Analysis of a Propeller Wake Flow Field Using Viscous Fluid Mechanics

The computational fluid dynamics （CFD） method is used to numerically simulate a propeller wake flow field in open water. A sub-domain hybrid mesh method was adopted in this paper. The computation domain was separated into two sub-domains, in which tetrahedral elements were used in the inner domain to match the complicated geometry of the propeller, while hexahedral elements were used in the outer domain. The mesh was locally refined on the propeller surface and near the wake flow field, and a size function was used to control the growth rate of the grid. Sections at different axial location were used to study the spatial evolution of the propeller wake in the region ranging from the disc to one propeller diameter （D） downstream. The numerical results show that the axial velocity fluctuates along the wake flow; radial velocity, which is closely related to vortices, attenuates strongly. The trailing vortices interact with the tip vortex at the blades＇ trailing edge and then separate. The strength of the vortex shrinks rapidly, and the radius decreases 20% at one diameter downstream.

Viscous Fluid Flowing around the Plate: Turbulence

Diffusion of momentum gives rise to viscosity. This article presents a solution in the explicit form of the equation of the momentum diffusion for a viscous fluid flowing around a plate taking into account deceleration. Three characteristic regions of a viscous flow have been described: the mantle, the body of the boundary layer, the viscous sublayer. In the mantle, the effect of viscosity is significant at a considerable distance from the plate. The momentum diffusion is focused in the body of the boundary layer. The diffusion force that produces the momentum of force giving rise to eddies is localized in the viscous sublayer. At the beginning of the plate, a moment of force twists the liquid along the flow, creating eddies that roll along the plate. For this reason, they are pressed against the surface of the plate. But at some distance from the beginning of the plate, the moment of force changes its orientation to the opposite and twists the vortices in the opposite direction, causing the vortices to roll along the plate against the flow. This causes the liquid to detach from the surface of the plate. This is the beginning of turbulence. The diameter of the vortex produced in the viscous sublayer is small being of the order of the thickness of the viscous sublayer. The vortex possesses a large angular velocity. Due to the momentum diffusion and the effect of the eddies combined in passing along the plate, its diameter increases up to the size of the thickness of the boundary layer and even more, whereas its angular velocity decreases down to the values really observed. The value of the critical Reynolds number of the transition from the laminar flow to the turbulent one has been found, and it agrees with the experimental data. The value of the shear stress produced by the viscous fluid on the plate surface has also been obtained. The way of measurement of the friction coefficient characterizing the effect of the plate on the flow has been proposed. It has been shown that the boundary condition of adhesion to the surface of a body flown around, that is applied in the estimation of viscous flows, contradicts the real processes of the flow.

MIXED COMPATIBLE ELEMENT AND MIXED HYBRID INCOMPATIBLE ELEMENT VARIATIONAL METHODS IN DYNAMICS OF VISCOUS BAROTROPIC FLUIDS

This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.