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At least 343 records · Page 19

Dramatic Slowdown of Bimolecular Reactions of Criegee Intermediates in Organic Aerosols

Although Criegee intermediates (CIs) play a central role in driving the transformation of organic molecules, their condensed-phase reaction kinetics remains poorly understood. While CIs undergo unimolecular decomposition to produce OH radicals, stabilized CIs participate in a host of other bimolecular reactions forming larger molecular weight products, including secondary ozonides (kSOZ), alkoxyalkyl hydroperoxides (kAlAHP), and acyloxyalkyl hydroperoxides (kAcAHP). Here, we demonstrate, using prior literature and new measurements of heterogeneous organic aerosol reactions using O3 or OH radicals, that these condensed-phase bimolecular reaction rate coefficients kSOZ (10-20 cm3·molecule-1·s-1), kAlAHP, and kAcAHP (10-19 cm3·molecule-1·s-1) are 7-10 orders of magnitude slower than analogous gas-phase reactions (∼ 10-10-10-13 cm3·molecule-1·s-1). This contrasts with current evidence that the rate coefficients for unimolecular steps in the condensed phase are similar in magnitude to those in the gas phase. Kinetic models using gas-phase-like bimolecular coefficients consistently overestimate the importance of bimolecular relative to unimolecular pathways while underpredicting the aerosol reactivity by up to 30-fold. The slowing of bimolecular reactivity in aerosols is likely due to solvation effects and the increased steric hindrance of larger molecular weight CIs and their scavengers in the condensed phase. These results challenge the conventional view that the high reactant density of an organic aerosol should favor bimolecular over unimolecular reactions, underscoring the need for more accurate CI condensed-phase rate constants for reliable modeling of oxidative processes across a diverse set of atmospheric and environmental systems.

Zeng, Meirong↗

An idealized model of homogeneous solid propellant combustion

The idealization of solid propellant combustion which consists of a single condensed-phase reaction and a single gas-phase reaction is discussed. A limiting-case solution to the gas-phase conservation equations is developed and tested by comparison with transformed thermocouple data. Closed-form expressions are derived for the burning rate and temperature sensitivity. Both quantities are linked explicitly to the solid and gas activation energies. It is concluded that the combustion phenomenology associated with the above idealization is still not fully understood. It is suggested that a careful study of the various limiting-case solutions tempered by a small set of numerical benchmark calculations might further such understanding.

Miller, M. S.↗

Modeling Macro- and Micro-Scale Turbulent Mixing and Chemistry in Engine Exhaust Plumes

Simulation of turbulent mixing and chemical processes in the near-field plume and plume-vortex regimes has been successfully carried out recently using a reduced gas phase kinetics mechanism which substantially decreased the computational cost. A detailed mechanism including gas phase HOx, NOx, and SOx chemistry between the aircraft exhaust and the ambient air in near-field aircraft plumes is compiled. A reduced mechanism capturing the major chemical pathways is developed. Predictions by the reduced mechanism are found to be in good agreement with those by the detailed mechanism. With the reduced chemistry, the computer CPU time is saved by a factor of more than 3.5 for the near-field plume modeling. Distributions of major chemical species are obtained and analyzed. The computed sensitivities of major species with respect to reaction step are deduced for identification of the dominant gas phase kinetic reaction pathways in the jet plume. Both the near field plume and the plume-vortex regimes were investigated using advanced mixing models. In the near field, a stand-alone mixing model was used to investigate the impact of turbulent mixing on the micro- and macro-scale mixing processes using a reduced reaction kinetics model. The plume-vortex regime was simulated using a large-eddy simulation model. Vortex plume behind Boeing 737 and 747 aircraft was simulated along with relevant kinetics. Many features of the computed flow field show reasonable agreement with data. The entrainment of the engine plumes into the wing tip vortices and also the partial detrainment of the plume were numerically captured. The impact of fluid mechanics on the chemical processes was also studied. Results show that there are significant differences between spatial and temporal simulations especially in the predicted SO3 concentrations. This has important implications for the prediction of sulfuric acid aerosols in the wake and may partly explain the discrepancy between past numerical studies (that employed parabolic or temporal approximations) and the measured data. Finally to address the major uncertainty in the near-field plume modeling related to the plume processing of sulfur compounds and advanced model was developed to evaluate its impact on the chemical processes in the near wake. A comprehensive aerosol model is developed and it is coupled with chemical kinetics and the axisymmetric turbulent jet flow models. The integrated model is used to simulate microphysical processes in the near-field jet plume, including sulfuric acid and water binary homogeneous nucleation, coagulation, non-equilibrium heteromolecular condensation, and sulfur-induced soot activation. The formation and evolution of aerosols are computed and analyzed. The computed results show that a large number of ultra-fine (0.3--0.6 nm in radius) volatile HSO4 - HO embryos are generated in the near-field plume. These embryos further grow in size by self coagulation and condensation. Soot particles can be activated by both heterogeneous nucleation and scavenging of H2SO4-H2O aerosols. These activated soot particles can serve as water condensation nuclei for contrail formation. Conditions under which ice contrails can form behind aircrafts are studied. The sensitivities of the threshold temperature for contrail formation with respect to aircraft propulsion efficiency, relative humidity, and ambient pressure are evaluated. The computed aerosol properties for different extent of fuel sulfur conversion to S(VI) (SO3 and H2SO4) in engine are examined and the results are found to be sensitive to this conversion fraction.

