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A train of high-speed microdrops impacting on a liquid pool can create a very deep and narrow cavity, reaching depths more than 1000 times the size of the individual drops. The impact of such a droplet train is studied numerically using boundary integral simulations. In these simulations, we solve the potential flow in the pool and in the impacting drops, taking into account the influence of liquid inertia, gravity and surface tension. We show that for microdrops the cavity shape and maximum depth primarily depend on the balance of inertia and surface tension and discuss how these are influenced by the spacing between the drops in the train. Finally, we derive simple scaling laws for the cavity depth and width.

To investigate the composition distribution that develops in continuously-cast steel during a grade change, an efficient, accurate, and user-friendly computational model has been developed. The model is fully transient and consists of three submodels, which account for mixing in the tundish, mixing in the liquid core of the strand, and

An experimental investigation of existing conditions of the threshold pressure gradient (TPG) for gas flow in waterbearing tight gas reservoirs was made and discussed, using cores at different water saturations prepared from the Sichuan gas field in China. The existence of TPG was proven, and the relationship between TPG and water saturation and absolute permeability were obtained by laboratory tests. TPG increases with higher water saturation and lower absolute permeability. Consequently, a mathematical model of low-velocity non-Darcy gas flow was established on the basis of conservation of mass and momentum equations. According to the analytical solution of non-Darcy radial flow derived here, an easy and accurate calculation method of the control radius is presented, which is most popular with reservoir engineers. Factors, such as TPG and isothermal compressibility, on effective deployment were also discussed. The analysis of calculation results demonstrates that peripheral reserves of the wellbore are difficult to deploy and formation energy is used mainly near the wellbore because of the existence of TPG, unlike in Darcy flow. The quantification of effective deployment of water-bearing tight gas reservoirs provides a theoretical foundation for reservoir evaluation and development design.

Mathematical models have been developed and applied to investigate the composition distributions that arise during steel grade changes in the continuous slab casting processes. Three-dimensional turbulent flow and transient mixing phenomena in the mold and the strand were calculated under conditions corresponding to a sudden change in grade. The composition distribution in the final slab was then predicted. Reasonable agreement was obtained between predicted and experimental concentration profiles in the slab centerlines. Intermixing in the center extends many meters below the transition point while intermixing at the surface extends above. Higher casting speed increases the extent of intermixing. Mold width, ramping of casting speed, and nozzle design have only small effects. Slab thickness, however, significantly influences the intermixing length of the slab.The axial transport of solute due to turbulent eddy motion was found to be many orders of magnitude greater than molecular diffusion and thus dominates the resulting composition distribution. Different elements, therefore, exhibited the same mixing behavior under the same casting conditions, despite having different molecular properties. Numerical diffusion caused by the finite difference schemes was investigated and confirmed to be much less important than turbulent diffusion. In the lower portion of the strand (lower than 3 meters below the meniscus), the convection and diffusion can be reasonably approximated as one dimensional axial flow.2

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