Numerical study of natural convection states in a horizontal concentric cylindrical annulus using SPH method

TL;DR

This study develops and validates an SPH method to simulate natural convection in a cylindrical annulus, revealing how flow stability and convection states vary with Rayleigh and Prandtl numbers.

Contribution

The paper introduces a validated SPH approach for natural convection, identifying four distinct convection states and their dependence on Rayleigh and Prandtl numbers.

Findings

Flow is stable at low Rayleigh numbers and unstable at high Rayleigh numbers.

Transition from stable to unstable states occurs at lower Rayleigh numbers for low Prandtl numbers.

Four convection states are identified: SP1, UP1, SPN, and UPN.

Abstract

Natural convection is of great importance in many engineering applications. This paper presents a smoothed particle hydrodynamics (SPH) method for natural convection. 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 numerical method is validated by comparing numerical results with experimental results from literature. The numerical and experimental results reach a good agreement. Then the SPH method is applied to study the natural convection in a horizontal concentric cylindrical annulus with Rayleigh number in the range of 10^2 to 10^7 and Prandtl number in the range of 0.01 to 10. In general, the flow is stable at low Rayleigh number but unstable at high Rayleigh number. The transition Rayleigh number from stable to unstable states is lower in the low Prandtl number cases than in the high Prandtl number cases. Four different convection states are identified in numerical simulations, namely, stable state with 1 plume (SP1), unstable state with 1 plume (UP1), stable state with n (n > 1) plumes (SPN), and unstable state with n (n > 1) plumes (UPN). The SP1 and UP1 states are observed for all Prandtl numbers, while the SPN and UPN states are only observed at Pr = 0.1 and 0.01.