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NASA NTRS2004

Numerical Simulations of Buoyancy Effects in low Density Gas Jets

This paper deals with the computational analysis of buoyancy effects in the near field of an isothermal helium jet injected into quiescent ambient air environment. The transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum were solved using a staggered grid finite volume method. Laminar, axisymmetric, unsteady flow conditions were considered for the analysis. An orthogonal system with non-uniform grids was used to capture the instability phenomena. Computations were performed for Earth gravity and during transition from Earth to different gravitational levels. The flow physics was described by simultaneous visualizations of velocity and concentration fields at Earth and microgravity conditions. Computed results were validated by comparing with experimental data substantiating that buoyancy induced global flow oscillations present in Earth gravity are absent in microgravity. The dependence of oscillation frequency and amplitude on gravitational forcing was presented to further quantify the buoyancy effects.

Satti, R. P.↗

NASA NTRS1991

Grid generation about complex three-dimensional aircraft configurations

The problem of obtaining three dimensional grids with sufficient resolution to resolve all the flow or other physical features of interest is addressed. The generation of a computational grid involves a series of compromises to resolve several conflicting requirements. On one hand, one would like the grid to be fine enough and not too skewed to reduce the numerical errors and to adequately resolve the pertinent physical features of the flow field about the aircraft. On the other hand, the capabilities of present or even future supercomputers are finite and the number of mesh points must be limited to a reasonable number: one which is usually much less than desired for numerical accuracy. One technique to overcome this limitation is the 'zonal' grid approach. In this method, the overall field is subdivided into smaller zones or blocks in each of which an independent grid is generated with enough grid density to resolve the flow features in that zone. The zonal boundaries or interfaces require special boundary conditions such that the conservation properties of the governing equations are observed. Much work was done in 3-D zonal approaches with nonconservative zonal interfaces. A 3-D zonal conservative interfacing method that is efficient and easy to implement was developed during the past year. During the course of the work, it became apparent that it would be much more feasible to do the conservative interfacing with cell-centered finite volume codes instead of the originally planned finite difference codes. Accordingly, the CNS code was converted to finite volume form. This new version of the code is named CNSFV. The original multi-zonal interfacing capability of the CNS code was enhanced by generalizing the procedure to allow for completely arbitrarily shaped zones with no mesh continuity between the zones. While this zoning capability works well for most flow situations, it is, however, still nonconservative. The conservative interface algorithm was also implemented but was not completely validated.

Klopfer, Goetz H.↗

NASA NTRS1989

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Meade, Andrew James, Jr.↗

NASA NTRS1973

Extended hydrodynamic theory of the peak and minimum pool boiling heat fluxes

The hydrodynamic theory of the extreme pool boiling heat fluxes is expanded to embrace a variety of problems that have not previously been analyzed. These problems include the prediction of the peak heat flux on a variety of finite heaters, the influence of viscosity on the Taylor and Helmoltz instability mechanisms with application to film boiling and to the peak heat flux in viscous liquids, the formalization of the analogy between high-current-density electrolysis and boiling, and the description of boiling in the low-gravity limit. The predictions are verified with a large number of new data.

Linehard, J. H.↗

NASA NTRS1980

On the solution of the unsteady Navier-Stokes equations for hypersonic flow about axially-symmetric blunt bodies

A formulation of the complete Navier-Stokes problem for a viscous hypersonic flow in general curvilinear coordinates is presented. This formulation is applicable to both the axially symmetric and three dimensional flows past bodies of revolution. The equations for the case of zero angle of attack were solved past a circular cylinder with hemispherical caps by point SOR finite difference approximation. The free stream Mach number and the Reynolds number for the test case are respectively 22.04 and 168883. The whole algorithm is presented in detail along with the preliminary results for pressure, temperature, density and velocity distributions along the stagnation line.

