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NASA NTRS1988

Dynamics of two fluids under periodic acceleration

The evolution of the interface between two fluids confined in a rectangular cavity is investigated numerically to predict its transient behavior. These computations address mixing characteristics of fluids under microgravity conditions, particularly g-jitter conditions resulting from aircraft vibration or crew motion, and have applications in solution crystal growth. The two-dimensional formulation employs the Boussinesq approximation and treats the mixing of two fluids as an initial value problem with a prescribed concentration field. For fluid mixing of practical applications inside a cavity, it is shown that nonlinear convective transport can dominate over both viscous and molecular diffusion. However, viscous diffusion can become important for low Reynolds number or certain cavity sizes. A stacking phenomenon is shown to occur for aspect ratios (Ar) approximately between 5 to 10. For aspect ratios in the neighborhood of 0.1 to 0.2, inner cells evolve at the interface with increasing time. For a square cavity of Ar = 1, chaotic mixing of the fluid appears to occur for a Stokes-Reynolds number greater than about 5.

Duval, Walter M. B.↗

NASA NTRS1990

Buoyancy-driven instability in a vertical cylinder: Binary fluids with Soret effect. I - General theory and stationary stability results

The buoyancy-driven instability of a monocomponent or binary fluid completely contained in a vertical circular cylinder is investigated, including the influence of the Soret effect for the binary mixture. The Boussinesq approximation is used, and the resulting linear stability problem is solved using a Galerkin technique. The analysis considers fluid mixtures ranging from gases to liquid metals. The flow structure is found to depend strongly on both the cylinder aspect ratio and the magnitude of the Soret effect. The predicted stability limits are shown to agree closely with experimental observations.

Hardin, G. R.↗

NASA NTRS1990

Numerical simulation of 3-D Benard convection with gravitational modulation

In this numerical study, randomly and sinusoidally modulated gravitational fields imposed on three-dimensional Rayleigh-Benard convection are investigated in an effort to understand the effects of vibration (G-Jitter) on fluid systems. The time-dependent, Navier-Stokes equations and the energy equation with Boussinesq approximations are solved by a semi-implicit, pseudospectral procedure. An analysis of energy balances indicates that with increasing modulation amplitude, transition from synchronous to relaxation oscillation goes through the subharmonic response. Random modulations are found to be less stabilizing than sinusoidal and are shown to impose three-dimensionality on the flow for some parameter ranges both at terrestrial and zero base gravity conditions.

Biringen, S.↗

NASA NTRS1990

Stability of an oscillated fluid with a uniform density gradient

Instabilities in a fluid with a constant density gradient that is subject to arbitrarily oriented oscillatory accelerations are considered. With the Boussinesq approximation and for the case of an unbounded fluid, transformation to Lagrangian coordinates allows the reduction of the problem to an ordinary differential equation for each three-dimensional wavenumber. The problem has three parameters: the nondimensional amplitude R of the base-state oscillation, the nondimensional level of background steady acceleration, which for some cases can be represented in terms of a local (in time) Richardson number Ri, and the Prandtl number Pr. Some general bounds on stability are derived. For Pr = 1 closed-form solutions are found for impulse (delta function) accelerations and a general asymptotic solution is constructed for large R and general imposed accelerations. The asymptotic solution takes advantage of the fact that at large R wave growth is concentrated at 'zero points'. These are times when the effective vertical wavenumber passes through zero. Kelvin-Helmholtz instabilities are found to dominate at low R, while Rayleigh-Taylor instabilities dominate at high R. At high R, the uniform shear of the Kelvin-Helmholtz case tends to distort and weaken instability waves. With unsteady flows, Ri = 1/4 is no longer an instability limit. Significant instabilities have been found for sinusoidal forcing for Ri up to 0.6.

