Direct Numerical Simulation of Forced Convective Heat Transfer From a Heated Rotating Sphere in Laminar Flows

Abstract

The laminar forced convection of a heated rotating sphere in air has been studied using a three-dimensional immersed boundary based direct numerical simulation method. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the rotating sphere, a moving Lagrangian grid is used, which tracks the rotational motion of the particle. A force density function or an energy density futiction is introduced to represent the momentum interaction or thermal interaction between the sphere and fluid. This numerical method is validated by comparing simulation results with analytical solutions of heat diffusion problem and other published experimental data. The flow structures and the mean Nusselt nttmbers for flow Reynolds number ratigitig from 0 to 1000 are obtained. We compared our simulation results of the mean Nusselt numbers with the correlations from the literature and found a good agreement for flow Reynolds number greater than 500; however, a significant discrepancy arises at flow Reynolds number below 500. This leads us to develop a new equation that correlates the mean Nusselt number of a heated rotating sphere for flows of Q < Re < 500.

A Resolved Eulerian–Lagrangian Simulation of Fluidization of 1204 Heated Spheres in a Bed With Heat Transfer

“…The DNS-IB has been implemented to solve particle motions and fluid velocity fields of particulate flows by Feng and Michaelides [8,9]. It has also been extended to solve heat transfer of moving particles with various applications [11][12][13]. Below, we provide a brief description of the method.…”

“…The strength of the forcing function is chosen to enforce the no-slip velocity boundary condition; it makes the treatment of solid-fluid momentum exchange much easier. Feng and Michaelides extended DNS-IB to study particulate flows with heat and mass transfer by introducing a thermal density function to enforce notemperature-jump conditions at the interface of particles and fluid [8,[11][12][13]. Using the DNS-IB, Deen et al [14] studied the heat transfer of particles in fixed and fluidized beds.…”

Mixed convective heat transfer from a heated sphere at an arbitrary incident flow angle in laminar flows

“…The immersed boundary method (IBM) [15] combined with a direct forcing scheme [16] has been implemented for solving particle motions and fluid velocity fields of particulate flows by Feng and Michaelides [17]. It has also been extended to solve heat transfer of moving particles in a viscous fluid by Feng and Michaelides [18,19] and by Feng [20]. For the present problem, the sphere is considered fixed with no rotational or translational velocity.…”

“…where For the velocity field of the entire domain, it follows the modified Navier-Stokes equation [20]:…”

“…The effect of the time step δt on the computed overall Nusselt number In our study on the heat diffusion from a heated sphere[24,20], we found that the size of the computational domain could significantly affect the temperature field in the outer region at longer times; however, it has an insignificant effect on the inner field and the overall Nusselt number. Maintaining the grid spacing and the time step δt = 0.0005, the effect of the domain size on the mixed convection for a completely upward flow (θ = 0°) on a heated sphere is further investigated by choosing three domain sizes: 8a×8a×24a, 10a×10a×20a, and 4a×20a×10a, respectively.…”