Research On The Characteristics Of Trajectories And Wake Structures Of Freely Falling Annular Disks In Quiescent Water

The freely rising or falling objects driven by gravity and buoyancy in quiescent fluids can be widely observed in nature,which contains complicated fluid dynamic phenomena including fluid-solid interaction,flow separation,generation and evolution of shear layer and vortex,interactions among vortices.Different from the fixed bodies in the incoming flow,the problems of freely moving bodies usually involve moving boundaries,unsteady flows and large separations,which can be hardly solved by the conventional fluid mechanics based on potential theory.Annular disks are typical non-streamlined bodies which contain intricate unsteady viscous flow mechanism involving the interactions among the vortex structures generated by the inner and outer rims when freely falling in quiescent fluids.In the present study,the characteristics of trajectories and wake structures during free-fall process of annular disks in quiescent water are investigated by combining numerical and experimental methods.The main research contents are as follows:The experimental approaches are set up to measure the trajectories,poses and wake structures of the free-fall annular disks.The 6 degrees of freedom during falling can be obtained by marked dots on the surface of the disk using stereoscopic vision method.Fluorescein-dye-based visualization is used to obtain the 3-D flow structures qualita-tively.And planar wake structures in the vertical and horizontal planes are measured by PIV quantificationally.Based on moving computational domain(MCD)and large eddy simulation(LES),the basic mathematical models and numerical methods for trajectories and wake structures of freely falling annular disks are established,and the application of numerical model and mesh independence are evaluated and validated by comparing with the experimental results.By dropping large amounts of annular disks with various geometrical parameters,the previous phase diagram describing the falling patterns of solid disks is expanded to 3-D parameter space,and the dimensionless moment of inertia~*,Reynolds number0)and inner to outer diameter ratioare shown regular distribution in the 3-D phase diagram.A new falling motion,SI motion(Straight Intermittent),is discovered,which is featured by the nearly vertical falling path,while the falling velocity is intermittent with short pauses.LI motion(Lateral Irregular)is the transitional motion from 1-D to 3-D motion,characterized by a irregular lateral movement.Then two kinds of 3-D motion documented in the literature,HH(hula-hoop)and HM(helical)motion,are compared.By investigating the wake flow structures,the periodic generation and shedding of the vortices are the reasons causing the different falling patterns,furthermore,Proper Orthogonal Decomposition(POD)analysis shows the existence of the vortical structures with various dimensions in the flow fields.To further investigate the influence of degrees of freedom on the flow structures,the flow fields behind the fixed annular disks in the uniform incoming flow are analysed under different Reynolds number,and the Streamline Probability Density Functions(SPDF)approach is utilised to study the sweeping features of the central jets.With the increment of Reynolds number,various flow characteristics are observed and the wake structures behind the disks are changed from steady to unsteady flow.Then the falling processes of the free-fall annular disks are analysed under corresponding Reynolds numbers,showing that the falling paths are changed from stable 1-D to 3-D motions.Based on the potential theory,added-mass force coefficient is calculated during the unsteady motion,and according to the Kelvin-Kirchhoff equations the added-mass force is separated from the total fluid force.The relations between the vortex motions and the fluid forces acting on the disks are studied.And the disparities of the wake structures under the same range of Reynolds number between the fixed and free-fall annular disks are summarized,revealing the influence of the degrees of freedom on the wake structures.Based on the established numerical methods,the main geometrical parameters,i.e.inner to outer diameter ratio,the dimensionless moment of inertia~*and solid to fluid density ratio?,are studied for their influence on the falling trajectories and wake structures.Inner to outer diameter ratiohas a major impact on the falling motion,where regular HH motion occurs at the lowand the path is irregular for the large.The dynamic process from the initial steady flow when starting falling to the unsteady flow is analysed under different,revealing the movement of the vortices.The rotation movement is affected mainly by~*,focusing on changes of the angular momentum and fluid torque with different~*.?has a minor impact on the falling motion,but in order to resist the increasing inertia force of the disks,the fluid forces exerted on the disks are increased accordingly.Furthermore,the mechanism of the horizontal trajectory procession of HH motion is studied.