LBM and Complex Flows
9:30am - 9:50am
Flow of plant protein doughs in extruder dies
Wageningen University & Research, Netherlands, The
In this contribution we present a numerical model of the flow of plant protein dough through an extruder die, as occurs in the production of plant-based meat replacers. This model is to be coupled to another model describing the flow of the material in the extruder screw section. The combined model will be used for process design.
The protein dough is assumed to behave as a Herschel-Bulkley fluid, having a yield stress, and exhibiting shear thinning. These parameters have been measured as function of moisture content and temperature. It follows that the yield stress depends on Tg/T, the ratio of the (moisture dependent) glass transition temperature and the actual temperature. The shear thinning exponent is independent of temperature or moisture content.
The cooling die receives the protein dough at high temperatures in the range of 120-160$^oC$, and it will be cooled down to temperatures of 60-100$^oC$. The extruder will be operated at a constant throughput. The cooling of the dough in the die will involve a strong increase of the yield stress. Hence, in the middle of the flow channel an unyielded plug flow will develop. Shear rate gradients develop in a small boundary layer along the wall. Above all, we expect a lubrication layer will develop along the wall due to expulsion of moisture, leading to wall slip. Towards the end the plug flow will cover the entire cross section of the die.
Hence, for proper process design the flow model needs to be coupled to an energy balance solving the temperature profile within the extruder die. There will be a two-way coupling between the flow model and the energy balance: the dough rheology is strongly temperature dependent,
and the viscous dissipation can increase temperature.
The flow model is implemented using Lattice Boltzmann model, which has the advantage that shear stresses are directly locally available, and it can later be extended to multiphase flow, as plant protein doughs consists often of two different biopolymers. The issue of the singularity in the effective viscosity in the Herschel-Bulkley model is resolved via a biviscosity regularization. Wall slip will be modelled using the general formalism by Kalyon. A scaling analysis of the governing equations show that a 2D model will suffice for process design purposes.
The overall boundary condition is complex, which is governed by a constant throughput. The related flow profile is an unknown, and will develop over the length of the extruder die, due to the non-isothermal conditions. The required pressure gradient is the desired outcome of the simulation, and thus it can be prescribed directly. Hence, as a boundary condition we impose a pressure gradient, which will be varied such that the flow profiles in all cross sections matches that of the imposed throughput.
9:50am - 10:10am
Investigation of the Capture of Coarse Air-borne Particles at different Fibre Aspect Ratios using Lattice Boltzmann Method
1Indian Institute of Technology Delhi; 2The University of Queensland
Air pollution is one of the most burning and life-threatening global issues, for which the fibrous air filters have emerged extensively as a remedial solution. In the present study, the capture dynamics of coarse airborne particles and associated variation of filtration performance parameters (efficiency and pressure drop) with respect to the variations in aspect ratio of a single rectangular fibre have been investigated numerically in two dimensions. With the length scales corresponding to the fibre and particles being a few microns each, the mesoscopic method, viz. lattice Boltzmann method (LBM) has been used for simulations of airflow across the fibre. For simulations of the motion of particles and their capture by fibre under the influence of aerodynamic drag and gravity, the Lagrangian approach has been used. One-way coupling has been employed between the airflow and particles (where only airflow field determines the motion of particles), and the inter-particle interactions have not been considered as the concentration of particles is pretty small. In case of LBM, the D2Q9 lattice configuration has been used. Also, the single relaxation time model has been used to define the collision operator via BGK approximation. The fibre-air interface has been provided with no-slip boundary condition via bounce-back scheme whereas the upper and lower boundaries of the computational domain have been provided with either symmetry or free-slip boundary condition using specular reflection. The study presents the characteristic variations observed in the filtration performance parameters as the fibre aspect ratio is varied.
10:10am - 10:30am
Compressible lattice Boltzmann methods based on numerical collision
University of Geneva/ Battelle, Switzerland
Over the past three decades, lattice Boltzmann methods (LBMs) have grown as serious alternatives to Navier-Stokes-Fourier (NSF) solvers for the simulation of isothermal and weakly compressible flows past realistic geometries. Nevertheless, most compressible LBMs available in the literature have difficulties to compete with NSF solvers due to an increased (1) size of the lattice required to get the correct macroscopic behavior, and/or (2) complexity of the numerical scheme to ensure stable simulations .
Recently, a GPU-accelerated and purely LB approach based on numerical equilibria was proposed as an efficient and accurate alternative. In this approach, equilibria are computed through a root-finding algorithm that imposes an arbitrary number of equilibrium moments, which alleviates common accuracy and stability limits encountered with relatively small lattices, polynomial equilibria and BGK collision model. Yet, the BGK approximation also leads to a number of physical and numerical limitations, e.g., fixed Prandtl number and stability issues.
In this talk, we propose to extend the numerical computation of equilibrium populations to their post-collision counterpart, hence, allowing for the direct control of diffusive fluxes through constraints on non-equilibrium moments. This idea was originally proposed in the context rarefied gas dynamics to impose the correct heat flux, and is further extended here to any non-equilibrium moment.
As a proof of concept, the D2Q37 lattice is adopted to study the effects of the numerical collision on both stability and accuracy. Particular attention is paid to the computation of gradients, which are used as constraints for non-equilibrium moments, and that can either be done locally (LB scheme) or thanks to a finite-difference scheme. The proposed approach can seamlessly run on CPUs or GPUs thanks to the recent upgrade of the C++ STL library and NVIDIA compiler. The numerical collision is tested for several benchmark problems of increasing complexity, and corresponding results provide a positive feedback to proceed further.