Fluid dynamics of frozen precipitation at the air–water interface

Precipitation in the forms of snow, hail, and rain plays a critical role in the exchange of mass, momentum and heat at the surfaces of lakes and seas. However, the microphysics of these interactions are not well understood. Motivated by recent observations, we study the physics of the impact of a single frozen canonical particle, such as snow and hail, onto the surface of a liquid bath using a numerical model. The descent, melting, bubble formation and thermal transport characteristics of this system are examined. Three distinct response regimes, namely particle impact, ice melting and vortex ring descent, have been identified and characterized. The melting rate and air content of the snow particle are found to be leading factors affecting the formation of a coherent vortex ring, the vertical descent of melted liquid and the vortex-induced transportation of the released gas bubble to lower depths. It is found that the water temperature can substantially alter the rate of phase change and subsequent flow and thermal transport, while the particle temperature has minimal effect on the process. Finally, the effects of the Reynolds, Weber and Stefan numbers are examined and it is shown that the Reynolds number modifies the strength of the vortex ring and induces the most significant effect on the flow dynamics of the snow particle. Also, the change of Weber number primarily alters the initial phases of snow–bath interaction while modifying the Stefan number of the snow particle essentially determines the system response in its later stages.

Investigation on Thrust Force Conversion Method of Oscillating Caudal Fin Based on Wake Vortex Field Structure

The wake field of the flexible oscillating caudal fin is investigated using the Digital Particle Image Velocity (DPIV) system. The distributions of the vorticity with different Strouhal numbers are presented, and a self-developed program is used for calculating the velocity circulation of the vortex ring. Quantitative analysis of the wake field such as velocity circulation of the vortex ring, vortex radius, and the center-to-center spacing of vortex pair is presented. A three-dimensional vortex ring chain model of oscillating caudal fin is introduced. A conversion model between velocity circulation and dynamic moment of the vortex ring is presented according to the vortex dynamics theory, and a self-developed program is used for the calculation, in which the conversion of the thrust force based on wake field of oscillating caudal fin is carried out. Comparisons of the results of the two kinds flexible caudal fins thrust force conversion with the result of tricomponent balance system have been done in this paper. The relative errors are 5.86% and 3.44%, respectively. It is shown that the thrust force conversion model of flexible oscillating caudal fin is accurate and reliable, and the method presented in the paper provides an effective model for the quantitative conversion between the flow field and the thrust force of the caudal fin.

Mathematical Modelling of the Elliptical Vortex Ring in a Viscous Fluid with the Vortex Filament Method

The article deals with modelling an elliptical vortex ring in a viscous fluid using the Lagrangian vortex filament method. The novelty is that earlier only inviscid flows restricted vortex filament method application. The proposed viscosity model uses an analogue of the diffusion rate method, which is widely applied to simulate plane-parallel and axisymmetric flows of viscous fluid. A transfer of the formula of a diffusion rate from two-dimensional flows to the model of spatial vortex filament is due to assumption that swirling of vortex lines (helicity of vorticity) is unavailable. Despite the laxity of the diffusion rate model for general spatial flows, its application enables taking into account the effect of viscous diffusion of vorticity, which provides expansion of vortex tubes in space. The paper formulates the vortex filament method in which the filaments are broken into the vortex segments. Such discretization enables turning from the equation of vorticity evolution in partial derivatives to a system of ordinary differential equations with respect to the parameters of the segments. Formulas to calculate a filament system-induced flow rate as well as formulas to perform approximate calculation of an analogue of the diffusion rate are given.The objective is to propose the viscosity model as an application to the vortex filament method by the example of modelling the evolution of an elliptical vortex ring in viscous fluid. The calculation results obtained by the vortex method are compared with the existing experiment and with the calculation performed by the grid method in the OpenFOAM package. A feature of the problem is that there are zones of nonzero helicity of vorticity where the proposed model of viscosity, strictly speaking, is not correct. It is shown that the results of calculations are in good agreement with each other and are in complete agreement with experiment. This allows saying that the effects of swirling vortex lines do not significantly affect the results of modelling a specific example of the spatial flow of viscous fluid by the proposed modification of the vortex filament method.