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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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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Evolution of Pore Structure and Permeability of Rocks Under Hydrothermal Conditions (Final Report)

The physical and transport properties of porous rocks can be altered by a variety of diagenetic, metamorphic, and tectonic processes, and the changes that result are of critical importance to such industrial applications as resource recovery, carbon dioxide sequestration, and waste isolation in geologic formations. The associated interrelationships between rocks, pore fluids and deformation are also key to understanding many natural processes, including dynamic metamorphism, fault mechanics, fault stability and pressure solution creep. In this project, we investigated the changes of permeability and pore geometry owing to inelastic deformation by solution-transfer, brittle fracturing and dislocation creep. In particular, we studied the coupling between pore fluids and deformation in fluid-filled quartz, calcite, mudstones and ultramafic rocks and examine the effects of coupled mechanical and chemical processes on the evolution of porosity and permeability under hydrothermal conditions. The investigations used a combination of techniques, that included triaxial laboratory experiments; uniaxial compressive loading with in situ observations of microstructure; permeability under hydrostatic compression; observations of microstructure using optical and electron microscopes, and micro-CT imaging; and numerical calculations. Laboratory experiments were designed to provide mechanical and transport data under conditions that isolate the particular mechanisms responsible for the changes. The data obtained were used to quantify changes in surface roughness, porosity, pore dimensions and their spatial fluctuations. The results of the experiments and data from image analyses were compared to the results of network, finite-difference and other numerical models to verify the validity of experimentally established relations between permeability and other rock properties. A bibliography for the period from 2015-2019 is appended below. New results obtained in the final year and the unfunded extension period are detailed below.

58 GEOSCIENCES↗
DOE OSTI2020

Design Optimization of A generic Fissile Solution for Mo99 production using Electron Beam-based Neutron Generator using MCNP+CFD

Molybdenum-99 ( 99 Mo) is a medical isotope used in 80% of all medical imaging procedures today. However, 99 Mo is not directly administered to patients for imaging; its decay product, technetium-99m ( 99 mTc), is a metastable isotope with a half-life of ~6 hours. Such a short half-life does not allow for production, separation, and application to a patient before decaying further. Therefore, the solution is to produce the precursor to 99 mTc, 99 Mo. 99 Mo has a half-life of 66 hours, long enough to produce the material and send it to the desired location before it fully decays. Under National Nuclear Security Administration’s (NNSA) highly enriched uranium (HEU) minimization mission, the Material Management and Minimization (M3) office leads the Molybdenum-99 (Mo-99) program. A major goal of the Mo-99 program is to develop methods of producing 99 Mo using low enriched uranium (LEU) opposed to the traditionally used HEU domestically in the U.S. Internationally, LEU is the new standard for use in research reactors and isotope production facility. In this study, we introduce a generic fissile solution system for 99 Mo production facility meeting the design requirement of 1) LEU usage as fissile material and 2) subcritical fissile system coupled with a horizontal electron beam (E-beam) accelerator. The focus of this research is to optimize a fissile solution configuration for maximum 99 Mo production yield using MCNP model, and ultimately implement the optimized design with computational fluid dynamics (CFD) model to understand thermal hydraulic behavior and solution convection characteristic. The report consists of two parts: 1) isotope yield calculation and criticality analysis with a wide range of parametric test matrix, and 2) thermal hydraulic analysis for solution mixing and cooling assessment.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1988

Analysis and interpretation of low gravity boiling experiments in the KC-135

Reduced gravity two phase flow boiling and condensing experiments were conducted in the NASA KC-135. In an attempt to gain a better understanding of two phase flow behavior in reduced gravity, the individual test runs were critically examined to determine their suitability to be taken as representative of two phase flow in microgravity. Selected runs were simulated using the two fluid thermal-hydraulic COBRA/TRAC computer code. The comparisons of these sophisticated codes with the observed flow behavior illustrate the generic shortcomings of current two phase modeling capabilities in application to reduced gravity conditions.

Cuta, Judith M.↗
NASA NTRS1999

Rheology of Foam Near the Order-Disorder Phase Transition

Foams are extremely important in a variety of industrial applications. Foams are widely used in fire-fighting applications, and are especially effective in fighting flammable liquid fires. In fact the Fire Suppression System aboard the Space Shuttle utilizes cylinders of Halon foam, which, when fired, force a rapidly expanding foam into the convoluted spaces behind instrument panels. Foams are critical in the process of enhanced oil recovery, due to their surface-active and highly viscous nature. They are also used as drilling fluids in underpressurized geologic formations. They are used as transport agents, and as trapping agents. They are also used as separation agents, where ore refinement is accomplished by froth flotation of the typically lighter and hydrophobic contaminants. The goal of the proposed investigation is the determination of the mechanical and rheological properties of foams, utilizing the microgravity environment to explore foam rheology for foams which cannot exist, or only exist for a short time, in 1g.

