Availability of the Boundary Condition for Vorticity

By applying a boundary condition for vorticity [1] in addition to that for velocity, a velocity distribution on a flat plate set in a parallel homogeneous flow has been numerically obtained through a one-way calculation from surface to infinity, without the “matching” procedure between an analysis from surface to infinity and that from infinity to surface. The numerical results obtained were in excellent agreement with those by Howarth [2]. The usage of the boundary condition for vorticity has raised the accuracy of velocity distribution near a plate’s surface and made it possible to realize the one-way calculation from surface to infinity.

Exploration of the mechanism of cavitation vortex rope and vortex development in the draft tube of tubular turbine units

Draft tube vortex rope is considered a special cavitation flow phenomenon in tubular turbine units.Cavitation vortex rope is one of the most detrimental factors affecting the safety of hydraulic turbines.In this study,ANSYS CFX software was utilized to numerically simulate the internal cavitation flow of a hydraulic turbine draft tube.The evolution of the cavitation vortex core was characterized by vortex line distribution and vorticity transport equation.The shape and number of blades influenced the revolving direction and distribution characteristics of the vortex close to the runner cone,which formed a counterclockwise-clockwise-counterclockwise distribution pattern.Simultaneously,there were many secondary flows in the draft tube.Mutual cancellation and dissipation between the flows was one of the reasons for reduction in vorticity.When the cross-sectional shape of the draft tube was changed,the vorticity was distributed from the center of the vortex rope to all parts of the cross-sectional draft tube,with extreme values at the center and at the walls.The vortex stretching and dilatation terms played a major role in the change in vorticity,with the baroclinic torque having an effect at the center of the vortex rope,this study is helpful to understand the flow of water in the draft tube and guide the design and optimization of the draft tube in engineering application.

LES method of the tip clearance vortex cavitation in a propelling pump with special emphasis on the cavitation-vortex interaction

The turbulent cavitating flow around the propelling pump tip clearance is numerically simulated using the large eddy simulation(LES)method coupled with the Zwart-Gerber-Belamri(ZGB)cavitation model to investigate the cavitation-vortex interaction mechanism.The calculated cavitation structures around the blades are in a remarkable agreement with the experimental results.The distributions of the tip clearance vortex under two cavitation conditions are obtained and compared.The results show that the cavitation development enhances the vorticity generation and the flow unsteadiness around the tip clearance of a propelling pump.Vortices are basically located around the cavitation areas,particularly in the tip clearance region,during the cavitation.The relative vorticity transport equation is applied for the cavitating turbulent flows and it is further indicated that the vortex stretching term makes the main contribution in the vortex production,and the baroclinic torque and dilation terms are important source terms for the vorticity generation in the cavitating flow.In addition,the viscous diffusion term and the Coriolis force term are significant in modifying the vorticity field inside the blade tip clearance.

Large eddy simulation of the transient cavitating vortical flow in a jet pump with special emphasis on the unstable limited operation stage

This paper studies the unsteady three-dimensional cavitating turbulent flow in a jet pump.Specifically,thefocus is on the unstable limited operation stage,and both the computational and experimental methods are used.In the experiments,the distribution of the wall pressure,as well as the evolution of cavitation over time,are obtained for a jet pump.Computation is carried out using the large eddy simulation,combined with a mass transfer cavitation model.The numerical results are compared with the experimental results,including the fundamental performances(the pressure ratio h and the efficiencyη),as well as the wall pressure distribution.Both the experimental and computational results indicate that the evolution of the cavitation over time in a jet pump is a quasi-periodic process during the unstable limited operation stage.The annular vortex cavitation inception,development and collapse predicted by the large eddy simulation agree fairly well with the experimental observations.Furthermore,the relationship between the cavitation and the vortex structure is discussed based on the numerical results,and it is shown that the development of the vortex structures in the jet pump is closely related to the evolution of the cavitation.The cavitation-vortex interaction is thoroughly analyzed based on the vorticity transport equation.This analysis reveals that the cavitation in a jet pump dramatically influences the distribution and the production of the vorticity.The process of the annular cavitation inception,development,and collapse involves a significant increase of the vorticity.