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NASA NTRS1993

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

Sutjahjo, Edhi↗

NASA NTRS1993

Pinching solutions of slender cylindrical jets

Simplified equations for slender jets are derived for a circular jet of one fluid flowing into an ambient second fluid, the flow being confined in a circular tank. Inviscid flows are studied which include both surface tension effects and Kelvin-Helmholtz instability. For slender jets a coupled nonlinear system of equations is found for the jet shape and the axial velocity jump across it. The equations can break down after a finite time and similarity solutions are constructed, and studied analytically and numerically. The break-ups found pertain to the jet pinching after a finite time, without violation of the slender jet ansatz. The system is conservative and admissible singular solutions are those which conserve the total energy, mass, and momentum. Such solutions are constructed analytically and numerically, and in the case of vortex sheets with no surface tension certain solutions are given in closed form.

Papageorgiou, Demetrios T.↗

NASA NTRS1994

Gas dynamics for accretion disk simulations

The behavior of accretion disks can largely be understood in terms of the basic physical processes of mass, energy, and momentum conservation. Despite this, detailed modeling of these systems using modern computational techniques is challenging and controversial. Disturbing differences exist between methods used widely in astrophysics, namely Eulerian finite-difference techniques and particle codes such as SPH. Therefore neither technique is fully satisfactory for accretion disk simulations. This paper describes a new fully Lagrangian method designed to resolve these difficulties.

Whitehurst, R.↗

NASA NTRS1994

Evolution of solitary density waves in stellar winds of early-type stars: A simple explanation of discrete absorption component behavior

We model the evolution of a density shell propagating through the stellar wind of an early-type star, in order to investigate the effects of such shells on UV P Cygni line profiles. Unlike previous treatments, we solve the mass, momentum, and energy conservation equations, using an explicit time-differencing scheme, and present a parametric study of the density, velocity, and temperature response. Under the assumed conditions, relatively large spatial scale, large-amplitude density shells propagate as stable waves through the supersonic portion of the wind. Their dynamical behavior appears to mimic propagating 'solitary waves,' and they are found to accelerate at the same rate as the underlying steady state stellar wind (i.e., the shell rides the wind). These hydrodynamically stable structures quantitatively reproduce the anomalous 'discrete absorption component' (DAC) behavior observed in the winds of luminous early-type stars, as illustrated by comparisons of model predictions to an extensive International Ultraviolet Explorer (IUE) time series of spectra of zeta Puppis (O4f). From these comparisons, we find no conclusive evidence indicative of DACs accelerating at a significantly slower rate than the underlying stellar wind, contrary to earlier reports. In addition, these density shells are found to be consistent within the constraints set by the IR observations. We conclude that the concept of propagating density shells should be seriously reconsidered as a possible explanation of the DAC phenomenon in early-type stars.

Waldron, Wayne L.↗

NASA NTRS1995

Numerical modeling of spray combustion with an advanced VOF method

This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.

Chen, Yen-Sen↗

NASA NTRS1995

General Fluid System Simulation Program to Model Secondary Flows in Turbomachinery

The complexity and variety of turbomachinery flow circuits created a need for a general fluid system simulation program for test data anomaly resolution as well as design review. The objective of the paper is to present a computer program that has been developed to support Marshall Space Flight Center's turbomachinery internal flow analysis efforts. The computer program solves for the mass. energy and species conservation equation at each node and flow rate equation at each branch of the network by a novel numerical procedure which is a combination of both Newton-Ralphson and successive substitution method and uses a thermodynamic property program for computing real gas properties. A generalized, robust, modular, and 'user-friendly' computer program has been developed to model internal flow rates, pressures, temperatures, concentrations of gas mixtures and axial thrusts. The program can be used for any network for compressible and incompressible flows, choked flow, change of phase and gaseous mixturecs. The code has been validated by comparing the predictions with Space Shuttle Main Engine test data.

Majumdar, Alok K.↗

NASA NTRS1994

Atomization simulations using an Eulerian-VOF-Lagrangian method

This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservations are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present innovative approach by simulating benchmark problems including the coaxial jet atomization.

