Non-expert summaryThe flushing of a viscous fluid from a pipe or cavity by a less viscous one is widely used in cleaning operations. This paper reports the numerical modelling of the transient displacement of a viscoplastic material from straight or suddenly constricted (square entry) concentric cylindrical tubes of finite length, simulating a gas at higher pressure displacing the geometry initially filled with liquid. A mixed finite element method is coupled with a quasi-elliptic mesh generation scheme in order to follow the very large deformations involved. The gas bubble grows in length and leaves a thin liquid film on the duct wall (so it does not remove all the liquid). The shape of the bubble is computed for various Reynolds and Bingham numbers (ratio of yield stress to viscous stress). The 'tip splitting' instability that can arise in flow of a gas along a tube filled with a viscous Newtonian fluids is suppressed with viscoplastic fluids at higher Bingham numbers. The shape of the bubble as it passes through the constriction is also studied.
Non-expert summaryThe use of a gas to purge a viscous liquid from a straight cylindrical pipe of finite length is investigated for the case where the liquid is viscoelastic. The rheology of the liquid is described using the Giesekus and the Phan-Thien-Tanner (PTT) models. The focus of the work is on the numerical aspects of the simulations. A parametric analysis is made in order to determine the effects of elastic and inertial forces, and the Newtonian viscosity, on the process.
Non-expert summaryThe use of pressurised air to displace a viscoplastic liquid from a complex duct geometry is simulated using detailed numerical modelling. The transient displacement of Newtonian and viscoplastic liquids by air in cylindrical tubes of finite length with a concentric expansion followed by a contraction in their cross section is considered. The change in diameter is not sudden. Various expansion and contraction ratios are studied. Papanastasiou's formula is employed to regularize the discontinuous Bingham model. Results are presented for a range of fluid and geometrical parameters, and some cases are compared to analytical results.
Non-expert summaryThe prediction of flow behaviour in complex geometries representative of industrial and other practical systems often requires the use of computational fluid dynamics (CFD) simulations. Two important pipe geometries are considered in this paper: a sudden and a gradual expansion or contraction. Steady state simulations using the STAR-CD package were used to predict the distribution of the mean shear stress imposed by a turbulent liquid flow from 1 inch to 2 inch cylindrical geometries (Reynolds number in the 1 inch pipe of 50,000), and the fluctuations in the shear stress. These calculated values are compared with estimates based on electrochemical mass transfer measurements. The data sets provide useful benchmarking results for other studies.
Non-expert summaryThe Lattice-Boltzman numerical method is used to solve the Navier-Stokes equations describing the displacement of a viscoplastic fluid from a cylindrical pipe by the injection of a Newtonian liquid. The equations are written in dimensionless form so no particular time or length scale is specified. Gravity and surface tension effects are included. The average velocity of the Newtonian liquid is such that its flow is laminar. The numerical code is able to resolve several features of the process: the growth of a 'finger' of Newtonian liquid as it pushes the viscoplastic fluid out and the development of waves at the liquid-fluid interface. The impact of key dimensionless groups, particularly the Bingham number (ratio of critical or yield stress to stress induced by the flow) and Reynolds number.