Holt, R. Glynn↗
NASA NTRS2018

Unstructured Grid Adaptation and Solver Technology for Turbulent Flows

Unstructured grid adaptation is a tool to control Computational Fluid Dynamics (CFD) discretization error. However, adaptive grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Issues that prevent the use of adaptive grid methods are identified by applying unstructured grid adaptation methods to a series of benchmark cases. Once identified, these challenges to existing adaptive workflows can be addressed. Unstructured grid adaptation is evaluated for test cases described on the Turbulence Modeling Resource (TMR) web site, which documents uniform grid refinement of multiple schemes. The cases are turbulent flow over a Hemisphere Cylinder and an ONERA M6Wing. Adaptive grid force and moment trajectories are shown for three integrated grid adaptation processes with Mach interpolation control and output error based metrics. The integrated grid adaptation process with a finite element (FE) discretization produced results consistent with uniform grid refinement of fixed grids. The integrated grid adaptation processes with finite volume schemes were slower to converge to the reference solution than the FE method. Metric conformity is documented on grid/metric snapshots for five grid adaptation mechanics implementations. These tools produce anisotropic boundary conforming grids requested by the adaptation process.

Park, Michael A.↗
NASA NTRS2004

Space Shuttle Upgrades Advanced Hydraulic Power System

Three Auxiliary Power Units (APU) on the Space Shuttle Orbiter each provide 145 hp shaft power to a hydraulic pump which outputs 3000 psi hydraulic fluid to 41 hydraulic actuators. A hydrazine fuel powered APU utilized throughout the Shuttle program has undergone many improvements, but concerns remain with flight safety, operational cost, critical failure modes, and hydrazine related hazards. The advanced hydraulic power system (AHPS), also known as the electric APU, is being evaluated as an upgrade to replace the hydrazine APU. The AHPS replaces the high-speed turbine and hydrazine fuel supply system with a battery power supply and electric motor/pump that converts 300 volt electrical power to 3000 psi hydraulic power. AHPS upgrade benefits include elimination of toxic hydrazine propellant to improve flight safety, reduction in hazardous ground processing operations, and improved reliability. Development of this upgrade provides many interesting challenges and includes development of four hardware elements that comprise the AHPS system: Battery - The battery provides a high voltage supply of power using lithium ion cells. This is a large battery that must provide 28 kilowatt hours of energy over 99 minutes of operation at 300 volts with a peak power of 130 kilowatts for three seconds. High Voltage Power Distribution and Control (PD&C) - The PD&C distributes electric power from the battery to the EHDU. This 300 volt system includes wiring and components necessary to distribute power and provide fault current protection. Electro-Hydraulic Drive Unit (EHDU) - The EHDU converts electric input power to hydraulic output power. The EHDU must provide over 90 kilowatts of stable, output hydraulic power at 3000 psi with high efficiency and rapid response time. Cooling System - The cooling system provides thermal control of the Orbiter hydraulic fluid and EHDU electronic components. Symposium presentation will provide an overview of the AHPS upgrade, descriptions of the four hardware elements, and a summary of development results to date.

Source record↗
NASA NTRS1991

Combustion of liquid fuel droplets in supercritical conditions

A comprehensive analysis of liquid-fuel droplet combustion in both sub- and super-critical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates finite-rate chemical kinetics and a full treatment of liquid-vapor phase equilibrium at the droplet surface. The governing equations and the associated interface boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to the supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influences on the fluid transport, gas/liquid interface thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibits a significant variation near the critical burning pressure, mainly as a result of reduced mass-diffusion rate and latent heat of vaporization with increased pressure. The influence of droplet size on the burning characteristics is also noted.