Chen, Yen-Sen↗

NASA NTRS1997

Analytical Modeling of Pressure Wall Hole Size and Maximum Tip-to-Tip Crack Length for Perforating Normal and Oblique Orbital Debris Impacts

This report presents the results of a study whose objective was to develop first-principles-based models of hole size and maximum tip-to-tip crack length for a spacecraft module pressure wall that has been perforated in an orbital debris particle impact. The hole size and crack length models are developed by sequentially characterizing the phenomena comprising the orbital debris impact event, including the initial impact, the creation and motion of a debris cloud within the dual-wall system, the impact of the debris cloud on the pressure wall, the deformation of the pressure wall due to debris cloud impact loading prior to crack formation, pressure wall crack initiation, propagation, and arrest, and finally pressure wall deformation following crack initiation and growth. The model development has been accomplished through the application of elementary shock physics and thermodynamic theory, as well as the principles of mass, momentum, and energy conservation. The predictions of the model developed herein are compared against the predictions of empirically-based equations for hole diameters and maximum tip-to-tip crack length for three International Space Station wall configurations. The ISS wall systems considered are the baseline U.S. Lab Cylinder, the enhanced U.S. Lab Cylinder, and the U.S. Lab Endcone. The empirical predictor equations were derived from experimentally obtained hole diameters and crack length data. The original model predictions did not compare favorably with the experimental data, especially for cases in which pressure wall petalling did not occur. Several modifications were made to the original model to bring its predictions closer in line with the experimental results. Following the adjustment of several empirical constants, the predictions of the modified analytical model were in much closer agreement with the experimental results.

Schonberg, William P.↗

NASA NTRS1998

A Generalized Fluid System Simulation Program to Model Flow Distribution in Fluid Networks

This paper describes a general purpose computer program for analyzing steady state and transient flow in a complex network. The program is capable of modeling phase changes, compressibility, mixture thermodynamics and external body forces such as gravity and centrifugal. The program's preprocessor allows the user to interactively develop a fluid network simulation consisting of nodes and branches. Mass, energy and specie conservation equations are solved at the nodes; the momentum conservation equations are solved in the branches. The program contains subroutines for computing "real fluid" thermodynamic and thermophysical properties for 33 fluids. The fluids are: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride and ammonia. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. Seventeen different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include: pipe flow, flow through a restriction, non-circular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, and a Joule-Thompson device. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. This paper also illustrates the application and verification of the code by comparison with Hardy Cross method for steady state flow and analytical solution for unsteady flow.

Majumdar, Alok↗

NASA NTRS1998

Flow Simulation in Secondary Flow Passages of a Rocket Engine Turbopump

This paper presents application of a Generalized Fluid System Simulation Program (GFSSP) to model fluid flow in a very complex secondary flow circuit of a rocket engine turbopump, SIMPLEX. SIMPLEX was a low cost turbopump designed, manufactured and tested to demonstrate the ability to reduce the overall cost and design cycle time of turbomachinery. GFSSP is a general purpose computer program for analyzing flowrate, pressure, temperature and concentration distribution in a complex flow network. The program employs a finite volume formulation of mass, momentum and energy conservation equations in conjunction with thermodynamic equation of state of a real fluid. The secondary flow passages modeled include flow between the impeller shroud and housing, impeller back face and housing, flow through labyrinth seal and bearing, return line flow to inducer and flow adjacent to front and back face of the turbine. Axial load on the bearing are calculated from the predicted pressure on all axial faces of the rotor. The predicted pressure and temperature distributions compared well with the test data.

Schallhorn, Paul↗

NASA NTRS1998

Numerical Modeling of Pressurization of a Propellant Tank

An unsteady finite volume procedure has been developed to predict the history of pressure, temperature and mass flow rate of the pressurant and propellant during the expulsion of the propellant from a tank. The time dependent mass, momentum and energy conservation equations are solved at the ullage space. The model accounts for the change in the ullage volume due to expulsion of the propellant. It also accounts for the heat transfer from the tank wall and propellant to the ullage gas. The procedure was incorporated in the Generalized Fluid System Simulation Program (GFSSP). The results of several test cases were then compared with a published correlation of pressurant requirements for a given displacement of propellant. The agreement between the predictions and the correlation was found to be satisfactory.

