Madhukar M. Rao

ELAFINT :a mixed Eulerian-Lagrangian method for fluid flows with complex and moving boundaries

In this work a mixed Eulerian–Lagrangian technique is devised, hereinafter abbreviated as ELAFINT (Eulerian–Lagrangian Algorithm For INterface Tracking). The method is capable of handling fluid flows in the presence of both irregularly shaped solid boundaries and moving/free phase boundaries. The position and shape of the boundary are tracked explicitly by the Lagrangian translation of marker particles. The field equations are solved on an underlying fixed grid as in Eulerian methods. The interface passes through the grid lay-out and details regarding the treatment of the cut cells so formed are provided. The issues involved in treating the internal boundaries are dealt with, with particular attention to conservation and consistency in the vicinity of the interface. The method is tested by comparing with solutions from well-tested body-fitted co-ordinate methods. Test cases pertaining to forced and natural convection in irregular geometries and moving phase boundaries with melt convection are presented. The capability developed here can be beneficial in solving difficult flow problems involving moving and geometrically complex boundaries.

Simulation of Transient Natural Convection Around an Enclosed Vertical Channel

Accurate numerical calculations have been conducted for buoyancy-driven two-dimensional flow of air between two vertical parallel isothermal plates, of aspect ratio 1, placed inside a rectangular enclosure. The Grashof number based on the channel half width is 105 . Insights have been obtained regarding the structure of the transient flow and thermal fields in a configuration of particular interest to electronics cooling. In the early stages of the transient the flowfield was found to be highly vortical and the net volume flow rate in the channel displayed an oscillatory behavior, periodically reversing its direction. However, the velocity profile adjacent to the heated plates maintained the same direction throughout the process, and hence the Nusselt number was relatively insensitive to the periodic flow reversal in the channel. Detailed studies of the transient flow field and the heat transfer results are presented.

Calculation of meniscus shapes and transport processes in float zone

Abstract The formation of the melt meniscus and convection heat transfer in the melt is a major issue in the float zone technique for growing single crystals. The present study investigates the issues of existence, multiplicity and physical realizability of the solutions, based on the concept of free energy minimization, to the Young-Laplace equation, representing the liquid menisci formed under equilibrium conditions. The physical realizability of the meniscus profile is sharply affected by the material properties and geometry, through the dimensionless parameters including Bond number and aspect ratio. A typical meniscus shape obtained at Bond numbers commonly encountered in practical configurations is selected for buoyancy driven convection and thermocapillary convection heat transfer studies. For the materials and geometries of interest, thermocapillary effects dominate over buoyancy effects. The impact of the convection pattern on the meniscus shape is reflected by the magnitude of the capillary number, which is found to be small in this case. Calculations were conducted over a range of Grashof numbers. Marangoni numbers and Prandtl numbers to gage the sensitivity of the solutions to the physical properties of the molten material. The relative strength of buoyancy-driven convection and thermocapillary convection has the greatest impact on the heat transfer results. The results reported here can help assess the suitability of a given float zone design.

Scaling procedure and finite volume computations of phase-change problems with convection

Abstract In this paper, solidification problems are investigated from two angles, namely, the issue of wide disparity of important length scales present in phase change processes, and the finite volume based computational techniques developed to simulate such processes. To appropriately handle phase change phenomena, a scaling analysis is presented to bring out the relevant physics at the macroscopic and morphological scales. It is demonstrated that an appropriate choice of the scale is necessary to obtain numerical solutions economically. Two different finite volume techniques are described in this paper. The first technique involves a mixed Eulerian/Lagrangian approach, where the interface is explicitly tracked by means of marker particles, and the field equations are solved on an underlying fixed, finite volume grid. The other approach is an enthalpy model which incorporates the interface information in a field variable called the phase-fraction. This volume averaged technique enables the implicit handling of the interface as part of the solution procedure at the cost of smearing out the discontinuity. Two different phase-fraction update techniques are presented and their relative effectiveness and performance discussed. A continuous ingot casting problem modelled by accounting for the interaction of phase-change and turbulent transport is also presented and compared with experimental results.

Modelling and simulation of phase change and thermofluid transport for spacecraft applications

Computational techniques were developed for prediction of transient two‐phase flow and were applied to predict material solidification with time‐dependent variation of gravity (G‐jitter) to simulate the environment encountered in an orbiting spacecraft. The effects of G‐jitter on the predicted wall heat fluxes and on the interface shape and motion are discussed.

Computational Fluid Dynamics with Moving Boundaries

This advanced-leveltext describes several computational techniques that can be applied to a variety of problems in thermo-fluid physics, multi-phase flow, and applied mechanics involving moving flow boundaries. Step-by-step discussions of numerical procedures include examples that employ algorithms to solve problems. 1990 edition.

Enthalpy based formulations for phase-change problems with application to g-jitter

Alternative formulations for the computational modelling of phase change have been investigated in the context of single region, enthalpy based mathematical models. All calculations were canied out on a fixed, Cartesian grid. Both, pure conduction driven phase change and buoyancy driven convective effects were considered. Two methods of phase fraction update were selected for detailed investigation the H-based and the T-based methods. Numerical experiments using the one dimensional conduction driven Stefan problem, revealed that while both methods gave identical results. the T-based method was superior in terms of computational efficiency. The T-based method was then extended to compute phase-change in the presence of buoyancy driven convection, and to compare with experimental information and assess its performance. Thereafter, the developed techniques were used to compute a g-jitter case with time-dependent variation of gravity to simulate the environment encountered in an orbiting spacecraft. The effects of g-jitter on the predicted wall heat fluxes and on the interface shape and motion are discussed. w