Smoothed Particle Hydrodynamics Modeling Of Meso-scale Liquid Drop Dynamics

Smoothed particle hydrodynamics (SPH) is a meshfree, adaptive, Lagrangian particlemethod.In the SPH method, the state of a system is represented by a set of particles, whichpossess individual material properties and interact with each other within a certain rangedefined as a support domain by a weight function or smoothing function. SPH featuresremarkably flexibility in handling complex flow fields and in including physical effects. Animportant advantage of SPH is that in SPH, there is no explicit interface tracking formultiphase or free surface flows–the motion of the fluid is represented by the motion of theparticles, and fluid surfaces or fluid-fluid interfaces move with particles representing theirphase defined at the initial stage. Therefore in SPH it is convenient to deal with free surfaces,moving interfaces, and deformable boundaries as well as large deformations that can beformidable to conventional grid-based numerical methods.In theory, the basic concept of the SPH method is introduced. Some detailed numericalaspects are discussed including the kernel approximation in continuous form and particleapproximation in discrete form, the properties for the smoothing functions and some of themost frequently used ones in the SPH literatures, the concept of support and influence domain,SPH formulations for Navier-Stokes equations, time integration, solid boundary treatment,particle interactions, artificial viscosity. laminar viscosity, molecular viscous, artificialcompressibility and equations of motion for particles.In numerical techniques, it is known that the conventional SPH method has beenhindered with low accuracy and the accuracy of the conventional SPH method is also closelyrelated to the distribution of particles. In order to improve computational accuracy, modifiedschemes for approximating density and kernel gradient are used. As surface tension effects arevery important for drop dynamics, in this paper, Molecular cohesive pressure of the van der Waals (vdW) model is used to deal with the surface tension. In addition, surface tensioneffects are modeled through constructing an inter-particle interaction force (IIF), which candescribe short-distance repulsion and long-range attraction. To deal with possible tensileinstability, which is associated with unphysical phenomena such as particle clustering orblowing away, an artificial stress is incorporated into the SPH equations of motion. A newkernel function is also used. With the surface tension effects modeled using aparticle-particle interaction force, the modified SPH method is used to investigate liquid dropimpacting onto solid surfaces. To well implement the solid boundary conditions and improvethe numerical accuracy, considering the advantages and disadvantages of the current boundarytreatment methods, we used a coupled dynamic solid boundary treatment (SBT) algorithm.In applications, this paper presents an improved SPH method for modeling theformations and oscillation of viscous liquid drop. in which the influence of the elongation andReynolds number on the amplitude and oscillation period is discussed. It is clearlydemonstrate that the tensile instability can be effectively removed. We find that forsmall-amplitude motions the combined dissipative effects of finite viscosity and heatconduction induce rapid decay of the oscillations after a few periods, while forlarge-amplitude motions wave damping is governed by the action of both viscous dissipationand surface tension forces. When the initial aspect ratio is increased for fixed Reynoldsnumber (Re), the amplitude of the oscillations increases and the first period is attained atprogressively longer times. When the Re number increases and wave damping is stronger. Forboth head-on and off-centre binary collision, it is clearly demonstrated that higher Re collisionvalues result in more elongated coalesced drops by the end of the first period of oscillation.The subsequent evolution will be governed by a long-term interplay between viscousdissipation and conversion into surface energy of the internal liquid movement. Theinfluences of Reynolds number on the both head-on and off-centre binary collision arediscussed. It is clearly demonstrated that higher collision values of Re translate into largersurface deformation and this modified SPH method can effectively model viscous dropdynamics.The modified SPH method is also applied to model impacting of liquid drop onto liquidsurface, It shows that the modified SPH method can effectively describe the dynamics ofdroplet splashing and the variation of the free surface, and that the accuracy of the results canbe stable；For impacting of liquid drop onto liquid films, the modified SPH method can also effectively describe the dynamics of droplet splashing and the variation of the free surface. Itis found that the dynamic processes after impact are sensitive to the initial drop velocity andthe liquid film thickness. It is also found that the critical Weber number for splashing issensitive to the liquid viscosity or Ohnesorge number and is insensitive to the liquid filmthickness. The numerical results are in close agreement with the theoretical and experimentalresults in literature；For impacting of liquid drop onto solid surface, we can conclude that themodified SPH method can well describe the dynamics process of morphology evolution andthe pressure field evolution with accurate and stable results. The spread factor increases withthe increase of the initial Weber number. The obtained numerical results are in closeagreement with available theoretical and experimental results in literature.