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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Linear Stability Analysis of Gravitational Effects on a Low-Density Gas Jet Injected into a High-Density Medium

The objective of this study was to determine the effects of buoyancy on the absolute instability of low-density gas jets injected into high-density gas mediums. Most of the existing analyses of low-density gas jets injected into a high-density ambient have been carried out neglecting effects of gravity. In order to investigate the influence of gravity on the near-injector development of the flow, a spatio-temporal stability analysis of a low-density round jet injected into a high-density ambient gas was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The Briggs-Bers criterion was combined with the spatio-temporal stability analysis to determine the nature of the absolute instability of the jet whether absolutely or convectively unstable. The roles of the density ratio, Froude number, Schmidt number, and the lateral shift between the density and velocity profiles on the absolute instability of the jet were determined. Comparisons of the results with previous experimental studies show good agreement when the effects of these variables are combined together. Thus, the combination of these variables determines how absolutely unstable the jet will be.

Lawson, Anthony L.↗
NASA NTRS1981

Equatorial superrotation in a thermally driven zonally symmetric circulation

Near the equator where the Coriolis force vanishes, the momentum balance for the axially symmetric circulation is established between horizontal and vertical diffusion, which, a priori, does not impose constraints on the direction or magnitude of the zonal winds. Solar radiation absorbed at low latitudes is a major force in driving large scale motions with air rising near the equator and falling at higher latitudes. In the upper leg of the meridional cell, angular momentum is redistributed so that the atmosphere tends to subrotate (or corotate) at low latitudes and superrotate at high latitudes. In the lower leg, however, the process is reversed and produces a tendency for the equatorial region to superrotate. The outcome depends on the energy budget which is closely coupled to the momentum budget through the thermal wind equation; a pressure (temperature) maximum is required to sustain equatorial superrotation. Such a condition arises in regions which are convectively unstable and the temperature lapse rate is superadiabatic. It should arise in the tropospheres of Jupiter and Saturn; planetary energy from the interior is carried to higher altitudes where radiation to space becomes important. Upward equatorial motions in the direct and indirect circulations (Ferrel-Thomson type) imposed by insolation can then trap dynamic energy for equatorial heating which can sustain the superrotation of the equatorial region.

Mayr, H. G.↗
NASA NTRS2000

Application of the Space-Time Conservation Element and Solution Element Method to One-Dimensional Convection-Diffusion Problems

In the space-time conservation element and solution element (CE/SE) method, the independent marching variables used comprise not only the mesh value of the physical dependent variables but also, in contrast to it typical numerical method, the Mesh values of the spatial derivatives of the physical variables The use of the extra marching variables results from the need to construct the two-level explicit and nondissipative schemes which are at the core of the CE/SE development. It also results from the need to minimize the stencil while maintaining accuracy. In this paper using the 1D(sub (alpha)-mu) scheme as an example, the effect of this added complication on consistency, accuracy and operation count is assessed. As part of this effort, an equivalent yet more efficient form of the alpha-mu scheme in which the independent marching variables are the local fluxes tied to each mesh point is introduced. Also, the intriguing relations that exist among the alpha-mu. Leapfrog, and DuFort-Frankel schemes are further explored. In addition, the redundance of the Leapfrog, DUFort-Frankel, and Lax scheme and the remedy for this redundance are discussed. This paper is concluded with the construction and evaluation of a CE/SE solver for the inviscid Burger equation.

