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

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Three-Dimensional, Multi-Phase Unsteady Flow of Water Undergoing Multiple Flow Regimes (Free Surface, Droplet, and Fluid Film)

Upgrades to the Mobile Launcher Rainbird nozzles were implemented for the Artemis II launch to increase water flow rates and improve the mobile launcher deck water coverage while minimizing the water throw distance to avoid impacting the Space Launch System (SLS) rocket nozzles. This analysis describes the use of a three-dimensional, multi-phase, free surface transient computational fluid dynamics (CFD) model to simulate the water flowing out through the Rainbird nozzle and ensure compliance with current Artemis requirements. Flow rates, pressures, velocities, nozzle throw distances and coverage areas were analyzed to ensure that system requirements are met. The completed results were used to make necessary modifications to the Ignition Overpressure Protection and Sound Suppression (IOP/SS) system Rainbird design by reshaping the nozzle used in the system.

CFD

Numerical Solution of Fluid Flow and Heat Tranfer Problems with Surface Radiation

This paper presents a numerical scheme, based on the finite element method, to solve strongly coupled fluid flow and heat transfer problems. The surface radiation effect for gray, diffuse and isothermal surfaces is considered. A procedure for obtaining the view factors between the radiating surfaces is discussed. The overall solution strategy is verified by comparing the available results with those obtained using this approach. An analysis of a thermosyphon is undertaken and the effect of considering the surface radiation is clearly explained.

S Ahuja

Cryogenic Flow Boiling in Microgravity: Effects of Reduced Gravity on Two-Phase Fluid Physics and Heat Transfer

With the growing interest in space exploration, cryogenic technologies involving two-phase flow and heat transfer are in high demand to successfully procure advanced space applications such as fuel depots and nuclear thermal propulsion (NTP) systems for deep space missions. However, the unique and extreme thermal properties of cryogenic fluids introduce distinct flow boiling fluid physics and energy transport phenomena, which differ significantly from those observed with conventional fluids. Understanding the unique two-phase physics in cryogenic flow boiling remains an ongoing challenge. Furthermore, the lack of readily available microgravity cryogenic steady-state heat transfer data hinders the assessment of gravitational effects on cryogenic flow boiling. This study aims to elucidate the gravitational effects on two-phase fluid physics and heat transfer by conducting the first-ever experimental measurement of cryogenic flow boiling performance using a steady-state heated method in a reduced gravity environment. Parabolic flight experiments were performed to acquire both heat transfer measurements and high-speed video of interfacial behaviors, under varying gravity levels (microgravity, hypergravity, Lunar gravity, and Martian gravity). The experiments involved flow boiling of liquid nitrogen (LN 2 ) with a near-saturated inlet along a circular heated tube of dimensions 8.5-mm inner diameter and 680-mm heated length. The operating parameters varied are mass velocity of 398.3 - 1342.8 kg/m2s, inlet quality of -0.08 to -0.01, and inlet pressure of 413.68 - 689.48 kPa. Captured microgravity flow patterns range from bubbly to annular, all having vapor structures that are larger than those under higher gravity levels. Under microgravity, absence of buoyancy yields symmetrical vapor structures without flow stratification, laying a physical foundation for the distinct two-phase heat transfer trends during LN 2 flow boiling in microgravity. Transient data collected during the flight parabolas exhibited decreasing heated wall temperature as the aircraft transitioned from hypergravity to microgravity phases. The temperature variation indicated an enhancement in flow boiling heat transfer with decreasing gravity levels and a reduction with increasing gravity levels. The effect of reduced gravity on cryogenic flow boiling heat transfer coefficient (HTC) is discussed based on steady state heat transfer analysis. Seminal HTC correlations are evaluated against the measured microgravity HTC data, of which one is identified for superior accuracy in predicting microgravity data. Finally, a new HTC correlation is proposed to improve accuracy of microgravity predictions, yet there still exists room for further improvement with future terrestrial flow boiling experiments at different flow orientations relative to Earth gravity.

