Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan The Vortex in Cell (VIC) method for bubbly flow, proposed in the authors' prior study, is improved to promote the numerical accuracy and efficiency. The improvements are concerned with a discretization method using staggered grids, a correction method for vorticity and a single-stage calculation method for the convection of vortex element. To enlarge the applicability of the VIC method, vortex elements without core structure are employed. The improved VIC method is applied to simulate a bubble plume. In a tank containing water, small air bubbles are released from the base of the tank. The bubbles rise due to the buoyant force, inducing the water flow around them. The simulation for the plume at the starting period highlights that the rising bubbles induce vortex rings at their top and that a bubble cluster appears owing to the entrainment of the bubbles into the vortex rings. The rising velocity for the top of the bubbles is proportional to the square-root for the flowrate of the released bubbles, being consistent with existing theoretical and numerical investigations. The simulation also demonstrates that the developed bubble plume having some characteristics of a jet is successfully captured.
This study is concerned with the improvements of the Vortex in Cell (VIC) method for incompressible flow simulation. A discretization method employing a staggered grid is proposed to ensure the consistency between the discretized equations as well as to prevent the numerical oscillation of the solution. A method to modify the vorticity is presented to compute the vorticity field satisfying the solenoidal condition. A single-stage calculation method for the convection of vortex element is also proposed to reduce the computational time. To demonstrate the validity and applicability of these methods, the flows in a cubic cavity are simulated by the VIC method. The simulation demonstrates that the solenoidal condition for the vorticity is satisfied and that the velocity fields are in good agreement with the existing results. The Taylor-Görtler-Like vortices are successfully captured at Re=3200. It is also confirmed that the calculation for the convection of vortex element requires less computational time than the 2-stage Runge-Kutta method.
Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan Direct numerical simulation (DNS) for a turbulent channel flow is performed by the Vortex in Cell (VIC) method.The Reynolds number based on the friction velocity and the channel half width is 180. The improvements for the VIC method proposed in the prior study are used. Staggaerd grid is employed to ensure the consistency between the discretized equations as well as to prevent the numerical oscillation of the solution. A method correcting the vorticity is used so that the resultant vorticity field satisfies the solenoidal condition. A single-stage calculation method for the convection of vortex element is also utilized to reduce the computational time. The simulated turbulence statistics such as the mean velocity, the turbulence intensity and the Reynolds shear stress are favorably compared with the existing DNS results. The streak structures and the streamwise vortices near the wall are also successfully captured. These computational results demonstrate that the improved VIC method is indeed applicable to the DNS of wall turbulence simulations.
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