Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “RAYLEIGH NUMBER”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

The spectrum of steady state turbulent convection.

Based on Heisenberg's statistical theory of turbulence, a model for steady state turbulent convection is herein proposed, and on the basis of this model, equations for the energy spectrum for steady state turbulent convection are derived. The spectrum is obtained from the solution of a nonlinear integral equation. After the integral equation is brought into a universally valid nondimensional form, it is transformed into a nonlinear first order differential equation to be solved numerically, with the Rayleigh number appearing as the only parameter. The energy spectrum has a substantial deviation from the Kolmogoroff law, as a result of the buoyancy force acting on the rising and falling eddies. The presented theory may be applicable to convection in planetary and stellar atmospheres wherein the radiative heat transport is small.

Winterberg, F.↗
NASA NTRS1974

Studies of heat source driven natural convection

Natural convection energy transport in a horizontal layer of internally heated fluid with a zero heat flux lower boundary, and an isothermal upper boundary, has been studied. Quantitative information on the time-mean temperature distribution and the fluctuating component of temperature about the mean temperature in steady turbulent convection are obtained from a small thermocouple inserted into the layer through the upper bounding plate. Data are also presented on the development of temperature at several vertical positions when the layer is subject to both a sudden increase and to a sudden decrease in power input. For changes of power input from zero to a value corresponding to a Rayleigh number much greater than the critical linear stability theory value, a slight hysteresis in temperature profiles near the upper boundary is observed between the heat-up and cool-down modes.

Kulacki, F. A.↗
NASA NTRS1974

Magneto-fluid-mechanics free convection turbulent flow

The present work is an experimental study of the influence of a uniform magnetic field on the structure of a free convection turbulent boundary layer in a conducting fluid. The boundary layer was formed along the heated vertical wall of a cell. The applied magnetic field was normal to the wall. The measured mean temperature profiles, temperature turbulent intensity distributions, and temperature spectra along the wall, indicated that transition from turbulent to laminar flow occurs at a constant value of the ratio (Rayleigh number)/(Hartmann number). The study of the recorded spectra indicated that the presence of the magnetic field enhances the mechanism of turbulent suppression due to the buoyancy forces. Finally, a possible mechanism by which turbulence is suppressed by the presence of a magnetic field is discussed.

Papailiou, D. D.↗
NASA NTRS1979

Sample stream distortion modeled in continuous-flow electrophoresis

Buoyancy-induced disturbances in an electrophoresis-type chamber were investigated. Five tracer streams (latex) were used to visualize the flows while a nine-thermistor array sensed the temperature field. The internal heating to the chamber was provided by a 400 Hz electrical field. Cooling to the chamber was provided on the front and back faces and, in addition, on both chamber side walls. Disturbances to the symmetric base flow in the chamber occurred in the broad plane of the chamber and resulted from the formation of lateral and axial temperature gradients. The effect of these gradients was to retard or increase local flow velocities at different positions in the chamber cross section, which resulted in lateral secondary flows being induced in the broad plane of the chamber. As the adverse temperature gradients increased in magnitude, the critical Rayleigh number was approached and reverse (separated) flow became apparent, which, subsequently, led to the onset of time variant secondary flows.

Rhodes, P. H.↗
NASA NTRS1979

Parameterized convection within the moon and the terrestrial planets

For a fluid layer or a self-gravitating fluid sphere uniformly heated from within, the internal temperature can be parameterized in terms of the appropriate Rayleigh number. The heat generation term includes both radioactive heat release and transient heating or cooling. This parameterization has been verified by comparisons with laboratory experiments. Thermal history calculations have been carried out for the earth, Venus, Mars, Mercury, and the moon. The results for the earth and Venus indicate that two scales of convection are occurring, one including the surface plates and the second occurring beneath the surface plates. In all cases the present heat flows are between seven and twelve per cent greater than the values obtained assuming a steady state balance between heat flow and internal heat generation.

Turcotte, D. L.↗
NASA NTRS1980

Bifurcation and stability in a model of moist convection in a shearing environment

The truncated spectral system (model I) of shallow moist two-dimensional convection discussed by Shirer and Dutton (1979) is expanded to eleven coefficients (model II) in order to include a basic wind. Cloud streets, the atmospheric analog of the solutions to model II, are typically observed in an environment containing a shearing basic motion field. Analysis of the branching behavior of solutions to mode II shows that, if the basic wind direction varies with height, very complex temporal behavior is possible as the modified Rayleigh number HR is increased sufficiently. The first convective solution is periodic, corresponding to a cloud band that propagates downwind; but secondary branching to a two-dimensional torus can occur for larger values of HR. Orientation band formulas are derived whose predictions generally agree with the results of previous studies.