Microgravity

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

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

stagnation heat flux

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

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

inviscid theory

Polymer coatings on zirconia microspheres via rotating flow fluid dynamics

Conventional tristructural isotropic (TRISO) coatings for nuclear fuels require multi-step and expensive formation processes; any breakage of the coatings may lead to fission species release. Polymer derived ceramic (PDC) coatings can be a suitable alternative to address these issues. In this study, allylhydridopolycarbosilane (SMP-10) coatings were created on yttria stabilized zirconia (YSZ) microspheres using a Rotating Flow Fluid Dynamics (RFFD) coating method. The effects of curing temperature, rotation speed, and coating cycle/time on the coating were analyzed. Surface functionalization of YSZ microspheres with NaOH resulted in good adhesion between the polymer precursor and the YSZ kernel particles. Spectroscopy analysis revealed complete curing of SMP-10 coated YSZ at 160 °C. Rotation speed and coating time significantly affect the coating characteristics. After 3 cycles at lower rotation speed (50 rpm) for 10 min each, the coating obtained was uniform and homogeneous. In comparison, the coating showed almost 10 times less eccentricity at a high rotation speed of 300 rpm. Compared with the coatings prepared at 300 rpm condition, the coatings have higher sphericity and lower eccentricity at 50 rpm. Overall, this study provides a novel and effective route for fabricating and curing SMP-10 precursor coatings on YSZ microspheres.

Ravi, Nivetha [University of Alabama, Birmingham]

Numerical Predictions of the Flow and Heat Transfer Characteristics in the Film Boiling Regime During Tube Quenching

Cryogenic fluid management plays a major role in refueling of spacecrafts while in space for NASA’s future human space exploration missions. Due to the low boiling points of cryogens, storage, transport and handling of these fluids becomes difficult and may result in inefficient operation of the space propulsion systems. For refueling applications in space, the cryogenic fluids have to be transported across different locations and hence, the transfer of cryogenic fluids through pipes become critical. The cryogenic chill-down process is characterized by different regimes of flow boiling, viz., film boiling, transition boiling and nucleate boiling. The prediction of these regimes in a single CFD framework available in the literature is challenging and the present work attempts to address this challenge by initially modeling the film boiling regime accurately and to incorporate an user-defined function for transition and nucleate boiling at a later stage. Hence, the aim of the present work is to numerically model and validate the film boiling regime of the chilldown curve for liquid nitrogen experiments available in the literature. The validations are carried out at different inlet mass fluxes to have a robust simulation methodology. A dispersed mixture model is used to predict the vapor-liquid interface dynamics with the phase change phenomena modeled using the Lee model.

line chilldown

Numerical Investigation of Fluid Flow and Space Charge in Liquid Argon Time Projection Chamber (LArTPC) Detectors

Overview This project focused on developing a high-fidelity numerical framework to simulate the multiphysics environment within Liquid Argon Time Projection Chamber (LArTPC) detectors. The primary objective was to characterize the complex interplay between ion transport, background fluid dynamics, and electric field distortions—a critical factor for the calibration and sensitivity of next-generation High Energy Physics experiments, such as DUNE. Technical Achievements The research successfully yielded a hybrid numerical space-charge solver utilizing a Cell-Centered Finite Volume Method (FVM) for ion transport coupled with a Finite Element Method (FEM) for electric potential. Key accomplishments include: • Verification & Validation: The 3-D solver was rigorously verified against 1-D analytical solutions, demonstrating high numerical accuracy in predicting space-charge-induced field deviations. • Field Distortion Analysis: 3D simulations revealed that space charge effects introduce significant non-uniformities in the electric field. Critically, the research identified that background LAr flow velocities, when comparable to ion drift velocities, markedly exacerbate these distortions. • Technology Transfer: The resulting source code and comprehensive user manuals were successfully transferred to collaborators at Fermilab, providing a portable computational tool for the broader scientific community. Challenges and Future Directions While the space-charge solver achieved all performance metrics, the integrated fluid dynamics modeling encountered convergence challenges stemming from the extreme 200-fold disparity in length scales between the detector's 37 mm inlet pipes and the 8-meter global domain. To address this, the project has identified a clear technical pivot toward Hierarchical Geometric Adaptive Mesh Refinement (HG-AMR). By implementing an h-type refinement strategy with hanging nodes, future iterations of this solver will be capable of resolving localized high-gradient inlet flows without the prohibitive computational costs of regular grids. This advancement, combined with data-driven uncertainty quantification based on MicroBooNE-style calibration, will enable the precise modeling of detector responses in large-scale cryogenic environments where direct measurement remains difficult. Impact The computational tools developed under this award provide a foundation for enhancing the energy resolution and spatial reconstruction of noble liquid detectors. By bridging the gap between theoretical fluid dynamics and experimental field calibration, this work supports the DOE’s mission to advance the frontiers of neutrino physics and dark matter detection.

