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NASA NTRS2016

Validation of High-Resolution CFD Method for Slosh Damping Extraction of Baffled Tanks

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involve the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations and knowledge were mainly carried out by extensive experimental studies. A Volume-Of-Fluid (VOF) based CFD program developed at NASA MSFC was applied to extract slosh damping in a baffled tank from the first principle. First, experimental data using water with subscale smooth wall tank were used as the baseline validation. CFD simulation was demonstrated to be capable of accurately predicting natural frequency and very low damping value from the smooth wall tank at different fill levels. The damping due to a ring baffle at different liquid fill levels from barrel section and into the upper dome was then investigated to understand the slosh damping physics due to the presence of a ring baffle. Based on this study, the Root-Mean-Square error of our CFD simulation in estimating slosh damping was less than 4.8%, and the maximum error was less than 8.5%. Scalability of subscale baffled tank test using water was investigated using the validated CFD tool, and it was found that unlike the smooth wall case, slosh damping with baffle is almost independent of the working fluid and it is reasonable to apply water test data to the full scale LOX tank when the damping from baffle is dominant. On the other hand, for the smooth wall, the damping value must be scaled according to the Reynolds number. Comparison of experimental data, CFD, with the classical and modified Miles equations for upper dome was made, and the limitations of these semi-empirical equations were identified.

Yang, H. Q.↗

NASA NTRS2016

Validation of High-Resolution CFD Method for Slosh Damping Extraction of Baffled Cryogenic Propellant Tanks

Propellant slosh is a potential source of disturbance critical to the stability of space vehicles. The slosh dynamics are typically represented by a mechanical model of a spring-mass-damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. A Volume-Of-Fluid (VOF) based Computational Fluid Dynamics (CFD) program developed at MSFC was applied to extract slosh damping in the baffled tank from the first principle. First the experimental data using water with sub-scale smooth wall tank were used as the baseline validation. It is demonstrated that CFD can indeed accurately predict low damping values from the smooth wall at different fill levels. The damping due to a ring baffles at different depths from the free surface was then simulated, and fairly good agreement with experimental measurement was observed. Comparison with an empirical correlation of Miles equation is also made.

Yang, H. Q.↗

NASA NTRS2016

Investigation of Damping Physics and CFD Tool Validation for Simulation of Baffled Tanks at Variable Slosh Amplitude

To meet the flight control damping requirement, baffles of various configurations have been devised to increase the natural viscous damping and decrease the magnitude of the slosh forces and torques. In the design of slosh baffles, the most widely used damping equation is the one derived by Miles, which is based on the experiments of Keulegan and Carpenter. This equation has been used in predicting damping of the baffled tanks in different diameters ranging from 12 to 112 inches. The analytical expression of Miles equation is easy to use, especially in the design of complex baffle system. Previous investigations revealed that some experiments had shown good agreements with the prediction method of Miles, whereas other experiments have shown significant deviations. For example, damping from Miles equation differs from experimental measurements by as much as 100 percent over a range of tank diameters from 12 to 112 inches, oscillation amplitudes from 0.1 to 1.5 baffle widths, and baffle depths of 0.3 to 0.5 tank radius. Previously, much of this difference has been attributed to experimental scatter. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between Miles equation and experimental measurement, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use CFD technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. A well validated CFD solver, developed at NASA MSFC, Loci-STREAM-VOF, is applied to study vorticity field around the baffle and around the fluid interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data are then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (h/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Yang, H. Q.↗

NASA NTRS2016

Investigation of Damping Physics and CFD Tool Validation for Simulation of Baffled Tanks at Variable Slosh Amplitude

Determination of slosh damping is a very challenging task as there is no analytical solution. The damping physics involves the vorticity dissipation which requires the full solution of the nonlinear Navier-Stokes equations. As a result, previous investigations were mainly carried out by extensive experiments. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between the empirical Miles equation and experimental measurements, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use Computational Fluid Dynamics (CFD) technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. Loci-STREAM-VOF, a well validated CFD solver developed at NASA MSFC, is applied to study the vorticity field around a baffle and around the fluid-gas interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data is then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (d/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Yang, H. Q.↗