Warsi, Z. U. A.↗

NASA NTRS1985

ISEE 1 and 2 observation of the spatial structure of a compressional Pc5 wave

A compressional Pc5 was observed on an ISEE 1 and 2 outbound path on September 28, 1981 at L = 5.6-7.3 near the magnetic equator at about 10 hr local time during the recovery phase of a geomagnetic storm. The wave propagated westward with a large azimuthal wave number of about 30 and exhibited in-phase oscillations of plasma density and magnetic field magnitude. During this event, component-dependent variations in phase and amplitude were observed for the magnetic field oscillations. The radial and compressional components had a constant phase and their amplitude was finite. In contrast, the azimuthal component changed its phase by 180 deg and its amplitude became zero during the middle of the wave event. The observation as indicating the spatial structure of the Pc5 wave is interpreted. The polarization reversal is likely to be caused by a crossing of a node of a standing wave located 4 deg above the geomagnetic equator.

Takahashi, K.↗

NASA NTRS1991

Pressure algorithm for elliptic flow calculations with the PDF method

An algorithm to determine the mean pressure field for elliptic flow calculations with the probability density function (PDF) method is developed and applied. The PDF method is a most promising approach for the computation of turbulent reacting flows. Previous computations of elliptic flows with the method were in conjunction with conventional finite volume based calculations that provided the mean pressure field. The algorithm developed and described here permits the mean pressure field to be determined within the PDF calculations. The PDF method incorporating the pressure algorithm is applied to the flow past a backward-facing step. The results are in good agreement with data for the reattachment length, mean velocities, and turbulence quantities including triple correlations.

Anand, M. S.↗

NASA NTRS1992

The platinum microelectrode/Nafion interface - An electrochemical impedance spectroscopic analysis of oxygen reduction kinetics and Nafion characteristics

The objectives of this study were to use electrochemical impedance spectroscopy (EIS) to study the oxygen-reduction reaction under lower humidification conditions than previously studied. The EIS technique permits the discrimination of electrode kinetics of oxygen reduction, mass transport of O2 in the membrane, and the electrical characteristics of the membrane. Electrode-kinetic parameters for the oxygen-reduction reaction, corrosion current densities for Pt, and double-layer capacitances were calculated. The production of water due to electrochemical reduction of oxygen greatly influenced the EIS response and the electrode kinetics at the Pt/Nafion interface. From the finite-length Warburg behavior, a measure of the diffusion coefficient of oxygen in Nafion and diffusion-layer thickness was obtained. An analysis of the EIS data in the high-frequency domain yielded membrane and interfacial characteristics such as ionic conductivity of the membrane, membrane grain-boundary capacitance and resistance, and uncompensated resistance.

Parthasarathy, Arvind↗

NASA NTRS1993

The compositional structure and the effects of exothermicity in a nonpremixed planar jet flame

Results are presented of direct numerical simulation (DNS) of a randomly perturbed compressible, spatially developing two-dimensional planar jet under the influence of a finite rate chemical reaction of the type F + O yields product. The objectives of the simulations are to assess the compositional structure of the flame and to determine the influence of reaction exothermicity by means of statistical sampling of the DNS generated data. It is shown that even with this idealized kinetics model the simulated results exhibit features in accord with experimental data. These results indicate that the Damkohler number is an important parameter in determining the statistical composition of the reacting field and that the results are not very sensitive to the mechanism by which this parameter is varied. It is demonstrated that as the intensity of mixing is increased and the effect of finite rate chemistry is more pronounced, the magnitudes of the ensemble mean and variance of the product mass fraction decrease and those of the reactants' mass fraction increase. Also, at higher mixing rates the joint probability density functions of the reactants' mass fractions shift towards higher values within the composition domain, indicating a lower reactedness.

