INVESTIGATION OF PROBLEMS IN THERMAL CONVECTION
Thermal convection - fluctuations in velocity, temperature and linear stability of horizontal surfaces
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Thermal convection - fluctuations in velocity, temperature and linear stability of horizontal surfaces
Hard turbulent convection is investigated using laboratory experiments and numerical simulations. In Newtonian mantle convection, the appearance of disconnected plumes marks the transition from soft to hard turbulence. For non-Newtonian rheology, the transition to hard turbulence takes place at much lower Nusselt numbers than it does for Newtonian rheology. This has important ramifications for the mantle. Large curvatures are developed in the trajectories of non-Newtonian plumes in the hard turbulent regime, in contrast to the trajectories of Newtonian plumes. When phase transitions are considered, mantle convection tends to become more layered with increasing Rayleigh numbers. The manner of mantle convection might have changed with time from a layered to a more whole mantle type of flow. Superplume events could have been caused by catastrophic overturns associated with strong gravitational instabilities in the transition zone.
Subsonic thermal convection or internal gravity waves from formal scale analysis of equations of motion in plane parallel atmosphere
Solution of thermal convection equations for thin layer of fluid
Numerical solution of thermal convection equations for velocity and temperature fluctuations as well as the stability analysis and heat transport for free boundary conditions
The spreading rates of convective thermals are linked to their net entrainment, and previous literature has suggested differences in spreading rates between moist and dry thermals. Here, growth rates of idealized numerically simulated axisymmetric dry and moist convective thermals are directly compared. In an environment with dry-neutral stratification, the increase of thermal radius with height dR / dz is a larger by a factor of 1.7 for dry thermals relative to moist thermals. The fractional change in thermal volume ε is also greater for dry thermals within a distance of ~4 radii from the initial thermal height. Values of dR / dz are nearly constant with height for both moist and dry thermals consistent with classical theory based on dimensional analysis. The simulations are also consistent with theory relating impulse, circulation, and spreading rate for dry thermals proposed in previous papers and extended here to moist thermals, predicting they will spread less than dry thermals. Tests adding heating to dry thermals, either spread uniformly across the thermal volume or concentrated in the inner core, indicate that dR / dz and ε are smaller for moist thermals because latent heating is confined mostly to their cores. Additional axisymmetric moist simulations using modified lapse rates and large-eddy simulations support this analysis. Overall, these results indicate that slow spreading rates are a fundamental feature of moist thermals caused by latent heating that alters the spatial distribution of buoyancy within them relative to dry thermals.
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.
Analytic approximation method for thermal convection at large Rayleigh numbers
The effect of thermal convection on the shape of solid-liquid interface was investigated in experiments conducted in a transparent Bridgman-type directional solidification furnace. The relationship was numerically modeled using a standard 2D finite-difference approach, with the solid-liquid deformable interface approximated by a blocking-off technique. The directional solidification furnace was used with pure succinonitrile (which is also transparent) contained in a long square ampoule made of borosilicate glass. With the furnace in the vertical configuration, a flat interface was observed, in agreement with the model. On the other hand, a highly distorted interface was obtained in the horizontal configuration; the numerical results showed a strong recirculating cell in front of the interface due to natural thermal convection. The results indicate that thermal convection is responsible for the interface distortion.
The question of whether or not thermal convection in the earth's mantle is chaotic is addressed. It is suggested that the high Prandtl number/high Raleigh number thermal convection associated with mantle convection is chaotic. To test this hypothesis, the route to chaos in a fluid with infinite Prandtl number is examined, using the Saltzman (1962) equations and the Lorenz (1963) equations. It is concluded that thermal convection at infinite Prandtl number becomes chaotic by means of symmetry-breaking pitchfork bifurcations and the appearance of Hopf bifurcations which produce unstable periodic orbits.
A method for thermally analyzing convectively cooled flight experiments is presented. A three-dimensional fluid flow analysis code is used to optimize air circulation patterns and to predict air velocities in thermally critical areas. The analysis results are compared with the performance characteristics of a typical isothermal free jet, and good agreement is found between velocity profiles and radial distributions for downstream flow mixing. Predicted air velocities from the fluid analysis are used to calculate forced convection coefficients for the flight experiment, and the coefficients are used in a finite difference thermal analysis code to describe the response of air temperature and heat loss for the Lidar Atmospheric Sensing Experiment during transient flight profiles. Recommendations are made for the future design of convectively cooled flight experiments.
Thermal convection in a closed chamber is driven by a warm bottom, a cold top, and side walls at various temperatures. Although wall fluxes are the source of convection energy, accurately modeling these fluxes (i.e., the wall model) is challenging. In large-eddy simulations (LESs), many wall models are traditionally derived from the canonical boundary layer, which may be unsuitable for thermal convection bounded by both horizontal and vertical walls. This study conducts a model intercomparison of dry convection in a cubic-meter chamber using three direct numerical simulations (DNSs) and four LESs with different wall models. The LESs employ traditional wall models, a new wall model employing physics-aware neural networks, and a refined grid near the walls. The experiment involves four cases with varying sidewall temperatures. Our results show that LESs capture the main flow features and the trends of mean fluxes. The physics-aware neural networks and refined wall grids can improve the temporally averaged local fluxes when the large-scale circulation has a preferred direction. Even without the local improvement of wall fluxes, the LES flow quantities (temperature and velocities) can still largely match those in DNSs, provided the mean flux largely matches the DNSs. Additionally, DNSs reveal that a variation in corner treatments has minimal impacts on the flow quantities away from corners. Finally, LESs underestimate the mean fluxes of the entire wall due to their inability to resolve corner regions, but their mean flux away from the corner can better match DNS.
Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.
Statistical theory of thermal convection at large Prandtl number
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.
A parallel implementation of the finite volume method for three-dimensional, time-dependent, thermal convective flows is presented.
Mercury corrosion and evaluation of corrosion products found in separators of three chromium molybdenum alloy boiling thermal convection loops
The dynamics of thermal convection in a rotating shear flow was studied using a three-dimensional time-dependent numerical model of the flow. The model assumes a sheared zonal wind in the form of an atmospheric jet stream and considers convective motions imbedded in this flow. It was found that rotation plays a vital role in the dynamics. Without rotation, the convective motions extract energy and momentum from the mean zonal flow. With rotation, the convective motions feed the energy and momentum into the mean flow. The results show how the small-scale convection might influence the large-scale dynamics of rotating stars and planets.