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
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.
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.
The solar nebula, from which the planets in our solar system formed, featured a disk of gas and dust grains in rapid, differential rotation, and at some stage was likely to have been unstable to thermal convection. This situation is suspected by many to lead to significant turbulent Reynolds stress production and angular momentum transport in such systems, and estimates of transport rates have been attempted from unsubstantiated phenomenological models. In order to determine the circumstances and physical conditions under which our own planetary system formed and to explain recent observations of young stellar systems, it is necessary to develop realistic models of heat and angular momentum transport for such flows. Developing an understanding of complicated flows featuring thermal convection, rotation, and shear is also of wide interest in stellar astrophysics and in planetary and terrestrial atmospheric studies. The ultimate objective is to develop workable models based on the numerical simulations for constructing global solar nebula models; viz., relatively simple prescriptions for heat and angular momentum fluxes from given system parameters (e.g., ratios of rotation, shear, and convective lapse rates) are characterized, quantified, and developed. Toward this end, our program has been to attempt to understand the behavior of the direct numerical simulations of Boussinesq convection, which, despite the complexity of the results, is still an overly simplified approximation to the real system and should be more amenable to analysis. These results are also intended to be tested against turbulence models, especially those designed for atmospheric boundary layers, and may provide a basis for subgrid-scale models. In order to make the numerical simulations more realistic with regard to the solar nebula problem, a fully compressible code that will allow incorporation of large density stratifications and realistic thermodynamic and radiative properties is developed. In order to explore the properties of these flows at the very high values of Re found in natural systems and the very low values of Pr found in most astrophysical contexts, we will need to employ large-eddy simulations for which we want to determine the most appropriate subgrid-scale model to incorporate.
Partial melting to generate the crust of a planet can create a buoyant residual layer at the top of the mantle which may have important implications for episodic planetary evolution. However, the rate of mixing of such a chemically buoyant layer with a thermally convecting mantle is an important unresolved question. Except for a few laboratory and numerical studies designed to address questions related to convection in the Earth's mantle, previous studies have generally treated on the mixing of passive tracers. The inhibiting role of chemical buoyancy on mixing is intuitively obvious but not fully understood quantitatively. In this study, we examine the dynamics of an intrinsically buoyant fluid layer at the top of a deeper, thermally convecting, infinite Prandtl number fluid that is heated from below.