Menon, Suresh↗

Large-scale characteristics of interstellar dust from COBE DIRBE observations

Observations from the COBE Diffuse Infrared Background Experiment of the 140 and 240 micrometer emissions from the Galatic plane region (absolute value of b less than 10 deg) are combined with radio surveys that trace the molecular (H2), neutral atomic (H I), and extended low-density (n(sub e) approximately 10 to 100/cm(exp 3)) ionized (H II) gas phases of the interstellar medium to derive physical conditions such as the dust temperature, dust-to-gas mass ratio, and far-infrared emissivity (1) averaged over these gas phases along each line of sight and (2) within each of these three gas phases. This analysis shows large-scale longitudinal and latitudinal gradients in the dust temperature and a decrease in dust temperature with increasing Galactocentric distance. The derived dust temperatures are significantly different from those derived in similar analyses using the Infrared Astronomical Satellite (IRAS) 60 and 100 micrometer data, suggesting that small (5 A approximately less than radius approximately less than 200 A) transiently heated dust particles contribute significantly o the Galactic 60 micrometer emission. It is found that 60% to 75% of the far-infrared luminosity arises from cold (approximately 17 to 22 K) dust associated with diffuse H I clouds, 15% to 30% from cold (approximately 19 K) dust associated with molecular gas, and less than 10% from warm (approximately 29 K) dust in extended low-density H II regions, consistent with the results of the IRAS analyses of the Galactic 60 and 100 micrometer emission. Within 2 deg of longitude of the Galactic center, the derived gas-to-dust mass ratio along the line of sight, G(sub d), reverses its general trend of decreasing G(sub d) toward the inner Galaxy and increases by a factor of approximately 2 to 3 toward the Galactic center. One possible explanation for this result is that the ratio of H2 column density to (12)CO intensity is lower in the Galactic center region than in the Galactic disk.

Sodroski, T. J.↗

Scientific support for an orbiter middeck experiment on solid surface combustion

The objective is to determine the mechanism of gas-phase flame spread over solid fuel surfaces in the absence of any buoyancy or externally imposed gas-phase flow. Such understanding can be used to improve the fire safety aspects of space travel by providing information that will allow judicious selections of spacecraft materials and environments to be made. The planned experiment consists of measuring the flame spread rate over thermally thin and thermally thick fuels in a closed container in the low-gravity environment of the Space Shuttle. Measurements consist of flame spread rate and shape obtained from two views of the process as recorded on movie film and surface and gas-phase temperatures obtained from fine-wire thermocouples. The temperature measurements along with appropriate modeling provide information about the gas-to-solid heat flux. Environmental parameters to be varied are the oxygen concentration and pressure.