42 ENGINEERING

Heat Transfer Enhancement in Cryogenic Quenching Process

This paper reports a heat transfer advancement in the cryogenic quenching process. An experiment was performed to evaluate the enhancement of quenching heat transfer by the use of metal tubes with low thermal conductivity coating layers. Four coating thicknesses with various coolant mass flow rates of liquid nitrogen were investigated. The results indicated that the tube inner surface coating greatly enhanced the quenching efficiency. The quenching efficiency was found to increase with increasing number of coating layers, and the efficiency also increased with decreasing mass flow rates. In general, the efficiencies cover a range between 40.6% and 80%. Comparing to the bare surface case, the percentage increase in the quenching efficiency was the minimum at 4.2% for a single coated layer at the highest flow rate and the maximum of 109.1% for four coated layers at the lowest flow rate. The coated tubes could save up to 53% in the amount of cryogen consumption.

two-phase flow

Self-generated electrokinetic flows from active-charged boundary patterns

We develop a hydrodynamic description of self-generated electrolyte flow in capillaries whose bounding walls feature nonuniform distributions of charge nonuniform active ionic fluxes. The hydrodynamic velocity arising in such a system has components that are forbidden by symmetry in the absence of charge and fluxes. However, when these two boundary mechanisms are simultaneously present, they can lead to a symmetry broken state where steady flows with both unidirectional and circulatory components emerge. We show that these flow states arise when modulated boundary patterns of charge and fluxes are offset by a flux-charge phase difference, which is associated with the separation between sites of their peak densities on the wall. Mismatch in diffusivity of cationic and anionic species can modify the flow states and becomes an enhancing factor when fluxes of both ion species are being produced together at the same site. We demonstrate that this mechanism can be realized with a microfluidic generator that is powered by enzyme-coated patches that catalyze reactants in the solution to produce fluxes of ions. The local ionic elevation or depletion, which disrupts a nonuniform double layer, promotes self-induced gradients yielding persistent body forces to generate bulk fluid motion. Our work quantifies a boundary-driven mechanism behind self-sustained electrolyte flow in confined environments that exists without any external bulk-imposed fields or gradients. It provides a theoretical framework for understanding the combined effect of active and charged boundaries that are relevant in biological or soft matter systems, and can be utilized in electrofluidic and iontronic applications.

active matter

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

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

Navier Stokes Equations

Fluid-Thermal-Structural Interactions Induced by an Asymmetric Shock-Wave/Boundary-Layer Interaction in a Mach-6 Compression Corner

An experimental study is conducted of the fluid-thermal-structural interaction of a clamped compliant panel exposed to a three dimensional shock-wave/boundary-layer interaction (SWBLI) induced by a Mach-6 compression ramp with a spanwise nonuniform incoming boundary layer. The nonuniform boundary layer was produced by placing trips on one side of the upstream flat plate, resulting in largely turbulent flow on the tripped side and transitional flow on the untripped side. Measurements of the flowfield confirmed that the tripped boundary layer contained elevated levels of unsteadiness, and the SWBLI was observed to vary from attached to fully separated as the ramp angle was increased from 10◦ to 38◦; the separation region on the tripped side of the panel was noticeably smaller, showing the elevated turbulence levels of the tripped-side flow to remain relatively localized rather than diffusing across the whole model. Full-field, time-resolved panel deformations were measured using high-speed photogrammetry and the vibrational response at each compression angle was characterized. Although the measured modes conformed largely to those from classical clamped-plate theory, some skewing of the mode shapes was observed. IR thermography highlighted regions of the compliant region where elevated temperatures were likely to promote thermal softening effects to the transient panel response. The quasi-static deformation and stress field was used to characterize the internal stress factor of each mode and showed a meaningful relationship between transient panel response and stress contained within each mode: modes with antinodes lying in high-stress areas of the plate tended to exhibit increases in vibrational frequency and decreases in vibrational power, whereas the opposite was true for modes with antinodes in low-stress areas.

