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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 19 records

Hot-Film and Hot-Wire Anemometry for a Boundary Layer Active Flow Control Test

Unsteady active flow control (AFC) has been used experimentally for many years to minimize bluff-body drag. This technology could significantly improve performance of rotorcraft by cleaning up flow separation. It is important, then, that new actuator technologies be studied for application to future vehicles. A boundary layer wind tunnel was constructed with a 1ft-x-3ft test section and unsteady measurement instrumentation to study how AFC manipulates the boundary layer to overcome adverse pressure gradients and flow separation. This unsteady flow control research requires unsteady measurement methods. In order to measure the boundary layer characteristics, both hot-wire and hot-film Constant Temperature Anemometry is used. A hot-wire probe is mounted in the flow to measure velocity while a hot-film array lays on the test surface to measure skin friction. Hot-film sensors are connected to an anemometer, a Wheatstone bridge circuit with an output that corresponds to the dynamic flow response. From this output, the time varying flow field, turbulence, and flow reversal can be characterized. Tuning the anemometers requires a fan test on the hot-film sensors to adjust each output. This is a delicate process as several variables drastically affect the data, including control resistance, signal input, trim, and gain settings.

Control Test↗

A Two-Dimensional Variational Analysis Method for NSCAT Ambiguity Removal: Methodology, Sensitivity, and Tuning

In this study, we apply a two-dimensional variational analysis method (2d-VAR) to select a wind solution from NASA Scatterometer (NSCAT) ambiguous winds. 2d-VAR determines a "best" gridded surface wind analysis by minimizing a cost function. The cost function measures the misfit to the observations, the background, and the filtering and dynamical constraints. The ambiguity closest in direction to the minimizing analysis is selected. 2d-VAR method, sensitivity and numerical behavior are described. 2d-VAR is compared to statistical interpolation (OI) by examining the response of both systems to a single ship observation and to a swath of unique scatterometer winds. 2d-VAR is used with both NSCAT ambiguities and NSCAT backscatter values. Results are roughly comparable. When the background field is poor, 2d-VAR ambiguity removal often selects low probability ambiguities. To avoid this behavior, an initial 2d-VAR analysis, using only the two most likely ambiguities, provides the first guess for an analysis using all the ambiguities or the backscatter data. 2d-VAR and median filter selected ambiguities usually agree. Both methods require horizontal consistency, so disagreements occur in clumps, or as linear features. In these cases, 2d-VAR ambiguities are often more meteorologically reasonable and more consistent with satellite imagery.

Hoffman, R. N.↗

Control of Fan Blade Vibrations Using Piezoelectrics and Bi-Directional Telemetry

A novel wireless device which transfers supply power through induction to rotating operational amplifiers and transmits low voltage AC signals to and from a rotating body by way of radio telemetry has been successfully demonstrated in the NASA Glenn Research Center (GRC) Dynamic Spin Test Facility. In the demonstration described herein, a rotating operational amplifier provides controllable AC power to a piezoelectric patch epoxied to the surface of a rotating Ti plate. The amplitude and phase of the sinusoidal voltage command signal, transmitted wirelessly to the amplifier, was tuned to completely suppress the 3rd bending resonant vibration of the plate. The plate's 3rd bending resonance was excited using rotating magnetic bearing excitation while it spun at slow speed in a vacuum chamber. A second patch on the opposite side of the plate was used as a sensor. This paper discusses the characteristics of this novel device, the details of a spin test, results from a preliminary demonstration, and future plans.