Altenkirch, Robert A.↗

Extinction of the Stagnation Point Diffusion Flame: Effect of Conductive Heat Loss into Solid Interior

The flammability boundary of a solid is U-shaped with the ordinate as ambient oxygen percentage (or total pressure) and the abscissa represents flow velocity, gravity level, stretch rate, etc. The left side of the flammability boundary is the quenching branch, and the right side is the blow-off branch. Quenching is due to a weak flame whose heat release from combustion cannot overcome the excessive heat losses from, for example, radiation. Blow-off is due to a short gas residence time that is smaller than the chemical reaction time (traditionally referred to as the small Damköhler number effect). For thick solids, the heat conduction into the solid interior has a long transient after ignition before the solid temperature reaches the steady state. During this slow transient, there is excessive (i.e. more than that at the steady state) gas phase heat conduction into the solid interior. From the viewpoint of the quasi-static gaseous flame, this is an additional heat loss that will affect the gas flame's flammability. In this work, a previously developed one-dimensional axisymmetric stagnation-point diffusion flame model is extended to account for the excessive heat loss into the solid beyond the steady burning state. A non-dimensional excessive conductive heat loss parameter Ψ is defined in the paper to account for the transient solid effect. For each Ψ, the gas phase is considered reaching a quasi-steady state. Extensive numerical computations have been performed to determine the extinction boundary and the characteristics of near-limit flames. The U-shaped flammability boundary is now a series of boundaries with Ψ as a parameter. Flame structures under the same environment condition but with different Ψ are compared. For a given oxygen ambient, the extinction boundary Ψ vs stretch rate is an inverted U-shape. The boundary consists of a blowoff branch and a radiative quenching branch. Extensive computed data including flame and pyrolysis temperatures, burning rate, flame standoff distance, species concentration, and reaction rate are presented along the extinction boundaries. Heat balance analysis is performed for both the gas phase and the gas-solid interface. Along the extinction boundary, the relative importance of conduction, convection, radiation, and chemical reaction are analyzed in detail.

Stagnation point diffusion flame↗

A stagnation pressure probe for droplet-laden air flow

It is often of interest in a droplet-laden gas flow to obtain the stagnation pressure of both the gas phase and the mixture. A flow-decelerating probe (TPF), with separate, purged ports for the gas phase and the mixture and with a bleed for accumulating liquid at the closed end, has been developed. Measurements obtained utilizing the TPF in a nearly isothermal air-water droplet mixture flow in a smooth circular pipe under various conditions of flow velocity, pressure, liquid concentration and droplet size are presented and compared with data obtained under identical conditions with a conventional, gas phase stagnation pressure probe (CSP). The data obtained with the CSP and TPF probes are analyzed to determine the applicability of the two probes in relation to the multi-phase characteristics of the flow and the geometry of the probe.

Murthy, S. N. B.↗

A theoretical investigation of gaseous absorption by water droplets from SO2-HNO3-NH3-CO2-HCl mixtures

A physical-chemical model is developed and used to investigate gaseous absorption by water droplets from trace gas mixtures. The model is an extension of that of Carmichael and Peters (1979) and includes the simultaneous absorption of SO2, NH3, HNO3, CO2, and HCl. Gas phase depletion is also considered. Presented results demonstrate that the absorption behavior of raindrops is strongly dependent on drop size, fall distance, trace gas concentrations, and the chemical and physical properties of the constituents of the mixture. In addition, when gas phase depletion is considered, the absorption rates and equilibrium values are also dependent on the precipitation rate itself. Also, the trace constituents liquid phase concentrations may be a factor of six or more lower when gas depletion is considered then when the depletion is ignored. However, the hydrogen ion concentration may be insensitive to the gas phase depletion.