Spectral Proper Orthogonal Decomposition

Validation of Accurate Cryogenic Fluid Vapor-Liquid Boundary Conditions Via Molecular Simulations

Vapor-liquid interfaces drive many important phenomena in cryogenic fluid management, including heat transfer, evaporation, and capillary flow. Design of cryogenic fluid systems, such as propellant storage, requires accurate predictions of fluid behavior, including evaporation rates. Many models have been proposed for heat and mass transfer at vapor liquid interfaces, but the accuracy of these models in the context of cryogenic fluids has not been performed. We use molecular dynamics simulations, which allow for nanometer scale resolution of fluid phenomena, to evaluate the accuracy of a variety of vapor-liquid boundary conditions at evaporating and condensing interfaces. We find that an anisotropic temperature distribution is a critical ingredient for accurate prediction of intensive evaporation and condensation.

Daniel Vigil

Screen Channel Liquid Acquisition Device Outflow Tests in Liquid Hydrogen

This paper presents experimental design and test results of the recently concluded 1-g inverted vertical outflow testing of two 325x2300 full scale liquid acquisition device (LAD) channels in liquid hydrogen (LH 2 ). One of the channels had a perforated plate and internal cooling from a thermodynamic vent system (TVS) to enhance performance. The LADs were mounted in a tank to simulate 1-g outflow over a wide range of LH 2 temperatures (20.3 – 24.2 K), pressures (100 – 350 kPa), and flow rates (0.010 – 0.055 kg/s). Results indicate that the breakdown point is dominated by liquid temperature, with a second order dependence on mass flow rate through the LAD. The best performance is always achieved in the coldest liquid states for both channels, consistent with bubble point theory. Higher flow rates cause the standard channel to break down relatively earlier than the TVS cooled channel. Both the internal TVS heat exchanger and subcooling the liquid in the propellant tank are shown to significantly improve LAD performance.

Fuel Depot

Active Fluids Form System-Spanning Filamentary Networks

Recent experimental realizations of liquid-liquid phase separation of active liquid crystals have offered an insight into the interaction between phase separation, ubiquitous in soft matter and biology, and chaotic active flows. Here, in this Letter, we use continuum theory to examine phase separation of an active liquid crystal and a passive fluid and report two new results. First, we provide an analytical derivation of the activity-induced suppression of the phase boundary of the coexistence region—a result first reported in simulations and experiments. We show that the shift in the critical point is a result of the balance between self-stirring active flows and phase-separating diffusive fluxes. Second, we show that this same balance is responsible for dramatically changing the morphology of the phase separated state, resulting in the emergence of a new mixed active phase consisting of a dynamical filamentous active network that invades the entire system area, trapping droplets of passive material. This structure exists even for very low volume fractions of active material. Our work provides an important step towards the goal of understanding how to use activity as a new handle for sculpting interfaces.

active nematics

High-Order Methods in NASA’s Next Generation of Computational Fluid Dynamics Tools

