Numerical Study of Double Diffusive Natural Convection in a Rectangular Cavity with Discrete Heat Sources Using Velocity-Vorticity Equations
D. Senthil Kumar1, K. Murugesan2 and Akhilesh Gupta3
1Research Scholar, Mechanical & Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee 247 667, India.
dskumar33@yahoo.com
2Asst. Professor Corresponding Author, Mechanical & Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee 247 667, India.
kirmufme@iitr.ernet.in
3Professor, Mechanical & Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee 247 667, India.
akhilfme@iitr.ernet.in
ABSTRACT
The combined effect of thermosolutal buoyancy forces due to temperature and concentration gradients causes fluid motion in a confined domain. Such a phenomenon is called double diffusive natural convection and it has relevance to oceanography, astrophysics, geology, nuclear reactor cooling, nuclear waste disposal, contaminant transport, crystal growth, chemical processing, etc. In vortex-dominated flows such as the double diffusive convection problems the vorticity advection is a fundamental process that determines the dynamics of the flow. Hence the stream function-vorticity and velocity-vorticity form of momentum equations are closer to physical reality. The main advantage of these vorticity formulations is that it is free from the pressure term, which is coupled indirectly with continuity constraint. Widely used stream function-vorticity formulation is limited only to two-dimensional domain and the kinematics variable velocity of the problem is indirectly computed unlike in velocity-vorticity form of momentum equations. In the present work numerical simulation of two-dimensional steady state double diffusive natural convection in a rectangular cavity with discrete heat sources on the bottom wall is carried out. The governing equations consist of vorticity transport equation, velocity Poisson equations, energy equation and concentration equation. The governing equations are discretized using Galerkin’s weighted residual finite element method using global matrix-free finite element algorithm. Since the above equations are coupled an iterative computational algorithm is used to obtain solution for the velocity, vorticity, temperature and concentration fields. Second order accurate Taylor’s series expansion scheme is employed to compute the vorticity boundary conditions. Validation results are obtained for a double diffusive natural convection in a square cavity and compared with results available in the literature. For the double diffusive problem considered in the present work, results are reported for the effect of buoyancy forces on the flow field for 103≤ Ra ≤105 and −10≤ N ≤ 10.
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