Adewuyi, Y. G.↗

Integration and validation of some modules for modelling of high-speed chemically reactive flows in two-phase gas-droplet mixtures

Three modules are integrated into the built-in OpenFOAM rhoCentralFoam solver towards accurate and efficient modelling of high-speed chemically reactive flows in two-phase gas-droplet mixtures within the OpenFOAM 10.0 framework. The first module is the mixture-averaged diffusion model. The second module is the built-in OpenFOAM Lagrangian solver coupled with optimised droplet drag coefficient and convective heat transfer coefficient sub-models. The last module is a sparse stiff chemistry solver based on dynamic adaptive hybrid integration (AHI-S). The optimised droplet sub-models are first verified in correct implementation for subsequent simulations in this work. Further, they show good accuracy against experimental and analytical data in the modelling of ammonia droplet acceleration and cooling in the flowing and/or low-temperature air. The accuracy and efficiency gains related to the mixture-averaged diffusion model and the AHI-S chemistry solver are examined by simulating 1-D detonation propagation in ammonia droplet-free/laden ammoniaoxygen mixtures. Numerical results of detonation propagation speed, gaseous temperature, density, and species distributions around the induction zone show good agreement with experimental data and analytical solutions. Compared to the built-in OpenFOAM diffusion model, the mixture-averaged diffusion model provides different numerical predictions of pulsating instabilities in detonation propagation. It shows better accuracy in depicting the detonation structure within the droplet-free section attributed to improved multi-component diffusion modelling. Compared to the built-in OpenFOAM solver EulerImplicit (backward Euler), the AHI-S chemistry solver reduces the computational cost by around 50%. It achieves satisfactory accuracy in calculating detonation propagation speed within the droplet-free section with the optimal efficiency when the safety factor, β, equals 0.5.

42 ENGINEERING↗

Structure of a Swirl-stabilized, Combusting Spray

Measurements of the structure of a swirl-stabilized, reacting spray are presented. The configuration consisted of a research air-assist atomizer located in the center surrounded by a coflowing air stream. Both the air assist and coflow streams had swirl imparted to them in the same direction with 45 degree angle swirlers. The fuel and air entered the combustor at ambient temperature and the combustor was operated in an unconfined environment. The gas phase was seeded with aluminum oxide particles in order to obtain velocity measurements. Velocity measurements for the gas phase are reported for both an isothermal, single-phase case without drops and a reacting spray case at axial distances from 2.5 to 350 mm downstream of the nozzle. Both mean and fluctuating values are reported. Heptane fuel was used for all the experiments. Drop size and velocity, and drop number flux are also reported for five axial distances downstream. Both mean and fluctuating values are reported for the drops. The measurements were performed using a two-component phase/Doppler particle analyzer. Profiles across the entire flowfield where velocities were significant are presented. Mean gas phase temperatures were also measured intrusively using a single pt/pt-13 percent rh thermocouple and are reported at axial distances from 2.5 to 200 mm downstream of the nozzle.

Bulzan, Daniel L.↗

Condensed phase details in the time-independent combustion of AP/composite propellants

The problem of nonmetallized ammonium perchlorate (AP)/composite propellant combustion is studied with the aim of coherently interpreting apparently diverse experimental data. Three fundamental hypotheses are introduced: the extent of propellant degradation at the vaporization step has to be specified through a scientific criterion; condensed phase degradation of AP to vaporizable fragments is the overall rate-limiting reaction; the rate of combustion in the gas phase is controlled by diffusive-mixing processes. Theoretical predictions of the regression rates of AP are seen to match well with experimental observations. Theoretical curves of regression rate are presented for a typical composite propellant. It is seen through analyses that either of the two familiar models for the gas phase (flame sheet approximation and uniform combustion) describes the general behavior adequately, hence de-emphasizing the role of gas phase details in propellant combustion.

Kumar, R. N.↗

Measurements and predictions of a liquid spray from an air-assist nozzle

Droplet size and gas velocity were measured in a water spray using a two-component Phase/Doppler Particle Analyzer. A complete set of measurements was obtained at axial locations from 5 to 50 cm downstream of the nozzle. The nozzle used was a simple axisymmetric air-assist nozzle. The sprays produced, using the atomizer, were extremely fine. Sauter mean diameters were less than 20 microns at all locations. Measurements were obtained for droplets ranging from 1 to 50 microns. The gas phase was seeded with micron sized droplets, and droplets having diameters of 1.4 microns and less were used to represent gas-phase properties. Measurements were compared with predictions from a multi-phase computer model. Initial conditions for the model were taken from measurements at 5 cm downstream. Predictions for both the gas phase and the droplets showed relatively good agreement with the measurements.

