Numerical simulation of natural convection using unsteady compressible Navier-stokes equations

Abstract

Purpose

Boussinesq approximation is widely used in solving natural convection problems, but it has severe practical limitations. Using Boussinesq approximation, the temperature difference should be less than 28.6 K. The purpose of this study is to get rid of Boussinesq approximation and simulates the natural convection problems using an unsteady compressible Navier-Stokes solver. The gravity force is included in the source term. Three temperature differences are used namely 20 K, 700 K and 2000 K.

Design/methodology/approach

The calculations are carried out on the square and sinusoidal cavities. The results of low temperature difference have good agreement with the experimental and previous calculated data. It is found that, the high temperature difference has a significant effect on the density.

Findings

Due to mass conservation, the density variation affects the velocity distribution and its symmetry. On the other hand, the density variation has a negligible effect on the temperature distribution.

Originality/value

The present calculation method has no limitations but its convergence is slow. The current study can be used in fluid flow simulations for nuclear power applications in natural convection flows subjected to large temperature differences.

Citation

El-Gendi, M.M. and M. Aly, A. (2017), "Numerical simulation of natural convection using unsteady compressible Navier-stokes equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 11, pp. 2508-2527. https://doi.org/10.1108/HFF-10-2016-0376