of critical heat flux (around 5.9% lower). The modified Cooper correlation with the optimized leading constant resulted in reliable prediction accuracy with a 5.3% mean absolute error percentage. Overall, these results indicate that the new dielectric fluid provides similar thermal performance to some legacy fluids.

2P50↗

NASA NTRS1985

Design and test of a pumped two-phase mounting plate

The design, fabrication, and testing of the full-scale development unit of a pumped two-phase mounting plate (TPMP) used in advanced two-phase spacecraft thermal control systems are described. The mounting plate is tested with R-11 in the evaporator mode for total heat loads of over 3000 watts and local heat fluxes over 4 W/sq cm, and in the condenser mode with condenser loads from 60 to 400 watts and inlet qualities from 8 to 94 percent. The calculated heat-transfer coefficients are between 0.66 and 1.0 W/sq cm/C and are nearly independent of the flow rate and heat load except at very low heat loads. It is shown that the TPMP can be run with inlet conditions down to 22 C subcooling without any significant gradients in the plate and that it performs well with nonuniform heat fluxes.

Grote, M. G.↗

DOE OSTI2024

Porous mesh manifold for enhanced boiling performance

High-performance electronics are continuously demanding cooling of higher heat fluxes. Phase-change cooling, including pool boiling, is a useful approach to address this challenge; however, competition between liquid and vapor flows generally limit the heat fluxes that can be dissipated. A range of strategies to control these flows have been investigated previously, including capillary guides. Here a manifold structure formed from a metallic mesh is investigated to control the disposition of liquid and vapor phases above a pool fed boiling surface enhanced with porous structures. Copper mesh forms defined liquid flow paths, using capillary action to guide and distribute liquid evenly over the heated surface, along with open channels to facilitate vapor escape. The mesh provides a novel structure for liquid guidance that imposes low resistance to liquid flow while occluding a minimal area of heated surface underneath. The manifold performance is characterized in boiling fed by a pool of water above a laser-textured aluminum nitride heat dissipation surface with pin–fin structures having heights of 110 µm and spacing of 30 µm with a heated area of 5 mm x 5 mm. A maximum heat flux of 490 W/cm 2 is reached with the manifold in the pool fed configuration, representing an increase of more than 65% over the porous pin fin surface alone. The maximum stable superheat observed for the manifold of 36K is 14K higher than that for the porous surface without the manifold. The factors limiting performance of the manifold are analyzed. High superheat is attributed to partial flooding of the boiling surface as suggested by the reduction in superheat using external suction. Similar systems and structures for enhanced two-phase cooling are compared.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1987

Test results of a pumped two-phase mounting plate with ammonia

The design, fabrication, and testing of full-scale prototype units of a two-phase mounting plate (TPMP), which will be used in a two-phase ammonia-based thermal control system for a large spacecraft, are described. The mounting plate uses an evaporator design in which liquid is mechanically pumped through porous feed tubes within the plate. The prototype TPMPs were tested with ammonia at heat loads over 3000 W (3.2 W/sq cm) and local heat fluxes of up to 4 W/sq cm. Calculated total heat transfer coefficients from these tests were between 0.8 and 1.0 W/sq cm per C. This represents a better than twenty-fold improvement over comparable single-phase heat transfer coefficients. Design diagrams are included.

Swanson, T. D.↗

NASA NTRS1992

A prototype heat pipe heat exchanger for the capillary pumped loop flight experiment

A Capillary Pumped Two-Phase Heat Transport Loop (CAPL) Flight Experiment, currently planned for 1993, will provide microgravity verification of the prototype capillary pumped loop (CPL) thermal control system for EOS. CAPL employs a heat pipe heat exchanger (HPHX) to couple the condenser section of the CPL to the radiator assembly. A prototype HPHX consisting of a heat exchanger (HX), a header heat pipe (HHP), a spreader heat pipe (SHP), and a flow regulator has been designed and tested. The HX transmits heat from the CPL condenser to the HHP, while the HHP and SHP transport heat to the radiator assembly. The flow regulator controls flow distribution among multiple parallel HPHX's. Test results indicated that the prototype HPHX could transport up to 800 watts with an overall heat transfer coefficient of more than 6000 watts/sq m-deg C. Flow regulation among parallel HPHX's was also demonstrated.

