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NASA NTRS1984

A convective model for turbulent mixing in rotating convection zones

The effects of rotation are included in an analytical model for the convective motions in a plane-parallel layer of an ideal fluid. The turbulent stress tensor, formed by taking products and averages of the various velocity components, is calculated for an arbitrary eddy size and shape. Heuristic formulae presented for determining the size and shape of the dominant eddy then give a fully specified stress tensor. Applications for this stress tensor in problems of stellar internal dynamics, heat flow, scalar diffusion, and dynamo theory are suggested. The resultant stresses tend to produce differential rotation profiles with rapidly rotating equators and interiors. The dynamo activity associated with these convective motions tends to occur near the lower boundary of the convection zone.

Hathaway, D. H.↗

NASA NTRS1995

Finite Element Analysis of Poroelastic Composites Undergoing Thermal and Gas Diffusion

A theory for time-dependent thermal and gas diffusion in mechanically time-rate-independent anisotropic poroelastic composites has been developed. This theory advances previous work by the latter two authors by providing for critical transverse shear through a three-dimensional axisymmetric formulation and using it in a new hypothesis for determining the Biot fluid pressure-solid stress coupling factor. The derived governing equations couple material deformation with temperature and internal pore pressure and more strongly couple gas diffusion and heat transfer than the previous theory. Hence the theory accounts for the interactions between conductive heat transfer in the porous body and convective heat carried by the mass flux through the pores. The Bubnov Galerkin finite element method is applied to the governing equations to transform them into a semidiscrete finite element system. A numerical procedure is developed to solve the coupled equations in the space and time domains. The method is used to simulate two high temperature tests involving thermal-chemical decomposition of carbon-phenolic composites. In comparison with measured data, the results are accurate. Moreover unlike previous work, for a single set of poroelastic parameters, they are consistent with two measurements in a restrained thermal growth test.

Salamon, N. J.↗

NASA NTRS1984

Turbulent compressible convection in a deep atmosphere. II - Two-dimensional results for main-sequence A5 and F0 type envelopes

In the present two-dimensional numerical study of turbulent compressible convection in the A5 and F0 main-sequence envelope types, ionization effects are included in the equation of state of the gas, and radiative transfer is modeled in a diffusive process with tabulated gas opacities. It is noted that the thermal effects of ionization significantly affect the dynamics of the flows and that an inversion of the mean density can be created and sustained in a dynamical situation. The substantial differences in the flows of A5 and F0 indicate development trends in the transition from the radiative to the convective mode of energy transport. As convection becomes more effective, the flow becomes more turbulent and the scaling effects of local scale heights become more significant.

Sofia, S.↗

NASA NTRS1987

A transport model of the turbulent scalar-velocity

Performance tests of the third-order turbulence closure for predictions of separating and recirculating flows in backward-facing steps were studied. Computations of the momentum and temperature fields in the flow domain being considered entail the solution of time-averaged transport equations containing the second-order turbulent fluctuating products. The triple products, which are responsible for the diffusive transport of the second-order products, attain greater significance in separating and reattaching flows. The computations are compared with several algebraic models and with the experimental data. The prediction was improved considerably, particularly in the separated shear layer. Computations are further made for the temperature-velocity double products and triple products. Finally, several advantages were observed in the usage of the transport equations for the evaluation of the turbulence triple products; one of the most important features is that the transport model can always take the effects of convection and diffusion into account in strong convective shear flows such as reattaching separated layers while conventional algebraic models cannot account for these effects in the evaluation of turbulence variables.

Amano, R. S.↗

NASA NTRS1988

Transport models of the turbulent velocity-temperature products for computations of recirculating flows

Amano, R. S.↗

NASA NTRS1991

The computation of standard solar models

Procedures for calculating standard solar models with the usual simplifying approximations of spherical symmetry, no mixing except in the surface convection zone, no mass loss or gain during the solar lifetime, and no separation of elements by diffusion are described. The standard network of nuclear reactions among the light elements is discussed including rates, energy production and abundance changes. Several of the equation of state and opacity formulations required for the basic equations of mass, momentum and energy conservation are presented. The usual mixing-length convection theory is used for these results. Numerical procedures for calculating the solar evolution, and current evolution and oscillation frequency results for the present sun by some recent authors are given.

