Threedimensional convection in cylindrical geometry
Abstract
A few convective flows inside cylindrical open or closed bodies are studied numerically. The simulations are carried out with a finite volume code, that solves for the governing NavierStokes and energy equations in conservative form. Convective and diffusive fluxes are discretized by the use of central differencing, and the solutions are obtained by marching in time. A new way of treating the axis of the cylinder is presented. The configurations considered scan a vast range of physical effects. The two most important problems analyzed are: three dimensional natural convection in the Czochralski melt, and three dimensional opposing mixed convection in an inclined pipe. The first problem is relevant to crystal growers. The knowledge of the free convective motion in the melt is important, since unsteady convective flows are responsible for striations in the crystal. In the idealized geometry considered, it is observed that the motion of a very low Prandtl number fluid is axisymmetric and has swirl, the azimuthal motion being concentrated close to the axis. Azimuthal components of velocity are caused by small perturbations that grow through a process of energy exchange between the radial and azimuthal directions. It is found that the onset of unsteadiness (oscillatory flow) is close to what is predicted by two dimensional axisymmetric simulations. In the second configuration, an inclined pipe in which natural and forced convection oppose each other, is considered. This problem has applications in all situations involving the transport of heated or cooled fluids, such as heat exchangers, thermosyphons, and heat pipes. The focus is on the dependence of the flow on the angle of inclination and Grashof number. In certain ranges of the flow parameters, the fluid separates at the wall and penetrates a cold region. Under these circumstances, the flow does not have any symmetry and is fully three dimensional.
 Publication:

Ph.D. Thesis
 Pub Date:
 March 1989
 Bibcode:
 1989PhDT........45B
 Keywords:

 Computerized Simulation;
 Convective Flow;
 Cylindrical Bodies;
 Czochralski Method;
 Flow Characteristics;
 Free Convection;
 Melts (Crystal Growth);
 Diffusivity;
 Energy Transfer;
 Finite Difference Theory;
 Forced Convection;
 Grashof Number;
 Heat Exchangers;
 Heat Pipes;
 Oscillations;
 Prandtl Number;
 Thermosiphons;
 Unsteady Flow;
 Fluid Mechanics and Heat Transfer