The validation region of the Boussinesq approximation for nuclear reactor operation and atmospheric pressure conditions

In natural convection problem, buoyancy term is important than other terms. An exact solution fully considering the buoyancy term has not existed until now. Some approximation is required to asses the engineering problem. The Boussinesq approximation is the simplest among the other methods. The approximation is derived based on the following: 1. Density is assumed constant except the momentum equation. 2. All other fluid properties are assumed constant. 3. Viscous dissipation is negligible. These assumptions constricted application region of the Boussinesq approximation. From condition 1 and 2, the approximation is constricted in the incompressible liquid region. Condition 3 constricted that the acoustic phenomena cannot be treated. The constriction, however, is so abstract as not to asses the validation of the Boussinesq approximation with the problems, directly. The present study allows an explicit region of the validity of the Boussinesq approximation. This means that a solution about natural convection can be meaningful only when the conditions under which the approximation is valid are explicitly known. Investigation of the explicit region was made by Spiegel and Veronis. They used an order of magnitude method for a perfect gas. Mihaljan derived the Boussinesq equations on the thin layer flow using the small parameter expansion technique. Gray expanded the Mihaljan's method to the liquid and considered all fluid properties to vary with temperature and pressure. Present study expanded the Gray's result to the condition of the nuclear reactor operation region and severe accident condition. The results will show the validity and limitation region of the Boussinesq approximation applicable to the severe accident analysis