Chang, Sin-Chung↗
NASA NTRS1968

Survey of the Relationship Between Theory and Experiment for Convective Heat Transfer From Rocket Combustion Gases

The problem of predicting the distribution of heat flux in a rocket engine is complicated by a flow field and thermodynamics so perturbed by as yet indescribable combustion effects that it continues to be necessary to utilize a simplified theoretical model against which to compare experimental results in order to gain insight. The most successful model applied to this problem is that of a compressible, turbulent, accelerating boundary layer flow with an arbitrary point of origin, and chemical reaction restricted to equilibrium recombination or diffusion-limited recombination on a catalytic wall. Analysis of this model was not possible without making several assumptions about the nature of the skin friction coefficient relationship and Reynold's analogy in an accelerating boundary layer flow. The paper summarizes the analysis of this model (together with detailed treatment of the special problems of variable properties, chemical reaction, and sources of transport properties), and describes several closed-form equations that have also been developed and applied to the problem. Described are results of several experiments with hot air flow made for the purpose of checking the validity of the assumptions in the boundary layer analysis. Most significant, however, are presentations of sample distributions of local heat flux measured in rocket engines operating with a wide range of conditions, propellants, injectors and sizes. When compared with predictions, these data show the significant range of deviation in heat flux that results from the combustion effects and which precludes a generally accurate prediction theory or correlation equation until the combustion process itself is correlated.

D R Bartz↗
NASA NTRS1998

Exact Solution to Stationary Onset of Convection Due to Surface Tension Variation in a Multicomponent Fluid Layer With Interfacial Deformation

Stationary onset of convection due to surface tension variation in an unbounded multicomponent fluid layer is considered. Surface deformation is included and general flux boundary conditions are imposed on the stratifying agencies (temperature/composition) disturbance equations. Exact solutions are obtained to the general N-component problem for both finite and infinitesimal wavenumbers. Long wavelength instability may coexist with a finite wavelength instability for certain sets of parameter values, often referred to as frontier points. For an impermeable/insulated upper boundary and a permeable/conductive lower boundary, frontier boundaries are computed in the space of Bond number, Bo, versus Crispation number, Cr, over the range 5 x 10(exp -7) less than or equal to Bo less than or equal to 1. The loci of frontier points in (Bo, Cr) space for different values of N, diffusivity ratios, and, Marangoni numbers, collapsed to a single curve in (Bo, D(dimensional variable)Cr) space, where D(dimensional variable) is a Marangoni number weighted diffusivity ratio.

Skarda, J. Raymond Lee↗
NASA NTRS1998

Algebraic Nonoverlapping Domain Decomposition Methods for Stabilized FEM and FV Discretizations

We consider preconditioning methods for convection dominated fluid flow problems based on a nonoverlapping Schur complement domain decomposition procedure for arbitrary triangulated domains. The triangulation is first partitioned into a number of subdomains and interfaces which induce a natural 2 x 2 partitioning of the p.d.e. discretization matrix. We view the Schur complement induced by this partitioning as an algebraically derived coarse space approximation. This avoids the known difficulties associated with the direct formation of an effective coarse discretization for advection dominated equations. By considering various approximations of the block factorization of the 2 x 2 system, we have developed a family of robust preconditioning techniques. A computer code based on these ideas has been developed and tested on the IBM SP2 using MPI message passing protocol. A number of 2-D CFD calculations will be presented for both scalar advection-diffusion equations and the Euler equations discretized using stabilized finite element and finite volume methods. These results show very good scalability of the preconditioner for various discretizations as the number of processors is increased while the number of degrees of freedom per processor is fixed.