Provenza, Andrew J.↗

Fluid System Stability Analysis Techniques

Fluid systems, or networks, consist of multiple components that work together to achieve some desired thermofluid state. For any generic application, this fluid state can be a combination of the fluid pressure, flow rate, enthalpy, or species concentration. Fluid system components, such as pumps and valves, are often governed by nonlinear differential equations, resulting in complex component-to-component interactions. System-level fluid network stability occurs when the flow through the system can maintain a steady-state solution in the presence of small perturbations, which depends on these component interactions. System instability, however, can go undetected until issues arise during integrated system testing. This presentation explores a method for system designers to think of the fluid network as an assembly of components, each with their own thermofluid surfaces of partial stability, called nullclines. The intersections of all nullclines yields system-level solutions, called equilibrium points. When designers define operating points, they are tuning system parameters so that these equilibrium points move to the desired location in the thermofluid state plane. However, linearization theory shows us that the dynamic behavior around these points can be unstable. The local stability of these equilibrium points can be assessed analytically with eigen-analysis, or numerically by propagating state-plane samples to construct a phase portrait. Investigating a phase portrait can help designers gain a qualitative understanding of a system’s dynamic performance. This understanding can then help inform requirement definitions, component selection, and operational procedures. This presentation includes an example of the phase portrait technique on a system featuring a centrifugal pump and a back-pressure regulator (BPR). Numerical modeling of this system suggests that equilibrium points on the left-hand side of the pump curve are dynamically unstable.

Fluid System↗

Fluid System Stability Analysis Techniques

Fluid systems, or networks, consist of multiple components that work together to achieve some desired thermofluid state. For any generic application, this fluid state can be a combination of the fluid pressure, flow rate, enthalpy, or species concentration. Fluid system components, such as pumps and valves, are often governed by nonlinear differential equations, resulting in complex component-to-component interactions. System-level fluid network stability occurs when the flow through the system can maintain a steady-state solution in the presence of small perturbations, which depends on these component interactions. System instability, however, can go undetected until issues arise during integrated system testing. This presentation explores a method for system designers to think of the fluid network as an assembly of components, each with their own thermofluid surfaces of partial stability, called nullclines. The intersections of all nullclines yields system-level solutions, called equilibrium points. When designers define operating points, they are tuning system parameters so that these equilibrium points move to the desired location in the thermofluid state plane. However, linearization theory shows us that the dynamic behavior around these points can be unstable. The local stability of these equilibrium points can be assessed analytically with eigen-analysis, or numerically by propagating state-plane samples to construct a phase portrait. Investigating a phase portrait can help designers gain a qualitative understanding of a system’s dynamic performance. This understanding can then help inform requirement definitions, component selection, and operational procedures. This presentation includes an example of the phase portrait technique on a system featuring a centrifugal pump and a back-pressure regulator (BPR). Numerical modeling of this system suggests that equilibrium points on the left-hand side of the pump curve are dynamically unstable.

Fluid System↗

Tuning Neural Network Models for Improved Prediction of Boundary Layer Transition

Boundary layer transition can strongly impact flight vehicle performance as it influences surface skin friction and aerodynamic heating, making accurate transition prediction a key to designing next generation aircraft. Artificial neural networks (ANNs) have shown promise toward predicting laminar-turbulent transition based on linear stability correlations. The computational efficiency of ANNs and the substantially reduced user involvement in relation to direct computations based on the linear stability theory (LST) makes them an attractive methodology for integrating the LST based correlations in computational fluid dynamics codes. Tollmien-Schlichting (TS) waves correspond to the dominant transition mechanism in 2D or weakly 3D subsonic boundary layers, such as those encountered in general aviation applications. Improvements to neural network model accuracy in predicting the amplification rates of TS instability waves have been investigated by leveraging recent machine learning developments in conjunction with surrogate optimization techniques and via suitable augmentation of the data used to train the networks. The optimized models trained on the modified dataset reduced the average transition location errors on different airfoils at several flow conditions by 51% of the original manually-tuned network’s errors on the same flow cases. The actual transition locations were derived from the Langley Stability and Transition Analysis Code (LASTRAC).

Machine Learning↗

A Machine Learning Ready Dataset of Acoustic Power Maps for Detection of Active Region Emergence

The development of an accurate forecast for solar eruptive activity has become increasingly important in order to prevent any potential impact on activities in space and the Earth's environment. It is therefore crucial to detect active regions before they appear on the solar surface and create early warning capabilities for upcoming Space Weather disturbances. In this work, 9TB of solar data (SDO/HMI dopplergrams, magnetograms and continuum intensity maps) involving the emergence of 61 NOAA solar active regions since 2010 were processed using the NASA HECC capabilities. An acoustic power maps time-series dataset was created (for four different frequency ranges and processed to take into account the solar sphere geometric effect ) which can be used for understanding the dynamics of the solar surface and train a variety of ML models. The calculated acoustic power maps carry precursor information associated with the decrease in continuum intensity on the solar surface, verifying older helioseismology research. Our results show that a Long Short-Term Memory (LSTMs) model, with a modest layer depth and the right hyperparameters tuned, when trained on this solar acoustic power maps dataset can predict without false negatives a drop in intensity (associated with the emergence of the active region), up to 18 hours in advance.