Shuen, J. S.↗
DOE OSTI2020

Liquid helium fluid dynamics studies. Final Technical Report

Future high energy physics accelerators depend on a number of advanced technologies to open the many doors of scientific discovery. Among these advanced technologies, superconducting magnets and superconducting radio frequency (SRF) cavities are the backbone of the accelerator and detector systems. But all these low temperature systems depend critically on successful and reliable operation of their supporting technologies, among which the liquid helium cooling system is of the utmost importance. To improve the quality of these systems both in terms of efficiency and reliability, a robust helium cryogenics research and development (R&D) effort is required. The proposed research to be conducted by the FSU cryogenics group aims to produce fundamental knowledge that meets this R&D need. The projects that we have completed over the past grant period at Florida State University consist of experimental research on liquid helium fluid dynamics and heat transfer problems relevant to the development of future superconducting particle physics accelerators. Liquid helium is the coolant used in all such facilities and in many of these facilities He II (the low temperature phase of liquid helium also known as superfluid helium) is preferred due to its outstanding heat transfer characteristics. The work consists of two main experimental studies that probe both fundamental as well as practical aspects of liquid helium cooling. The first is a broad and fundamental study of the heat and mass transfer processes that can occur during a sudden catastrophic loss of vacuum (SCLV) incident in a superconducting accelerator. SCLV refers to the remote but extremely critical accident scenario where atmospheric pressure air is allowed to flood into the insulating vacuum system and impinge on the liquid helium cooled surfaces in the accelerator. Safe performance and recovery from such accidents is essential to the reliable operation of superconducting accelerators. The dynamics of this process is quite complex and so our approach is to conduct a series of well-orchestrated experiments that probe the various physical phenomena that can occur during an SCLV event. The experiments are coupled with analytic and numerical analysis in an effort to develop a general understanding of the process and to assist with future accelerator design and development. The second activity is directed toward fundamental understanding of heat and mass transfer in He II, which is essential to the design of superconducting magnets and radio frequency cavities in accelerators. The work consists of flow visualization of the dynamics of He II using laser assisted techniques. Two complementary techniques are used to study the fundamentals of the turbulent state. The first technique uses neutrally buoyant solid hydrogen particles to probe the flow fields of the superfluid and normal fluid components. The other technique uses laser excited He2* molecules as tracers of the normal fluid motion within the He II. The activities also included an effort to use visualization techniques to locate transient hot spots in radio frequency superconducting cavities. Such work provides valuable information about the heat transfer process in He II and its impact on the performance of superconducting devices. The research effort at Florida State University is not directly in support of a specific high energy physics experiment or facility. Rather, the work is general and coordinated with HEP accelerator laboratories to provide valuable insight that can assist with future accelerator development.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Local Rearrangement in Adsorption Layers of Nanoconfined Ethane

Fluids under nanoconfinement control many environmental and engineering processes. In particular, nanoconfined ethane commonly occurs in hydrocarbon production and gas separation applications. While previous research has measured the pore critical properties and self-diffusivity of nanoconfined ethane, the relationship between molecular organization and phase behavior in nanoporous media persists as a knowledge gap. Through experimental adsorption measurements and molecular dynamics simulations, we report the impact of pore wall proximity, pore size, and temperature on the structure of nanoconfined ethane. Finally, we offer evidence for an energetically favorable rearrangement of ethane molecules in the adsorption layer that may contribute to more accurate gas-in-place estimates and more efficient design of gas separation membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Multi-GPU immersed boundary method hemodynamics simulations

Large-scale simulations of blood flow that resolve the 3D deformation of each comprising cell are increasingly popular owing to algorithmic developments in conjunction with advances in compute capability. Among different approaches for modeling cell-resolved hemodynamics, fluid structure interaction (FSI) algorithms based on the immersed boundary method are frequently employed for coupling separate solvers for the background fluid and the cells within one framework. GPUs can accelerate these simulations; however, both current pre-exascale and future exascale CPU-GPU heterogeneous systems face communication challenges critical to performance and scalability. In this paper, we describe, to our knowledge, the largest distributed GPU-accelerated FSI simulations of high hematocrit cell-resolved flows with over 17 million red blood cells. We compare scaling on a fat node system with six GPUs per node and on a system with a single GPU per node. Through comparison between the CPU- and GPU-based implementations, we identify the costs of data movement in multiscale multi-grid FSI simulations on heterogeneous systems and show it to be the greatest performance bottleneck on the GPU.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Direct observation of ultrafast cluster dynamics in supercritical carbon dioxide using X-ray Photon Correlation Spectroscopy