Ku, Jentung↗

DOE OSTI2025

MOSCATO Development and Integration in Fiscal Year 2025: Implementation of Multiphase, Multiphysics Modeling Capabilities for Molten Salt Systems

MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy corrosion for molten salt systems. In FY25, significant developments were made to the code package, enhancing its capabilities for modeling all relevant phenomena within operating moltens salt reactors (MSRs). The developments and activities in FY25 included: 1. Implementation of Level-Set methods to enable modeling of single-bubble behavior in molten salts. In FY25, the Level-Set two-phase flow modeling implementation was improved to simulate single bubble behavior with molten salt media. The large density and viscosity ratios between typical gases and molten salt liquids present challenges for these types of numerical solvers. With enhancements to the pressure projection method, MOSCATO’s Level-Set solver was able to be successfully validated to experiments related to helium bubble rise in stagnant molten salt. The simulated bubble rising velocity showed reasonable good agreement with experimental measurements. The bubble shape and dynamics were also visually compared with experimental snapshots, demonstrating a good qualitative match. 2. Generation of mass transfer correlations for multiphase flow systems. To enable calculations of the tritium transport across the interface between gas bubbles and salt, we modeled high- Schmidt-number mass transfer around a sphere across a broad range of Reynolds numbers. The mesh near the sphere surface was highly refined to resolve steep concentration gradients caused by the low diffusion coefficient. Literature-based mass transfer correlations were compared with the numerical results, and modifications were proposed to improve agreement, particularly at higher Schmidt numbers. These mass transfer correlations were subsequently provided to other national laboratories to help enable high quality mass transfer simulations using lower-order solvers under development within the NEAMS program. 3. Preliminary implementation of a bubbly flow solver. To model bubbly flow in molten salt, we implemented a bubbly flow solver for void fractions less than 5%. To do so, an algebraic relative velocity model that assumes small bubbles with rapid momentum equilibration was added to MOSCATO to compute bubble velocities. Preliminary comparisons with experimental data showed reasonable agreement, and further improvements are underway. 4. Generation of mass transfer correlations for MSRE subchannel The Molten-Salt Reactor Experiment (MSRE) was a landmark historical project that demonstrated the feasibility of molten-salt reactor technology. The MSRE campaign also generated a significant body of experimental data and reports that continue to support molten-salt–related research. In this report, the MSRE core subchannel was used as the reference geometry for a mass transfer study performed with MOSCATO. The geometry and computational mesh were adapted from a previous study, providing adequate resolution for the relatively low Reynolds number in this case. Additional mesh refinement was applied to reach higher Schmidt numbers, enabling the derivation of a reliable mass-transfer correlation for the present scenario. 5. Simulations of oxygen ingressions into molten salt. In the previous fiscal year, we initiated a study to simulate oxygen ingression in stagnant salt. As oxygen enters the salt through its surface, it reacts with Ce 3+ to form solid CeO 2 and other reaction products. To more fully capture the complex diffusion-convection-reaction mechanisms, capabilities for modeling natural convection in the salt vessel were added. These were needed as the flow of the ingressed gas induced flow in the salt caused by surface shear and non-isothermal effects. With these updated physics in place, we were able to successfully reproduce the experimental results for the rate of change of CeCl 3 concentrations versus time. 6. Flow corrosion model validation. In FY24, MOSCATO’s corrosion model was validated against static corrosion experiments. In FY25, this work was extended to a flow corrosion experiment, where FLiNaK salt was driven by natural convection, with initial salt impurities to initiate corrosion. Despite uncertainties in parameters such as elemental diffusion coefficients in the alloy and unknown H + concentrations, the simulations achieved good agreement with experimental results, especially in predicting sample mass losses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Non-dimensional performance and safety parameters for heat pipes