Bulzan, Daniel L.↗

Measurements and predictions of a liquid spray from an air-assist nozzle

Droplet size and gas velocity were measured in a water spray using a two-component Phase/Doppler Particle Analyzer. A complete set of measurements was obtained at axial locations from 5 to 50 cm downstream of the nozzle. The nozzle used was a simple axisymmetric air-assist nozzle. The sprays produced, using the atomizer, were extremely fine. Sauter mean diameters were less than 20 microns at all locations. Measurements were obtained for droplets ranging from 1 to 50 microns. The gas phase was seeded with micron sized droplets, and droplets having diameters of 1.4 microns and less were used to represent gas-phase properties. Measurements were compared with predictions from a multi-phase computer model. Initial conditions for the model were taken from measurements at 5 cm downstream. Predictions for both the gas phase and the droplets showed relatively good agreement with the measurements.

Bulzan, Daniel L.↗

Finite-Rate Ablation Boundary Conditions for Carbon-Phenolic Heat-Shield

A formulation of finite-rate ablation surface boundary conditions, including oxidation, nitridation, and sublimation of carbonaceous material with pyrolysis gas injection, has been developed based on surface species mass conservation. These surface boundary conditions are discretized and integrated with a Navier-Stokes solver. This numerical procedure can predict aerothermal heating, chemical species concentration, and carbonaceous material ablation rate over the heatshield surface of re-entry space vehicles. In this study, the gas-gas and gas-surface interactions are established for air flow over a carbon-phenolic heatshield. Two finite-rate gas-surface interaction models are considered in the present study. The first model is based on the work of Park, and the second model includes the kinetics suggested by Zhluktov and Abe. Nineteen gas phase chemical reactions and four gas-surface interactions are considered in the present model. There is a total of fourteen gas phase chemical species, including five species for air and nine species for ablation products. Three test cases are studied in this paper. The first case is a graphite test model in the arc-jet stream; the second is a light weight Phenolic Impregnated Carbon Ablator at the Stardust re-entry peak heating conditions, and the third is a fully dense carbon-phenolic heatshield at the peak heating point of a proposed Mars Sample Return Earth Entry Vehicle. Predictions based on both finite-rate gas- surface interaction models are compared with those obtained using B' tables, which were created based on the chemical equilibrium assumption. Stagnation point convective heat fluxes predicted using Park's finite-rate model are far below those obtained from chemical equilibrium B' tables and Zhluktov's model. Recession predictions from Zhluktov's model are generally lower than those obtained from Park's model and chemical equilibrium B' tables. The effect of species mass diffusion on predicted ablation rate is also examined.

Chen, Y.-K.↗

Structure of a swirl-stabilized combusting spray

Measurements of the structure of a swirl-stabilized, reacting spray are presented. The configuration consisted of a research air-assist atomizer located in the center surrounded by a co-flowing airstream. Both the air-assist and co-flowing streams had swirl imparted to them in the same direction with 45-deg angle swirlers. The fuel and air entered the combustor at ambient temperature and the combustor was operated in an unconfined environment. The gas phase was seeded with aluminum-oxide particles in order to obtain velocity measurements. Mean velocity measurements for the gas phase are reported for both an isothermal, single-phase case without drops and a reacting spray case at axial distances from 2.5 to 50 mm downstream of the nozzle. Heptane fuel was used for all the experiments. Drop size and mean velocity and drop number flux are also reported for five axial distances downstream. The measurements were performed using a two-component phase/Doppler particle analyzer. Profiles across the entire flowfield where velocities were significant are presented. Mean gas-phase temperatures were also measured intrusively using a single pt/pt-13%rh thermocouple and are also reported at axial distances from 2.5 to 50 "im downstream of the nozzle.