Supercritical fluids exhibit distinct thermodynamic and transport properties, making them of particular interest for a wide range of scientific and engineering applications. These anomalous properties emerge from structural heterogeneities due to the formation of molecular clusters at conditions above the critical point. While the static behavior of these clusters and their effects on the thermodynamic response functions have been recognized, the relation between the ultrafast cluster dynamics and transport properties remains elusive. By measuring the intermediate scattering function in carbon dioxide at conditions near the critical point with X-ray photon correlation spectroscopy, we directly capture the cross-over dynamics between 4 and 13 picoseconds, revealing the transition between ballistic and diffusive motion. Complementary analysis using large-scale molecular dynamics simulations reveals that this behavior arises from collisions between unbound molecules and clusters. This study provides direct evidence of the ultrafast momentum exchange between clusters, which has significant impact on transport properties, solvation processes, and reaction kinetics in supercritical fluids.

carbon capture and storage↗
NASA NTRSDate not supplied

Validation of Cryogenic Propellant Tank Self-Pressurization by Leveraging Reduced Order Modeling within Computational Fluid Dynamics Simulation

Validation of cryogenic propellant tank self-pressurization was performed using a hybrid Computational Fluid Dynamics (CFD) and reduced order modeling methodology. Data from a liquid hydrogen ground test conducted at the K-site facility at the National Aeronautics and Space Administration (NASA) Glenn Research Center was used for the validation effort. Liquid phase dynamics were explicitly resolved with a CFD tool. Vapor phase dynamics were modeled as a point mass that communicated heat from the tank wall to the liquid phase via a boundary condition used at the gas-liquid interface. The method proved to be more accurate, robust, and efficient than explicit resolution of the dynamics using a standard Volume of Fluid (VOF) methodology. The subject pressurization process was found to be heavily dependent upon both the relatively high liquid temperature gradient near the gas-liquid interface and the natural convection flow path. Modeling the gas-liquid interface as an immovable surface eliminated temperature gradient destroying gas-liquid interface velocities observed in VOF simulations, and correspondingly enabled more rapid simulation since interface advection was not allowed. The single phase computational domain also facilitated the ability to demonstrate spatial resolution convergence of natural convection cells within the liquid which significantly impacted the tank pressurization rate. This work was used to demonstrate the critical physics for tank self-pressurization and numerical methodologies that may be used to best resolve those physics. The findings informed development and operation of production level CFD tools used in the Fluid Dynamics Branch at NASA Marshall Space Flight Center.

J. M. Brodnick↗
DOE OSTI2021

Linear and nonlinear viscoelasticity of concentrated thermoresponsive microgel suspensions

We present an integrated experimental and theoretical study of the dynamics and rheology of self-crosslinked, slightly charged, temperature responsive soft poly(N-isopropylacrylamide) (pNIPAM) microgels over a wide range of concentration and temperature spanning the sharp change in particle size and intermolecular interactions across the lower critical solution temperature (LCST). Dramatic, non-monotonic changes in viscoelasticity are observed as a function of temperature, with distinct concentration dependence in the dense fluid, glassy, and soft-jammed regimes. Motivated by our experimental observations, we formulate a minimalistic model for the size dependence of a single microgel particle and the change of the interparticle interaction from purely repulsive to attractive upon heating. Using microscopic equilibrium and time-dependent statistical mechanical theories, theoretical predictions are quantitatively compared with experimental measurements of the shear modulus. Good agreement is found for the nonmonotonic temperature behavior that originates as a consequence of the competition between reduced microgel packing fraction and increasing interparticle attractions. Furthermore, testable predictions are made for nonlinear rheological properties such as the yield stress and strain. To our knowledge, this is the first attempt to quantitatively understand in a unified manner the viscoelasticity of dense, temperature-responsive microgel suspensions spanning a wide range of temperatures and concentrations.

42 ENGINEERING↗
DOE OSTI2021

Turbulence theories and statistical closure approaches

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Dynamic structural and microstructural responses of a metal–organic framework type material to carbon dioxide under dual gas flow and supercritical conditions

The structural and microstructural responses of a model metal–organic framework material, Ni(3-methyl-4,4'-bipyridine)[Ni(CN) 4 ] (Ni-BpyMe or PICNIC-21), to CO 2 adsorption and desorption are reported for in situ small-angle X-ray scattering and X-ray diffraction measurements under different gas pressure conditions for two technologically important cases. These conditions are single or dual gas flow (CO 2 with N 2 , CH 4 or H 2 at sub-critical CO 2 partial pressures and ambient temperatures) and supercritical CO 2 (with static pressures and temperatures adjusted to explore the gas, liquid and supercritical fluid regimes on the CO 2 phase diagram). The experimental results are compared with density functional theory calculations that seek to predict where CO 2 and other gas molecules are accommodated within the sorbent structure as a function of gas pressure conditions, and hence the degree of swelling and contraction in the associated structure spacings and void spaces. Furthermore, these predictions illustrate the insights that can be gained concerning how such sorbents can be designed or modified to optimize the desired gas sorption properties relevant to enhanced gas recovery or to addressing carbon dioxide reduction through carbon mitigation, or even direct air capture of CO 2 .