Jacqmin, David↗

NASA NTRS1991

Nonadiabatic and three-dimensional effects in compressible turbulent boundary layers

A defect stream function formulation for nonadiabatic flow with small crossflow is developed. The first-integral property of this formulation provides for two removal of the streamline curvature term in the governing equation so that the form of the reduced equation for small crossflow is the same as that for two dimensional flow. The combined law of the wall and wake is used in place of the no-slip boundary condition. The tangential velocity equation for law-of-the-wall flow is shown to be the same for three-dimensions as for two when the Boussinesq approximation applies, and a closed form solution for the crossflow angle in the inner region is obtained. Analytic solutions for nonadiabatic, compressible, equilibrium flow with a Clauser outer-region eddy-viscosity model are obtained, and excellent agreement with experimental skin friction and velocity profile data for nonadiabatic, compressible flat-plate flow is achieved. An analytic solution for a linear inner-region eddy-viscosity model is also obtained; the wake function part of this solution is found to be inconsistent with the empirically established law of the wake.

Barnwell, Richard W.↗

NASA NTRS1991

Time-accurate finite difference solutions to the incompressible Navier-Stokes/energy equations

Two new algorithms for solving coupled Navier-Stokes and energy equations are presented. The algorithms are compared with available Navier-Stokes solutions for the model problem of a driven-cavity-flow over a range of Reynolds numbers. It is noted that the algorithms represent two different implementations of the fractional step approach to the solution of the coupled Navier-Stokes and energy equations using the Boussinesq approximation.

Mirfakhraee, Ali↗

NASA NTRS1991

Prediction of jet mean flow structure in support of HSCT noise suppression concepts

The paper describes the application of techniques based on computational fluid dynamics to the simulation of jet flowfields. A solution code for the Reynolds-averaged Navier-Stokes equations is supplemented by conventional two-equation turbulence models based on the Boussinesq approximation. The axisymmetric SCIPVIS code is enhanced with the PARCH and CRAFT codes to examine plug-jet flowfields and imperfectly expanded axisymmetric free round jets. The sensitivity of shock/boundary layer interactions is observed in simulations of the plug case, and the adaptive gridding in the disk region and turbulence levels generated at the triple point are identified as areas in the Mach case that require improvement. Jet-wave structure in the region beyond the first several shock cells can be predicted, and turbulence modeling can be undertaken with respect to improving compressibility, length scale, vorticity, and energy budget. The mean flow structure of imperfectly expanded jets can be studied to develop related noise suppression concepts for the High-Speed Civilian Transport (HSCT).

Sinha, N.↗

NASA NTRS1991

Vertical solidification of dendritic binary alloys

Three numerical techniques are employed to analyze the influence of thermosolutal convection on defect formation in directionally solidified (DS) alloys. The finite-element models are based on the Boussinesq approximation and include the plane-front model and two plane-front models incorporating special dendritic regions. In the second model the dendritic region has a time-independent volume fraction of liquid, and in the last model the dendritic region evolves as local conditions dictate. The finite-element models permit the description of nonlinear thermosolutal convection by treating the dendritic regions as porous media with variable porosities. The models are applied to lead-tin alloys including DS alloys, and severe segregation phenomena such as freckles and channels are found to develop in the DS alloys. The present calculations and the permeability functions selected are shown to predict behavior in the dendritic regions that qualitatively matches that observed experimentally.

Heinrich, J. C.↗

NASA NTRS1992

The program FANS-3D (finite analytic numerical simulation 3-dimensional) and its applications

In this study, the program named FANS-3D (Finite Analytic Numerical Simulation-3 Dimensional) is presented. FANS-3D was designed to solve problems of incompressible fluid flow and combined modes of heat transfer. It solves problems with conduction and convection modes of heat transfer in laminar flow, with provisions for radiation and turbulent flows. It can solve singular or conjugate modes of heat transfer. It also solves problems in natural convection, using the Boussinesq approximation. FANS-3D was designed to solve heat transfer problems inside one, two and three dimensional geometries that can be represented by orthogonal planes in a Cartesian coordinate system. It can solve internal and external flows using appropriate boundary conditions such as symmetric, periodic and user specified.

