On the validity of Boussinesq approximation in transient simulation of single-phase natural circulation loops

Application of One-dimensional numerical models with Boussinesq approximation is a common approach for stability evaluation of single-phase natural circulation loops. Present work focuses on assessing the viability of such approximation during nonlinear stability appraisal following transient simulation. Accordingly a 3-D computational model of a rectangular loop is developed, with heating at bottom horizontal arm and isothermal sink around the top. Transient conservation equations are solved, performing simulations both with complete variation of all relevant thermophysical properties and the simple Boussinesq model. System exhibits unstable behavior with increase in both heater power and sink temperature, the nature of the temporal response being significantly affected by the coolant-side condition. Boussinesq model predicts instability for substantially lower power levels, along with bidirectional pulsing in flow rate and presence of secondary motion at the corners of the horizontal arm. The system also takes much longer time to initiate the flow, compared to the model with complete property variation, the deviation being larger at enhanced power levels. Hence the Boussinesq approximation provides a highly-conservative estimate of the stability boundary and is not a practicable tool for transient analyses of single-phase loops, particularly at higher powers.