Steinberger, C. J.↗

NASA NTRS1997

Physics of Rotation Powered Pulsars and Their Nebulae

This letter is my progress report for the Astrophysics Theory grant. The first goal of the research supported by this grant is to produce a time dependent theory of the unsteady relativistic collisionless shock wave terminating the relativistic wind from a pulsar, and compare the predicted surface brightness fluctuations to Hubble Space Telescope observations of the wisps in the Crab Nebula. The second goal is to model the production of electron-positron pairs over the polar caps of rotation powered pulsars, and use the results to predict the heating of the surface due to particle trapping and bombardment of the atmosphere at the base of the polar field lines. We have succeeded in creating a one dimensional hybrid code, in which the electron-positron pairs incident on the shock structure are modeled as a relativistic, adiabatic, ideal MHD fluid, while the heavy ions are treated as particles using a particle-in-cell algorithm. The electromagnetic fields are evaluated from the currents and charge densities in the pairs and the ions, while the particles and the fluid accelerate in response to the computed self-consistent electromagnetic fields. The results are promising, in that the underlying ion cyclotron instability generates finite amplitude, propagating magnetosonic waves in the pairs, whose wavelengths and frequencies, when translated into physical units, are comparable to the observed running waves of brightness observed by HST near the Crab pulsar. The code is undergoing a number of tests, to assure us that this preliminary correspondence is not an artifact. In the coming year, the observational appearance of the models will be computed and compared to the HST observations of the Crab now in hand, and used to predict the HST results which will be obtained the year after next. WE also developed a one dimensional cascade theory for pair creation over pulsars' polar caps. A linear integral equation describing the synchrotron cascade has been derived and solved by iterative techniques, in the case when a high energy electron moving parallel to a star centered dipole magnetic field initiates the cascade through curvature gamma ray emission.

Arons, Jonathan↗

NASA NTRS2023

Progressive Damage and Failure Analysis of Thermoplastic Composites in Low Velocity Impact Using MAT299

As part of the NASA Hi-Rate Composite Aircraft Manufacturing (HiCAM) Project, state-of-the-art progressive damage and failure analysis (PDFA) tools developed for use with thermosets are being evaluated for use in modeling alternative material systems, like thermoplastics. Experimental low-velocity impact data of a thermoplastic material system, AS4D/PEKK-FC, is presented and includes characterization of the impact damage mechanisms as well as associated load and displacement data. Following the presentation of experimental results, two simulation approaches using the PDFA tool MAT299 in the commercial off-the-shelf finite element software LS-DYNA are employed to predict damage area and force-displacement responses of thermoplastic panels subjected to various impact energies. The first modeling method uses solid elements with a high-density mesh and a ply-by-ply modeling approach similar to previously published work for thermosets. This method has the capability of capturing individual crack development, progression, and delamination on a per ply basis. The second modeling method uses TSHELL elements that have in-plane dimensions that are an order of magnitude larger than the elements used in the solid element approach and reduces the number of elements through the thickness of the laminate. The second method produces a lower-fidelity model with reduced run times that is incapable of monitoring every delamination plane and damage within each ply. Results from both simulation methods are compared to experiment, and limitations of the methods are discussed.

Composite material↗

NASA NTRS2023

Progressive Damage and Failure Analysis of Thermoplastic Composites in Low Velocity Impact Using MAT299

Composite material↗

NASA NTRS1987

Navier-Stokes computations of prolate spheroids at angle of attack

Three-dimensional viscous flow calculations are made for a 6:1 prolate spheroid at conditions for which detailed experimental data are available. The computations are made with two finite-volume algorithms for the compressible Navier-Stokes equations, one using central differencing for the convective and pressure terms and the other using an upwind-biased flux-difference-splitting approach. The effects of grid density and artificial dissipation on the accuracy of the numerical results are included. Generally good agreement of the computations with the experimental results is obtained over a range of Reynolds numbers and angles-of-attack, up to 30 deg, although the results at lower Reynolds numbers are sensitive to the assumed transition location.

Vatsa, V. N.↗

NASA NTRS1988

Numerical simulation of nonaxisymmetric adiabatic accretion flow

The hydrodynamics of gas flow past a finite-sized gravitating central object is studied in the adiabatic approximation in two spatial dimensions. The flow morphology is shown to depend on the ratio (epsilon) of the axisymmetric accretion radius to the length scale of the density variation. For small to intermediate epsilon values the flows are highly time dependent, and for large epsilon values a quasi-steady state is obtained.

