Ranga Narayanan

Free surface convection in a bounded cylindrical geometry

Abstract Surface tension-driven convection and buoyancy-driven convection in a bounded cylindrical geometry with a free surface are studied for a range of aspect ratios and Nusselt numbers. Linear theory and some aspects of a nonlinear analysis are utilized to determine the critical Marangoni and Rayleigh numbers, the structure of the convective motion, the direction of flow, and the nature of the bifurcation branching. The analysis is based on a somewhat different method for treating free convection problems, the use of Greens functions to reduce the problem to the solution of an integral equation.

Comments on the numerical investigation of Rayleigh and Marangoni convection in a vertical circular cylinder

Convection in a cylindrical container was simulated with a three‐dimensional, time‐dependent code. For the case of purely Rayleigh convection, a completely rigid cylinder with adiabatic vertical walls and conducting horizontal walls was considered. The calculations showed that the individual velocity components could be in a transient state, while the total heat transfer was steady. This occurred in cases where the maximum azimuthal component of velocity was very small in magnitude, in comparison to the other two components, and this component decreased in time. On the other hand, the total kinetic energy along with the heat transfer reached a steady value. Consequently the present results have been shown to be at variance with the calculations of Neumann [J. Fluid Mech. 214, 559 (1990)]. Marangoni convection was modeled with a free flat surface on the upper side, assuming the superimposed second layer to be passive. The numerically obtained critical Marangoni numbers and flow patterns were compared favor...

A tutorial on the Rayleigh–Marangoni–Bénard problem with multiple layers and side wall effects

A brief review in the form of a tutorial is presented on convective instabilities that arise from thermocapillary and buoyancy effects. This tutorial primarily focuses on the effect of multiple layers and side walls on the nature of the convective flows and associated patterns. A comprehensive explanation of the physics of this type of convection is followed by a discussion of the mathematical features of bifurcation associated with the problem and some of the recent experimental studies. (c) 1999 American Institute of Physics.

The microgravity environment: its prediction, measurement, and importance to materials processing

Abstract One of the primary benefits of conducting scientific research in space is to take advantage of the low acceleration environment. For experimenters conducting space research in the field of materials science the quality of the science return is contingent upon the extremely low frequency acceleration environment (⪡ 1 Hz) aboard the spacecraft. Primary contributors to this low frequency acceleration environment (commonly referred to as the steady-state acceleration environment) include aerodynamic drag, gravity-gradient, and rotational effects. The space shuttle was used on the STS-75 mission as a microgravity platform for conducting a material science experiment in which a lead tin telluride alloy was melted and regrown in the Advanced Automated Directional Solidification Furnace under different steady-state acceleration environment conditions by placing the shuttle in particular fixed orientations during sample processing. The two different shuttle orientations employed during sample processing were a bay to Earth, tail into the velocity vector shuttle orientation and a tail to Earth, belly into the velocity vector shuttle orientation. Scientists have shown, through modeling techniques, the effects of various residual acceleration vector orientations to the micro-buoyant flows during the growth of compound semiconductors. The signatures imposed by these temporally dependent flows are manifested in the axial and radial segregation or composition along the crystal.

Oscillation phase relations in a Bridgman system

The thermal conditions under which convection in a tin melt undergoes the transition from steady flow to time-dependent flow are investigated. Previously, it has been shown that crystals that are directionally solidified from a time-dependent melt will have a larger defect density and increased chance of compositional striations. Thus, it is important for this transition to be well characterized. The experimental results to be presented were obtained from a two-zone Bridgman furnace with a middle insulation zone. Thermocouples were placed on the axis and on the outer wall of a cylindrical vitreous silica tube which contained molten tin. The phase relations between temperature oscillations measured at different positions in the cell are discussed. Fourier transforms are used to investigate the increasing complexity of convection as the temperature gradient is increased.

Observations on Interfacial Convection in Multiple Layers without and with Evaporation

A tutorial is presented on convective instabilities that arise from thermocapillary and buoyancy effects in the presence of evaporation. It focuses on the effect of multiple layers on the nature of the instabilities. A comprehensive explanation of the physics of this type of convection is accompanied by results from calculations and their interpretation.

The detection of solutal convection during electrochemical measurement of the oxygen diffusivity in liquid tin

Electrochemical titration was used as a means to determine the mass diffusivity of oxygen in liquid tin at various temperatures. Solutal convection was present depending on the conditions, and this was inferred from an enhancement in the effective diffusivity. The experiments were conducted in two different modes of operation, and in each case, we attempted to align the oxygen concentration gradient such that it was parallel to the gravitational field. In the first mode, the concentration gradient was such that the fluid was heavy at the bottom and lighter at the top, and in the second, the reverse was true. The second mode was potentially unstable and sometimes gave rise to substantial convection for large values of the oxygen concentration gradient. The measured effective diffusivities were then higher than the corresponding measurements in the first mode of operation. Activation energies in two different temperature ranges were obtained by using an Arrhenius relationship.

Rayleigh convection in a closed cylinder—Experiments and a three‐dimensional model with temperature‐dependent viscosity effects

In this paper our most recent research results on natural convection in a closed cylinder, where our interest focuses on pattern structure dependence on aspect ratio and on temperature‐dependent viscosity, are summarized. The main results are (a) the experiments on the onset pattern and conditions for pure Rayleigh convection in circular cylinders compare favorably with linearized stability results of Hardin et al. [Int. J. Num. Methods Fluids 10, 79 (1990)], as well as three‐dimensional nonlinear calculations made by us; and (b) experiments and nonlinear calculations indicate a variation of the patterns at and near the codimension two points when large temperature differences are introduced, so as to cause a substantial change in viscosity.

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Greens functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.

The Faraday instability in miscible fluid systems

The Faraday instability arising in distinct miscible fluid layers, when the parametric forcing is parallel to the gravity vector, is analysed. A time-dependent density gradient is established from the moment the fluid layers are placed in contact with one another. The operating parameters in a miscible Faraday system are the frequency of parametric forcing and the wait time between the initial contact of fluids and the commencement of oscillations. Using a linearized theory that invokes a quasi-steady approximation, the vibrational threshold required for the onset of Faraday instability is evaluated for these parameters and several observations are made. First, the criticality is observed to occur at a sub-harmonic frequency. Second, the large magnitude of the concentration gradient at early wait times is found to make the thin layers highly unstable. Third, the stability increases with forcing frequency, owing to the increased dissipation of the resulting choppy waves. All these observations qualitatively agree with experiments. Finally, a calculation reveals that an increase in gravity increases the critical wavelength of flow onset and results in the reduction of critical input acceleration.