Ulrich, Roger K.↗

NASA NTRS1995

Two-Flux and Green's Function Method for Transient Radiative Transfer in a Semi-Transparent Layer

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment, and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green's function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.

Siegel, Robert↗

NASA NTRS1990

Hopf bifurcation in the driven cavity

The algorithm employed in the present incompressible two-dimensional calculations of an impulsively-started lid-driven cavity has its basis in the time-dependent stream-function equation. While a Crank-Nicholson differencing scheme is used for the diffusion terms, the Adams-Bashforth scheme is used for the convection terms. The periodic asymptotic solutions obtained for Reynolds numbers of 5000 and 10,000 are found to be precisely periodic; it is demonstrated that they have reached asymptotic states. The indicators of that achievement are discussed.

Goodrich, John W.↗

NASA NTRS2002

Volcanic Plume Heights on Mars: Limits of Validity for Convective Models

Previous studies have overestimated volcanic plume heights on Mars. In this work, we demonstrate that volcanic plume rise models, as currently formulated, have only limited validity in any environment. These limits are easily violated in the current Mars environment and may also be violated for terrestrial and early Mars conditions. We indicate some of the shortcomings of the model with emphasis on the limited applicability to current Mars conditions. Specifically, basic model assumptions are violated when (1) vertical velocities exceed the speed of sound, (2) radial expansion rates exceed the speed of sound, (3) radial expansion rates approach or exceed the vertical velocity, or (4) plume radius grossly exceeds plume height. All of these criteria are violated for the typical Mars example given here. Solutions imply that the convective rise, model is only valid to a height of approximately 10 kilometers. The reason for the model breakdown is hat the current Mars atmosphere is not of sufficient density to satisfy the conservation equations. It is likely that diffusion and other effects governed by higher-order differential equations are important within the first few kilometers of rise. When the same criteria are applied to eruptions into a higher-density early Mars atmosphere, we find that eruption rates higher than 1.4 x 10(exp 9) kilograms per second also violate model assumptions. This implies a maximum extent of approximately 65 kilometers for convective plumes on early Mars. The estimated plume heights for both current and early Mars are significantly lower than those previously predicted in the literature. Therefore, global-scale distribution of ash seems implausible.

Glaze, Lori S.↗

NASA NTRS1986

Effects of three-dimensional heliospheric structures on cosmic-ray modulation

The theory of cosmic-ray transport in the heliosphere contains four distinct physical processes - diffusion, convection, adiabatic cooling, and drifts. The last of these has only recently been evaluated. Extrapolation of present understanding of the regions near the heliospheric equator to high heliographic latitudes leads to the conclusion that particle drift in the large-scale magnetic field plays an important role in cosmic-ray modulation. The large-scale, three-dimensional structure of the interplanetary magnetic field is therefore very important in understanding cosmic rays. Several key observed modulation effects are summarized, each of which is a natural consequence of drift, but which requires special assumptions if drift plays no role. It is concluded that particle drifts play an important and possibly dominant role in transport in the heliosphere.

Jokipii, J. R.↗

NASA NTRS1990

Steady-state thermal-solutal convection and diffusion in a simulated float zone

Models describing the steady-state thermal diffusion in a pure system, the thermal-solutal diffusion in a binary system, and heat and momentum transverse in a pure system are presented. The geometry of the model is described by a 2D Cartesian coordinate system that is applicable for crystal sheets. The melting, solidifying, and melt/gas interfacial shapes as well as the thermal, flow, and solutal profiles are analytically evaluated as functions of the heat and ambient temperature profiles and material properties. The solution procedure involves a coupled asymptotic/numerical approach which reduces the coupled set of partial differential equations to ordinary type. The results should be applicable in situations where melt flows are not intense enough to change the thermal field in pure systems, or where the physical properties of the melt are such that the convective field is decoupled from the thermal field, the latter being established primarily by diffusion.