NASA NTRS2016

Modeling Droplet Heat and Mass Transfer during Spray Bar Pressure Control of the Multipurpose Hydrogen Test Bed (MHTB) Tank in Normal Gravity

A CFD model for simulating pressure control in cryogenic storage tanks through the injection of a subcooled liquid into the ullage is presented and applied to the 1g MHTB spray bar cooling experiments. An Eulerian-Lagrangian approach is utilized to track the spray droplets and capture the interaction between the discrete droplets and the continuous ullage phase. The spray model is coupled with the VOF model by performing particle tracking in the ullage, removing particles from the ullage when they reach the interface, and then adding their contributions to the liquid. A new model for calculating the droplet-ullage heat and mass transfer is developed. In this model, a droplet is allowed to warm up to the saturation temperature corresponding to the ullage vapor pressure, after which it evaporates while remaining at the saturation temperature. The droplet model is validated against the results of the MHTB spray-bar cooling experiments with 50% and 90% tank fill ratios. The predictions of the present T-sat based model are compared with those of a previously developed kinetic-based droplet mass transfer model. The predictions of the two models regarding the evolving tank pressure and temperature distributions, as well as the droplets' trajectories and temperatures, are examined and compared in detail. Finally, the ullage pressure and local vapor and liquid temperature evolutions are validated against the corresponding data provided by the MHTB spray bar mixing experiment.

mass transfer↗

NASA NTRS2016

Modeling Ullage Dynamics of Tank Pressure Control Experiment during Jet Mixing in Microgravity

A CFD model for simulating the fluid dynamics of the jet induced mixing process is utilized in this paper to model the pressure control portion of the Tank Pressure Control Experiment (TPCE) in microgravity1. The Volume of Fluid (VOF) method is used for modeling the dynamics of the interface during mixing. The simulations were performed at a range of jet Weber numbers from non-penetrating to fully penetrating. Two different initial ullage positions were considered. The computational results for the jet-ullage interaction are compared with still images from the video of the experiment. A qualitative comparison shows that the CFD model was able to capture the main features of the interfacial dynamics, as well as the jet penetration of the ullage.

active control↗

NASA NTRS2018

Validity of Miles Equation in Predicting Propellant Slosh Damping in Baffled Tanks at Variable Slosh Amplitude

Yang, H. Q.↗

NASA NTRS2018

Validity of Miles Equation in Predicting Propellant Slosh Damping in Baffled Tanks at Variable Slosh Amplitude

Yang, H. Q.↗

NASA NTRSDate not supplied

CFD Modeling of Phase Change and Pressure Drop during Violent Sloshing of Cryogenic Fluid in a Small-Scale Tank

This paper presents the development of a two-phase CFD model that is used to study sloshing of a cryogenic fluid (LN2) undergoing phase change generated by lateral acceleration and its effects on the ensuing heat and mass transfer and pressure drop in a small-scale tank. In this model the interface is captured using the volume-of-fluid (VOF) method [1]. Kinetic-theory based Schrage relation [2] is used for calculating phase change mass transfer at the liquid-vapor interface. Computational results are compared to the data provided by a non-isothermal sloshing experiment with phase change conducted by the University of Tokyo and JAXA in 2018 using liquid Nitrogen in a transparent tank. The effect of different thicknesses of a liquid temperature stratification layer created at the interface on the pressure drop during sloshing was studied experimentally. CFD results for interface movement and tank pressure are presented and compared in this paper to experimental data for the cases with the smallest and largest liquid temperature stratification thickness.

phase change↗

NASA NTRSDate not supplied

CFD Modeling of Cryogenic Chilldown in a Complex Channel under Normal and Low Gravity Conditions

