At the initial stage of injection, the injection flow has not yet broken up and in a range of small atmosphere pressure (16∼500KPa), the tip of the injection flow always forms a shape of mushroom. ^{[1] [2]} Moreover, the umbrella of the mushroom is always very big and its root is always very thin, especially when the atmosphere pressure is relatively low (88KPa, or 100mmHg). These phenomena are not known popularly and the reason of mushroom formation is not clear. In this paper, with the MARS method for simulating free surface, analysis of injection flow is practiced. The phenomena are reproduced and the reason is cleared that the formation of the mushroom is induced by the momentum exchange between the injection fuel flow with very high speed and the very complex flow of the air.

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We proposed an improved immiscible lattice BGK model for simulating multiphase flows. The surface tension effect was recovered by introducing a force term based on the appropriate continuum physics. The anti-diffusion scheme in the mixed region was applied to reduce the side-effect of recoloring step and control the thickness of the interface. The simulation of a static bubble was used as a test case. Laplace's law, spurious velocities and isotropy property were examined. The results show that our model has more advantages for simulations of immiscible fluids over the existing immiscible lattice BGK models. Furthermore, the simulations of droplet formation in a Cross-junction microchannel were performed and compared with the experiments. The numerical results show good agreements with the experimental ones for the evolution of the droplet.

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A numerical method for solving Navier-Stokes equations and combined with a phase-field interface model is applied to flow problems of motion of an incompressible isothermal two-phase fluid with a high density ratio on a solid surface. Based on the free-energy theory, a fluid interface is described as a finite volumetric zone across which the physical properties vary continuously. The wettability of a solid surface is taken into account through a simple boundary condition derived from the increase in free energy on the surface. The phase-field approach simplifies the capture of motions of a fluid interface on a surface (contact line). The major findings from the simulations are as follows: (1) the contact-line motions of the liquid column under gravity are well predicted in comparison with the available data; (2) the static contact angle is flexibly controlled by a parameter of the wetting potential of the surface; (3) the capillary force is evaluated appropriately; (4) the acceleration of the two-phase flow in a channel with a local hydrophilic surface is predicted and observed to be in qualitative agreement with the experimental data; and (5) the displacement and breakup of a single drop on a flat solid wall are well predicted qualitatively. These results prove that the phase-field method can be employed for simulating air-water flows on a surface with heterogeneous wettability.

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A lattice Boltzmann method (LBM) for two-phase viscoelastic fluid flows is proposed. The method is mainly an extension of the LBM for two-phase flows with large density differences proposed by Inamuro et al. [Journal of Computational Physics Vol. 198, No. 2 (2004), pp. 628-644]. The viscoelastic effects are introduced by the constitutive equation based on the Maxwell model, which has a spring and a dashpot connected with each other in series. The method is applied to simulations of a drop under shear flow in viscoelastic fluids and of a bubble rising in viscoelastic fluids. In the simulation of drop deformation under shear flows, the effects of viscoelasticity on the deformation and orientation angle are evaluated. In the simulation of bubble rising in viscoelastic fluids, a cusp configuration at the trailing edge is investigated and compared with the theoretical prediction and other numerical results.

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