Numerical prediction of three-dimensional thermally driven flows in a rotating frame

Abstract

An original approach has been used to solve the three-dimensional unsteady incompressible flow in a uniformly rotating frame. The governing equations of fluid motion are discretized using a control-volume procedure, which ensures the satisfaction of global conservation laws. Pressure and velocities are calculated iteratively at each time-level, yielding a semi-implicit scheme. Buoyancy effects are included by using the Boussinesq approximation. The current form of the energy equation neglects the presence of internal energy point sources and sinks, viscous dissipation of energy and work done by the body force. The model is tested by using it to simulate the three-dimensional incompressible flow in a fluid annulus rotating with uniform angular velocity, with differential heating provided by maintaining the side-walls of the convection chamber at separate temperatures. Fluid heat transports obtained from the model agree well with those obtained from experimental measurement.