SMD↗

Interannual Variability of Martian Global Dust Storms: Simulations with a Low-Order Model of the General Circulation

We present simulations of the interannual variability of martian global dust storms (GDSs) with a simplified low-order model (LOM) of the general circulation. The simplified model allows one to conduct computationally fast long-term simulations of the martian climate system. The LOM is constructed by Galerkin projection of a 2D (zonally averaged) general circulation model (GCM) onto a truncated set of basis functions. The resulting LOM consists of 12 coupled nonlinear ordinary differential equations describing atmospheric dynamics and dust transport within the Hadley cell. The forcing of the model is described by simplified physics based on Newtonian cooling and Rayleigh friction. The atmosphere and surface are coupled: atmospheric heating depends on the dustiness of the atmosphere, and the surface dust source depends on the strength of the atmospheric winds. Parameters of the model are tuned to fit the output of the NASA AMES GCM and the fit is generally very good. Interannual variability of GDSs is possible in the IBM, but only when stochastic forcing is added to the model. The stochastic forcing could be provided by transient weather systems or some surface process such as redistribution of the sand particles in storm generating zones on the surface. The results are sensitive to the value of the saltation threshold, which hints at a possible feedback between saltation threshold and dust storm activity. According to this hypothesis, erodable material builds up its a result of a local process, whose effect is to lower the saltation threshold until a GDS occurs. The saltation threshold adjusts its value so that dust storms are barely able to occur.

Pankine, A. A.↗

Improved Re-Configurable Sliding Mode Controller for Reusable Launch Vehicle of Second Generation Addressing Aerodynamic Surface Failures and Thrust Deficiencies

In this report we present a time-varying sliding mode control (TV-SMC) technique for reusable launch vehicle (RLV) attitude control in ascent and entry flight phases. In ascent flight the guidance commands Euler roll, pitch and yaw angles, and in entry flight it commands the aerodynamic angles of bank, attack and sideslip. The controller employs a body rate inner loop and the attitude outer loop, which are separated in time-scale by the singular perturbation principle. The novelty of the TVSMC is that both the sliding surface and the boundary layer dynamics can be varied in real time using the PD-eigenvalue assignment technique. This salient feature is used to cope with control command saturation and integrator windup in the presence of severe disturbance or control effector failure, which enhances the robustness and fault tolerance of the controller. The TV-SMC is developed and tuned up for the X-33 sub-orbital technology demonstration vehicle in launch and re-entry modes. A variety of nominal, dispersion and failure scenarios have tested via high fidelity 6DOF simulations using MAVERIC/SLIM simulation software.

Shtessel, Yuri B.↗

Convex Optimization Guidance for Precision Landing on Titan

Precision landing is an anticipated technology for future interplanetary missions. Autonomous spacecraft Entry, Descent and Landing (EDL) on the surface of a planetary body with a degree of precision in the order of meters is highly challenging. In this paper, a successive convexification guidance algorithm is utilized to simulate autonomous precision landing sequences on Saturn’s moon Titan. Due to its unique geophysical features, studying the science of matter within Titan’s atmosphere and beneath its surface is one of NASA’s most important planetary science objectives. As part of the Space Exploration Technology Directorate, a parafoil is proposed for landing on Titan due to its cost effectiveness, ease of deployment, low mass compared to the prospective payload and capabilities of precise autonomous delivery. This paper focuses on path optimization and guidance law development for high-fidelity dynamics parafoil tuning in the dense and adverse wind atmosphere of Titan, defined as a nonlinear and nonconvex optimal control problem. The powerful successive convexification method is used to solve the problem accordingly. The algorithm is designed such that the converged solution adheres to the nonlinear dynamics and kinematics in accordance with the original formulation, while respecting the state and control constraints. The six-degree-of-freedom (6DoF) simulations results show that this robust method is suitable for autonomous interplanetary applications.