Future NASA architectures have baselined cryogenic propulsion systems as well as cryogenic fluid management to support lunar missions and ultimately to support future missions to Mars. These missions will require chilling hardware down prior to engine restart as well as chilling lines and tanks prior to transferring and refueling these propulsion elements in orbit. In lieu of expensive tests conducted on-orbit, accurate predictive computational models of these chilldown processes can be used to reduce system and propellant mass as well as mission risk. To gain confidence in these computational models, appropriate anchoring and validation to experimental data in a relevant environment needs to be performed. Recent ground and sub-orbital flight experiments conducted by the Japan Aerospace Exploration Agency (JAXA) investigated chilldown of a complex channel resembling a turbopump bearing cavity at low flow rates. This work presents Computational Fluid Dynamics (CFD) model development of the chilldown experiment employing two-phase flow boiling models available in commercial CFD software STAR-CCM+ using Volume of Fluid (VOF) and the traditional Euler-Euler multiphase flow solvers. Comparisons of the numerical and experimental results under normal and low-gravity conditions are presented. An assessment of solid wall temperatures and phase distribution yielded important insights into multiphase solver choice, dependence on gravity environment, and challenges associated with cryogenic flow boiling prediction and validation.

CFD↗

NASA NTRS2021

Experimental and Computational Investigation of Flow Boiling in Microgravity

This study explores use of Computational Fluid Dynamics (CFD) to predict near-saturated flow boiling of FC-72 in microgravity. The computational method employs transient analysis to predict detailed interfacial behavior and heat transfer characteristics along a rectangular channel heated along two opposite walls. Predicted results are validated against experimental temperature measurements and high-speed video images captured during a series of parabolic aircraft maneuvers for three sets of operating conditions which include variations of both mass velocity and wall heat flux. The computational method is based on the multi-phase volume of fluid (VOF) model, which is combined with appropriate phase change and turbulence models, and accounts for both shear-lift force on bubbles and conjugate heat transfer along the heating walls. A key advantage of the CFD method is ability to capture details that are very difficult to measure experimentally, including detailed spatial variations of bubble shape, void fraction, mixture fluid temperature, liquid velocity, and vapor velocity, results for which are presented for each of the three test cases. Different flow regimes predicted along the heated length exhibit a number of dominant mechanisms including bubble nucleation, bubble growth, coalescence, vapor blankets, interfacial waviness, and residual liquid sub-layer, all of which agree well with experiment. Vapor velocity is shown to increase appreciably along the heated length because of increased void fraction, while liquid velocity experiences large fluctuations. Non-equilibrium effects are accentuated with increasing mass velocity, contributing minor deviations of fluid temperature from simulations compared to those predicted by the analytical method. Predicted wall temperature is fairly uniform in the middle of the heated length but increases in the entrance region, due to sensible heat transfer in the subcooled liquid, and decreases toward the exit, mostly because of flow acceleration resulting from increased void fraction.

two-phase cooling; flow boiling; CFD; microgravity↗

NASA NTRSDate not supplied

Validation of CFD Model Prediction of Flow Boiling Regime Transitions during LN2 Line Chilldown

Propellant storage and transfer during future long-duration missions will involve fuel depot operations in which a donor depot tank is used to fill a receiver spacecraft tank with a cryogenic propellant. Prior to the on-Orbit filling operation both the receiver tank and the transfer line must be cooled. The line chilldown process involves transition between boiling regimes in microgravity that will be quite different from their 1g ground-based counterparts. Since the cryogenic propellant itself will be used to perform the chilldown process, the time constants to cool the wall and the amount of fuel that will be used become important design considerations. In this light, the focus of the present work is to understand the flow boiling characteristics of a cryogenic fluid, namely, liquid nitrogen, during the chill-down of a transfer line using CFD modelling and simulations. The cryogenic chill-down process involves different flow boiling regimes: film boiling, transition boiling and nucleate boiling. The prediction of transition between these regimes in a CFD framework is new and challenging. The present work addresses this challenge by employing a volume-of-fluid (VOF) based methodology with Lee phase change model to predict the film boiling regime of the chill-down process in ANSYS Fluent®. The transition and nucleate boiling regimes are predicted by incorporating a sub-grid model developed by Craft Tech that accounts for bubble nucleation, growth, shedding frequency, and departure diameter. The sub-grid model is implemented into Fluent via a user-defined function for wall-fluid heat flux calculations. The sub-grid model is similar in formulation to the well-known Rensselaer Polytechnic Institute (RPI) boiling model. The model constants are tested for different operating conditions and designated values are reported. The CFD model is validated against published experimental data for liquid nitrogen chill-down of a heated stainless-steel pipe in 1g. Predicted results showing good agreement of wall temperature, rewetting temperature, and transition between film and nucleate boiling with the experimental measurements are presented and discussed.

