TRANSIENT ANALYSIS OF NATURAL CONVECTION FLOW IN ENCLOSURES AND ITS APPLICATION TO SOLAR COLLECTORS AND BUILDINGS

Abstract

A higher order accurate numerical method for solving viscous incompressible Navier-Stokes equations is developed and its application to analyse the transient natural convection flow in enclosures is discussed. The inherent numerical errors in the current numerical methods such as factorization error, linearization error and discretization error, have essentially limited the accuracy of these methods upto second order only. Though vorticity – streamfunction methods have been developed to avoid the factorization error, the vorticity boundary conditions are not known in advance and are derived quantities only. A generalised solution methodology based on existing Vorticity – Streamfunction methods is developed to show that the vorticity boundary condition being implemented is explicit in nature. A novel numerical solution method of Vorticity – Streamfunction formulation is proposed by implementing the Vorticity boundary conditions implicitly. The developed method is applied over various types of boundaries encountered in natural convection flows such as regular (square/rectangular) boundary enclosures, non-rectangular/Irregular boundary enclosures and boundary with obstructions. The results obtained closely match with standard reference results available in literature demonstrating the 2nd order overall accuracy. Convergence behaviour of implicit vorticity boundary conditions show that present method exhibits faster convergence and better stability over conventional vorticity – streamfunction formulation. The developed numerical method is extended to allied convection phenomenon such as conjugate convection, double diffusive convection and mixed convection. In all the studied cases the developed numerical method was validated with standard benchmark results and found that the developed numerical method could accurately predict the fluid flow behaviour accurately with second order convergence upto the boundary.