Majumdar, Alok↗

NASA NTRS1998

Application of Parametrized Post-Newtonian Methods to the Gravitational IS of Satellite Energy Exchange Data

Project Satellite Energy Exchange (SEE) is a free-flying, high altitude satellite that utilizes space to construct a passive, low-temperature, nano-g environment in order to accurately measure the poorly known gravitational constant G plus other gravitational parameters that are difficult to measure in an earth-based laboratory. Eventually data received from SEE must be analyzed using a model of the gravitational interaction including parameters that describe deviations from general relativity and experiment. One model that can be used to fit tile data is the Parametrized post- Newtonian (PPN) approximation of general relativity (GR) which introduces ten parameters which have specified values in (GR). It is the lowest-order, consistent approximation that contains non linear terms. General relativity predicts that the Robertson parameters, gamma (light deflection), and beta (advance of the perihelion), are both 1 in GR. Another eight parameters, alpha(sub k), k=1,2,3 and zeta(sub k), k=1,2,3,4 and Xi are all zero in GR. Non zero values for alpha(sub k) parameters predict preferred frame effects; for zeta(sub k) violations of globally conserved quantities such as mass, momentum and angular momentum; and for Xi a contribution from the Whitehead theory of gravitation, once thought to be equivalent to GR. In addition, there is the possibility that there may be a preferred frame for the universe. If such a frame exists, then all observers must measure the velocity omega of their motion with respect to this universal rest frame. Such a frame is somewhat reminiscent of the concept of the ether which was supposedly the frame in which the velocity of light took the value c predicted by special relativity. The SEE mission can also look for deviations from the r(exp -2) law of Newtonian gravity, adding parameters alpha and lamda for non Newtonian behavior that describe the magnitude and range of the r(exp -2) deviations respectively. The foundations of the GR supposedly agree with Newtonian gravity to first order so that the parameters alpha and lamda are zero in GR. More important, however, GR subsequently depends on this Newtonian approximation to build up the non linear higher-order terms which forms the basis of the PPN frame work.

Smalley, Larry L.↗

NASA NTRS1999

Numerical Prediction of Transient Axial Thrust and Internal Flows in a Rocket Engine Turbopump

This paper presents the application of the Generalized Fluid System Simulation Program (GFSSP) to model the time-dependent flow in a complex secondary flow circuit of the turbopump of the Fastrac engine currently under development at Marshall Space Flight Center. GFSSP is a general purpose computer program for analyzing steady-state and time-dependant flowrates, pressures, temperatures, and concentrations in a complex flow network. The program employs a finite volume formulation of mass, momentum and energy conservation equations in conjunction with the thermodynamic equation of state of real fluids. GFSSP was used to calculate the axial thrust and internal flow distribution of the Fastrac engine turbopump during the start and shut down transients. The models discussed in this paper use boundary conditions that were extracted from turbopump test data. The GFSSP predicted turbopump secondary flow passage pressures and temperatures were compared with actual measured values.

VanHooser, Katherine↗

NASA NTRS1999

A Sectored-One-Dimensional Model for Simulating Combustion Instabilities in Premix Combustors

A one-dimensional, CFD based combustor simulation has been developed that exhibits self-excited, thermoacoustic oscillations in premixed combustor geometries that typically have large, abrupt changes in cross sectional area. The combustor geometry is approximated by dividing it into a finite number of one-dimensional sectors. Within each sector, the equations of motion are integrated numerically, along with a species transport and a reaction equation. Across the sectors, mass and energy are conserved, and momentum loss is prescribed using appropriately compatible boundary conditions that account for the area change. The resulting simulation and associated boundary conditions essentially represent a one-dimensional, multi-block technique. Details of the simulation code are presented herein. Results are then shown comparing experimentally observed and simulated operation of a particular combustor rig that exhibited different instabilities at different operating points. It will be shown that the simulation closely matched the rig data in oscillation amplitudes, frequencies, and operating points at which the instabilities occurred. Finally, advantages and limitations of the simulation technique are discussed.

Paxson, Daniel E.↗

NASA NTRS1999

Numerical Modeling of Pressurization of a Propellant Tank

An unsteady finite volume procedure has been developed to predict the history o pressure, temperature and mass flow rate of the pressurant and propellant during the expulsion of the propellant from a tan. The time dependent mass, momentum and energy conservation equations are solved at the ullage space. The model accounts for the change in the ullage volume due to expulsion of the propellant. It also accounts for the heat transfer from the tank wall and propellant to the ullage gas. The procedure was incorporated in the Generalized Fluid System Simulation Program (GFSSP). The results of several test cases were then compared with a published correlation of pressurant requirements for a given displacement of propellant. The agreement between the predictions and the correlation was found to be satisfactory.