Shirer, H. N.↗
NASA NTRS1980

Material properties for mantle convection consistent with observed surface fields

An attempt is made to derive constraints on mantle convection from observed surface fields: plate velocities, gravity, topography and heat flow. The spherical harmonic spectra of the fields are expressed in terms of a spectral magnitude and slope, and requirements for the minimal representation of the equations for mantle convection are discussed. The effects of the boundary layer represented by the surface fields on convection at the mantle surface and at deeper levels are then examined, and a mean value of the effective mantle viscosity of approximately 10 to the 23rd g/cm per sec is obtained, together with values of 10 to the 8th and 10 to the 7th for the Rayleigh numbers of whole mantle and upper mantle convection, respectively. Consideration is then given to the compositional, thermal and rheological aspects of mantle convection, and it is pointed out that constraints on the depth and other properties of convection will require more detailed modeling using the relationships between the harmonic coefficients of the surface fields.

Kaula, W. M.↗
NASA NTRS1981

Numerical modeling of diffusive-convective physical vapor transport in cylindrical vertical ampoules

Diffusive-convective physical vapor transport (PVT) in cylindrical, vertical ampoules of aspect ratio (length/radius) between 0.5 and 10 was modeled numerically. The transport of a crystal forming component through an inert component that undergoes zero net transport was considered. Systems were treated in which: (1) with unequal molecular weight of the components and with temperature gradients typically employed in PVT, convective flow arises dominantly from solutal density gradients; and (2) with equal molecular weight of the components, convective flow can arise only from thermal expansion. It was found that, due to the diffusion-induced horizontal density gradients, buoyancy-driven convective flows are superimposed on the diffusive-advective fluxes without threshold. Net recirculation sets in adjacent to the growing interface, in contrast to the corresponding monocomponent situation where marginally stable convective modes fill the whole fluid space. Depending on the orientation of the main transport direction with respect to gravity, convection can either reduce or enhance the diffusion-induced radial concentration gradients. Significant enhancement of the net transport rate was found to occur only when the whole vapor space between source and growing crystal is filled by a convective recirculation roll. Solutal and thermal convection results are similar; yet for quantitative discussions, thermal and solutal Rayleigh numbers are not interchangeable in contrast to convective situations that lack net mass transport across the fluid space.

Markham, B. L.↗
NASA NTRS1981

Transient thermal convection in microgravity

The unsteady two-dimensional thermal convection in a cylinder due to a transient acceleration solved for a step-function excitation. From this, the solution was obtained for an arbitrary time-dependent acceleration. The solutions are valied for sufficiently low Rayleigh numbers and therefore, relevant to microgravity fields. As an example, two graphs are presented for he convection resulting from the movement of an astronaut inside the Shuttle. The analysis can be applied to obtain any other convective flows such as those caused by g-jitter or variable rotation of the Shuttle.

Dressler, R. F.↗
NASA NTRS1981

Topographic forcing of supercritical convection in a porous medium such as the oceanic crust

Experiments carried out with a Hele-Shaw cell indicate that above the critical Rayleigh number, topography does not control the convection pattern, except when the topographic wavelength is comparable to the depth of water penetration. Scaled to the depth of the layer, the convective wavenumbers are restricted to values between 2.5 and 4.8 - a range that brackets pi, the natural wavenumber for convection in a porous slab with planar, isothermal, impermeable boundaries. Topographies within this range are found to control the circulation pattern perfectly, with downwelling under valleys and upwelling aligned with topographic height. Other topographies do not force the pattern, although it is noted that in some cases the convection wavenumber may be a harmonic of the topographic wavenumber. It is pointed out that unforced circulation cells wander and vary in size because they are not locked to the topography.

Hartline, B. K.↗
NASA NTRS1983

Natural convection in an enclosed cavity

The problem of buoyancy driven flow in a vertical, rectangular cavity whose vertical sides are at different temperatures and whose horizontal sides are insulated is addressed. An application of the dynamic A.D.I. method to obtain numerical solutions to this problem is described. For large non-dimensional temperature differences characterized by the Rayleigh number the flow patterns develop strong boundary layers. These boundary layers are resolved by applying the D.A.D.I. method to the discretization of this problem on a non-uniform grid.

Phillips, T. N.↗
NASA NTRS1982

Nonlinear modal analysis of penetrative convection

It is pointed out that thermal convection in many astrophysical and geophysical settings occurs in an unstable layer bounded above and below by regions which are stably stratified. The convective motions may extend a substantial distance into the adjacent stable zones. If the motions have little direct effect upon the mean stratification of the stable zone, then they are usually referred to as convective overshooting. The primary objective of the present investigation is to study the dynamics of overshooting at very large Rayleigh numbers, mainly with stellar applications in mind. Numerically this is only feasible if severe simplifications are made in the description of what are likely to be turbulent motions. The approach employed in the investigation utilizes nonlinear modal equations in which the vertical and temporal structure of the convection is described accurately at the expense of the horizontal structure. A summary of the salient properties of penetrative convection is provided on the basis of the results of the conducted studies.

