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 73 records · Page 4

Presentation material for Progress in Simulated Water Well Performance on Mars

This presentation reports on the results of some experimental work regarding the establishment and operation of water wells on Mars. These results were accomplished since this group reported on this concept at the AIAA Space conference in 2018. These experiments were conducted to improve the understanding of a Rodwell’s performance under Mars surface conditions. The motivation to improve this understanding results from the leverage that access to large quantities of water, already on Mars, gives to future human missions to that planet. Previous work by this group has described the likely location of these water deposits and the extensive history of terrestrial use of the Rodwell technique. The results reported in this presentation indicate several key points. First, it has been demonstrated that a stable pool of water can be maintained under Martian surface environmental conditions using an approach comparable to terrestrial Rodwells. Next, it was unexpectedly learned that the water pool exhibits some of the same structural characteristics – specifically an ice shelf just above the water pool – that are seen in terrestrial Rodwells. This finding directly affected the way in which test data was reduced. And finally the experimental data was used to generate equations for convection-driven evaporation and convective heat transfer. The evaporation results were found to follow the same trends as published results for experiments in terrestrial environments. But the results reported here have also extended the range of these trends into much smaller Rayleigh Number ranges than anything previously reported. It was also found that convective heat transfer does not following published results even in the same Rayleigh Number range. A suggested explanation for this result has been proposed based on phenomenon described in the literature, but this group continues to look at the results to see if a better explanation can be found.

Mars↗

Convection in the Physical Vapor Transport Process: Thermosolutal - Part 2

We consider the effect of an inert gas on the diffusive-convective physical vapor transport process. We investigate the case when the temperature gradient is stabilizing and the concentration gradient is destabilizing for a wide parametric range. When an inert gas is present, the thermal and solutal convection oppose each other. The solutal field is destabilizing while the thermal field and the advective-diffusive flux stabilize the flow field. When the pressure of the inert component is increased, the stabilizing effect of the advective-diffusive flux is decreased. The intensity of convection as well as the oscillatory transient time increases. Below, the critical Rayleigh number, the nonlinear dynamics of the flow field show an oscillatory approach to steady state. For parametric values in the neighborhood of the critical Rayleigh number, the flow field undergoes a chaotic transient which settles to a periodic state. The asymptotic state of the flow field shows that growth and amalgamation of cells yields an overturning motion which results in an asymmetric cellular structure. The low gravity environment yields the stabilizing advective-diffusive flow which results in uniform temperature and concentration gradients near the crystal interface.

Duval, Walter M. B.↗

The relationship between plate velocity and trench viscosity in Newtonian and power-law subduction calculations

The relationship between oceanic trench viscosity and oceanic plate velocity is studied using a Newtonian rheology by varying the viscosity at the trench. The plate velocity is a function of the trench viscosity for fixed Rayleigh number and plate/slab viscosity. Slab velocities for non-Newtonian rheology calculations are significantly different from slab velocities from Newtonian rheology calculations at the same effective Rayleigh number. Both models give reasonable strain rates for the slab when compared with estimates of seismic strain rate. Non-Newtonian rheology eliminates the need for imposed weak zones and provides a self-consistent fluid dynamical mechanism for subduction in numerical convection models.

King, Scott D.↗

Subsolidus convection in the mantles of terrestrial planets

The role of heat transport by solid state mantle convection in determining the past and present thermal states of terrestrial planets is examined. Mantle convection models have relied on two-dimensional and axisymmetric three-dimensional numerical calculations incorporating the temperature and pressure dependence of mantle rheology and its non-Newtonian nature. Convection at high Rayleigh numbers has been investigated through theoretical scaling arguments and boundary layer theories; nevertheless, computational limits prevent modeling of the fully three-dimensional, time-dependent, very high Rayleigh number convection which probably prevails in terrestrial planets. Radar measurements of Venus, as well as Voyager exploration of the Galilean satellites, should also provide information on mantle convection.

Schubert, G.↗

Local and Global Bifurcations of Flow Fields During Physical Vapor Transport: Application to a Microgravity Experiment

The local bifurcation of the flow field, during physical vapor transport for a parametric range of experimental interest, shows that its dynamical state ranges from steady to aperiodic. Comparison of computationally predicted velocity profiles with laser doppler velocimetry measurements shows reasonable agreement in both magnitude and planform. Correlation of experimentally measured crystal quality with the predicted dynamical state of the flow field shows a degradation of quality with an increase in Rayleigh number. The global bifurcation of the flow field corresponding to low crystal quality indicates the presence of a traveling wave for Ra = 1.09 x 10(exp 5). For this Rayleigh number threshold a chaotic transport state occurs. However, a microgravity environment for this case effectively stabilizes the flow to diffusive-advective and provides the setting to grow crystals with optimal quality.

