On the Use of SPH Method for Simulating Gas Bubbles Rising in Viscoelastic Liquids

Abstract

The upward motion and deformation of a single large-scale two-dimensional planar gas bubble rising in an otherwise quiescent viscoelastic liquid obeying the Oldroyd-B rheological model is numerically investigated using the weakly-compressible smoothed particle hydrodynamics (WC-SPH) method. It is shown that unlike the incompressible version of this mesh-less method (I-SPH), the WC-SPH method combined with the continuum surface force (CSF) idea for modelling surface tension is well capable of capturing the cusped-shape trailing edge during its rise in viscoelastic liquids. The failure of the I-SPH method for predicting the cusp is attributed to the several stages of weighted arithmetic and harmonic interpolations used for smoothing the transport parameters of the constituents. The WC-SPH code developed in the present work has enabled us to obtain results at high density and viscosity ratios not reported in similar works. The results suggest that WC-SPH is better suited than I-SPH for handling bubble rise problem in viscoelastic liquids even at large density and viscosity ratios typical of underwater explosions.

Computational modeling of multiphase viscoelastic and elastoviscoplastic flows

“…Following these authors, the values of the nondimensional parameters are R e = 1.419, E o = 35.28, W i = 8.083, B i = 0, β = 0.07, k ρ = 0.1, k μ = 0.1, and χ = 0.3. The droplet interface shapes that we obtained at t = 0.13 s together with the ones by Zainali et al and Vahabi and Sadeghy are depicted in Figure . It can be seen in the figure that the present result is consistent with the one reported by Vahabi and Sadeghy; on the contrary, Zainali et al have not observed the cusped trailing edge, which is however a common feature for the case of Newtonian droplet in viscoelastic medium at high polymer concentrations …”

“…Shape of a Newtonian droplet rising in an Oldroyd‐B fluid at t = 0.13 s. The present results (∘) are compared with the results of Zainali et al (×) and the results of Vahabi and Sadeghy (▿). ( R e = 1.419, E o = 35.28, W i = 8.083, B i = 0, β = 0.07, k ρ = 0.1, k μ = 0.1, χ = 0.3, with 120 × 240 grid points) [Colour figure can be viewed at wileyonlinelibrary.com]…”

“…The no‐slip boundary conditions are applied at the horizontal walls. It should be noted that Prieto used the free‐slip boundary conditions on the vertical walls, whereas Zainali et al and Vahabi and Sadeghy imposed the no‐slip boundary conditions. The nondimensional parameters pertaining to this problem are defined as the Reynolds number R e = ρ 1 U g L / μ 1 , the E tv s number , the Weissenberg number W i = λ U g / L , the Bingham number B i = τ y / ρ g L , the viscosity ratio k μ = μ 2 / μ 1 , the density ratio k ρ = ρ 2 / ρ 1 , and the confinement ratio χ = 2 R / L x .…”

“…Finally, some sample simulations are presented for a Newtonian droplet moving in an EVP fluid. The physical properties pertinent to the problem are the same as in the work of Zainali et al and Vahabi and Sadeghy except for a nonzero Bingham number; indeed, the Bingham number is varied between B i = 0 and 0.1. Figure shows shapshots at t = 0.13 s of the streamlines inside the computational domain for the fully Newtonian case (N) and for the EVP fluid with B i = 0,0.01 and 0.1.…”

“…The Oldroyd-B model is used in the present work to facilitate direct comparison with the results by Prieto, 101 Zainali et al, 102 and Vahabi and Sadeghy. 103 The fully Newtonian case is a classical benchmark (see, eg, the work of Hysing et al 104 ). The domain is rectangular with the width L x = 1 and the height L y = 2.…”