Zahn, J.-P.↗
NASA NTRS1982

Toward a unified theory of atmospheric convective instability

A nonlinear three-dimensional truncated spectral model of shallow and moist Boussinesq convection indicates that parallel instability and thermal forcing are linked, in view of the fact that only one convective mode exists in which either or both mechanisms are operating to generate convection in the planetary boundary layer. It is also established that the wind field causes two-dimensional roll convection formation, an alignment of the convection with the wind in a preferred manner, and a propagation speed that is related to the wind component perpendicular to the roll axis. Latent heating is responsible for the decrease of the critical value of the environmental lapse rate in accordance with the slice method stability criterion. When only the upper part of the upward branch is moist and all of the downward branch is dry, latent heating also causes a finite-amplitude convective solution for Rayleigh number values lower than the critical value of linear analysis.

Shirer, H. N.↗
NASA NTRS1982

Single-mode theory of diffusive layers in thermohaline convection

A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed independence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. The convection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys of numerical solutions are presented for a selection of Rayleigh numbers R, stability parameters lambda and horizontal wavenumbers. The solutions yield a buoyancy flux ratio chi that is insensitive to lambda, in accord with laboratory experiments. However chi increases with increasing R, in contradiction to laboratory observations.

Gough, D. O.↗
NASA NTRS1983

A model to determine open or closed cellular convection

The horizontal asymmetry of cellular convection is demonstrated to be detectable by consideration of the vertical asymmetry of the driving force. A two-dimensional numerical model for convection in an internally heated and cooled fluid is presented, based on equations for the conservation of temperature and vorticity. Attention is focused on the steady-state finite-amplitude solutions for fixed Rayleigh number, Prandtl number, and aspect ratio. Temperature in the model corresponds to potential temperature under dry conditions and the equivalent potential temperature under saturated conditions. Slowly varying convection driven by asymmetric boundary fluxes is expressed in terms of steady-state convection driven by an asymmetric internal heat source. It is shown that heating near the ground produces open convection patterns where most of the fluid is descending, while cooling near the top of the flow leads to closed cellular patterns with a preponderance of ascending fluid. Extension of the model to three dimensions is indicated.

Helfand, H. M.↗
NASA NTRS1984

On the geodynamic setting of kimberlite genesis

The emplacement of kimberlites in the North American and African continents since the early Palaeozoic appears to have occurred during periods of relatively slow motion of these continents. The distribution of kimberlites in time may reflect the global pattern of convection, which forces individual plates to move faster or slower at different times. Two-dimensional numerical experiments on a convecting layer with a moving upper boundary show two different regimes: in the first, when the upper boundary velocity is high, heat is transferred by the large-scale circulation and in the second, when the upper boundary velocity is lower, heat is predominantly transferred by thermal plumes rising from the lower boundary layer. For a reasonable mantle solidus, this second regime can give rise to partial melting beneath the moving plate, far from the plate boundaries. The transition between these modes takes place over a small range of plate velocities; for a Rayleigh number of 1,000,000 it occurs around 20 mm/yr. It is suggested that the generation of kimberlite magmas may result from thermal plumes incident on the base of a slowly moving plate.

England, P.↗
NASA NTRS1982

Natural convection in melt crystal growth - The influence of flow pattern on solute segregation

The results of two lines of research aimed at calculating the structure of the flows driven by buoyancy in small-scale crystal growth systems and at understanding the coupling between these flows, the shape of the solidification interface, and dopant segregation in the crystal are reviewed. First, finite-element methods are combined with computer-aided methods for detecting multiple steady solutions to analyze the structure of the buoyancy-driven axisymmetric flows in a vertical cylinder heated from below. This system exhibits onset of convection, multiple steady flows, and loss of the primary stable flow beyond a critical value of the Rayleigh number. Second, results are presented for calculations of convection, melt/solid interface shape, and dopant segregation within a vertical ampoule with thermal boundary conditions that represent a prototype of the vertical Bridgman growth system.

Brown, R. A.↗
NASA NTRS1984

Time-dependent models of single- and double-layer mantle convection

Time-dependent numerical models of two-dimensional convection which simulate mantle convection are presented. Starting from a fluid initially at rest with a purely conductive temperature profile, it is found that for a Rayleigh number of ten million, the model experiences a transient period of double-layer convection which lasts on the order of hundreds of millions of years when scaled to the earth's mantle. It is suggested that transient periods of double-layer convection in the earth's mantle may have existed in the past, whether or not such a period exists today.

Boss, A. P.↗