This analysis has studied natural convection for the temperature-dependent viscosity of fluids inside porous media between two concentric spheres by numerically solving the Brinkman-Darcy-Forchheimer model, vorticity transport, and energy equations. Parameters included Rayleigh numbers (5.0 Â 10 3 -8.0 Â 10 4 ) at radius ratios of 1.5, 2.0, and 3.5 with porosities of 0.4 and 0.9 for variable-viscosity fluids with Prandtl numbers (158, 405, and 720) when the Darcy number was changed at 0.1 and 0.001. The results showed that the mean Nusselt number varied with Rayleigh number, porosity, radius ratio, and variable viscosity but did not change with the Darcy number.
According to the field measurement in 2012, the bathymetry in the area of Port Mailiao, located in the middle of Taiwan's west coast, shows an erosion with size distribution about 500m by 100m. The maximum scour depth is 26m (from22m eroded to -48m). Although scour has become a serious threat to breakwater structures and the safety of navigation, it is able to be predicted rapidly by applying the CFD numerical simulation, with low cost and high reliability. In the study, the numerical simulation of currents and wave fields, and wave-current interaction on flow fields were performed by the commercial code FLOW-3D in purpose to investigate the causes of erosion by using Typhoon waves of 50-year return period at Port Mailiao open sea and data extracted from Acoustic Doppler Current Profiler as the requirements of tidal boundaries, a fixed-bed bottom boundary was generated by sounding data of the year 1996 , and the harbor CAD physical model as the requirement of closing boundary. Moreover, sensitivity of both grid independence and numerical domain were tested to reach a steady flow field. The results of the study indicate that a shed vortex form at leeside of the breakwater during tidal cycle is conformed to currents data with numerical modeling. Furthermore, describe the distribution of velocity profiles, excess shear stress and tidal currents by visualization, the application of scour potential model with the Stokes 5th order wave boundary is found to give more reasonable results.
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