Executive Summary : | The present research proposal reports the theoretical study on stability analysis of non-isothermal annular Poiseuille flow (NAPF) between two concentric cylinders under a uniform transverse magnetic field through high-performance numerical simulation. The electrically conducting NAPF appears in several magnetohydrodynamic (MHD) applications such as the design of liquid metal blankets for fusion reactors, heat exchangers, oil industry, and MHD-based thermal electronic devices. In general, the magnetic field stabilizes the flow, but the thermal buoyancy force destabilizes the flow. The complexity in flow arose due to the buoyancy force and applied magnetic field competition. The hydrodynamic stability analysis provides a better understanding of the flow characteristics. Instabilities in the flow often lead to the onset of turbulent motion. In the theoretical framework, the following essential theories are available for the examination of the instability properties through a numerical simulation. 1. Linear stability analysis 2. Weakly nonlinear stability analysis (or Finite Amplitude Analysis) 3. Large Eddy Simulation (LES) 4. Direct Numerical Simulation (DNS) The linear stability analysis is a mathematical cum theoretical investigation, which determines the point of instability. Linearly unstable solutions cannot be accomplished when the larger amplitudes are obtained in the flow. In this situation, nonlinear effects appear to describe the resulting flows. A weakly nonlinear analysis gives the next step beyond the linear stability analysis to understand the different types of instabilities in the flow. This analysis is only valid near the linear stability boundary and provides valuable information about the type of bifurcation in the flow. To understand the turbulent motion, the most widespread numerical methods, namely large-eddy simulation (LES) and direct numerical simulation (DNS), are important computational techniques. There are some issues associated with the solution of the Navier-Stokes equations by DNS/LES. The major drawbacks of DNS are extreme numerical simulation cost. At the same time, the linear and weakly nonlinear stability analyses are attractive (mathematical point of view) and easy to adopt. These analyses provide useful information about flow field, size of the disturbance, and types of bifurcations (supercritical/subcritical). In the present proposal, we will be examined the stability properties of MHD non-isothermal annular Poiseuille flow analysis through linear and weakly nonlinear stability analyses. A high order, more accurate Chebyshev spectral collocation method will be used to develop a numerical code for simulation of the magneto-convection instabilities. The evolution of magneto-convection instabilities is complicated and challenging in fluid dynamics research due to the buoyancy force and magnetic field competition. This study will be highly beneficial for improving the fidelity of numerical simulation. |