Boiling regimes↗

NASA NTRSDate not supplied

Multiphase Simulations of the SLS Launch Environment

NASA’s Space Launch System (SLS), which will send astronauts back to the Moon in the next few years, is powered by four RS-25 engines and two RSRMV solid rocket boosters (SRBs). During launch the SLS propulsion system generates intense acoustics and other powerful waves, such as ignition overpressure (IOP) which, if unmitigated, have the potential to damage the vehicle and possibly cause loss of mission or crew. To protect the vehicle from these powerful waves, the SLS launch pad design includes an ignition overpressure/sound suppression (IOP/SS) system which sprays 270,000 gallons per minute of water very close to the SRB and RS-25 nozzles. The SRB and RS-25 engine plumes, and the proximity of the IOP/SS water, create a complex multiphase (gas and liquid) environment during the SLS ignition sequence. The interplay among these systems creates challenges related to water spray into/onto engine nozzles, potential debris transport, and additional transient loads due to strong plume-water interactions - all of which the SLS vehicle must be able to withstand. Prior to the Artemis I launch, the SLS multiphase liftoff environment was largely unknown due to differences from the Space Shuttle and other programs. Some data was available from tests of individual systems, but no integrated testing or analysis was available. Even post-launch analysis of Artemis I cannot provide a full understanding of the complex physics involved due to limited (or obstructed) camera views and instrumentation. Computational fluid dynamics (CFD) is being used to investigate the details of the multiphase environment which could not be measured, help comprehend the data gathered from the launch, and ultimately identify phenomena that are a concern for future flights. Project Details Engineers at NASA’s Marshall Space Flight Center (MSFC) have executed simulations using the Loci/STREAM-Volume of Fluid (VoF) multiphase CFD solver to understand this environment. Initial efforts successfully validated the CFD solver on various tests, giving confidence to simulate the SLS multiphase liftoff environment prior to the Artemis I launch. The CFD simulation of the SLS ignition sequence was conducted in three phases. First the IOP/SS water system was simulated for approximately 6 seconds to reach a quasi-steady state. Next, the RS-25 engine plumes were activated and held at full power for 1 second. Lastly, the SRB booster was activated and the simulation was carried out until just prior to vehicle motion. This simulation process mimics the conditions that exist at launch. Results and Impact The SLS ignition sequence simulation results provide deep understanding of the underlying physics occuring during launch. Observations from the simulation include reduction of water splashing into/onto the engine nozzles, change in angling of the dense water sheets, and the origin of the powerful ignition overpressure (IOP) wave. These observations directly inform the SLS program on subjects including plume-water induced side loads, debris transport, and the acoustic launch environment. Additionally, with post launch comparison of CFD observations to flight data, these tools can be applied to launch vehicles and environments other than SLS with confidence. Why HPC Matters The SLS ignition sequence CFD simulations are conducted on meshes up to hundreds of millions of cells on thousands of processors for weeks at a time. These simulations generate terabytes of data that must also be stored and archived for future use on HPC systems. Simply put, the CFD simulations would not be possible without NASA HPC resources. What’s Next Comparisons between the Artemis I flight data and the CFD simulations will be continued to both improve confidence in the CFD results and provide deeper understanding into the SLS multiphase launch environment. This will be used to provide insight for decision making for the first manned SLS flight, Artemis II. Future simulations will target new configurations of the SLS IOP/SS water required to support the more powerful variants of the SLS vehicle, such as Block 1B. Additionally, this capability provides NASA the ability to investigate launch environments for vehicles other than SLS to support other missions.

