Numerical simulation of the head-on collision of two drops in a vertical channel

Abstract

The head-on collision between two oil drops in a vertical channel is investigated numerically by using a volume-of-fluid method. Three-dimensional simulations are examined for laminar, fully developed, unsteady, and incompressible fluid flow. The effects of the Weber and Reynolds numbers and the density ratio on the collision dynamics are investigated before and after the drop coalescence. The results show that the deformation of drops increases and gap thickness decreases as the Weber and Reynolds numbers increase. The drops collide with each other faster for higher density ratios. It is found that the drops elongation has a sinusoidal behavior after collision due to the tendency of the drops to gain a spherical shape. Also, the results demonstrate that the elongation increases with increasing of the Weber and Reynolds numbers and decreasing of the density ratio. Keywords Drop collision • Two-phase flow • VOF method • Reynolds number • Weber number • Eotvos number List of symbols b The minor semi-axes of the drop (m) D Drop diameter (m) e* The drop elongation (m) Eo Eotvos number F Force (N) g Gravity acceleration H Channel height (m) k Curvature l The major semi-axes of the drop (m) L Channel length (m) n Normal vector (m) Oh Ohnesorge number p Pressure (Pa) Re Reynolds number t Time (s) t* Dimensionless time u Velocity (m/s) We Weber number x Position (m) Greek letters η Density ratio λ Viscosity ratio μ Dynamic viscosity (N. s/m 2) ν Kinematic viscosity (m 2 /s) ρ Density (kg/m 3) σ Surface tension (N/s) Subscripts 1, 2 Number of drop d Drop f Fluid rel Relative st Surface tension

An Overview of Multi-Phase Flow Numerical Methods

“…Similar to the E-E method, the volume fraction of each fluid in each computational cell is captured in the computational domain. The same as the E-E method, α = 0 when the computational cell is occupied by the dispersed phase, α = 1 when the computational cell is occupied by the continuous phase, and 0 < α < 1 when the cell involves the interface between the two dispersed and continuous phases [18][19][20][21]. For instance, Hassanzadeh et al [19] employed the VOF to simulate the head-on collision of two drops falling in a vertical channel (Fig.…”

Simulation of Sand Particles Flow Using a Weakly Compressible Smoothed Particle Hydrodynamics Method (WCSPH)

“…Hence, the most important point in this problem is to model free surface. Since the specification of the free surface is not readily possible in mesh-based methods, various techniques such as Volume-of-Fluid (VOF) [1][2], front-tracking [3][4][5][6][7][8] and Level Set (LS) are employed for tracking the free surface. If the profile of the free surface significantly changes, the structure of mesh network is completely destroyed.…”