Numerical Capture and Study Towards the Suppression of Taylor Column in Rotating Fluids with Forced Convection

Abstract

The thesis embodies a novel investigation and study of the numerical capture of Taylor newlinecolumn phenomena in rotating fluids and its analysis under different circumstances newlinewhich includes forced convection heat transfer and the application of a uniform magnetic newlinefield. Taylor column is an interesting flow phenomenon that occurs as a result of newlinethe interaction between the Coriolis and the inertial forces. The governing equations newlinerepresenting such a system are a set of highly non-linear coupled elliptic partial differential newlineequations. Obtaining analytical solutions in a closed form to such equations newlinemay not be possible and one has to resort to a numerical scheme which is of high accuracy newlineand efficiency. A comprehensive literature survey doesn t provide any convincing newlineresults claiming the numerical capture of the Taylor column phenomenon and its subsequent newlineflow physics. The non-linear terms involved in the governing equations owing to newlinethe presence of convection and fluid rotation makes it more challenging, and therefore, newlinea powerful numerical scheme is needed. One reason for not being able to numerically newlinecapture the phenomena could be the use of existing lower-order accurate schemes by newlineearlier researchers. In this thesis, we have imposed Higher Order Compact Scheme newline(HOCS) which ensures fourth order accurate results, and hence, we have successfully newlinecaptured the Taylor column phenomena. newlineThis setup allows us to capture the Taylor column phenomena for the steady flow newlinepast a translating sphere in the upstream region at critical values of inverse Rossby newlinenumber 1/Ro (= 2Ta/Re, where Re is Reynolds number and Ta is Taylor number) newlinealong with the subsequent formation of a cyclonic vortex in the downstream region. The newlineresults for both cases of low and high inverse Rossby number (1/Ro) are presented to newlineunfurl each event with in-depth physical rationale.