Mooij, Edwin↗

Weather Research and Forecasting Model Wind Sensitivity Study at Edwards Air Force Base, CA

NASA prefers to land the space shuttle at Kennedy Space Center (KSC). When weather conditions violate Flight Rules at KSC, NASA will usually divert the shuttle landing to Edwards Air Force Base (EAFB) in Southern California. But forecasting surface winds at EAFB is a challenge for the Spaceflight Meteorology Group (SMG) forecasters due to the complex terrain that surrounds EAFB, One particular phenomena identified by SMG is that makes it difficult to forecast the EAFB surface winds is called "wind cycling". This occurs when wind speeds and directions oscillate among towers near the EAFB runway leading to a challenging deorbit bum forecast for shuttle landings. The large-scale numerical weather prediction models cannot properly resolve the wind field due to their coarse horizontal resolutions, so a properly tuned high-resolution mesoscale model is needed. The Weather Research and Forecasting (WRF) model meets this requirement. The AMU assessed the different WRF model options to determine which configuration best predicted surface wind speed and direction at EAFB, To do so, the AMU compared the WRF model performance using two hot start initializations with the Advanced Research WRF and Non-hydrostatic Mesoscale Model dynamical cores and compared model performance while varying the physics options.

Watson, Leela R.↗

Quantifying Leak Rates and Vacuum Impact on Granular Soil Column Pneumatic Seal

Introduction: All In-Situ Resource Utilization (ISRU) regolith reactor systems that aim to extract gases or vapors must maintain a seal along the flow path of the regolith from the inlet hopper to where extracted gases or vapors are generated. Using a column of regolith at the inlet has been proposed as an alternative to systems using series of mechanical valves to reduce mass and complexity. Preliminary investigations into the use of regolith itself as a barrier to escaping fluids have been conducted, which this research seeks to expand upon. Different vertical regolith simulant plug diameters and heights were tested under vacuum with dry nitrogen to observe leak rates and approximate steady state pressure gradient equilibria. The effect of absolute ambient pressure was also studied by repeating tests at incremental pressures ranging from 10e-5 Torr up to 1 atm to corroborate ambient bench tests from previous work. The impact of regolith dynamics was addressed to emulate continuous-feed regolith reaction processes by measuring leak rates through continuously draining simulant columns. OB-1 lunar highlands regolith simulant was used. Experimental Setup: Regolith simulant columns were constructed using a motorized butterfly valve separating upper acrylic tubes of various diameters from a larger, lower aluminum pipe plenum (See Figure 1). The butterfly valve was cracked open such that gas could freely pass through whereas regolith would bridge and stay suspended as a cohesive plug above in the acrylic portion. These assemblies were loaded into a vacuum chamber, and a compressed dry nitrogen line was routed into the lower plenum. Pressure transducers measured the absolute pressure of the lower plenum, which was compared to absolute chamber pressure to monitor the pressure gradient across the regolith simulant. A precision mass flow controller enabled fine control of plenum pressure. The plenum pressure was quasi-statically increased to set points informed by previous work [1] before shutting off the gas supply to allow the now pressurized gas volume to dissipate through the simulant into the chamber in what was referred to as a ‘leak test.’ In a separate set of tests, the pressure was allowed to quasi-statically build until visual disturbances in the soil were observed via remote camera feeds. Initial leak rate tests were repeated on the disturbed soil to observe changes in leak rates between initial as-poured and post-bubbling soil conditions. This test schedule was applied to simulant columns of three different diameters (approximately 2, 4, and 6 inches) as well as two different heights (around 8 and 16 inches) and was repeated at least three times for each configuration. Plenums were also pressurized while the butterfly valves were opened slightly further to facilitate slow, controlled, constant flowrate draining of the simulant to observe the impact that continuous-feed systems might have on leak rate through the regolith column. Finally, the regolith columns were reset and refilled and static leak rate tests were repeated approximately every decade in ambient pressure from 10e-5 Torr up to ambient conditions to observe the impact of transitioning out of the molecular flow regime on regolith column seal performance. Analysis: Trends with respect to each factor examined were constructed and reported alongside commentary on the most likely responsible physical phenomena. Confidence intervals were applied to the predictive findings of the data by quantifying instrumentation error and accounting for probabilistic impacts of curve fitting the generic exponential function onto pressure decay data. The leak rate is assumed directly proportional to the exponential term coefficient, while the steady-state static pressure gradient is assumed to be the asymptotic limit of each curve fit. Finally, a generic model developed by Ogino et al. [2] and later tuned for ambient testing was re-tuned using vacuum data to estimate leak rates on the lunar surface. Results: Pressure decay rates decreased up to 27-fold under vacuum when compared to ambient pressure, as shown in Figure 2. Simulant column diameter was found to exponentially correlate to both regolith column leak rate and steady-state equilibrium pressure delta. Height was found to be linearly related to leak rate –doubling the regolith column height consistently yielded around a 40% reduction in leak rate. Dynamic regolith draining was found to slightly increase leak rate, although to a lower degree than expected. Conclusion: Because of the transition into molecular gas flow through regolith, vacuum testing is required to properly estimate performance. Regolith columns should be designed as narrow as possible to avoid bridging and minimize leak rate, and as tall as is feasible to both further reduce leak rate and to help prevent bubbling, which has been shown to degrade the quality of the regolith seal. Disrupted soil was found to exhibit higher leak rates than pristine, as-poured soil, indicating the need to consider the impact of recovery from depressurization events. Regolith columns appear equally feasible for both dosed and continuous-feed reactors.

