John I. Hochstein

Volume tracking of interfaces having surface tension in two and three dimensions

Solution algorithms are presented for tracking interfaces with piecewise linear (PLIC) volume-of-fluid (VOF) methods on fixed (Eulerian) two-dimensional (2-D) structured and three-dimensional (3-D) structured and unstructured grids. We review the theory of volume tracking methods, derive appropriate volume evolution equations, identify and present solutions to the basic geometric functions needed for interface reconstruction and volume fluxing, and provide detailed algorithm templates for modern 2-D and 3-D PLIC VOF interface tracking methods. We discuss some key outstanding issues for PLIC VOF methods, namely the method used for time integration of fluid volumes (operator splitting, unsplit, Runge-Kutta, etc.) and the estimation of interface normals. We also present our latest developments in the continuum surface force (CSF) model for surface tension, namely extension to 3-D and variable surface tension effects. We identify and focus on key outstanding CSF model issues that become especially critical on fine meshes with high density ratio interfacial flows, namely the surface delta function approximation, the estimation of interfacial curvature, and the continuum surface force scaling and/or smoothing model. Numerical results in two and three dimensions are used to illustrate the properties of these methods.

Accurate solution algorithms for incompressible multiphase flows

A number of advances in modeling multiphase incompressible flow are described. These advances include high-order Godunov projection methods, piecewise linear interface reconstruction and tracking and the continuum surface force model. Examples are given.

Prediction of self-pressurization rate of cryogenic propellant tankage

The SOLA-ECLIPSE code is being developed to enable prediction of the behavior of cryogenic propellants in spacecraft tankage. A brief description of the formulations used for modeling heat transfer and for determining the thermodynamic state is presented. Code performance is verified through comparison to experimental data for the self-pressurization of scale-model liquid hydrogen tanks. SOLA-ECLIPSE is used to examine the effect of initial subcooling of the liquid phase on the self-pressurization rate of an on-orbit full-scale liquid hydrogen tank typical for a chemical-propu lsion orbit transfer vehicle. The computational predictions show that even small amounts of subcooling will significantly decrease the self-pressurization rate. Further, if the cooling is provided by a thermodynamic vent system, it is concluded that small levels of subcooling will maximize propellant conservation.

Fluid capture by a permanent ring magnet in reduced gravity

Recent advances in magnet technology suggest that magnetic positive positioning of liquids may become a viable technology for future spacecraft systems. Development of a new computational tool for simulating this process is presented as are results from experimental and computational studies of the process. Comparison of simulation predictions to known solutions for simple configurations and to experiment data, support the conclusion that the computational tool provides a good model of magnetic positive positioning. Sequences oFpredicted flow fields that extend the parameter space of the experimental investigation are presented and conclusions are drawn about the expeiiments, the simulation, and magnetic positive positioning.

Numerical modeling of on-orbit propellant motion resulting from an impulsive acceleration

In-space docking and separation maneuvers of spacecraft that have large fluid mass fractions may cause undersirable spacecraft motion in response to the impulsive-acceleration-induced fluid motion. An example of this potential low gravity fluid management problem arose during the development of the shuttle/Centaur vehicle. Experimentally verified numerical modeling techniques were developed to establish the propellant dynamics, and subsequent vehicle motion, associated with the separation of the Centaur vehicle from the shuttle orbiter cargo bay. Although the shuttle/Centaur development activity was suspended, the numerical modeling techniques are available to predict on-orbit liquid motion resulting from impulsive accelerations for other missions and spacecraft.

Microgravity Geyser and Flowfield Prediction

Modeling and prediction of flow fields and geyser formation in microgravity cryogenic propellant tanks was investigated. A computational simulation was used to reproduce the test matrix of experimental results performed by other investigators, as well as to model the flows in a larger tank. An underprediction of geyser height by the model led to a sensitivity study to determine if variations in surface tension coefficient, contact angle, or jet pipe turbulence significantly influence the simulations. It was determined that computational geyser height is not sensitive to slight variations in any of these items. An existing empirical correlation based on dimensionless parameters was re-examined in an effort to improve the accuracy of geyser prediction. This resulted in the proposal for a re-formulation of two dimensionless parameters used in the correlation; the non-dimensional geyser height and the Bond number. It was concluded that the new non-dimensional geyser height shows little promise. Although further data will be required to make a definite judgement, the reformulation of the Bond number provided correlations that are more accurate and appear to be more general than the previously established correlation.

