(186d) Non-Newtonian Flow Simulation Using Lattice Boltzmann Method

Authors: 
Kim, D., Carnegie Mellon University
Biegler, L. T., Carnegie Mellon University
Jhon, M. S., Carnegie Mellon University


The non-Newtonian fluid flow analysis is important for industrial applications dealing with polymeric and suspension systems as well as biological fluids. There are plenty of analysis tools developed commercially for Newtonian computational fluid dynamics, however very few numerical tools are available for non-Newtonian fluid flow systems. The lattice Boltzmann method (LBM) has emerged as a promising numerical tool for simulating complex fluid flows and energy transport [1]. There are numerous advantages of LBM such as clear physical pictures, an inherently transient nature, multi-scale/phenomena simulation capabilities, and fully parallel algorithms.

In view of these merits, we developed a novel 3D mathematical tool based on LBM for non-Newtonian fluid flows. In the framework of Newtonian LBM, the relaxation time is simply obtained by kinematic viscosity (dependent on temperature, but not on local shear rate). To generalize the analysis for non-Newtonian fluid flow systems, the relaxation times are modified to incorporate the shear rate dependence. We adopted two non-Newtonian models, namely the truncated power law and the Bird-Carreau models, to demonstrate the essence of our LBM formulation [2].

To handle the complex geometries we adopt the Taylor series expansion and least squares based LBM, which is a meshless approach [3]. The distribution functions at each non-uniform mesh point are explicitly updated by an algebraic formulation, where 27 neighboring nodes are used in the current simulation. To validate our non-Newtonian LBM scheme, we performed a 2D non-Newtonian Poiseuille flow simulation by varying the power-law exponent n, and compared our LBM results with analytic solutions. To further demonstrate the capabilities of our novel LBM tool, we simulated the 3D Poiseuille flow in a square duct. The bounce-back scheme was used for the solid wall boundaries and the extrapolation scheme was adopted for the pressure boundaries at the inlet and outlet. It was shown that the velocities of non-Newtonian fluids (n < 1) increased in comparison to Newtonian fluids (n = 1) due to the shear thinning behavior. Our LBM formulation described this behavior accurately for the non Newtonian fluid flow models.

After performing the benchmark studies of 2D/3D Poiseuille flows, we simulated velocity profiles of cavity geometry for n = 0.5. For this complex flow, a circular vortex develops inside the cavity in the reentrant corner geometry. The circulation core moves to lower-left direction when the flow exhibits non-Newtonian characteristics. A plug-like velocity profile is obtained, which is a special phenomenon for shear-thinning flows [4]. The velocity profile obtained exhibits an asymmetry for non-Newtonian fluid flow since the convection effect becomes more dominant. We will further examine oscillatory plate and blood flows. Oscillating bottom plate makes a non-Newtonian fluid fluctuate in a regular pattern [5]. Through inlet perturbation, the blood flow inside a blood vessel can be modeled [6]. Our non-Newtonian fluid flow LBM code can be applied for industrial systems dealing with complex fluid flow by proper modification.

REFERENCES

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[6] H. Fang, Z. Wang, Z. Lin, and M. Liu, Phys. Rev. E., Vol. 65, 051925, 2002.