Assessment of the boussinesq approximation for buoyancy-driven flows

The numerical simulation of buoyant flows often makes use of the Boussinesq approximation. This is particularly true when Direct Numerical Simulation is used for the analysis of heat transfer loops or other applications of natural convection flows. Boussinesq approximation consists of considering the density strictly constant, adding the buoyant force to the momentum balance and coupling an equation for the temperature to the incompressible Navier-Stokes system that has to be solved. In this paper, the validity of the Boussinesq approximation is investigated in some details via numerical simulations. The test cases chosen include a differentially heated cavity and two buoyant heated loops with internal heating. Results show clearly that the error on some performance parameters depends linearly on the compressibility parameter βΔΤ The error in some cases can be 20% or higher, but it is drastically reduced to a few percent by the use of a 2ⁿͩ order formulation of the Boussinesq source term. Nevertheless, some flow features are strictly tied to the compressible coupling and are not captured in a Boussinesq framework