Bravo, Ramiro H.↗

NASA NTRS1992

Direct simulation of the stably stratified turbulent Ekman layer

The Navier-Stokes equations and the Boussinesq approximation were used to compute a 3D time-dependent turbulent flow in the stably stratified Ekman layer over a smooth surface. The simulation data are found to be in very good agreement with atmospheric measurements when nondimensionalized according to Nieuwstadt's local scaling scheme. Results suggest that, when Reynolds number effects are taken into account, the 'constant Froud number' stable layer model (Brost and Wyngaard, 1978) and the 'shearing length' stable layer model (Hunt, 1985) for the dissipitation rate of turbulent kinetic energy are both valid. It is concluded that there is good agreement between the direct numerical simulation results and large-eddy simulation results obtained by Mason and Derbyshire (1990).

Coleman, G. N.↗

NASA NTRS1994

Local shear instabilities in weakly ionized, weakly magnetized disks

We extend the analysis of axisymmetric magnetic shear instabilities from ideal magnetohydrodynamic (MHD) flows to weakly ionized plasmas with coupling between ions and neutrals caused by collisions, ionization, and recombination. As part of the analysis, we derive the single-fluid MHD dispersion relation without invoking the Boussinesq approximation. This work expands the range of applications of these instabilities from fully ionized accretion disks to molecular disks in galaxies and, with somewhat more uncertainty, to protostellar disks. Instability generally requires the angular velocity to decrease outward, the magnetic field strengths to be subthermal, and the ions and neutrals to be sufficiently well coupled. If ionization and recombination processes can be neglected on an orbital timescale, adequate coupling is achieved when the collision frequency of a given neutral with the ions exceeds the local epicyclic freqency. When ionization equilibrium is maintained on an orbital timescale, a new feature is present in the disk dynamics: in contrast to a single-fluid system, subthermal azimuthal fields can affect the axisymmetric stability of weakly ionized two-fluid systems. We discuss the underlying causes for this behavior. Azimuthal fields tend to be stabilizing under these circumstances, and good coupling between the neutrals and ions requires the collision frequency to exceed the epicyclic frequency by a potentially large secant factor related to the magnetic field geometry. When the instability is present, subthermal azimuthal fields may also reduce the growth rate unless the collision frequency is high, but this is important only if the field strengths are very subthermal and/or the azimuthal field is the dominant field component. We briefly discuss our results in the context of the Galactic center circumnuclear disk, and suggest that the shear instability might be present there, and be responsible for the observed turbulent motions.

Blaes, Omer M.↗

NASA NTRS1996

Non-linear k-epsilon-v(sup 2)(bar) modeling with application to high-lift

The k-epsilon-v(sup 2)(bar) model has been investigated to quantify its predictive performance on two high-lift configurations: 2D flow over a single-element aerofoil, involving closed-type separation; 3D flow over a prolate spheroid, involving open-type separation. A 'code-friendly' modification has been proposed which enhances the numerical stability, in particular, for explicit and uncoupled flow solvers. As a result of introducing Reynolds-number dependence into a coefficient of the s-equation, the skin-friction distribution for the by-pass transitional flow over a flat plate is better predicted. In order to improve deficiencies arising from the Boussinesq approximation, a nonlinear stress-strain constitutive relation was adopted, in which the only one free constant is calibrated on the basis of DNS data, and the Reynolds-stress anisotropy near the wall is fairly well represented.

Lien, F. S.↗

NASA NTRS1997

A Numerical Method for Incompressible Flow with Heat Transfer

A numerical method for the convective heat transfer problem is developed for low speed flow at mild temperatures. A simplified energy equation is added to the incompressible Navier-Stokes formulation by using Boussinesq approximation to account for the buoyancy force. A pseudocompressibility method is used to solve the resulting set of equations for steady-state solutions in conjunction with an approximate factorization scheme. A Neumann-type pressure boundary condition is devised to account for the interaction between pressure and temperature terms, especially near a heated or cooled solid boundary. It is shown that the present method is capable of predicting the temperature field in an incompressible flow.

