Droplet Deformation In Shear Flow Research Articles

Parallel Immersed Boundary Method for Two-Phase Flows on DCU Clusters

The immersed boundary method (IBM) is widely used in simulating multiphase flows. DCU (Deep Computing Unit) acceleration device is a kind of GPU-like device, which is developed by GPU technology authorised by AMD. To achieve an efficient numerical simulation of two-phase flows, we develop a parallel DCU-based immersed boundary method using the MPI+HIP programming model. To solve the slow convergence problem caused by domain partitioning in multigrid methods, a coarse grid aggregation (CGA) technique is effectively employed. We adopt a nonblocking communication approach with HIP streams to overlap computation and communication. To validate the proposed method running on DCU clusters, we conducted two numerical experiments of droplet deformation in shear flow and the rising bubble. Performance tests show that a speedup of 181 times more than the CPU version can be achieved with 32 DCUs in a 1024 × 512 × 512 mesh grid.

A fast and practical adaptive finite difference method for the conservative Allen–Cahn model in two-phase flow system

We present a simple and practical adaptive finite difference method for the conservative Allen–Cahn–Navier–Stokes system. For the conservative Allen–Cahn equation, we use a temporally adaptive narrow band domain embedded in the uniform discrete rectangular domain. The narrow band domain is defined as a neighboring region of the interface. The Navier–Stokes equation is solved in a fully discrete domain with the coarse grid than that for the CAC equation. Various benchmark numerical experiments, such as the pressure jump, droplet deformation in shear flow, falling droplet, and rising bubble, are performed to show that the proposed method is efficient and practical for the simulations of two-phase incompressible flow.

Numerical study of droplet deformation in shear flow using a conservative level-set method

This paper is concerned with a numerical study on the behavior of a single Newtonian droplet suspended in another Newtonian fluid, all subjected to a simple shear flow. Conservative finite-volume approximation on a collocated three-dimensional grid along with a conservative Level-set method are used to solve the governing equations. Four parameters of capillary number (Ca), Viscosity ratio (λ), Reynolds number (Re) and walls confinement ratio are used to physically define the problem. The main focus of the current study is to investigate the effect of viscosity on walls critical confinement ratio. In this paper, the phrase critical is used to specify a state of governing parameters in which divides the parameter space into the subcritical and supercritical regions where droplets attain a steady shape or breakup, respectively. To do so, first, we validate the ability of proposed method on capturing the physics of droplet deformation including: steady-state subcritical deformation of non-confined droplet, breakup of supercritical conditioned droplet, steady-state deformation of moderate confined droplet, subcritical oscillation of highly-confined droplet, and the effect of viscosity ratio on deformation of the droplet. The extracted results are compared with available experimental, analytical and numerical data from the literature. Afterward, for a constant capillary number of 0.3 and a low Reynolds number of 1.0, subcritical (steady-state) and supercritical (breakup) deformations of the droplet for a wide range of walls confinement in different viscosity ratios are studied. The results indicate the existence of two steady-state regions in a viscosity ratio-walls confinement ratio graph which are separated by a breakup region.

A contoured continuum surface force model for particle methods

A surface tension model is essential to simulate multiphase flows with deformed interfaces. This study develops a contoured continuum surface force (CCSF) model for particle methods. A color function that varies sharply across the interface to mark different fluid phases is smoothed in the transition region, where the local contour curvature can be regarded as the interface curvature. The local contour passing through each reference particle in the transition region is extracted from the local profile of the smoothed color function. The local contour curvature is calculated based on the Taylor series expansion of the smoothed color function, whose derivatives are calculated accurately according to the definition of the smoothed color function. Two schemes are proposed to specify the smooth radius: fixed scheme, where 2×re (re = particle interaction radius) is assigned to all particles in the transition region; and varied scheme, where re and 2×re are assigned to the central and edged particles in the transition region respectively. Numerical examples, including curvature calculation for static circle and ellipse interfaces, deformation of square droplet to a circle (2D and 3D), droplet deformation in shear flow, and droplet coalescence, are simulated to verify the CCSF model and compare its performance with those of other methods. The CCSF model with the fixed scheme is proven to produce the most accurate curvature and lowest parasitic currents among the tested methods.

Effect of confinement on droplet deformation in shear flow

The dynamics of a single droplet under shear flow between two parallel plates is investigated by using the immersed boundary method. The immersed boundary method is appropriate for simulating the drop-ambient fluid interface. We apply a volume-conserving method using the normal vector of the surface to prevent mass loss of the droplet. In addition, we present a surface remeshing algorithm to cope with the distortion of droplet interface points caused by the shear flow. This mesh quality improvement in conjunction with the volume-conserving algorithm is particularly essential and critical for long time evolutions. We study the effect of wall confinement on the droplet dynamics. Numerical simulations show good agreement with previous experimental results and theoretical models.

Numerical investigation of Newtonian and non-Newtonian multiphase flows using ISPH method

We have presented a multiphase incompressible smoothed particle hydrodynamics method with an improved interface treatment procedure. To demonstrate the effectiveness of the interface treatment which can handle multiphase flow problems with high density and viscosity ratios, we have modeled several challenging two phase flow problems; namely, single vortex flow, square droplet deformation, droplet deformation in shear flow, and finally the Newtonian bubble rising in viscous and viscoelastic liquids. The proposed interface treatment includes the usage of (i) different smoothing functions (in this work, cubic spline kernel function for discretizing equations associated with the calculation of the surface tension force while the quintic spline for the discretization of governing equations and the relevant boundary conditions), and (ii) a new discretization scheme for calculating the pressure gradient. It is shown that with the application of the improved interface treatment, it becomes possible to model multiphase flow problems with the density and viscosity ratios up to 1000 and 100 respectively while using standard projection method. The utilization of cubic spline for the continuum surface force model significantly improves the quality of the calculated interface, thereby eliminating the interphase particle penetrations, and in turn leading to the calculation of more accurate velocity and pressure fields.