Fryxell, B. A.↗

NASA NTRS1992

Numerical study of the small scale structures in Boussinesq convection

Two-dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high order accurate Essentially Nonoscillatory (ENO) scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. The numerical results suggest that the collapse of the bubble cap is unlikely to occur in resolved calculations. The strain rate corresponding to the intensification of the density gradient across the front saturates at the bubble cap. We also found that the cascade of energy to small scales is dominated by the formulation of thin and sharp fronts across which density jumps.

Weinan, E.↗

NASA NTRS1993

Performance assessment of low pressure nuclear thermal propulsion

An increase in Isp for nuclear thermal propulsion systems is desirable for reducing the propellant requirements and cost of future applications, such as the Mars Transfer Vehicle. Several previous design studies have suggested that the Isp could be increased substantially with hydrogen dissociation/recombination. Hydrogen molecules (H2), at high temperatures and low pressures, will dissociate to monatomic hydrogen (H). The reverse process (i.e., formation of H2 from H) is exothermic. The exothermic energy in a nozzle increases the kinetic energy and therefore, increases the Isp. The low pressure nuclear thermal propulsion system (LPNTP) system is expected to maximize the hydrogen dissociation/recombination and Isp by operating at high chamber temperatures and low chamber pressures. The process involves hydrogen flow through a high temperature, low pressure fission reactor, and out a nozzle. The high temperature (approximately 3000 K) of the hydrogen in the reactor is limited by the temperature limits of the reactor material. The minimum chamber pressure is about 1 atm because lower pressures decrease the engines thrust to weight ratio below acceptable limits. This study assumes that hydrogen leaves the reactor and enters the nozzle at the 3000 K equilibrium dissociation level. Hydrogen dissociation in the reactor does not affect LPNTP performance like dissociation in traditional chemical propulsion systems, because energy from the reactor resupplies energy lost due to hydrogen dissociation. Recombination takes place in the nozzle due primarily to a drop in temperature as the Mach number increases. However, as the Mach number increases beyond the nozzle throat, the static pressure and density of the flow decreases and minimizes the recombination. The ideal LPNTP Isp at 3000 K and 10 psia is 1160 seconds due to the added energy from fast recombination rates. The actual Isp depends on the finite kinetic reaction rates which affect the amount of monatomic hydrogen recombination before the flow exits the nozzle. A LPNTP system has other technical issues (e.g. flow instability and two-phase flow) besides hydrogen dissociation/recombination which affect the systems practicality. In this study, only the effects of hydrogen dissociation/recombination are examined.

Gerrish, Harrold P., Jr.↗

NASA NTRS1994

Characteristics of the field-aligned current system in the nighttime sector during auroral substorms

Fujii et al. (1994) obtained characteristics of the electrodynamic parameters, that is, field-aligned currents, electric fields, and electron precipitation, which are associted with auroral substorm events in the nighttime sector, through a unique analysis that places the ionospheric measurements of these parameters into the context of a generic substorm determined from global auroral images. In this paper we investigate in considerably more detail the characteristics of the field-aligned currents using data from the same set of passes as the previuos study. We show for the first time that the net upward field-aligned currents throughout the surge and surge horn are sufficient to account for most if not all of the converging currents of the auroral electrojets. Current densities are largest in the surge and surge horn. Current region continuity does not appear to exist across the substorm bulge region. Much of the auroral substorm field-aligned current is composed of filamentary currents and finite current segments at large angles to each other. The westward electrojet may contain large gradients in intensity both in local time and latitude due to sets of localized field-aligned currents. The net downward current for several hours to the west of the surge is insufficient to account for the eastward electrojet, consistent with the concept that this electrojet originates primarily on the dayside. Our pattern of field-aligned currents associated with the surge has common features and also differs significantly from the patterns previously derived from data from radars and ground-based magnetometer arrays. Our pattern is considerably more complex, probably due to the much higher resolution in latitude of the satellite data. It is also larger in area, since our average substorm is much larger than those pertaining to the previous patterns, giving a substorm wedge considerably wider than that obtained from the radar and array data.

Hoffman, R. A.↗

NASA NTRS1995

Protostellar Collapse with a Shock

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(exp -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Tsai, John C.↗