Simulation and Prediction of Realistic Magnetic Positive Positioning for Space Based Fluid Management Systems

BACKGROUND For more than 30 years, analytical, experimental, and computational studies have been performed to seek reliable technologies for managing cryogenic propellants in reduced gravity. Passive and impulsive systems have been utilized for monopropellant management onboard small satellites. Passive systems depend on surface tension forces generated by specific geometries, such as screens, vanes, and channels, inside the tank, to hold the propellant within specific locations inside the tank. One disadvantage of the passive system is the increased weight of the spacecraft due to the vane/screen/channel structures. Active systems achieve reorientation by firing external thrusters that accelerate the spacecraft tank relative to the liquid. The advantage propulsive methods have over passive systems is that propellant can be repositioned to meet mission requirements. However, implementation requires the addition of auxiliary thrusters, fuels, and controls. Experimental and computational studies have shown that a sufficiently strong magnetic field can influence a magnetically susceptible liquid. An improved simulation integrates an electromagnetic field model and incompressible flow model to predict fluid reorientation using realistic magnetic fields. Flow fields are presented incorporating several realistic magnetic fields to verify and validate the connectivity of the integrated system. Conclusions are drawn about the fidelity of the integrated simulation in modeling magnetically induced fluid flows. The simulation is used to model the application of magnetic positive positioning of LOX in a reduced gravity experiment utilizing a realistic magnetic field. Preflight experiment predictions of the performance of the magnetic field in reorienting LOX are presented and recommendations are made for future design.

Microgravity Propellant Tank Geyser Analysis and Prediction

An established correlation for geyser height prediction of an axial jet inflow into a microgravity propellant tank was analyzed and an effort to develop an improved correlation was made. The original correlation, developed using data from ethanol flow in small-scale drop tower tests, uses the jet-Weber number and the jet-Bond number to predict geyser height. A new correlation was developed from the same set of experimental data using the jet-Weber number and both the jet-Bond number and tank-Bond number to describe the geyser formation. The resulting correlation produced nearly a 40% reduction in geyser height predictive error compared to the original correlation with experimental data. Two additional tanks were computationally modeled in addition to the small-scale tank used in the drop tower testing. One of these tanks was a 50% enlarged small-scale tank and the other a full-scale 2 m radius tank. Simulations were also run for liquid oxygen and liquid hydrogen. Results indicated that the new correlation outperformed the original correlation in geyser height prediction under most circumstances. The new correlation has also shown a superior ability to recognize the difference between flow patterns II (geyser formation only) and III (pooling at opposite end of tank from the bulk fluid region).

Approaches to Validation of Models for Low Gravity Fluid Behavior

Abstract This paper details the author experiences with the validation of computer models to predict low gravity fluid behavior. It reviews the literature of low gravity fluid behavior as a starting point for developing a baseline set of test cases. It examines authors’ attempts to validate their models against these cases and the issues they encountered. The main issues seem to be that: Most of the data is described by empirical correlation rather than fundamental relation; Detailed measurements of the flow field have not been made; Free surface shapes are observed but through thick plastic cylinders, and therefore subject to a great deal of optical distortion; and Heat transfer process time constants are on the order of minutes to days but the zero-gravity time available has been only seconds. Introduction Each of the authors of this paper has extensive experience modeling low-gravity flow with Computational Fluid Dynamics. Dr. Chato, (refs. 1 and 2) working mostly with a NASA developed phase field model of the free surface, (ref. 3) Drs. Hochstein and Marchetta with the Volume of Fluid (refs. 4 and 5)-Continuum Surface Force (ref. 6) code ECLIPSE, and Dr. Kassemi with the finite element code FIDAP (ref. 7). All codes have their strengths and weaknesses and each author has had some success with his approach. One of the major hurdles each has encountered is a lack of validation data with which to compare his results with. Although much drop tower work was conducted in the sixties and seventies, it is typically published in a form which does not contain enough information to analyze the flow field. Most data is published in a few static photographs and the bulk of the data is compressed into an empirical correlation. Most of the raw drop tower film has been lost to the ravages of time. Even when film is available, flow visualization is not, so the velocity field is inferred rather than measured. At best, one can look at the injection of dye and infer the fluid motion roughly from that. The purpose of this paper is to examine what research is available and open a dialog within the research community as to where to go from here.

Temperature fields due to jet induced mixing in a typical OTV tank

The Eclipse Code is being developed as a general tool for analysis of cryogenic propellant behavior in spacecraft tankage. The focus of the work being reported is on prediction of temperature fields due to introduction of a cold jet along the centerline of a typical Orbit Transfer Vehicle tank. A brief description of the formulations used for modeling heat transfer and turbulent flow is presented. Code performance is verified through comparison to experimental data for mixing in small scale tanks. An unexpected difficulty in computing long duration flows is reviewed. Preliminary results for a partially filled full scale tank are obtained by approximating the free surface by a spherical solid boundary.