Numerical Simulations of Incompressible Flows Around a Rotating Circular Cylinder with Convective Heat Transfer Using the Immersed Boundary Method

An adaptive immersed boundary method (IBM) for simulating non-isothermal incompressible flows with convective heat transfer involving a rotating circular cylinder is developed. Both Dirichlet- (isothermal) and Neumann (zero heat flux)-type temperature boundary conditions are implemented. In addition to the discrete momentum forcing and energy forcing adopted to effectively satisfy the prescribed velocity and temperature boundary conditions, a mass source/sink term is introduced into the continuity equation to meet the mass conservation at the immersed boundary. The Navier–Stokes equations are solved using the fractional step method implemented on a staggered Cartesian grid system. Time stepping is performed using a second-order Adams–Bashforth/backward-differentiation method, while spatial derivatives are approximated with a second-order centered scheme. Testing of the flow induced by a rotating disk demonstrates that the spatial accuracy of the presented algorithm is second-order. Furthermore, the proposed method is validated by forced convective flow past a rotating isothermal circular cylinder. Finally, mixed Rayleigh–Bénard convection in a square cavity with an embedded adiabatic rotating circular cylinder is simulated, showing that heat transport can be greatly enhanced by increasing the rotating rate and radius of the cylinder at larger Prandtl numbers in the laminar regime.