Explicit incompressible SPH algorithm for modelling channel and lid-driven flows

Abstract

In this paper, explicit incompressible Smoothed Particle Hydrodynamics (ISPH) algorithm is used to simulate two-dimensional channel flow, channel flow in the presence of a square solid object and lid-driven square cavity flow for both Newtonian and non-Newtonian fluids. It is demonstrated that 2640 particles are sufficient to predict the behavior of channel flow. As the power low index decreases, more iteration is needed to reach steady state conditions. The results reveal that only 1600 particles are required for reasonable prediction of lid-driven square cavity flow at Re = 100 and 400 and 6400 particles is required to predict it at Re = 1000. It is also concluded that the ISPH method has a high ability to predict the behavior of non-Newtonian power law fluids. Keywords Smoothed particle hydrodynamics (SPH) method • Incompressible SPH • Three-phase algorithm • Channel flow • Lid-driven cavity flow List of symbols D Deformation tensor g Acceleration due to gravity (m/s 2) h Smoothing length (m) H Channel width (m) L Channel length (m) L 0 Initial particle distance (m) m Mass (kg) n Power law index P Pressure (Pa) r ij Distance between the particles i and j (m) Re Reynolds number t Time (s) u Velocity vector (m/s) V Volume of particle (m 3) W n Kernel function x, y Coordinates (m) Greek symbols ρ Density (kg/m 3) µ Viscosity (Ns/m 2) µ eff Effective viscosity (Ns/m 2) τ Shear stress (Pa)

A shift model based on particle collisions – preserving kinetic energy and potential energy in a constant force field – to avoid particle clustering in SPH

“…In the Fig. 14 to16 velocity profiles obtained with FS and CS at Re = 100, 400, 1000 and medium resolution (∆𝑥 = 1/160 m) are compared, and again validated against the results from Ghia et al [37]. The results of FS and CS are nearly the same and in a good agreement with those of Ghia.…”

“…In the Fig. 11 to13 the velocity profiles at Re = 100, 400, 1000 are presented, as obtained with CS for three resolutions (∆𝑥 = 1/80 m, ∆𝑥 = 1/160 m and ∆𝑥 = 1/240 m) and validated against simulations obtained with a multigrid finite volume method from Ghia et al [37]. The figures show that with increasing resolution, the results are closer to those of Ghia et al [38].…”

“…The lid driven cavity is a typical shear driven flow, where no-slip boundaries play a significant role. Several researchers have used this case to validate their SPH methods [28,[35][36][37]. The parameters are commonly chosen as follows.…”

Deep Neural Network Modeling for CFD Simulations: Benchmarking the Fourier Neural Operator on the Lid-Driven Cavity Case

“…We used the lid-driven cavity problem [31][32][33][34] to generate data for the models. Liddriven cavity flow is well known in the CFD research field because it provides complex flow structures and interactions and can be run in both laminar and turbulent flow regimes.…”