Abstract
SummaryA new axisymmetric lattice Boltzmann model is proposed for non‐Newtonian fluid flows. The model incorporates the additional axisymmetric contributions into the evolution equation by introducing a force term. The precise form of the Navier‐Stokes equations in the cylindrical polar coordinate system is derived through Chapman‐Enskog analysis, and the consistency in dimension with the lattice Boltzmann equation is retained in the introduction of force terms. The model is used to simulate the flows in a straight pipe and an annulus channel for various power‐law indexes and Reynolds number. The velocity profiles in the straight pipe and annulus channel are presented and shown to be in excellent agreement with analytical results. The 4:1 axisymmetric contraction flow was studied as well. The results show that the reattachment length increases as the power‐law indexes for a shear‐thickening fluid. The opening angle increases substantially with the increase of the power‐law index for both a shear‐thinning fluid and a shear‐thickening fluid. The velocity profiles and vortex sizes of contraction flows agree very well with those of the finite element analysis. Results demonstrate that the proposed method is very effective to analyze the axisymmetric flows of a non‐Newtonian fluid.
Published Version
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