Travis Rivord↗

NASA NTRSDate not supplied

Validation of Ullage Collapse Due to Violent Lateral Slosh

Understanding the coupling between thermodynamics and propellant sloshing is important for cryogenic upper stages, especially during the lift-off phase and in missions including multiple engine restarts, as the fluid dynamic condition of the propellant is mainly influenced by various flight maneuvers. This paper describes the development and validation of a Volume of Fluid (VOF)-based CFD solver, Loci/STREAM-VOF, to the ullage collapse under violent later slosh conditions. Loci/STREAM-VOF is shown to be able to capture detailed slosh dynamics, including slosh frequency, non-linear slosh damping, and violent surface breakup due to forced acceleration. The comparison of surface shape and small drops formed during large amplitude slosh with experimental imagery shows excellent agreement throughout the sloshing period. Comparison of temperature histories in the ullage, at the gas-liquid interface, and inside liquid with the experiment conducted at JAXA also show very good agreement. The simulation points to a stratified temperature field inside the liquid near the interface, critical to the ullage pressure after the collapse. The predicted pressure collapse matches well with the experimental value due to sloshing. Parametric sensitivity studies suggest that high-fidelity Loci/STREM-VOF simulations can play an essential role in predicting the actual thermodynamics of ullage collapse when following the recommended simulation methodology.

H Q Yang↗

NASA NTRSDate not supplied

CFD Model Development of a Cryogenic Storage Tank Self-Pressurization in Normal Gravity and Validation against SHIIVER Experiment

Two-Phase flow and heat transfer simulations with interfacial phase change of the Structural Heat Intercept, Insulation, and Vibration Evaluation Rig (SHIIVER) self-pressurization experiment were conducted using storage tank CFD model in the framework of the ANSYS Fluent CFD code. The simulations were performed for the 70% fill level case with MLI on domes and no vapor cooling. All the phase change calculations in these simulations were generated by in-house Schrage-based evaporation-condensation model. The calculations were performed using both the VOF and Sharp Interface multiphase 2Daxisymmetric models. A number of parametric and sensitivity studies were performed to check the various aspects of the CFD model. These studies helped to understand the effects of varying several parameters on the tank pressure and temperature during self-pressurization. These parameters include: the effect of turbulence modeling and turbulence damping at the interface; the effect of constant vs. temperature dependent fluid properties; the effect of accommodation coefficient; the effect of modeling phase change at the interface and the effect of the fill level.

Computational Fluid Dynamics↗

NASA NTRSDate not supplied

Predictions of Line Chilldown Boiling Regime Transitions by a Coupled CFD-Sub-Grid Boiling Model Validated against 1G LN2 Experiments

Propellant storage and transfer during future long-duration missions will involve fuel depot operations in which a donor depot tank is used to fill a receiver spacecraft tank with a cryogenic propellant. Prior to the on-Orbit filling operation both the receiver tank and the transfer line must be cooled. The line chilldown process involves transition between boiling regimes in microgravity that will be quite different from their 1g ground-based counterparts. Since the cryogenic propellant itself will be used to perform the chilldown process, the time constants to cool the wall and the amount of fuel that will be used become important design considerations. In this light, the focus of the present work is to capture the flow boiling characteristics of a cryogenic fluid, namely, liquid nitrogen, during the chill-down of a transfer line using CFD modelling and simulations. The cryogenic chill-down process involves different flow boiling regimes: film boiling, transition boiling and nucleate boiling. The prediction of transition between these regimes in a CFD framework is new and challenging. The present work addresses this challenge by employing a volume-of-fluid (VOF) based methodology with Lee phase change model to predict the film boiling regime of the chill-down process in ANSYS Fluent®. The transition and nucleate boiling regimes are predicted by incorporating a sub-grid model that accounts for bubble nucleation, growth, shedding frequency, and departure diameter. The sub-grid model is implemented into Fluent via a user-defined function for wall-fluid heat flux calculations. The sub-grid model is similar in formulation to the well-known Rensselaer Polytechnic Institute (RPI) boiling model. The CFD model is validated against published experimental data for liquid nitrogen chill-down of a heated stainless-steel pipe in 1g. Predicted results shows good agreement of wall temperature, rewetting temperature, and transition between film and nucleate boiling with the experimental measurements for several different LN2 flowrates in the vertical orientation. The strengths and weaknesses of this modeling approach are presented and discussed.

