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NASA NTRS1991

A numerical study of the direct contact condensation on a horizontal surface

The results of a numerical study of the direct contact condensation on a slowly moving horizontal liquid surface are presented. The geometrical configuration and the input conditions used to obtain numerical solutions are representative to those of experiments of Celata et al. The effects of Prandtl number (Pr), inflow Reynolds number, and Richardson number on the condensation rate are investigated. Numerical predictions of condensation rate for laminar flow are in good agreement with experimental data. The effect of buoyancy on the condensation rate is characterized by Richardson number. A correlation based on the numerical solutions is developed to predict the average condensation Nusselt number in terms of Richardson number, Peclet number, and inflow Reynolds number.

Hasan, M. M.↗

NASA NTRS1991

Are the Equatorial Highlands on Venus formed by mantle plume diapirs?

Several origins have been proposed for the Equatorial Highlands on Venus, including spreading centers and plume-related uplift. Recently, the spreading center hypothesis has been shown to be incompatible with the measured geoid and topography variations over the highlands. It is also difficult to reconcile the range of geoid anomalies over the highlands with a steady-state plum model. There is a large variation in admittance values (geoid/topography ratios) among highland regions. This variation suggests that different uplifted regions represent distinct stages in a time dependent process. It has been proposed that the Beta Regio, Thetis Regio, Ovda Regio, and Artemis Plateau Equatorial Highland Regions are formed by large mantel diapirs. According to this model, topography and geoid height decrease with increasing age of the highland, as the diapir spreads out beneath the lithosphere. In order to determine if the diapir model is compatible with the sequence of tectonic and volcanic events recorded in the surface geology of the highlands, a series of finite difference calculations were made of the ascent and partial melting of a spherical thermal diapir in an incompressible, infinite Prandtl number, isoviscous fluid.

Olson, Peter↗

NASA NTRS1991

Calculations and curve fits of thermodynamic and transport properties for equilibrium air to 30000 K

A self-consistent set of equilibrium air values were computed for enthalpy, total specific heat at constant pressure, compressibility factor, viscosity, total thermal conductivity, and total Prandtl number from 500 to 30,000 K over a range of 10(exp -4) atm to 10(exp 2) atm. The mixture values are calculated from the transport and thermodynamic properties of the individual species provided in a recent study by the authors. The concentrations of the individual species, required in the mixture relations, are obtained from a free energy minimization calculation procedure. Present calculations are based on an 11-species air model. For pressures less than 10(exp -2) atm and temperatures of about 15,000 K and greater, the concentrations of N(++) and O(++) become important, and consequently, they are included in the calculations determining the various properties. The computed properties are curve fitted as a function of temperature at a constant value of pressure. These curve fits reproduce the computed values within 5 percent for the entire temperature range considered here at specific pressures and provide an efficient means for computing the flowfield properties of equilibrium air, provided the elemental composition remains constant at 0.24 for oxygen and 0.76 for nitrogen by mass.

Gupta, Roop N.↗

NASA NTRS1992

A near-wall four-equation turbulence model for compressible boundary layers

A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon(sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, the numerical predictions are in very good agreement with measurements and there are significant improvements in the predictions of mean flow properties at high Mach numbers.

Sommer, T. P.↗

NASA NTRS1992

Streamwise vortices in heated boundary layers

The nonlinear instability of the boundary layer on a heated flat plate placed in an oncoming flow is investigated. Such flows are unstable to stationary vortex instabilities and inviscid traveling wave disturbances governed by the Taylor-Goldstein equation. For small temperature differences the Taylor-Goldstein equation reduces to Rayleigh's equation. When the temperature difference between the wall and free stream is small the preferred mode of instability is a streamwise vortex. It is shown in this case that the vortex, assumed to be of small wavelength, restructures the underlying mean flow to produce a profile which can be massively unstable to inviscid traveling waves. The mean state is shown to be destabilized or stabilized to inviscid waves depending on whether the Prandtl number is less or greater than unity.

Hall, Philip↗

NASA NTRS1990

The structure of turbulent channel flow with passive scalar transport

The simulation of turbulent channel flow, with various passive markers, was examined to investigate the local mechanisms of passive scalar transport. We found significant differences between the local transport of heat and momentum, even when the molecular and turbulent Prandtl numbers are of order one. These discrepancies can be attributed to the role of the pressure. We also found that the heat is a poor marker of the vorticity field outside of the near wall region and that scalar transport over significant distances results from the aggregate effect of many turbulent eddies.

Guezennec, Y.↗

NASA NTRS1990

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Glass, Christopher E.↗

NASA NTRS1991

Recent developments in oscillatory thermocapillary flows

Recent research aimed at understanding the transition of thermocapillary flows from steady to oscillatory states is described. Particular attention is given to conditions for the onset of the oscillations and how they are influenced by changes in configuration such as geometry and thermal signature. It is shown that, for high Prandtl number fluids, the oscillations are caused by the coupling among the imposed thermal signature, the surface flow, and the surface deformations. The surface deformations cause a time lag between the surface and bulk-return flows and alter the driving force (surface-temperature gradient).

Ostrach, Simon↗

NASA NTRS1991

Buoyancy effects of a growing, isolated dendrite

The buoyancy effect of a growing isolated dendrite on the solidification process in the undercooling liquid material was investigated by developing an analytic solution to the growth/convection problem in powers of a buoyancy parameter G. The solution depends on the Prandtl number P and the Stefan number S (undercooling) for the local velocity and thermal fields and also the buoyant alteration of the interface shape. Results suggest that buoyancy effect for metals (low P) may be qualitatively different from that for organics (high P).