Majumdar, Alok↗

NASA NTRS2002

Numerical Modeling of Cavitating Venturi: A Flow Control Element of Propulsion System

In a propulsion system, the propellant flow and mixture ratio could be controlled either by variable area flow control valves or by passive flow control elements such as cavitating venturies. Cavitating venturies maintain constant propellant flowrate for fixed inlet conditions (pressure and temperature) and wide range of outlet pressures, thereby maintain constant, engine thrust and mixture ratio. The flowrate through the venturi reaches a constant value and becomes independent of outlet pressure when the pressure at throat becomes equal to vapor pressure. In order to develop a numerical model of propulsion system, it is necessary to model cavitating venturies in propellant feed systems. This paper presents a finite volume model of flow network of a cavitating venturi. The venturi was discretized into a number of control volumes and mass, momentum and energy conservation equations in each control volume are simultaneously solved to calculate one-dimensional pressure, density, and flowrate and temperature distribution. The numerical model predicts cavitations at the throat when outlet pressure was gradually reduced. Once cavitation starts, with further reduction of downstream pressure, no change in flowrate is found. The numerical predictions have been compared with test data and empirical equation based on Bernoulli's equation.

Majumdar, Alok↗

NASA NTRS2003

Lidar Measurements of Wind, Moisture and Boundary Layer Evolution in a Dryline During IHOP2002

Variability in the convective boundary layer moisture, wind and temperature fields and their importance in the forecasting and understanding of storms have been discussed in the literature. These variations have been reported in relation to frontal zones, stationary boundaries and during horizontal convective rolls. While all three vary substantially in the convective boundary layer, moisture poses a particular challenge. Moisture or water vapor concentration (expressed as a mass mixing ratio, g/kg), is conserved in all meteorological processes except condensation and evaporation. The water vapor mixing ratio often remains distinct across an air -mass boundary even when the temperature difference is indistinct. These properties make it an ideal choice in visualizing and understanding many of the atmosphere's dynamic features. However, it also presents a unique measurement challenge because water vapor content can vary by more than three orders of magnitude in the troposphere. Characterization of the 3D-distribution of water vapor is also difficult as water vapor observations can suffer from large sampling errors and substantial variability both in the vertical and horizontal. This study presents groundbased measurements of wind, boundary layer structure and water vapor mixing ratio measurements observed by three co-located lidars. This presentation will focus on the evolution and variability of moisture and wind in the boundary layer during a dry line event that occurred on 22 May 2002. These data sets and analyses are unique in that they combine simultaneous measurements of wind, moisture and CBL structure to study the detailed thermal variability in and around clear air updrafts during a dryline event. It will quantify the variation caused by, in and around buoyant plumes and across a dryline. The data presented here were collected in the panhandle of Oklahoma as part of the International BO Project (IHOP-2002), a field experiment that took place over the Southern Great Plains (SGP) of the United States from 13 May to 30 June 2002. The chief goal of IHOP-2002 is to improve characterization of the four-dimensional (4-D) distribution of water vapor and its application to improving the understanding and prediction of convection

Demoz, Belay↗

NASA NTRS2003

Dynamical Study of Prebiotic Processing by Comet Impact

Comets and meteoroids that bombarded the Earth, other planets and moons are considered possible deliverers of prebiotic materials manufactured in space. Simultaneously, chemical processing can be initiated by the large kinetic energy imparted to the planetary atmosphere during comet/meteoroid entry. The efficiency of organic synthesis and the diversity of products by impact shock are known to decrease as the reducing power of the atmosphere decreases. It is generally accepted that rich organic products are produced in a methane atmosphere whereas a carbon dioxide atmosphere is reported to yield a dearth of products In order to understand the details of impact chemistry and how it depends on the atmospheric composition, we carried out simulations of the chemistry initiated by comet/meteoroid impact upon a planetary atmosphere using different atmospheric compositions. The simulations were done by solving the set of coupled equations for mass, momentum, and energy conservations, chemical kinetics, and transport, that describe a high-energy impact shock, subsequent expansion and cooling of the hot shocked gas by mixing with the ambient gas, and the eventual steady state composition.

Huo, Winifred M.↗