Duval, W. M. B.↗

Experimental Study of Combined Forced and Free Laminar Convection in a Vertical Tube

An apparatus was built to verify an analysis of combined forced and free convection in a vertical tube with uniform wall heat flux and to determine the limits of the analysis. The test section was electrically heated by resistance heating of the tube wall and was instrumented with thermocouples in such a way that detailed thermal entrance heat-transfer coefficients could be obtained for both upflow and downflow and any asymmetry in wall temperature could be detected. The experiments showed that fully developed heat-transfer results, predicted by a previous analysis, were confirmed over the range of Rayleigh numbers investigated. The concept of "locally fully developed" heat transfer was established. This concept involves the assumption that the fully developed heat-transfer analysis can be applied locally even though the Rayleigh number is varying along the tube because of physical-property variations with temperature. Thermal entrance region data were obtained for pure forced convection and for combined forced and free convection. The analysis of laminar pure forced convection in the thermal entrance region conducted by Siegel, Sparrow, and Hallman was experimentally confirmed. A transition to an eddy motion, indicated by a fluctuation in wall temperature was found in many of the upflow runs. A stability correlation was found. The fully developed Nusselt numbers in downflow were below those for pure forced convection but fell about 10 percent above the analytical curve. Quite large circumferential variations in wall temperature were observed in downflow as compaired with those encountered in upflow, and the fully developed Nussalt numbers reported are based on average wall temperatures determined by averaging the readings of two diametrically opposite wall thermocouples at each axial position. With larger heating rates in downflow the wall temperature distributions strongly suggested a cell flow near the bottom. At still larger heating rates the wall temperatures varied in a periodic way.

Hallman, Theodore M.↗

Magnetic Field Effect on Convective Fluid Flow in a Vertical Bridgman System

We studied the magnetic field effects on convective fluid flow in a differentially heated HgCdTe Bridgman growth system with linearly stratified vertical HgTe concentration. We followed J. E. Hart's system set-up, boundary conditions, and formulation. We obtained analytical steady parallel flow solutions for fluid flow's velocity and solutal concentration. These solutions depend only on solutal Rayleigh number. Our analytical solutions had different expressions from that of Hart's, but had similar numerical simulation results for the mean fluid velocity and solutal concentration gradient as a function of solutal Rayleigh number. We studied the effects of a transverse magnetic field on the fluid flow of the Bridgman growth systems both on the ground and in the space. The simulation results and comparison with experimental results will be presented.

Wang, J. C.↗

Effects of truncation in modal representations of thermal convection

The Galerkin (including single-mode and Lorenz) equations were examined for convection in a sphere to determine which physical processes are neglected when the equations of motion are truncated too severely. The conclusions were tested by calculating solutions to the equations of motion for different values of the Rayleigh number and for different values of the limit of the horizontal spatial resolution. It was shown that the transitions from steady state to periodic, then to aperiodic convection depend not only on the Rayleigh number but also very strongly on the horizontal resolution. One of the effects of truncation is to enhance the high wavenumber end of the kinetic energy and thermal variance spectra. The numerical examples indicate that as long as the kinetic energy spectrum decreases with wavenumber, a truncation gives a qualitatively correct solution.

Marcus, P. S.↗

The role of hard turbulent thermal convection in the Earth's early thermal evolution

In the last several years great progress was made in the study of a new transition in thermal convection, called hard turbulence. Initial experiments were conducted with helium gas, then with water. It was shown that for base-heated Newtonian convection a transition occurred at Rayleigh numbers between 10(exp 7) and 10(exp 8). This transition is characterized by the appearance of disconnected plume structures in contrast to continuous plumes with mushroom-shaped tops found for lower Rayleigh numbers. This new hydrodynamic transition is expected to play an important role in reshaping our concepts of mantle convection in the early stages of planetary evolution. We have conducted two-dimensional calculations for large and small aspect-ratio configuration to see whether such a transition would take place for infinite Prandtl number fluids.

Hansen, Ulli↗

Onset of Convection in Ice I with Composite Newtonian and Non-Newtonian Rheology: Application to the Icy Galilean Satellites

Ice I exhibits a complex rheology at temperature and pressure conditions appropriate for the interiors of the ice I shells of Europa, Ganymede, and Callisto. We use numerical methods and existing parameterizations of the critical Rayleigh number to determine the conditions required to trigger convection in an ice I shell with the stress-, temperature- and grain size- dependent rheology measured in laboratory experiments by Goldsby and Kohlstedt [2001]. The critical Rayleigh number depends on the ice grain size and the amplitude and wavelength of temperature perturbation issued to an initially conductive ice I shell. If the shells have an assumed uniform grain size less than 0.4 mm, deformation during initial plume growth is accommodated by Newtonian volume diffusion. If the ice grain size is between 0.4 mm and 3 cm, deformation during plume growth is accommodated by weakly non-Newtonian grain boundary sliding, where the critical ice shell thickness for convection depends on the amplitude of temperature perturbation to the _0.5 power. If the ice grain size exceeds 2 cm, convection can not occur in the ice I shells of the Galilean satellites regardless of the amplitude or wavelength of temperature perturbation. If the grain size in a convecting ice I shell evolves to effective values greater than 2 cm, convection will cease. If the ice shell has a grain size large enough to permit flow by dislocation creep, the ice is too stiff to permit convection, even in the thickest possible ice I shell. Consideration of the composite rheology implies that estimates of the grain size in the satellites and knowledge of their initial thermal states are required when judging the convective instability of their ice I shells.

