| The translation of the drop or the drop impacting onto a pool is always the focus in the fluid mechanics field.These two phenomena are widely observed both in nature and industrial processes.Natural objects are commonly referred to the formation and falling of raindrops and volcanic falling tephra.Engineering applications typically include the blending of molten polymers,emulsion topological changes,cooling and condensation process,spray coating and ink-jet printers,etc.In those applications,the falling velocity,morphology and disintegration during the translating and falling of the droplet are fascinating for researchers,while the shape evolutions,the secondary droplet formation and their mechanisms are crucial and difficult points in sight.Since the development of International Thermonuclear Experimental Reactor(ITER)project have appealed great effort to the conception of organs external to the Tokamak machine,namely the blanket and the divertor.Within the liquid divertor,particularly,which is located at the bottom of the vacuum vessel,is covered by thin liquid lithium film designed to bear large heat and neutron loads as well as divert impurities.In their designs,liquid metal jets ejected by nozzles are also proposed.All those situations provide the possibility of formation of moving droplets in the magnetic field.These droplets translate in a magnetic field and will probably impact onto the liquid film on the divertor;besides,the influences of these phenomena are unknown for the operation of the divertor.Thus,the investigations for the mechanism of the drop translating or impacting onto a pool under a magnetic field are of great importance.Among all research methods,numerical simulations have strong adaptability and flexibility,while the theoretical researches rely on certain kinds of simplifications and assumptions,and experimental studies need to deal with complex experimental settings and nontransparent liquid metal,which increases measurement difficulty.However,it is also a big challenge for numerical simulations dealing with magnetohydrodynamic flows with free surfaces due to the complex coupling between the flow field,the magnetic field and the free surface effect.Owing to the numerical methods developed in our research team for the simulation of multiphase magnetohydrodynamics(MHD)flows,in the first part of this thesis,a single liquid metal droplet translating in a magnetic field is numerically investigated.Its dynamic behaviors,such as the decrease in the translating velocity,the deformation of shape,and the flow inside the droplet are discussed,while the influences of the magnetic field are also reported.Basically,it is found that if the droplet keeps spherical shape during the translating,the magnetohydrodynamic effects are identical whether the nonuniform magnetic field is linearly increased or decreased along the falling direction of the droplet,and the numerical results are in good agreement with the analytical solutions.However,in most of the cases that the droplet deformations cannot be ignored,their shapes evolve into two categories: being prolate or oblate depended on the direction of the magnetic field gradient.Besides,the aspect ratio of the droplet and the deceleration of its falling velocity are also related to three factors: the initial velocity of the droplet,the gradient and the global strength of the magnetic fields.Moreover,it is observed the shape of the droplet to oscillate after exiting a linearly decreasing magnetic field,and the oscillatory frequency complies with mode 2.After that,it is also considered other circumstances by adjusting the inclination between the magnetic field and the gravitational direction,finding the trajectory of the droplet to deviate from the rectilinear path.Moreover,the evolutions of the vortex structures at the tail of the droplet are presented when the inclined angle is varied.To make things clearer during the translating of the droplet,the energy conversion process is also analyzed,to show that the Joule dissipating is gradually dominating over other energy components as the droplet falls.In the second part of this thesis,an electric-conducting droplet impacting onto a deep pool of same liquid under an external vertical magnetic field is investigated.The numerical method is employed in an axisymmetric coordinate system to maximize computational efficiency.The induced Lorentz force is treated as an external body force.The ejecta morphology and evolution of vortex structures are investigated.It is also discovered the swing of the early ejecta.The influences of the magnetic field are also summarized for each vortex pattern.In a wide parameter spaces of Reynolds numbers(700 ? 12000)and Weber numbers(40 ? 500),impact phenomena are divided to three regimes: no vortex shedding,main vortex shedding and Kármán vortex street.The increased magnetic field or surface tension always act to restrain the splash.They can both exhibit a transition from no vortex shedding to main vortex shedding.However,in the high Reynolds numbers region surface tension is to strongly suppress all kinds of ejecta but has little impact on vortex rings,while the magnetic field is to weaken the vortex rings and slower the outward radial movement of the ejecta.Interestingly,as the vortex rings are shedding continuously to form the Kármán vortex street structure,the first jet ejecta tends to swing between the narrow gap near the neck region,while its frequency shows strong correlation on Von Kármán vortex street and is apt to be influenced by the magnetic field.Finally,a drop impacting onto a pool in a horizontal magnetic field is simulated in a three-dimensional coordinate.Anisotropy of the splash ejecta is observed and analyzed in details.A liquid layer similar to Hartmann layer in duct flow can be found in the direction perpendicular to the magnetic field,and thus a depression of splash is observed,while the splash is not dampened by the Lorentz force in the parallel direction because of the induced electric current stagnation at the other direction. |
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