Sa, Jong-Youb↗

NASA NTRS1999

Modeling Studies of PVT Growth of ZnSe: Current Status and Future Course

Bulk growth of wide band gap II-VI semiconductors by physical vapor transport (PVT) has been developed and refined over the past several years at NASA Marshall Space Flight Center. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using a two-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and a compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles are provided. The simulations show that the Stefan flux dominates the system flow field and the subtle gravitational effects can be gauged by subtracting this flux from the calculated profiles. Shear flows, due to solutal buoyancy, of the order of 50 microns/s for the liorizont,-d growth orientation and 10 microns/s for the vertical orientation are predicted. Whether these flows can fully account for the observed gravity related growth morphological effects and inhomogeneous solute and dopant distributions is a matter of conjecture. A template for future modeling efforts in this area is suggested which incorporates a mathematical approach to the tracking of the growth front based on energy of formation concepts.

Ramachandran, N.↗

NASA NTRS1999

Double Diffusive Convection in Materials Processing

A great number of crystals grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity (g-jitter). As a specific example, past HgCdTe crystal growth space experiments by Lehoczky and co-workers indicate radial compositional asymmetry in the grown crystals. In the case of HgCdTe the rejected component into the melt upon solidification is HgTe which is denser than the melt. The space grown crystals indicate the presence of three dimensional flow with the heavier HgTe-rich material clearly aligned with the residual gravity (0.55-1.55 micro g) vector. This flow stems from double-diffusive convection, namely, thermal and solutal buoyancy driven flow in the melt. The study of double-diffusive convection is multi-faceted and rather vast. In our investigation, we seek to focus on one specific aspect of this discipline that is of direct relevance to materials processing especially crystal growth, namely, the side ways heating regime. This problem has been widely studied, both experimentally and numerically, in the context of solar ponds wherein the system is characterized by a linear salt (solutal) gradient with an imposed lateral temperature gradient. The induced flow instabilities arise from the wide disparity between the fluid thermal diffusivity and the solute diffusivity. The extension of the analysis to practical crystal growth applications has however not been rigorously made and understood. One subtle but important difference in crystal growth systems is the fact that die system solute gradient is non-linear (typically exponential). Besides, the crystal growth problem has the added complexities of solidification, both lateral and longitudinal thermal gradients and segregation phenomena in systems where binary and ternary compounds are being grown. This paper treats the side ways heating problem alone in a model fluid system. Results from detailed numerical calculations, mainly two dimensional are provided. The interactions between a non-linear solute gradient and an imposed transverse thermal gradient are investigated. The buoyancy effects are treated in the traditional Boussinesq approximation and also in a more complete density formulation to address recent concerns of the first approach especially in simulations of the system response in a reduced gravity environment. Detailed flow, temperature and solute field plots along with heat and mass transfer results are presented in the paper. Implications to practical crystal growth systems as discerned from the modeling results are also explored and reported.

Ramachandra, Narayanan↗

NASA NTRS1999

Numerical Modeling of Crystal of ZnSe by Physical Vapor Transport - Towards a more Comprehensive Formulations

Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of PVT growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided. The effect of gravity on the process from numerical computations shows subtle effects although experimental evidence from vertically and horizontally grown samples show dramatic evidence of gravitational effects. The shortcomings of the problem formulation will be discussed and a framework will be provided leading up towards a more comprehensive model of PVT systems.

Ramachandran, N.↗

NASA NTRS1998

Crystal Growth of ZnSe by Physical Vapor Transport: A Modeling Study

Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of Physical Vapor Transport (PVT) growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe arc reported in this paper. The PVI process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The preliminary results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided.

Ramachandran, Narayanan↗

NASA NTRS1994

Incompressible Navier-Stokes Computations with Heat Transfer

The existing pseudocompressibility method for the system of incompressible Navier-Stokes equations is extended to heat transfer problems by including the energy equation. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. Both forced and natural convection problems are examined. Numerical results from turbulent reattaching flow behind a backward-facing step will be compared against experimental measurements for the forced convection case. The validity of Boussinesq approximation to simplify the buoyancy force term will be investigated. The natural convective flow structure generated by heat transfer in a vertical rectangular cavity will be studied. The numerical results will be compared by experimental measurements by Morrison and Tran.

Kiris, Cetin↗