Numerical simulation of mixed convection in vertical concentric cylinders

We conduct numerical simulation of mixed convection in a gap between rotating hot inner cylinder and stationary cold outer cylinder to investigate flow regimes at various intensities of rotational speed and buoyancy in terms of Reynolds number and Grashof number. For the current study, a projection method with explicit Adams-Bashforth and implicit Crank-Nicolson schemes was adopted. Flows with various Reynolds numbers are investigated at fixed Grashof number, and flow pattern is examined through streamlines and iso-surfaces of helicity. Phase plots constructed by velocity components, Nusselt number and torque reveal the transition between different flow regimes. With Grashof number less than 3000, the flow go through a sequence of axisymmetric, spiral and Taylor-Couette flow as Reynolds number increases, while the flow with Grashof number 4000 shows complex pattern including quasi-periodic flows and chaos in a wide range of Reynolds number. Transition to chaos is investigated using the budget analysis of centrifugal and buoyant forces, indicating that competition between the two driving forces causes chaos.