Numerical study of natural convection in a horizontal concentric annulus using smoothed particle hydrodynamics

Abstract

Natural convection is of great importance in many engineering applications. This paper presents a smoothed particle hydrodynamics (SPH) method for natural convection simulation. The conservation equations of mass, momentum and energy of fluid are discretized into SPH equations. The body force due to the change of density in a temperature field is considered by the Boussinesq approximation. The SPH method is validated by experimental results in temperature distribution. Then the SPH method is applied to characterize the natural convection in a horizontal cylindrical annulus with varying both Rayleigh number (102 to 107) and Prandtl number (0.01 to 10), while in literature the effect of Prandtl number was usually not considered. In general, the flow is stable at low Rayleigh number but unstable at high Rayleigh number. The numerical results show that the transition Rayleigh number, from stable to unstable, varies with Prandtl number. Four different convection states are identified from numerical simulations, namely, stable state with one plume, unstable state with one plume, stable state with multiple plumes, and unstable state with multiple plumes. The two one-plume states are observed for all Prandtl numbers, while the two multiple-plume states are observed only for Pr = 0.1 and 0.01. It is believed that high thermal diffusivity (low Pr) enhances heat transfer, which modifies the flow and induces instability. An exception case is observed at Pr = 0.1 – the flow is unstable at Ra = 104 but stable at Ra = 105, which can be explained by vortex interactions. Therefore, the flow states depend on not only the Rayleigh and Prandtl numbers but also the vortex interactions.