Canright, D.↗

NASA NTRS1992

Stability analysis of surface tension effects on a double-diffusive layer

The linear stability characteristics of a fluid layer with simultaneous temperature and concentration gradients in a reduced gravity field are examined. The surface tension of the fluid is assumed to be a linear function of temperature and concentration. It is concluded that a small amount of gravity may damp out oscillatory instability or may alter its dynamics so that instability appears as steady convection. The onset of salt-finger instability may be in the overstable mode due to the surface tension method. The Lewis and Prandtl numbers of the material have a strong influence on the stability boundaries and onset characteristics of the system.

Chen, C. F.↗

NASA NTRS1992

Dynamo action in stratified convection with overshoot

Results are presented from direct simulations of turbulent compressible hydromagnetic convection above a stable overshoot layer. Spontaneous dynamo action occurs followed by saturation, with most of the generated magnetic field appearing as coherent flux tubes in the vicinity of strong downdrafts, where both the generation and destruction of magnetic field is most vigorous. Whether or not this field is amplified depends on the sizes of the magnetic Reynolds and magnetic Prandtl numbers. Joule dissipation is balanced mainly by the work done against the magnetic curvature force. It is this curvature force which is also responsible for the saturation of the dynamo.

Nordlund, Ake↗

NASA NTRS1992

Mixed convection in a horizontal rectangular channel - Experimental and numerical velocity distributions

Mixed convection in a rectangular channel (width/height = 2) with bottom-heated and top-cooled sections is studied by laser Doppler anemometry in nitrogen at Ra = 22,200 and Re = 18.75, 36, and 54. At the lower Re values, symmetry breaking is observed in steady but spatially oscillating flows that prevail over a certain distance from the leading edge of the differentially heated section. Further downstream, unsteady flows are found even for Re = 18.75. Numerical models are used to investigate the effects of adiabatic, conducting (with a conductive-convective heat transfer coefficient), and perfectly conducting side walls; channel tilts and Prandtl number dependence. Good agreement between calculations and experiment is obtained for longitudinal convective roll velocities. The transverse velocities are found to be independent of Re.

Nyce, Thomas A.↗

NASA NTRS1992

Effect of free surface shape on combined thermocapillary and natural convection

Combined thermocapillary and natural convection in an open square cavity with differentially-heated side walls is studied numerically as well as experimentally. The test fluid is silicone oil with Prandtl number of 105. The shape of fluid-free surface is made either flat or curved to study its effect on the flow. A finite difference scheme to deal with a curved free surface is developed. The experimental results shown agree with the numerical results. With the curved-free surface, the flow and local heat transfer rate are reduced in the corner regions, and a sharp peak in heat transfer rate at the top edge of the cold wall disappears.

Kamotani, Yasuhiro↗

NASA NTRS1992

On the structure of cellular solutions in Rayleigh-Benard-Marangoni flows in small-aspect-ratio containers

Multiple steady flow patterns occur in surface-tension/buoyancy-driven convection in a liquid layer heated from below (Rayleigh-Benard-Marangoni flows). Techniques of numerical bifurcation theory are used to study the multiplicity and stability of two-dimensional steady flow patterns (rolls) in rectangular small-aspect-ratio containers as the aspect ratio is varied. For pure Marangoni flows at moderate Biot and Prandtl number, the transitions occurring when paths of codimension 1 singularities intersect determine to a large extent the multiplicity of stable patterns. These transitions also lead, for example, to Hopf bifurcations and stable periodic flows for a small range in aspect ratio. The influence of the type of lateral walls on the multiplicity of steady states is considered. 'No-slip' lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to 'slippery' sidewalls) through the occurrence of saddle node bifurcations. In this way 'no-slip' sidewalls induce a selection of certain patterns, which typically have the largest Nusselt number, through secondary bifurcation.

Dijkstra, Henk A.↗

NASA NTRS1992

Turbulent transport of a passive-scalar field by using a renormalization-group method

A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.

Hossain, Murshed↗

NASA NTRS1993

Centrifuge in space fluid flow visualization experiment

A prototype flow visualization system is constructed to examine buoyancy driven flows during centrifugation in space. An axial density gradient is formed by imposing a thermal gradient between the two ends of the test cell. Numerical computations for this geometry showed that the Prandtl number plays a limited part in determining the flow.

Arnold, William A.↗

NASA NTRS1993

Structure of axisymmetric mantle plumes

The structure of axisymmetric subsolidus thermal plumes in the earth's lower mantle is inferred from calculations of axisymmetric thermal plumes in an infinite Prandtl number fluid with thermally activated viscosity. The velocity and temperature distribution is determined for axisymmetric convection above a heated disk in an incompressible fluid cylinder 2,400 km in height and 1,200 km in diameter. Several calculations of plumes with heat transport in the range 100-400 GW, similar to the advective heat transport at the Hawaiian hotspot, are presented. Hotspot formation by plumes originating at the base of the mantle requires both large viscosity variations and a minimum heat transport.

Olson, Peter↗

NASA NTRS1991

Two-dimensional numerical modeling and solution of convection heat transfer in turbulent He II

Numerical schemes are employed to investigate heat transfer in the turbulent flow of He II. FEM is used to solve a set of equations governing the heat transfer and hydrodynamics of He II in the turbulent regime. Numerical results are compared with available experimental data and interpreted in terms of conventional heat transfer parameters such as the Prandtl number, the Peclet number, and the Nusselt number. Within the prescribed Reynolds number domain, the Gorter-Mellink thermal counterflow mechanism becomes less significant, and He II acts like an ordinary fluid. The convection heat transfer characteristics of He II in the highly turbulent regime can be successfully described by using the conventional turbulence and heat transfer theories.

Zhang, Burt X.↗