Bulzan, Daniel L.↗

Structure of nonevaporating sprays. I - Initial conditions and mean properties

Structure measurements were completed within the dilute portion of axisymmetric nonevaporating sprays. Measurements included: mean velocities, velocity fluctuations, and Reynolds stress of the gas phase; and mean velocities, fluctuating velocities, mass flux, and diameter distributions of the drop phase. The measurements were used to evaluate three typical methods of analyzing sprays: (1) a locally homogeneous flow (LHF) analysis, where slip between the phases is neglected; (2) a deterministic separated flow (DSF) analysis, where slip is considered but effects of drop interactions with turbulence are ignored; and (3) a stochastic separated flow (SSF) analysis, where effects of both slip and turbulence are considered using random-walk computations for drop motion. Measurements of initial conditions of both phases near the injector, mean gas-phase properties, and liquid flux distributions are described herein. Best agreement between predictions and measurements was obtained with the SSF model, which provided a reasonable representation of turbulent dispersion of drops. A companion paper presents additional measurements of drop continuous phase properties.

Solomon, A. S. P.↗

Theoretical studies of the extraterrestrial chemistry of biogenic elements and compounds

Organic compounds, molecules related to those in living systems, are found in many different extraterrestrial environments. The study of organic astrochemistry is important to exobiology both because it demonstrates the ubiquity of processes which led to life on Earth and because the dust clouds where molecules are found are analogs of the solar nebula from which the Earth formed. In the long chain of events leading from the Big Bang, and a universe composed of atomic hydrogen and helium, to the emergence of life on Earth, molecular interstellar clouds are an early link, the most primitive objects which display any significant organic chemistry. One such cloud was the direct precursor to the solar system and to all objects which it contains. Theoretical methods are ideally suited to studying interstellar cloud chemistry. They have been applied to determine spectroscopic constants of candidate interstellar molecules, mechanisms of ion-molecule reactions, and composition of dust grains. Accurate predictions of rotational constants and dipole moments of long-chain carbon molecules HC13N, HC15N, and C5O have been made to aid in determining the size limit of gas-phase interstellar molecules. Models of gas-phase interstellar chemistry use reaction rate constants measured at room temperature and extrapolated to interstellar temperatures. The temperature dependence of NH3(+)+H2 yields NH4(+)+H is anomalous, however, with a minimum rate at about 100K, casting doubt on the extrapolation procedures. The temperature dependence has now been explained.

Defrees, D. J.↗

Modeling and Simulation of Tank Pressure Control using Zero-Boil Off Active Thermal Control for LOXSAT Technology Demonstration Mission