The use of heat pipes in safety-critical systems such as nuclear microreactors dictates the development of generalized, practical, scalable performance and safety parameters. Traditional dimensional metrics, while informative, lack the universality required for comparative analysis across varying designs and operating regimes. Here, this work introduces a comprehensive set of non-dimensional parameters to characterize heat pipe performance and safety, including capillary performance, effective thermal conductivity, response time, exergetic efficiency, allowable temperature gradients, allowable rate of temperature change, priming coefficients, and factor of safety. A reference heat pipe design representative of microreactor applications was analyzed via the developed parameters using both traditional analytical models and Sockeye simulations under transient and steady-state conditions. Sodium, potassium, and water were evaluated as working fluids to demonstrate the applicability of the framework across a broad temperature range. The proposed non-dimensional parameters effectively captured key thermal-hydraulic behaviors and safety concerns, as was demonstrated via Sockeye simulations. This framework supports the development of design optimization strategies, operational protocols, and safety assurance practices for advanced reactor systems and other high-reliability applications.

42 - ENGINEERING↗

DOE OSTI2025

Integrated Molten Salt Reactor Modeling Capabilities in NEAMS Thermal Hydraulics Tools

The DOE neams program supports a full range of computational thermal fluids analysis capabilities and code developments for a broad range of advanced reactor concepts. The research and development approach under the thermal fluids technical area synergistically combines three length and time scales in a hierarchical multi-scale approach. To enable multi-scale thermal fluids capability using these codes, a key joint effort has been underway to develop an integrated system- and engineering-scale thermal fluids analysis capability, through integration of SAM and Pronghorn codes, both based on the MOOSE framework. This report summarizes recent advances in developing an integrated system- and engineering-scale modeling capability for the msr concept, which has gained significant interest in recent years. A consistent framework was established by coupling Pronghorn and SAM through the Saline interface, with thermophysical properties provided by the Molten Salt Thermal Property Database (MSTDB-TP). Further improvements were made to the coupling schemes and domain-overlapping strategies, enhancing the stability and robustness of multi-code simulations. Verification and validation efforts demonstrate the accuracy of this integration across a range of benchmark problems, including one-dimensional heated pipe flows, three-dimensional natural convection loops with evolving isotopic compositions, and \gls{msre} demonstration cases. Within Pronghorn, new capabilities were introduced to model corrosion and noble-metal plating phenomena, supported by an extended thermal-hydraulics framework and refined turbulence treatments. To capture two-phase flow behavior, a multiphase Euler–Euler model was implemented in Pronghorn, including advanced closure relations, high-resolution advection techniques, and capillary force reconstruction. Preliminary verification cases confirm the fidelity of the approach, while planned validation efforts target canonical multiphase benchmarks and application to msr components such as the msre pump bowl. Finally, updates to SAM’s msr mass transfer modeling were extended to consider noble gas migration into porous structures like graphite. The point kinetics model was updated to include reactivity feedback contributions from any defined species, such as xenon. The gas transport model was expanded for applicability to gas mixtures, bubble efflux phenomena, and species transport between liquid and gas phases. A selection of multi-scale Sherwood number correlations from MOSCATO/NekRS and multi-phase correlations from literature have been added for improved accuracy in calculating mass transfer coefficients. A companion effort on developing system-level redox corrosion has also been incorporated into SAM. Collectively, these enhancements strengthen the predictive capability of SAM and Pronghorn for simulating MSR thermal-hydraulics, corrosion, multiphase behavior, and fission-product transport, providing a more complete toolset for design, safety analysis, and licensing support of next-generation \gls{msr}s.