ISRU↗

Sky-Scanning Sun-Tracking Airborne Radiometer (3STAR): Instrument Design, Flight Testing, and Tracking Performance

The Sky-Scanning, Sun-Tracking Airborne Radiometer (3STAR) adapts commercial radiometer technology developed for the ocean color research community to airborne measurement of spectrally resolved solar irradiance and sky radiance. These atmospheric observations are used to derive aerosol optical depth (AOD), supporting localized AOD inputs for atmospheric correction of satellite and airborne data over terrestrial and aquatic (including optically dark) targets. The ability to regionally “tune” atmospheric correction schemes with relevant spatial AOD supports constraining atmospheric correction of remote sensing reflectance. Very wide dynamic range has been achieved for multi-channel band-pass-filter-radiometers originally designed for deployment into the water column. By actively tracking and directly pointing to the Sun, the light attenuation by aerosol particles in the atmospheric column can be quantified. These measurements improve knowledge of atmospheric constituents and the atmospheric corrections required to improve remote sensing capabilities for interpreting reflectance measurements from the Earth surface. 3STAR incorporates a custom Sun-tracking/sky-scanning pointing head, a Sun-tracking camera, and a commercially available, cylindrical, 19-channel radiometer tube assembly. An accurate and responsive mount and tracking system has been developed and certified to NASA and Naval Air Systems Command (NAVAIR) airworthiness standards for deployment into the aircraft slipstream. Ground and flight testing indicate typical tracking errors of less than 0.1 degrees, well within the field of view of the radiometer as required to minimize measurement uncertainty from alignment error. Preliminary AOD measurements compare to within 0.013 with 15 measurements from an Aerosol Robotic Network (AERONET) Cimel instrument at 500 nm wavelength and low solar angle.

Atmosphere↗

Land Surface Microwave Emissivity Dynamics: Observations, Analysis and Modeling

Land surface microwave emissivity affects remote sensing of both the atmosphere and the land surface. The dynamical behavior of microwave emissivity over a very diverse sample of land surface types is studied. With seven years of satellite measurements from AMSR-E, we identified various dynamical regimes of the land surface emission. In addition, we used two radiative transfer models (RTMs), the Community Radiative Transfer Model (CRTM) and the Community Microwave Emission Modeling Platform (CMEM), to simulate land surface emissivity dynamics. With both CRTM and CMEM coupled to NASA's Land Information System, global-scale land surface microwave emissivities were simulated for five years, and evaluated against AMSR-E observations. It is found that both models have successes and failures over various types of land surfaces. Among them, the desert shows the most consistent underestimates (by approx. 70-80%), due to limitations of the physical models used, and requires a revision in both systems. Other snow-free surface types exhibit various degrees of success and it is expected that parameter tuning can improve their performances.

