Non-Boussinesq Integral Model for Horizontal Turbulent Strongly Buoyant Plane Jets

Abstract

Horizontal buoyant jets are fundamental flow regimes for hydrogen safety analyses in the nuclear power plants. Integral model is an efficient, fast running engineering tool that can be used to obtain the jet trajectory, centerline dilution and other properties of the flow. In the published literature, most of the integral models that are used to predict the horizontal buoyant jet behavior employ the Boussinesq approximation, which limits the density range between the jets and the ambient. CorJet, a long researched, developed, and established commercial model, is such a Boussinesq model, and has proved to be accurate and reliable to predict the certain buoyant jet physics. In this study, Boussinesq and non-Boussinesq integral models with modified entrainment hypothesis were developed for modeling horizontal turbulent strongly buoyant plane jets. All the results and data where the Boussinesq model is valid will collapse to CorJet when they are properly normalized, which implies that the calculation is not sensitive to density variations in Boussinesq model. However, non-Boussinesq results will never collapse to CorJet analyses using the same normalized scaling, and the results are dependent on the density variation. The reason is that CorJet employs the Boussinesq approximation in which density variations are only important in the buoyancy term. For hydrogen safety analyses, the large density variation between hydrogen and the ambient, which is normally the mixture of air and steam, will make the Boussinesq approximation invalid, and the effect of the density variation on the inertial mass of the fluid can not neglected. This study highlights the assumption of the Boussinesq approximation as a limiting, simplified theory for strongly buoyant jets. A generalized scaling theory for horizontal strongly buoyant jet seems not to exist when the Boussinesq approximation is not applicable. This study also reveals that the density variation between jets and the ambient should be less than 10% to accurately model horizontal buoyant jets when the Boussinesq approximation is applied. Verification of this integral model is established with available data and comparisons over a large range of density variations with the CFD codes GASFLOW and Fluent. The model has proved to be an efficient engineering tool for predicting horizontal strongly buoyant plane jets.