SOME PROBLEMS ON VISCOUS POTENTIAL FLOW ANALYSIS OF KELVIN-HELMHOLTZ INSTABILITY

Abstract

In potential flow it is neither necessary nor useful to put the viscosity to zero. In viscous potential theory, viscosity is not neglected and irrotational flow of a viscous fluid satisfies Navier-Stokes equations. However, in inviscid potential theory, viscosity is neglected when considering irrotational solutions of Navier-Stokes equations. Tangential stresses are not considered in viscous potential theory and viscosity enters through normal stress balance. Viscous potential flow gives better approximation than inviscid potential flow. Viscous potential flow analysis of linear and nonlinear Kelvin-Helmholtz instability with heat and mass transfer has not been considered in earlier study. It is also important in study of electrohydrodynamic stability, magnetohydrodynamic stability and flow through porous medium. Hence "Viscous Potential Flow Analysis of Some Problems on Kelvin-Helmholtz instability" is studied in this thesis. The chapterwise summary of the thesis is as follows: Chapter 1 is introductory in nature. In Chapter 2, Viscous potential flow analysis of Kelvin-Helmholtz instability with heat and mass transfer has been carried out. A condition for neutral stability is obtained. It is given in terms of critical value of relative velocity. Effect of viscosity ratio, heat transfer coefficient, and vapor fraction has been studied. A part of this paper has been published in Physica A (2007). In Chapter 3, Viscous potential flow analysis of Kelvin-Helmholtz instability with heat and mass transfer in presence of a horizontal electric field has been carried out. Stability criterion is given by a critical value of relative velocity of two fluids as well as critical value of the applied electric field. Various graphs with respect to physical parameters, such as wave number, viscosity ratio, ratio of dielectric constants of two fluids, heat transfer coefficients have been drawn and effect of various parameters have been described. In Chapter 4, Magnetoviscous potential flow analysis of Kelvin-Helmholtz instability with heat and mass transfer has been considered. A critical value of magnetic field as well as relative velocity is obtained. A detail analysis in terms of all physical parameters such as wave number, viscosity ratio, ratio of magnetic permeability and heat transfer coefficients has been made. In Chapter 5, Viscous potential flow analysis of Kelvin-Helmholtz instability of cylindrical interface in presence of heat and mass transfer has been carried out. A comparison with plane geometry configuration considered in Chapter 2 has been made. Effect of vapor fraction, Reynolds number and heat transfer coefficient has been studied. In Chapter 6, Viscous potential flow analysis of nonlinear Kelvin- Helmholtz instability with heat and mass transfer has been studied. Nonlinear analysis has been carried out using multiple scale method. A partial differential equation governing the nonlinear wave has been obtained. A comparison with linear theory considered in chapter 2 has been made. In Chapter 7, Viscous potential flow analysis of Kelvin-Helmholtz instability in porous media has been carried out. A new dispersion relation has been obtained. Analysis has been carried out in terms of various physical parameters such as Reynolds number, Bond number, Darcy number and porosity of the medium. Finally in Chapter 8, based on present study, conclusions are drawn and future research work in this direction is suggested