Modeling↗

Direct Numerical Simulations of Boundary Layer Transition on a Flat Plate

In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows associated with geometrically complex configurations. However, success in terms of accuracy and reliability has been limited to cases where the effects of turbulence and transition could be modeled in a straightforward manner. Even in simple flows, the accurate computation of skin friction and heat transfer using existing turbulence models has proved to be a difficult task, one that has required extensive fine-tuning of the turbulence models used. In more complex flows (for example, in turbomachinery flows in which vortices and wakes impinge on airfoil surfaces causing periodic transitions from laminar to turbulent flow) the development of a model that accounts for all scales of turbulence and predicts the onset of transition is an extremely difficult task. Fortunately, current trends in computing suggest that it may be possible to perform direct simulations of turbulence and transition at moderate Reynolds numbers in some complex cases in the near future. This presentation will focus on direct simulations of transition and turbulence using high-order accurate finite-difference methods. The advantage of the finite-difference approach over spectral methods is that complex geometries can be treated in a straightforward manner. Additionally, finite-difference techniques are the prevailing methods in existing application codes. An application of high-order-accurate finite-difference methods to direct simulations of transition and turbulence in a spatially evolving boundary layer subjected to high levels of freestream turbulence will be presented.

Rai, Man Mohan↗

Direct Simulations of Transition and Turbulence Using High-Order Accurate Finite-Difference Schemes

In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows associated with geometrically complex configurations. However, success in terms of accuracy and reliability has been limited to cases where the effects of turbulence and transition could be modeled in a straightforward manner. Even in simple flows, the accurate computation of skin friction and heat transfer using existing turbulence models has proved to be a difficult task, one that has required extensive fine-tuning of the turbulence models used. In more complex flows (for example, in turbomachinery flows in which vortices and wakes impinge on airfoil surfaces causing periodic transitions from laminar to turbulent flow) the development of a model that accounts for all scales of turbulence and predicts the onset of transition may prove to be impractical. Fortunately, current trends in computing suggest that it may be possible to perform direct simulations of turbulence and transition at moderate Reynolds numbers in some complex cases in the near future. This seminar will focus on direct simulations of transition and turbulence using high-order accurate finite-difference methods. The advantage of the finite-difference approach over spectral methods is that complex geometries can be treated in a straightforward manner. Additionally, finite-difference techniques are the prevailing methods in existing application codes. In this seminar high-order-accurate finite-difference methods for the compressible and incompressible formulations of the unsteady Navier-Stokes equations and their applications to direct simulations of turbulence and transition will be presented.

Rai, Man Mohan↗

Direct Numerical Simulations of Boundary Layer Transition on a Flat Plate

In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows associated with geometrically complex configurations. However, success in terms of accuracy and reliability has been limited to cases where the effects of turbulence and transition could be modeled in a straightforward manner. Even in simple flows, the accurate computation of skin friction and heat transfer using existing turbulence models has proved to be a difficult task, one that has required extensive fine-tuning of the turbulence models used. In more complex flows (for example, in turbomachinery flows in which vortices and wakes impinge on airfoil surfaces causing periodic transitions from laminar to turbulent flow) the development of a model that accounts for all scales of turbulence and predicts the onset of transition is an extremely difficult task. Fortunately, current trends in computing suggest that it may be possible to perform direct simulations of turbulence and transition at moderate Reynolds numbers in some complex cases in the near future. This presentation will focus on direct simulations of transition and turbulence using high-order accurate finite-difference methods. The advantage of the finite-difference approach over spectral methods is that complex geometries can be treated in a straightforward manner. Additionally, finite-difference techniques are the prevailing methods in existing application codes. An application of accurate finite-difference methods to direct simulations of transition and turbulence in a spatially evolving boundary layer subjected to high levels of freestream turbulence will be presented.

Rai, Man Mohan↗

Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments relies upon the global momentum conservation of the fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. Numerical examples illustrate the method's application to predicting bulk fluid motion including lateral propellant slosh in low-g conditions.

Orr, Jeb S.↗