Barth, Timothy J.↗
NASA NTRS2003

Modeling Candle Flame Behavior In Variable Gravity

The burning of a candle, as typical non-propagating diffusion flame, has been used by a number of researchers to study the effects of electric fields on flame, spontaneous flame oscillation and flickering phenomena, and flame extinction. In normal gravity, the heat released from combustion creates buoyant convection that draws oxygen into the flame. The strength of the buoyant flow depends on the gravitational level and it is expected that the flame shape, size and candle burning rate will vary with gravity. Experimentally, there exist studies of candle burning in enhanced gravity (i.e. higher than normal earth gravity, g(sub e)), and in microgravity in drop towers and space-based facilities. There are, however, no reported experimental data on candle burning in partial gravity (g < g(sub e)). In a previous numerical model of the candle flame, buoyant forces were neglected. The treatment of momentum equation was simplified using a potential flow approximation. Although the predicted flame characteristics agreed well with the experimental results, the model cannot be extended to cases with buoyant flows. In addition, because of the use of potential flow, no-slip boundary condition is not satisfied on the wick surface. So there is some uncertainty on the accuracy of the predicted flow field. In the present modeling effort, the full Navier-Stokes momentum equations with body force term is included. This enables us to study the effect of gravity on candle flames (with zero gravity as the limiting case). In addition, we consider radiation effects in more detail by solving the radiation transfer equation. In the previous study, flame radiation is treated as a simple loss term in the energy equation. Emphasis of the present model is on the gas-phase processes. Therefore, the detailed heat and mass transfer phenomena inside the porous wick are not treated. Instead, it is assumed that a thin layer of liquid fuel coated the entire wick surface during the burning process. This is the limiting case that the mass transfer process in the wick is much faster than the evaporation process at the wick surface.

Alsairafi, A.↗
NASA NTRS1982

Finite analytic numerical solution of axisymmetric Navier-Stokes and energy equations

Convective heat transfer for steady state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature and heat transfer coefficients for flow with Reynolds number of 5.0, 100.0, 1000.0, and 2000.0, and Prandtl number of 0.1, 1.0, and 10.0 with uniform grid sizes are reported for axisymmetric pipe with sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic solution is stable, converges rapidly, and simulates the convection of fluid flow accurately since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values thereby minimizing the false numerical diffusion.

Chen, C.-J.↗
NASA NTRS1993

Effects of thermal-solutal convection on temperature and solutal fields under various gravitational orientations

Semiconductor crystals such as Hg(1-x)CD(x)Te grown by unidirectional solidification Bridgmann method have shown compositional segregations in both the axial and radial directions. Due to the wide separation between the liquidus and the solidus of its pseudobinary phase diagram, there is a diffusion layer of higher HgTe content built up in the melt near the melt-solid interface which gives a solute concentration gradient in the axial direction. The value of effective diffusion coefficient calculated from fitting of the data to 1D model varies with Hg(1-x)Cd(x)Te growth conditions. This indicates that the growth condition of the Hg(1-x)Cd(x)Te is not purely diffusion controlled. Because of the higher thermal conductivity in the melt than that in the crystal in the growth system, there is a thermal leakage through the fused silica crucible wall near the melt-solid interface. This gives a thermal gradient in the radial direction. Hart, and Thorpe, Hutt and Soulsby have shown that under such conditon a fluid will become convectively unstable as a result of different diffusitivities of temperature and solute. It is quite important to understand the effects of this thermosolute convection on the compositonal segregation in both axial and radial directions in the unidirectionally solidified crystals under various gravitational directions. To reach this goal, we start with a simplified problem to study the effects of thermal-solutal convection on the temperature and solutal fields under various gravitional orientations. We begin by reviewing model governing equations.

Wang, Jai-Ching↗
NASA NTRS2006

Comparison of the Radiative Two-Flux and Diffusion Approximations

Approximate solutions are sometimes used to determine the heat transfer and temperatures in a semitransparent material in which conduction and thermal radiation are acting. A comparison of the Milne-Eddington two-flux approximation and the diffusion approximation for combined conduction and radiation heat transfer in a ceramic material was preformed to determine the accuracy of the diffusion solution. A plane gray semitransparent layer without a substrate and a non-gray semitransparent plane layer on an opaque substrate were considered. For the plane gray layer the material is semitransparent for all wavelengths and the scattering and absorption coefficients do not vary with wavelength. For the non-gray plane layer the material is semitransparent with constant absorption and scattering coefficients up to a specified wavelength. At higher wavelengths the non-gray plane layer is assumed to be opaque. The layers are heated on one side and cooled on the other by diffuse radiation and convection. The scattering and absorption coefficients were varied. The error in the diffusion approximation compared to the Milne-Eddington two flux approximation was obtained as a function of scattering coefficient and absorption coefficient. The percent difference in interface temperatures and heat flux through the layer obtained using the Milne-Eddington two-flux and diffusion approximations are presented as a function of scattering coefficient and absorption coefficient. The largest errors occur for high scattering and low absorption except for the back surface temperature of the plane gray layer where the error is also larger at low scattering and low absorption. It is shown that the accuracy of the diffusion approximation can be improved for some scattering and absorption conditions if a reflectance obtained from a Kubelka-Munk type two flux theory is used instead of a reflection obtained from the Fresnel equation. The Kubelka-Munk reflectance accounts for surface reflection and radiation scattered back by internal scattering sites while the Fresnel reflection only accounts for surface reflections.

