Previous laboratory experiments and associated numerical models of laminar flows forced by oscillatory, along-shelf background currents are extended to include some of the effects of boundary-generated turbulence. The experiments are conducted in the 13-m-diameter rotating-flow facility in Grenoble, France. Two pairs of case studies, one at a large forcing velocity (designated as FAST) for which the boundary layers are fully turbulent during part of the flow cycle and one at relatively smaller forcing (SLOW) for which transitional boundary layers are operative at the higher speeds of the background flow, are conducted. Smooth and artificially roughened boundaries are considered, respectively, for each of these pairs. Phase-averaged and time-mean velocity, vertical vorticity, and horizontal divergence fields are found to be qualitatively similar to those of previous laminar experiments. The similarities in the time-mean fields are that (i) within the canyon they are dominated by cyclonic vorticity with maxima centered near the shelf break; (ii) within and in the vicinity of the canyon the general circulation pattern includes a net transport into the canyon through its mouth, a net upwelling in the canyon interior, a transport away from the canyon over the shelf break along both sides of the canyon, and, by inference, a return flow to the deep ocean; and (iii) the interior time-mean flow is characterized by a well-defined coastal current whose axis follows the shelf in the vicinity of the shelf break, with the coast on the right. It is found that the measurements of the characteristic speed of the residual or time-mean flow within the canyon for the transitional and fully turbulent experiments do not follow the scaling law derived earlier for laminar experiments. An alternative scaling analysis for large-Reynolds-number flows is thus derived. Although sufficient numbers of experiments are not available to test the hypothesis fully, the measurements available for the fully turbulent flows are consistent with the theory advanced.

Evaporating fronts propagate through porous media during drying processes, underground coal gasification, geothermal energy production from hot dry rock, and around nuclear waste repositories. Present work will focus on the one-dimensional heat transfer at the interface between vapor saturated porous matrix and water saturated porous region and evaluate the conditions for which various approximations yield an accurate representation of front velocity. An implicit finite difference scheme is utilized to simulate the propagation of an evaporating front in a porous medium saturated with water and undergoing the phase change process. The assumption of local thermal equilibrium (LTE) which results in a one-equation model and a simple two-equation model that does not assume LTE are examined by comparison with a quasi-analytic numerical model. We consider the case for low Reynolds number, hence Nusselt number is assumed constant. Results illustrate that the one-equation model does not yield accurate results even if the length scale for diffusion in the solid phase is relatively small. The one-equation model predicts faster front propagation than the two-equation model. It is illustrated that the one-equation model yields satisfactory results only when thermophysical properties characterized by the volume weighted ratio of thermal diffusivities is reduced to an order of magnitude less than those for the applications of interest. In addition, consistent with the established “rule of thumb”, for Biot < 0.1, the traditional two-equation model which makes the lumped capacitance assumption for the solid phase compares well with a two-equation model that more accurately predicts the time dependent diffusion in the solid phase using Duhamel’s theorem.

No abstract

High intensity drying is used to characterize those situations for which the drying medium is sufficiently above the saturation temperature of water to preclude the existence of a two-phase zone. In the present work, three models are applied to high intensity drying of porous materials. The three models are: (1) a traditional one-equation model that assumes local thermal equilibrium (LTE); (2) a two-equation model that utilizes lumped capacitance assumption to predict the heat transfer to the solid phase; and (3) a two-equation model that utilizes a more precise quasi-analytical approach to more accurately characterize the conduction in the solid phase. In addition, the relationship between pressure and the drying conditions and material properties is examined since elevated pressure that can occur during high intensity drying is potentially destructive. An implicit finite difference scheme is utilized to determine the drying rate in a porous medium saturated with water and undergoing the phase change process. The case for low local Reynolds number is considered, hence Nusselt number is assumed constant. Results illustrate that the one-equation model does not yield accurate results when the thermophysical properties characterized by the volume weighted ratio of thermal diffusivities, C > 10 (within 5% error). Hence, a two-equation model is suggested. In addition, consistent with the established “rule of thumb,” for Biot number, Biv < 0.1, the traditional two-equation model which makes the lumped capacitance assumption for the solid phase compares well with a two-equation model that more accurately predicts the time dependent diffusion in the solid phase using Duhamel’s theorem. The peak pressures observed during drying for a range of Darcy number and surface heat flux are presented.