36 MATERIALS SCIENCE↗
DOE OSTI2024

Data-driven closure modeling for hypersonic turbulent flows

The Reynolds-averaged Navier–Stokes (RANS) equations remain a workhorse technology for simulating compressible fluid flows of practical interest. Due to model-form errors, however, RANS models can yield erroneous predictions that preclude their use on mission-critical problems. This report summarizes work performed from FY22-FY24 focused on improving RANS models for hypersonic flows using data-driven modeling and scientific machine learning. In this work we: 1. Investigate the current capabilities of RANS models in Sandia’s parallel aerodynamics and re-entry code (SPARC) for hypersonic flows with a focus on shock boundary layer interactions (SBLIs), 2. Assess several established corrections that exist in the literature aimed at improving predictions for SBLIs, 3. Develop improved models for the Reynolds stress tensor using tensor-basis neural networks, 4. Develop a neural-network-based variable turbulent Prandtl number model to reduce errors in wall heating in SBLIs. 5. Begin future investigations including employing the LIFE framework to improve wall heating predictions in SBLIs as well as the ensemble Kalman filter. We find that current RANS models in SPARC are deficient for complex SBLI flows. In particular, no current model jointly predicts wall heat flux, wall shear stress, and wall pressure with reasonable accuracy. Existing corrections help, but do not alleviate this issue altogether. The development of improved models for the Reynolds stress tensor via tensor-basis neural networks results in more predictive RANS models across a suite of low-speed and high-speed cases. For hypersonic boundary layers, the inclusion of the wall-normal Reynolds stress via TBNNs has an appreciable impact on the wall-normal momentum balance and wall quantities. However, we find that improvements to the Reynolds stress tensor do not address the over-prediction in wall heat flux in SBLIs. We find that a neural-network-based variable turbulent Prandtl number model systematically and substantially improves wall heating predictions for a range of SBLI cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Evaluation of Deep Learning Model Architectures for Point-of-Care Ultrasound Diagnostics

Point-of-care ultrasound imaging is a critical tool for patient triage during trauma for diagnosing injuries and prioritizing limited medical evacuation resources. Specifically, an eFAST exam evaluates if there are free fluids in the chest or abdomen but this is only possible if ultrasound scans can be accurately interpreted, a challenge in the pre-hospital setting. In this effort, we evaluated the use of artificial intelligent eFAST image interpretation models. Widely used deep learning model architectures were evaluated as well as Bayesian models optimized for six different diagnostic models: pneumothorax (i) B- or (ii) M-mode, hemothorax (iii) B- or (iv) M-mode, (v) pelvic or bladder abdominal hemorrhage and (vi) right upper quadrant abdominal hemorrhage. Models were trained using images captured in 27 swine. Using a leave-one-subject-out training approach, the MobileNetV2 and DarkNet53 models surpassed 85% accuracy for each M-mode scan site. The different B-mode models performed worse with accuracies between 68% and 74% except for the pelvic hemorrhage model, which only reached 62% accuracy for all model architectures. These results highlight which eFAST scan sites can be easily automated with image interpretation models, while other scan sites, such as the bladder hemorrhage model, will require more robust model development or data augmentation to improve performance. With these additional improvements, the skill threshold for ultrasound-based triage can be reduced, thus expanding its utility in the pre-hospital setting.

47 OTHER INSTRUMENTATION↗
NASA NTRS1995

Effect of entry of subcooled cryogen on thermal stratification in a cryogenic storage tank

The purpose of this study was to predict if subcooled cryogenic liquid entering the bottom of a storage tank will destroy the thermal stratification of the tank. After an extensive literature search, a formula for maximum critical Reynolds Number which used to predict the destratification of a cryogenic tank was found. Example of calculations and graphics to determine the mixing of fluid in the tank were presented.

Wang, Pao-lien↗