Spuckler, Charles M.↗
NASA NTRS1989

An embedded grid formulation applied to delta wings

An embedded grid algorithm for the Euler and/or Navier-Stokes equations is developed and applied to delta wings at high angles of attack in low speed flow. The Navier-Stokes code is an implicit, finite volume algorithm, using flux difference splitting for the convective and pressure terms and central differencing for the viscous and heat transfer terms. Calculations are compared with detailed experimental results over an angle of attack range up to and beyond the maximum lift coefficient, corresponding to vortex breakdown at the trailing edge, for a delta wing nominally of unit aspect ratio. The results indicate that the overall flowfield, including surface pressures, surface streamlines, and vortex trajectories, can be simulated accurately with the global grid version of the present algorithm. However, comparison of computed velocities and vorticity with experimentally measured off-body values at an angle of attack of 20.5 deg indicates the core region is substantially more diffuse in the computations than that measured with either a five-hole probe or a laser velocimeter. Embedded grids, used to improve the numerical discretization in the core region, are formulated within the framework of the implicit, upwind-biased multi-grid algorithm. Structured levels of local nested refinements are made. Three-dimensional results for both Euler and Navier-Stokes calculations are shown, with up to 3 levels of embedded refinement. The embedding procedure was effective in eliminating a crossflow secondary separation produced in the Euler solutions on coarse grids.

Thomas, James L.↗
NASA NTRS1994

Modeling the effect of water on mantle rheology

To study the thermal history of the Earth we use a parameterized model of mantle convection. This model includes a mathematical description of de- and regassing processes of water from the Earth's mantle. The rates of this processes are considered to be directly proportional to the seafloor spreading rate. The kinematic viscosity of the mantle depends on the temperature/pressure as well as on the volatile content. Dissolved volatiles such as water weaken the minerals by reducing their activation energy for solid state creep. Karato and Toriumi showed a power law dependence between creep rate and water fugacity derived from experimental results. Therefore, we use such flow parameters of diffusion creep in olivine under wet and dry conditions to calculate the mantle viscosity as a function of the water content. Because the creep rate is proportional to the concentration of water-related point deflects we assume that the water fugacity is proportional to the water weight fraction. An equation for the steady-state strain rate under wet conditions is established. To assess the unknown constant K in this equation, we use flow law parameters given by Karato and Wu as well as the results of McGovern and Schubert.

Bounama, CH.↗
NASA NTRS2013

Coarsening in Solid-liquid Mixtures: Overview of Experiments on Shuttle and ISS

The microgravity environment on the Shuttle and the International Space Station (ISS) provides the ideal condition to perform experiments on Coarsening in Solid-Liquid Mixtures (CSLM) as deleterious effects such as particle sedimentation and buoyancy-induced convection are suppressed. For an ideal system such as Lead-Tin in which all the thermophysical properties are known, the initial condition in microgravity of randomly dispersed particles with local clustering of solid Tin in eutectic liquid Lead-Tin matrix, permitted kinetic studies of competitive particle growth for a range of volume fractions. Verification that the quenching phase of the experiment had negligible effect of the spatial distribution of particles is shown through the computational solution of the dynamical equations of motion, thus insuring quench-free effects from the coarsened microstructure measurements. The low volume fraction experiments conducted on the Shuttle showed agreement with transient Ostwald ripening theory, and the steady-state requirement of LSW theory was not achieved. More recent experiments conducted on ISS with higher volume fractions have achieved steady-state condition and show that the kinetics follows the classical diffusion limited particle coarsening prediction and the measured 3D particle size distribution becomes broader as predicted from theory.