Cryogenic Fluid Management↗

NASA NTRSDate not supplied

CFD Modeling & Validation of Single Bubble Growth During Cavitation in Zero Gravity

Cryogenic Fluid Management (CFM) in zero gravity represents a vital area of research as NASA pursues future long-duration space missions. Success of these missions relies heavily on the ability to store and transfer the cryogenic liquid fuels efficiently and safely. In the Zero Boil-Off Tank (ZBOT-1) Experiment in 2018, unexpected and intense phase change occurred at the screened Liquid Acquisition Device (LAD) during tank pressure control that was later attributed to cavitation. The cavitation ultimately resulted in pump failure. Since cryogen cavitation during storage and transfer of propellants in microgravity has been a source of serious concern for the aerospace community, a series of drop tower experiments with liquid methane were also performed at the University of Bremen to carefully study cavitation from a single bubble nucleus in an engineered micron-sized wall cavity. As the test cell is depressurized during the 10-second drop, cavitation causes bubble growth from the nucleus. Here, in a collaboration between the Case Western Reserve University and University of Bremen, we present a two-phase Computational Fluid Dynamics (CFD) model of bubble growth from a single wall cavity during depressurization in microgravity. Both 2D axisymmetric and 3D parametric simulation case studies are performed to show the evolution of the bubble growth. The model uses a Volume of Fluid (VOF) approach with and without adaptive mesh refinement and adaptive time stepping to capture the growth dynamics using an explicit formulation with algebraic reconstruction of the interface. CFD results show good agreement with corresponding experiment. Based on the velocity, temperature, and volume fraction fields generated by the validation case studies, detailed discussion and analysis of fluid flow and heat transfer during bubble growth process are presented to delineate the intricacies of the cavitation process. Strengths and shortcomings of the present numerical approach in capturing this phenomenon are also highlighted.

Two Phase Flow↗

NASA NTRSDate not supplied

Loci/STREAM Sharp Interface Model Validation of Cryogenic Propellant Tank Self-Pressurization

This paper documents a model validation effort for the prediction of cryogenic propellant tank selfpressurization physics using the Loci/STREAM sharp interface CFD model developed at NASA MSFC. Cryogenic fluid management (CFM) applications for long duration spaceflight missions require accurate modeling of heat transfer and thermodynamics. Therefore, detailed validation of those physics is important to ensure simulation accuracy. In the past, the MSFC Propulsion Fluid Dynamics Branch has validated and used the Loci/STREAM Volume of Fluid (VOF) module extensively for propellant slosh applications, which are dominated by fluid motion. For cases where the interface gas/liquid interface is essentially static, the Loci/STREAM sharp interface was developed for more rapid and efficient CFM analysis. In the present study, Loci/STREAM sharp interface simulations were compared with the NASA K-site self-pressurization experiment of a flight weight, partially full, LH2 tank in normal gravity. This study investigated several parametric effects and made a number of important observations on the performance of the Loci/STREAM sharp interface method: - First, a homogeneous model was derived to verify the CFD model. The homogeneous model assumes both gas and liquid phases are uniform and are at saturation temperature. The predicted pressure rise rates at 3.5 W/m2 and 2.0 W/m2 with a 49% fill level are all lower than the experimental measurement. This is expected due to the observed temperature stratification near the gas-liquid interface during testing. - The k-w and k-e turbulence models predict comparable pressurization rates, which are much lower than the experiment measurement. On the other hand, the pressure values and pressurization rates from both models are almost the same as those of the homogeneous model. The current turbulence model is too diffusive and is not capable of capturing the thermal stratification in the liquid and ullage. - When using the laminar flow model, the pressurization rate is found to be very close to the experimental value when a quasi-steady flow field is allowed to develop by continuously venting the tank prior to pressurization as was done during testing. On the other hand, without initial venting, the rate is not constant. Additionally, the development time to reach a quasi-steady flow field differed from the experiment due to the lack of turbulent mixing away from the gas-liquid interface that is expected in reality. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 15% of the experimental value for 49% fill level at 3.5 W/m 2 and is within 18% for 2.0 W/m 2 heat loading. - Using the laminar flow model and appropriate initial conditioning, the pressurization rate is within 18% of the experimental value for a 29% fill level and within 15% for an 83% fill level.

H. Q. Yang↗