The missions of the National Aeronautics and Space Administration (NASA) routinely produce unique requirements and challenges for development and application of Computational Fluid Dynamics (CFD) methods. NASA presently embodies four distinct Mission Directorates: Aeronautics Research, Exploration Systems, Science, and Space Operations. These missions generate requirements for systems that operate in a wide variety of environments. They range from the high-speed flight of aerodynamically optimized vehicles operating in the earth’s atmosphere to spacecraft designed for missions that don’t favor aerodynamic optimization, some operating in the atmosphere of planets and planetary moons such as Mars and Venus or Saturn’s moon Titan. Systems supporting these vehicles, such as rocket and jet propulsion, reaction control systems, fluid and thermal transfer systems, etc. can also generate their own unique set of flow phenomena that challenge today’s CFD methodology. Through the NASA Engineering and Safety Center (NESC), NASA annually conducts state-of-the-discipline assessments in fifteen distinct engineering disciplines. These assessments are performed by the NASA Technical Fellows that lead Technical Discipline Teams (TDT) of recognized experts in these fifteen areas. In the Aerosciences discipline, three topics have been identified as the top challenges for the discipline: aero-plume interaction prediction, unsteady separated flows, and aerothermodynamic prediction. These challenge areas are defined by the Agency’s high-risk projects and problems on which the NESC is requested to perform independent testing, analysis, and assessments. When viewed as a whole, these tests, analyses, and assessments provide a clear view of the recurring technical challenges facing Agency engineers and researchers and can be used to guide future research and technology development. The present state-of-the-art in the application of CFD at NASA is the use of Reynolds-Averaged Navier- Stokes (RANS) solvers, primarily executed in a steady-state mode of operation. In isolated cases, Unsteady RANS (URANS) solvers have been employed when steady RANS solutions produce poorly converging or oscillating results or in cases, such as aeroelastic analysis, which require unsteady aerodynamic simulation. For most traditional external and internal aerodynamic flows, structured overset grids or unstructured grids are employed to minimize geometric modeling and grid generation times. Grid adaptation, primarily as a series of coarse-grain intermediate processing steps is also seeing use on particularly complex flow problems and configurations. In the case of aerothermodynamic flows, engineers have been forced to continue to employ structured grid techniques as the present unstructured grid methodology has proven inadequate in the prediction of surface heating. In the area of aero-plume interaction modeling, two-gas, frozen chemistry simulation is generally the state-of-the- art, with some production solvers capable of predicting flows with only a single gas component. Prediction of flows falling into the afore-mentioned top Aerosciences technical challenges have severely stressed the present state-of-the-art in CFD prediction and for some problems, such as unsteady separated flows and aero-plume interaction cases, engineers have begun employing Large Eddy Simulation (LES) and Hybrid RANS/LES techniques. In some isolated aero-propulsion interaction cases, chemically reacting flow simulations have been applied. These methods are highly evolutionary and engineers have little experience in their application, so they cannot be heavily relied upon in today’s application environment. Therefore, this leads one to muse over which numerical technologies will be included in the CFD tools that will be employed 30 years in the future. This presentation will describe specific technical problems that have stressed NASA’s traditional CFD methods to their breaking point and will link these issues to the Agency’s top Aerosciences technical challenges. The discussion will then shift to the characteristics of future CFD solvers that will be required to attack these challenges and how these characteristics differ from the present state-of-the- art. High-order methods certainly appear to have a place in the development of future CFD tools and some of the physical characteristics of our most challenging problems suggest that high-order methods are the only way to effectively solve them. But there are some relatively severe implementation issues that face these methods, particularly in the area of general applicability and robust operation as an engineering tool. Desired characteristics of next-generation CFD solvers will be discussed and the author’s view of which emerging numerical technologies might be employed to address these attributes will also be presented

David M Schuster

Rewet Temperature Correlations for Liquid-Nitrogen Boiling Pipe Flows Across Varying Flow Conditions and Orientations

In many convective liquid-vapor phase change heat transfer engineering applications, cryogenic fluids are widely used in industrial processes, spacecraft and cryosurgery systems, and so on. For example, cryogens are usually used as liquid fuels such as liquid hydrogen and oxygen in the rocket industry, liquid nitrogen (LN2) and helium are frequently used to cool superconducting magnetic device for medical applications. In these systems, proper transport, handling, and storage of cryogenic fluids are of extreme importance. Among all the cryogenic transport processes performed in room temperatures, quenching, also termed chilldown, is a unavoidable initial, transient phase-change heat transfer process that brings the system down to the cryogenic condition. The Leidenfrost temperature or rewet temperature that signals the end of film boiling is practically considered the completion point of a quenching process. Therefore, rewet temperature has been considered the most important parameter for the engineering design of cryogenic thermal management systems. As most of the previous correlations for predicting the Leidenfrost temperature and the rewet temperature have been basically developed for water, they are shown to disagree with recent liquid nitrogen pipe chilldown experiments in upward and downward flow directions over a wide range of flow rates, pressures, and degrees of inlet subcooling. In addition to a complete review of the literature, two new correlations are presented in this work, one based on bubble growth and another based on the theoretical maximum limit of superheat. Each correlation performs well over the entire data set.

liquid nitrogen