| In the paper, computational results of the attempt to explain the phenomenon of skin-friction reduction due to microbubble injection are presented. The numerical simulations are consisted of two parts: the first is to simulate the friction reduction by microbubbles on a flat plate; the second is to simulate initially the friction reduction on the approximated ship model with the flat bottom. The model of FPSA (Inter-Phase Slip Algorithm) provided in PHOfvMCS, the software used in Computational Fluid Dynamics, which solves the Navier-Stokes equations of each phase with the interphase interactions between two phase of water and air, including the interphase drag forces, interphase lift forces, interphase pressure and virtual mass forces, is employed with the difference scheme of UPWIND and the orthonormal grid. Under considering the impact of bubbles on the turbulence, the K-? model modified with the presence of microbubbles is employed, postulating the turbulent kinetic energy K and the dissipation rate ? are the properties of continuous phase.In the simulation of friction reduction on a flat plate, since the effects, including the order of magni tude of several interact ions between water and microbubbles and correlated coefficient models of interactions, on the results are unknown, which are rather important in establishing the simplified model put into the theory and engineering practice, the results about them are presented as the preparation for the further study. Two main physical surroundings for two different injecting means are simulated. In the 1 ight of results, the interphase pressure can be ignored and the interphase lift force plays a trifling role in the friction reduction, while the gravity-buoyancy, the interphase drag force and the virtual mass force are influential, especially in the bigger bubble. As the moving particle in the turbulence boundary layer, the resistance on microbubble from water may be fallen inside the scope of the Stokes Law. However, the computed results shows that the spherical bubble drag as an alternative is suitable better than the Stokes.Besides, as results shown under considering factors affecting the friction reduction, with the increase of microbubble diameter within100?w and the grads of air volume fraction in injection normal to the plate, the magnitude of friction reduction will be increased. There is an important parameter, the air injection ratio, which is the ratio of the injection air volume to the injection area multiplied with the free-stream speed. The results predict the local friction reduction increases with the air injection ration hut decreases with the distance-away from the injection, which is in conformity with experiments.As the first step towards further exploring the mechanism of the friction reduction induced hy microhubhles for an approximated ship-model, in the calculations with the goal of knowing the relationship of the air injection ratio with the friction reduction qualitatively, the simulations is in comparison with the experiment in which the length of ship with a flat bottom is 10m under the same condition of free-steam veloci ties of 5w/s and 7m/s within a certai n scope of the air injection ratio. Results indicated that the friction reduction of ship flat bottom is proportional to the air injection ratio and adversely proportional to the distance from the injection. In addition, the free surface approximated with zero flux also is investigated in the field of velocity near the free surface and the bow, which is reliable from results. |
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