Ostwald ripening↗
NASA NTRS2002

Solutal Convection Around Growing Protein Crystal and Diffusional Purification in Space

This work theoretically addressed two subjects: 1) onset of convection, 2) distribution of impurities. Onset of convection was considered analytically and numerically. Crystal growth was characterized by slow surface incorporation kinetics, i.e. growth kinetic coefficient beta (cm/s) small as compared to the typical bulk diffusion rate, D(sub 1)/h, where D(sub 1) is diffusivity of major crystallizing protein and h is the crystal size. Scaling type analysis predicted two laws on how the convection rate, v, essentially the Peclet number, Pe exactly equal to vh/D(sub 1), depends on dimensionless kinetic coefficient a exactly equal to beta h/D(sub 1). Namely: Pe = C(sub 2/5)(aRa(sup 2/5)) and Pe = C(sub 1) aRa. Here, Reynolds number Ra = rho(sub 1)(sup 0)gh(sup 3)(rho(sub p) - rho(sub w))/rho(sup p)rho(sub 1)vD(sub 1), v being solution viscosity. The constants C(sub 2/5), exactly equal to 0.28 and C(sub 1) exactly equal to 10(exp -2) found from the full scale computer simulation for a cylindrical crystal inside big cylindrical vessel. The linear boundary conditions connecting protein and impurity concentration at the interface with the flux to/from the interface was applied. No-slip condition for Navier-Shocker equations was employed. With these conditions, flow and concentration distributions were calculated. Validity of the Pe(Ra) dependencies follows for wide range of parameters for which numerical calculations have been accomplished and presented by various points.

Chernov, A. A.↗
NASA NTRS1989

Monte Carlo simulation of particle acceleration at astrophysical shocks

A Monte Carlo code was developed for the simulation of particle acceleration at astrophysical shocks. The code is implemented in Turbo Pascal on a PC. It is modularized and structured in such a way that modification and maintenance are relatively painless. Monte Carlo simulations of particle acceleration at shocks follow the trajectories of individual particles as they scatter repeatedly across the shock front, gaining energy with each crossing. The particles are assumed to scatter from magnetohydrodynamic (MHD) turbulence on both sides of the shock. A scattering law is used which is related to the assumed form of the turbulence, and the particle and shock parameters. High energy cosmic ray spectra derived from Monte Carlo simulations have observed power law behavior just as the spectra derived from analytic calculations based on a diffusion equation. This high energy behavior is not sensitive to the scattering law used. In contrast with Monte Carlo calculations diffusive calculations rely on the initial injection of supra-thermal particles into the shock environment. Monte Carlo simulations are the only known way to describe the extraction of particles directly from the thermal pool. This was the triumph of the Monte Carlo approach. The question of acceleration efficiency is an important one in the shock acceleration game. The efficiency of shock waves efficient to account for the observed flux of high energy galactic cosmic rays was examined. The efficiency of the acceleration process depends on the thermal particle pick-up and hence the low energy scattering in detail. One of the goals is the self-consistent derivation of the accelerated particle spectra and the MHD turbulence spectra. Presumably the upstream turbulence, which scatters the particles so they can be accelerated, is excited by the streaming accelerated particles and the needed downstream turbulence is convected from the upstream region. The present code is to be modified to include a better description of particle scattering (pitch-angle instead of hard-sphere) and as iterative procedure for treating the self-excitation of the MHD turbulence.