Barr, A. C.↗

Numerical simulation of small-scale thermal convection in the atmosphere

A Boussinesq system is integrated numerically in three dimensions and time in a study of nonhydrostatic convection in the atmosphere. Simulation of cloud convection is achieved by the inclusion of parametrized effects of latent heat and small-scale turbulence. The results are compared with the cell structure observed in Rayleigh-Benard laboratory conversion experiments in air. At a Rayleigh number of 4000, the numerical model adequately simulates the experimentally observed evolution, including some prominent transients of a flow from a randomly perturbed initial conductive state into the final state of steady large-amplitude two-dimensional rolls. At Rayleigh number 9000, the model reproduces the experimentally observed unsteady equilibrium of vertically coherent oscillatory waves superimposed on rolls.

Somerville, R. C. J.↗

Effect of Rayleigh accelerations applied to an initially moving fluid

The General Interpolant Method computer code was used to analyze two-dimensional unsteady thermal convection in circular cylinders under variable low-g conditions associated with space flight. When an acceleration vector was applied parallel to the thermal gradient, in the case of a fluid at rest, no convection resulted for the stable direction, and an instability led to Rayleigh convection for the opposite direction. However, when the acceleration had a component orthogonal to the gradient, convection resulted at any Rayleigh number. The effect on convection of both types of acceleration, applied concurrently or sequentially, was investigated, including the case when the resultant vector varied in direction with time. An analysis of experimental results shows that for space flight conditions, the Rayleigh accelerations induce significant, but not dominating, changes in the established convection even when the Rayleigh number is less than critical.

Dressler, R. F.↗

Buoyancy-driven flows of a radiatively participating fluid in a vertical cylinder heated from below

The effect of radiative energy transport on the onset and evolution of natural convective flows is studied in a Rayleigh-Benard system. Steady, axisymmetric flows of a radiatively participating fluid contained in a rigid-walled, vertical cylinder which is heated on the base, cooled on top, and insulated on the side wall are calculated by using the Galerkin FEM. Bifurcation analysis techniques are used to investigate the changes in the flow structure due to internal radiation. The results of this two-parameter study - where the Rayleigh number, Ra and optical thickness, tau, are varied - apply to fluids ranging from opaque to nearly transparent with respect to IR radiation. For any nonopaque fluid, internal radiation eliminates the static state that without radiation, exists for all values of the Rayleigh number. This heat transfer mechanism also destroys a symmetry of the system that relates clockwise and counterclockwise flows. The connectivity between characteristic flow families and the range of Ra where families are stable are found to depend greatly on tau. Results demonstrate the inadequacy of characterizing the behavior of this system using simple notions of radiative transfer in optically thick or thin media; the nonlinear interaction of radiation and flow are far more complicated than these asymptotic limits would imply.

Salinger, A. G.↗

Transitions to chaos in two-dimensional double-diffusive convection

The partial differential equations governing two-dimensional thermosolutal convection in a Boussinesq fluid with free boundary conditions have been solved numerically in a regime where oscillatory solutions can be found. A systematic study of the transition from nonlinear periodic oscillations to temporal chaos has revealed sequences of period-doubling bifurcations. Overstability occurs if the ratio of the solutal to the thermal diffusivity tau is less than 1 and the solutal Rayleigh number Rs is sufficiently large. Solutions have been obtained for two representative values of tau. For tau = 0.316, R(s) = 10,000, symmetrical oscillations undergo a bifurcation to asymmetry, followed by a cascade of period-doubling bifurcations leading to aperiodicity, as the thermal Rayleigh number R(T) is increased. At higher values of R(T), the bifurcation sequence is repeated in reverse, restoring simple periodic solutions. As R(T) is further increased more period-doubling cascades, followed by chaos, can be identified. Within the chaotic regions there are narrow periodic windows, and multiple branches of oscillatory solutions coexist. Eventually the oscillatory branch ends and only steady solutions can be found. The development of chaos has been investigated for tau = 0.1 by varying R(T) for several different values of R(s). When R(s) is sufficiently small there are periodic solutions whose period becomes infinite at the end of the oscillatory branch. As R(s) is increased, chaos appears in the neighborhood of these heteroclinic orbits. At higher values of R(s), chaos is found for a broader range in R(T). A truncated fifth-order model suggest that the appearance of chaos is associated with heteroclinic bifurcations.

