Buoyant jet and two-phase jet-plume modeling for application to large water pools

Abstract

Models of a single-phase liquid-into-liquid buoyant jet and a two-phase vapor-into-liquid turbulent jet-plume injected in horizontal orientation were developed for analyzing the dynamics of the mixing characteristics and thermal response for shallow submergence of the source in large pools. These models were developed from the Reynolds averaged Navier–Stokes equations in the cylindrical system for steady axisymmetric flow and incorporated the integral plume theory. The bases for the general assumptions such as self-similarity and use of Gaussian profiles to represent the velocity field across the effluent cross-section are examined. Subroutines were developed to reproduce the governing differential equations formulated from the continuity, momentum and conservation of buoyancy or energy equations which treats the jet-plume's half-width, velocity and temperature as variables and seek solutions of these variables along the jet-plume trajectory. Information on empirical closure relations obtained from experimental data such as the coefficient-of-entrainment, bubble slip velocity, momentum amplification factor, and plume spread-ratios for buoyancy and density-defect which are available for adiabatic cases were applied to the case of steam-into-water. Solutions were obtained without cross-flow in a linearly stratified ambient and then with cross-flow in a homogeneously mixed ambient for the single-phase formulation that represents a complete condensation scenario of a buoyant jet. The model was finally extended to the turbulent two-phase jet-plume case and the results were compared to available jet-plume pool condensation data. The analysis and results proved to be comparable to experimental data in predicting the pool surface temperature to within 0.5 °C, however, temperature fluctuations along the jet-plume path were not adequately captured by the model since an oscillating input component was not incorporated in the model formulation; indeed the pool surface temperature proved to be of higher importance, which was adequately captured by the model.