42 - ENGINEERING↗

DOE OSTI2026

Deflagration to Detonation Transition Update: XDDT Code Modularization

A legacy FORTRAN 77 implementation of the Baer–Nunziato two-phase mixture theory for deflagration-to-detonation transition (DDT) in reactive granular materials—hereafter the XDDT (eXplosive DDT) code—has been modularized to Fortran 90 with modular structure, external input files, and adaptive mesh capability. During validation, two code defects were identified and corrected: an inconsistency in the nodal solid pressure evaluation and a nonphysical burn-front tracking criterion. The ignition criterion was also corrected to use the granular surface temperature from the interface heat transfer model, matching the original Baer implementation. An initial attempt to validate against Figure 3 of the original Baer and Nunziato (1986) paper revealed that the code’s detonation velocity on a 201-node mesh (5.5 km/s) was approximately 21% below the expected Chapman–Jouguet value for 70% TMD HMX (∼7 km/s). Validation was redirected to the piston-driven DDT experiments of McAfee et al. (1989), Shot B-9036, for which well-characterized ionization-pin data are available. With the compaction-burn coefficient calibrated to 𝐶 𝛼 = 75, the XDDT code reproduces the DDT transition time to within 0.4% and produces a steady-state detonation velocity within 4% of the McAfee experimental value of 6.36 km/s. The burn model was generalized to support pressure-dependent exponents, enabling application to nitrocellulose-based ball propellants (TS3659) with a cube-root pressure dependence. Validation against the Sandusky/Baer PDC82 piston-impact experiment yielded a reactive wave velocity of 2.3–2.8 km/s, in good agreement with the experimental value of ∼2.2 km/s, and wave coalescence within 5% of the experimental timing. The mathematical model, input parameter requirements, and a roadmap for extending XDDT to PETN with an autocatalytic burn model are presented.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2025

A Finite Element Method for Compressible and Turbulent Multiphase Flow Instabilities with Heat Transfer

We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

Assessment of analytical techniques for predicting solid propellant exhaust plumes

The calculation of solid propellant exhaust plume flow fields is addressed. Two major areas covered are: (1) the applicability of empirical data currently available to define particle drag coefficients, heat transfer coefficients, mean particle size and particle size distributions, and (2) thermochemical modeling of the gaseous phase of the flow field. Comparisons of experimentally measured and analytically predicted data are made. The experimental data were obtained for subscale solid propellant motors with aluminum loadings of 2, 10 and 15%. Analytical predictions were made using a fully coupled two-phase numerical solution. Data comparisons will be presented for radial distributions at plume axial stations of 5, 12, 16 and 20 diameters.

Tevepaugh, J. A.↗

NASA NTRS1985

A swirl flow evaporative cold plate

A forced flow evaporative cold plate is under development for future application to the thermal bus concept being pursued by NASA for Space Station Thermal Control. The vaporizer is a swirl-flow device employing a spiral tube coil geometry sandwiched between conductive metal plates upon which electric components could be mounted. This concept is based on the inherent phase separation that occurs in a two phase stream in curvilinear flow. This is a zero 'g' design with one 'g' all-attitude capability and is capable of high heat transfer coefficients, good isothermality, and the ability to function at heat fluxes approaching 5w/sq cm on the cold plates (10w/sq cm on the tube wall) with Freon 114. The advantages of this design over other two phase evaporator approaches are high heat flux capability, simplified control requirements, insensitivity to micro-gravity oscillations, and inexpensive manufacturability. The program included design, fabrication, and test of such a cold plate utilizing an existing test stand developed for two-phase thermal management system (TPTMS) testing. Test results analysis and conclusions are included.

Niggemann, R. E.↗

NASA NTRS1990

High heat flux single phase heat exchanger

This paper presents the results obtained to date in a program to develop a high heat flux, single-phase heat exchanger for spacecraft thermal management. The intended application is a net generation interface heat exchanger to couple the crew module water thermal bus to the two-phase ammonia main thermal bus in the Space Station Freedom. The large size of the interface heat exchanger is dictated by the relatively poor water-side heat transfer characteristics. The objective of this program is to develop a single-phase heat transfer approach which can achieve heat fluxes and heat transfer coefficients comparable to those of the evaporation ammonia side. A new heat exchanger concept has been developed to meet these objecties. The main feature of this heat exchanger is that it can achieve very high heat fluxes with a pressure drop one to two orders of magnitude lower than those of previous microchannel or jet impingement high heat flux heat exchangers. This paper describes proof-of-concept experiments performed in air and water and presents analytical model of the heat exchanger.

Valenzuela, Javier A.↗