Temperature distribution of shallow water FLNG cooling water outfalls

Abstract

FLNG cooling water outfalls can be characterized as high momentum buoyant jets, relatively close to the surface. The buoyant jet trajectories, spreading rates and surface distribution very much depend on the jet outflow characteristics. A study with the CFD software OpenFOAM has been carried out into the mixing and transport processes of buoyant jets. It is shown that OpenFOAM can be used to model the three dimensional trajectories of buoyant jets and their far-field buoyant plume distribution. Two dominant mixing processes are the result of the high initial jet momentum. First, the high momentum jet results in large turbulent jet entrainment rates. Second, the relatively shallow high momentum jets result in large horizontal surface currents. These currents horizontally advect the buoyant plume into the far-field and result in steep vertical velocity gradients, which induce vertical mixing of the buoyant plume. The momentum length scale, Lm proves to be an important parameter to characterize buoyant jets. The momentum length scale represents a distance along the jet trajectory, where buoyancy effects become dominant over initial jet momentum. For these jet characteristics it is found that the dimensionless surface temperature rise follows a logistic distribution function to the momentum length scale, after the point of surface impingement. The relative surface temperature results become constant for increasing values of the momentum length scale. This is the result of increased mixing by the jet turbulent entrainment and steep vertical velocity gradient. From the logistic distribution an empirical relation is found which can accurately predict the surface temperature rise as a function of the outfall velocity, outfall diameter, outfall temperature, outfall angle and distance from the jet orifice. The outfall depth appears to have no significant influence on the surface temperature rise for the conditions used in this study. The empirical equation proves to give reliable results for distances larger than 1.5 times the value of the momentum length scale and jet submergence smaller than 7.5 times the jet diameter. The robustness of the equation is also tested for extreme value outfall scenarios. The equation overestimates the temperature rise for small outflow diameters, combined with high initial jet temperatures. For other considered extreme values, the equation proves to give reliable results. Moreover, it is also demonstrated that the standard k-epsilon turbulence closure can be successfully used to model the buoyant jet centerline velocities, jet trajectories, spreading rates and centerline dilution rates of a round turbulent buoyant jet.