Campbell, Roy K.↗
NASA NTRS1982

The flux ejection dynamo with small diffusivity. I - Basic properties. II - Illustrative examples

In the first part of this paper, the flux ejection dynamo in an infinitely broad convective layer of finite depth is treated in the limit of electrical conductivity, where the convective layer upper surface is open to empty space while the lower surface is closed to the passage of fluid and field. The idealized convective overturning used allows an exact description of the symmetry and distribution of the magnetic field carried with the fluid. The total flux of the mean horizontal field grows linearly with the number of convective cycles. A discussion is given of the boundary conditions to be applied to an astronomical body whose flux ejection dynamo operates at its surface. In the second part, examples are presented which illustrate the consequences of reverse flux ejection from the surface of a convective layer of conducting fluid. Reverse flux ejection generally has the opposite effect of magnetic buoyancy, burying the fields rather than bringing them through the surface. Reverse flux injection at the surface of an alpha-omega dynamo profoundly alters the character of the solutions of dynamo equations.

Parker, E. N.↗
NASA NTRS1994

On the Behavior of Three-dimensional Wave Packets in Viscously Spreading Mixing Layers

We consider analytically the evolution of a three-dimensional wave packet generated by an impulsive source in a mixing layer. The base flow is assumed to be spreading due to viscous diffusion. The analysis is restricted to small disturbances (linearized theory). A suitable high-frequency ansatz is used to describe the packet; the key elements of this description are a complex phase and a wave action density. It is found that the product of this density and an infinitesimal material volume convecting at the local group velocity is not conserved: there is a continuous interaction between the base flow and the wave action. This interaction is determined by suitable mode-weighted averages of the second and fourth derivatives of the base-flow velocity profile. Although there is some tendency for the dominant wave number in the packet to shift from the most unstable value toward the neutral value, this shift is quite moderate. In practice, wave packets do not become locally neutral in a diverging base flow (as do instability modes), therefore, they are expected to grow more suddenly than pure instability modes and do not develop critical layers. The group velocity is complex; the full significance of this is realized by analytically continuing the equations for the phase and wave action into a complex domain. The implications of this analytic continuation are discussed vis-a-vis the secondary instabilities of the packet: very small scale perturbations on the phase can grow very rapidly initially, but saturate later because most of the energy in these perturbations is convected away by the group velocity. This remark, as well as the one regarding critical layers, has consequences for the nonlinear theories.

Balsa, Thomas F.↗
NASA NTRS2002

Effect of Wind Velocity on Flame Spread in Microgravity

A three-dimensional, time-dependent model is developed describing ignition and subsequent transition to flame spread over a thermally thin cellulosic sheet heated by external radiation in a microgravity environment. A low Mach number approximation to the Navier Stokes equations with global reaction rate equations describing combustion in the gas phase and the condensed phase is numerically solved. The effects of a slow external wind (1-20 cm/s) on flame transition are studied in an atmosphere of 35% oxygen concentration. The ignition is initiated at the center part of the sample by generating a line-shape flame along the width of the sample. The calculated results are compared with data obtained in the 10s drop tower. Numerical results exhibit flame quenching at a wind speed of 1.0 cm/s, two localized flames propagating upstream along the sample edges at 1.5 cm/s, a single line-shape flame front at 5.0 cm/s, three flames structure observed at 10.0 cm/s (consisting of a single line-shape flame propagating upstream and two localized flames propagating downstream along sample edges) and followed by two line-shape flames (one propagating upstream and another propagating downstream) at 20.0 cm/s. These observations qualitatively compare with experimental data. Three-dimensional visualization of the observed flame complex, fuel concentration contours, oxygen and reaction rate isosurfaces, convective and diffusive mass flux are used to obtain a detailed understanding of the controlling mechanism, Physical arguments based on lateral diffusive flux of oxygen, fuel depletion, oxygen shadow of the flame and heat release rate are constructed to explain the various observed flame shapes.

Prasad, Kuldeep↗