Knobloch, E.↗

Exploring the impact of surface topography on Rayleigh-Bénard dry convection in the Pi cloud chamber using OpenFOAM: In cylindrical and rectangular geometries

The Pi convection-cloud chamber can generate steady-state turbulence in both rectangular and cylindrical shapes via Rayleigh-Bénard convection (RBC) by maintaining warm bottom and cold top surfaces. Although most experiments in the Pi chamber were conducted in cylindrical shapes, all previous Pi chamber simulations were conducted in a rectangular shape due to the limitations of those models to discretize a cylindrical domain when using the finite difference method therein. Here, we use OpenFOAM, an open-source finite-volume-based Computational Fluid Dynamics (CFD) software package, to conduct Large-Eddy Simulation (LES) of dry RBC in the Pi chamber at high Rayleigh numbers (10 8 to 10 9 ). Results show that large-scale circulation (LSC) direction varies in the chamber with a constant side wall temperature. Imposing a slight temperature imbalance at the side wall ranging from 0.1 to 0.7 degrees can lock the LSC, aligning better with Pi chamber observations, particularly at higher Rayleigh numbers. In addition, we examine the impact of surface topography on LSC and heat transfer in RBC systems within cylindrical and rectangular shapes under varying conditions. Results show that roughing top/bottom surfaces by adding bars of a few tens millimeters height can strengthen thermal plumes and enhance temperature fluctuations in the chamber. Furthermore, we observe that different bar height configurations lead to notable changes in LSC orientation and thermal stratification, highlighting the complex interactions between surface features and convection patterns. This finding highlights how surface topography and chamber geometry affect Rayleigh-Bénard convection, improving understanding of turbulent heat transfer and atmospheric boundary-layer processes. Direct Numerical Simulations (DNS) are also conducted to validate LES results. In conclusion, while LES effectively captures qualitative behaviors seen in DNS, it tends to underestimate velocity variances near walls, illustrating a trade-off between computational efficiency and accuracy.

54 ENVIRONMENTAL SCIENCES↗

Effect of Fluid Flow on Zinc Electrodeposits from Acid Chloride Electrolytes

Zinc was deposited potentiostatically from acid chloride baths. Once bath chemistry and electrochemistry were controlled, the study was focused on convective mass transfer at horizontal electrodes and its effect on cell performance. A laser schlieren imaging technique allowed in situ observations of flow patterns and their correlation with current transients. Convection was turbulent and mass transfer as a function of Rayleigh number was well correlated by: Sh = 0.14 R to the 1/3 power. Similarly, convection initiation time was correlated by DT/d squared = 38 Ra to the -2/3 power. Time scale of fluctuations was about half the initiation time. Taking the boundary layer thickness as a characteristic length, a critical Rayleigh number for the onset of convection was deduced: Ra sub CR = 5000. Placing the anode on the top of the cathode completely changed the flow pattern but kept the I-t curves identical whereas the use of a cathode grid doubled the limiting current. A well defined plateau in the current voltage curves suggested that hydrogen evolution has been successfully inhibited. Finally, long time deposition showed that convection at horizontal electrodes increased the induction time for dentrite growth by at least a factor of 2 with respect to a vertical wire.

Abdelmassir, A. A.↗

Unsteady convection in tin in a Bridgman configuration

When a quiescent fluid is heated sufficiently from below, steady convection will begin. Further heating will cause oscillatory and then turbulent flow. Theoretical results predict that the frequency of oscillation will depend on the square root of the Rayleigh number in the fluid. In the current work, liquid tin was heated from below for three aspect ratios, h/R = 3.4, 5.3, and 7.0. The experimental results are curve-fit for the square-root relation and also for a linear relation. The fit of the expression is evaluated using a correlation coefficient. An estimate for the first critical Rayleigh number (onset of steady convection) is obtained for both expressions. These values are compared to previous experimental results.

Knuteson, David J.↗

Surface tension effects on the onset of double-diffusive convection

Experiments have been carried out to determine the critical thermal Rayleigh number for onset of convection in a horizontal layer of density-stratified fluid with a free surface when heated from below. Three different aqueous solutions were used: salt, glycerol, and acetic acid. The rates of change in surface tension with concentration for these three solutions are positive, nearly zero, and negative, respectively. Compared to the rigid-rigid boundaries, the critical thermal Rayleigh number was found to be larger by 11.2 percent for the salt solution and smaller by 10.0 percent for the glycerol solution. With the acetic acid solution, however, the effect of the free surface was found to be negligible.

Chen, C. F.↗