To-date, research and modeling of cryogenic fluid management technologies (CFM) for spaceflight has been limited to ground tests, short-duration zero-g simulations (e.g. drop towers), and small-scale experiments on-orbit. There has not been a large-scale flight demonstration of a flight-like system. As future NASA missions to take humans further from Earth will require large, in-space cryogenic propulsion vehicles, it is imperative to begin collecting flight data for these systems to accurately model and design future vehicles. To meet this goal, NASA awarded tipping point technology demonstration awards to Eta Space, Lockheed Martin, Space Exploration Technologies (SpaceX), and United Launch Alliance (ULA) to demonstrate on-orbit storage and transfer of cryogenic propellant. For its award, Eta Space is developing LOXSAT-1. It is a small satellite that will be launched on a Rocket Lab Electron rocket. The spacecraft consists of a Rocket Lab Photon spacecraft bus with a primary payload of a spherical liquid oxygen (LOX) storage tank with thermodynamic control systems. The primary objective of the mission is to demonstrate zero-boil-off storage of liquid oxygen. To accomplish this objective, the payload is equipped with an active thermal control system fluid loop that consists of propellant management device (PMD), positive-displacement pump, heat exchanger connected to a cryocooler, and a spray bar mixing injector. When the fluid loop is operating, fluid is drawn from the tank by the PMD and pumped through the heat exchanger, lowering the fluid temperature below the fluid temperature in the tank. This subcooled liquid is then injected back into the tank through the spray bar. The subcooled injected liquid has two effects. If it is sprayed into the ullage space, the injected liquid will form into jets or droplets and exchange heat with the ullage gas. This will cool and condense the gas, reducing the pressure in the tank. Additionally, the liquid that is not sprayed through the ullage, as well as any remaining liquid spray from the ullage, will rejoin the liquid mass of the tank, lowering the bulk temperature of the liquid. These combines effects provide for zero-boil off pressure control by lowering the tank pressure and the liquid saturation pressure simultaneously, ensuring the liquid stays subcooled. To model these complex mechanics and predict the performance of the active thermal control system, NASA is providing Eta Space with 3 parallel models of the tank. The approach of providing 3 different models allows for cross-checking and comparisons between the three to better understand how different modeling assumptions and selection semi-empirical factors affects the modeling result. Additionally, developing 3 models provides three different schemes for numerical simulation, providing confidence that results depict real physical phenomenon and not numerical quirks of the program. Within the tank thermodynamics, there are two primary areas of heat transfer we concern ourselves with: the heat transfer between the ullage space and the droplet spray, and between the ullage space and bulk liquid. For the droplet heat transfer, there are multiple sets of assumptions that can be made and correlations that can be used. Currently, two working models - the TankSIM model and Easy5 model – provide for an overview of the different approaches available. The TankSIM model and Easy5 model use two different models for droplet heating and evaporation that illustrate how the models use different types of mechanisms to arrive at the same answer. For the TankSIM model, droplets are treated as spheres of constant radius. Heat is transferred from the ullage to the droplet and warms the droplet until it reaches saturation, then the droplet begins evaporating and reducing its radius and mass. To calculate the heat transfer coefficient between the droplet and ullage, the Ranz-Marshall correlation is used. To determine the number of droplets in the ullage, a resident mass approach is used. This approach averages the number of droplets such that residuals at the start-up and shut-off of the spray bar cancel out. This same approach is used in the Easy5 model. The GFSSP model implements a linked list to track individual droplet “nodes” within the model. For the Easy5 model, the droplet is assumed to have an interface at a temperature equal to the saturation temperature corresponding to the pressure of the gas phase. The heat transfer from the gas to the interface and the interface to the droplet bulk is then calculated, and the net mass transfer between the droplet and interface is determined by performing an energy balance across the interface. For the gas side of the interface, the Ranz-Marshall correlation is used. For the liquid side of the interface, a variety of correlations were tried, including Kronig and Brink (1950) and effective conductivity models. As a result of these assumptions, the Easy5 model currently predicts faster depressurization, as at saturated vapor conditions, the heat transfer coeffect on the liquid side for the Easy5 model is greater than the heat transfer coefficient predicted by Ranz-Marshall used in the TankSIM code. This greater heat flux translates into faster condensation of the saturated ullage gas. At the bulk liquid to ullage interface, the models are in much closer agreement. Both models model the ullage as a sphere centered within the bulk liquid in the tank, and both use the energy-jumping boundary condition to model heat and mass transfer across the interface. There are slight differences in how the interface temperature is calculated, however. The Easy5 model assumes the temperature of the interface is equal to the saturation temperature associated with the pressure of the gas phase. The TankSIM model calculates this temperature with Alabovskii’s equation, which provides a correction factor for interface temperatures. Analysis tasks are focused on determining rates of depressurization within the tank during active cooling operation. To maintain net positive suction head at the pump inlet, the tank pressure cannot fall faster than the saturation pressure associated with the temperature of the bulk liquid. Additionally, there is interest in analyzing the performance of the loop at different pump speeds and cryocooler input powers. Adjusting the flowrate affects both the performance of the heat exchanger between the cryocooler and pumped liquid, and the heat transfer between the droplet spray and the ullage. Ideally, a pump speed and cryocooler power can be selected that will allow the tank to operate in zero-boil-off mode with a very narrow range of storage pressure.

Cameron J. Hines↗