Young, G. W.↗

NASA NTRS1977

Gravitational effects on chemically reacting laminar boundary layer flows over a horizontal flat plate

A theoretical study of the chemically reacting laminar boundary layer flow over a horizontal flat plate with gravitationally induced buoyant force is presented. A diffusion flame sheet model was used to describe the combustion process. The effects of gravity on the purely force convection flow can be characterized by a dimensionless coordinate quantity, which is involved in the generation of the governing equations. A numerical solution of the zero and first order governing equations subject to the appropriate physical boundary conditions was obtained. It is shown that the cross stream buoyancy induced body force acts effectively to produce a streamwise pressure gradient in the fluid adjacent to the plate surface. It is concluded that buoyancy plays an important role in boundary layer diffusion flames.

Lavid, M.↗

NASA NTRS1991

Analysis of a dusty wall jet

An analysis is given for the entrainment of dust into a turbulent radial wall jet. Equations are solved based on incompressible flow of a radial wall jet into which dust is entrained from the wall and transported by turbulent diffusion and convection throughout the flow. It is shown that the resulting concentration of dust particles in the flow depends on the difference between the applied shear stress at the surface and the maximum level of shear stress that the surface can withstand (varies as rho(sub d)a(sub g)D) i.e., the pressure due to the weight of a single layer of dust. The analysis is expected to have application to the downflow that results from helicopter and VTOL aircraft.

Lim, Hock-Bin↗

NASA NTRS1985

The modulation features of the long-period cosmic ray variations in connection with the sign change of the general magnetic field of the Sun

On the basis of the model and experimental investigations, the spatial distribution of cosmic ray anisotropy for the different epochs of solar activity is studied. A solution is offered to the anisotropic diffusion equation with regard to the electromagnetic conditions for the periods of minimum and maximum solar activity and cosmic ray particle drift in a regular interplanetary magnetic field. It is shown that the long period changes amplitude and phase of the diurnal variations of cosmic rays is limited not only by convection and diffusion of particles but also by the drift effect before and after the sing change of the general magnetic field of the Sun. The calculated model is compared with the results obtained on the basis of an analysis of the experimental data from the neutron super monitor station, and it is shown that for the periods when the lines of magnetic force of the Sun come from the Northern Hemisphere the phase of the first harmonic diurnal variation is shifted forwards to an earlier time.

Iskra, K.↗

NASA NTRS1996

Two-Flux Green's Function Analysis for Transient Spectral Radiation in a Composite

An analysis is developed for obtaining transient temperatures in a two-layer semitransparent composite with spectrally dependent properties. Each external boundary of the composite is subjected to radiation and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. This produces internal reflections at the boundaries and the internal interface; the reflections are assumed diffuse. Spectral results using the Green's function method are verified by comparing with numerical solutions using the exact radiative transfer equations. Transient temperature distributions are given to illustrate the effect of radiative heating on one side of a composite with external convective cooling. The protection of a material from incident radiation is illustrated by adding scattering to the layer adjacent to the radiative source.

Siegel, Robert↗

NASA NTRS1997

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

Bune, Andris V.↗

NASA NTRS1980

Velocity and concentration distribution in a Stefan diffusion tube

Numerical solutions for the diffusion- and gravity-driven flow in a cylindrical Stefan tube were obtained from the coupled diffusion and Navier-Stokes equations of Peclet numbers 0.3, 1 and 5. Distributions of binary component concentrations and velocities were calculated. The mass average velocity is parabolic in nature, except at high Peclet numbers. The solvent is not stagnant but recirculates, even in the absence of gravity. Radial concentration gradients develop which act convectively destabilizing. Consequences for the deduction of diffusion coefficients from Stefan tube experiments are discussed.

Markham, B. L.↗

NASA NTRS1994

Incorporating interfacial phenomena in solidification models

A general methodology is available for the incorporation of microscopic interfacial phenomena in macroscopic solidification models that include diffusion and convection. The method is derived from a formal averaging procedure and a multiphase approach, and relies on the presence of interfacial integrals in the macroscopic transport equations. In a wider engineering context, these techniques are not new, but their application in the analysis and modeling of solidification processes has largely been overlooked. This article describes the techniques and demonstrates their utility in two examples in which microscopic interfacial phenomena are of great importance.

Beckermann, Christoph↗