Three-dimensional simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re) and Bingham number (Bn). These results reveal the flow behavior of Bingham plastics

A study of the quadratic molecular stress function constitutive model in simulation

Constitutive models that conform to separable KBKZ specification have been shown to fit steady-state strain hardening rheological data in planar and uniaxial elongational flows, but with inaccuracy in the rate of strain hardening. The single parameter Molecular Stress Function model of Wagner [Rheol. Acta, 39 (2000), 97-109] has been shown to accurately fit the rise-rate in experimental data for a number of strain hardening and strain softening materials. We study this models accuracy against the well characterised IUPAC LDPE data, and present a method for full implementation of this model for flow solution which is suitable for incorporating into existing separable KBKZ software. A new method for particle tracking in arbitrarily aligned meshes, which is efficient and robust, is given. The Quadratic Molecular Stress Function (QMSF) model is compared to existing separable KBKZ based models, including one which is capable of giving planar strain hardening; the QMSF is shown to fit experimental rheological and contraction flow data more convincingly. The issue of `negative correction pressures¿ notable in some Doi-Edwards based models is addressed. The cause is identified, and leads to a logical method of calculation which does not give these anomalous results

A modification of the convective constraint release mechanism in the molecular stress function model giving enhanced vortex growth

The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [J. Rheol. 45 (2001), 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J. non-Newt. Fluid Mech., 3 (1977), 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements

Dynamic Sealing Using Magneto-Rheological Fluids

Micropumps are microfluidic components which are widely used in applications such as chemical analysis, biological sensing and micro-robots. However, one obstacle in developing micropumps is the extremely low efficiency relative to their macro-scale counterparts. This paper presents a dynamic sealing method for external gear pumps to reduce the volumetric losses through the clearance between the tips of gears and the housing by using magneto-rheological (MR) fluids. By mitigating these losses, we are able to achieve high efficiency and high volumetric accuracy with current mechanical architectures and manufacturing tolerances. Static and dynamic sealing using MR fluids are investigated theoretically and experimentally. Two Mason numbers $Mn\left(p\right)$ and $Mn\left(\Omega\right)$ which are defined in terms of pressure gradient of the flow and velocity of the moving boundary respectively are used to characterize and evaluate the sealing performance. A range of magnetic field intensities is explored to determine optimal sealing effectiveness, where effectiveness is evaluated using the ratio of volumetric loss and friction factor. Finally, we quantify the effectiveness of this dynamic sealing method under different working conditions for gear pumps.Comment: 9 pages; 10 figures

Simulation of two- and three-dimensional viscoplastic flows using adaptive mesh refinement

This paper presents a finite element solver for the simulation of steady non-Newtonian flow problems, using a regularized Bingham model, with adaptive mesh refinement capabilities. The solver is based on a stabilized formulation derived from the variational multiscale framework. This choice allows the introduction of an a posteriori error indicator based on the small scale part of the solution, which is used to drive a mesh refinement procedure based on element subdivision. This approach applied to the solution of a series of benchmark examples, which allow us to validate the formulation and assess its capabilities to model 2D and 3D non-Newtonian flows.Postprint (author's final draft

Simulations of extensional flow in microrheometric devices

We present a detailed numerical study of the flow of a Newtonian fluid through microrheometric devices featuring a sudden contraction–expansion. This flow configuration is typically used to generate extensional deformations and high strain rates. The excess pressure drop resulting from the converging and diverging flow is an important dynamic measure to quantify if the device is intended to be used as a microfluidic extensional rheometer. To explore this idea, we examine the effect of the contraction length, aspect ratio and Reynolds number on the flow kinematics and resulting pressure field. Analysis of the computed velocity and pressure fields show that, for typical experimental conditions used in microfluidic devices, the steady flow is highly three-dimensional with open spiraling vortical structures in the stagnant corner regions. The numerical simulations of the local kinematics and global pressure drop are in good agreement with experimental results. The device aspect ratio is shown to have a strong impact on the flow and consequently on the excess pressure drop, which is quantified in terms of the dimensionless Couette and Bagley correction factors. We suggest an approach for calculating the Bagley correction which may be especially appropriate for planar microchannels

Computation of entropy generation in dissipative transient natural convective viscoelastic flow

Entropy generation is an important aspect of modern thermal polymer processing optimization. Many polymers exhibit strongly non-Newtonian effects and dissipation effects in thermal processing. Motivated by these aspects in this article a numerical analysis of the entropy generation with viscous dissipation effect in an unsteady flow of viscoelastic fluid from a vertical cylinder is presented. The Reiner-Rivlin physical model of grade two (second grade fluid) is employed which can envisage normal stress variations in polymeric flow-fields. Viscosity variation is included. The obtained governing equations are resolved using implicit finite difference method of Crank-Nicolson type with well imposed initial and boundary conditions. Key control parameters are the second-grade viscoelastic fluid parameter (β), viscosity variation parameter (γ) and viscous dissipation parameter (ε). Also, group parameter (BrΩ-1), Grashof number (Gr) and Prandtl number (Pr) are examined. Numerical solutions are presented for steady-state flow variables, temperature, time histories of friction, wall heat transfer rate, entropy and Bejan curves for distinct values of control parameters. The results specify that entropy generation decreases with augmenting values of β, γ and Gr. The converse trend is noticed with increasing Pr and BrΩ-1. Furthermore, the computations reveal that entropy and Bejan lines only occur close to the hot cylinder wall