The Axisymmetric Lattice Boltzmann Model Creation For Non-newtonian Fluid Flow And Numerical Simulation

The numerical simulation of non-Newtonian fluid is very important in engineering application and has been made great progress.However,there are still many challenges.Recently LBM has become a powerful tool for simulating various physical phenomena and shows excellent prospects in flow simulation.Establishing axisymmetric lattice Boltzmann models method is a key research area.In this paper,new axisymmetric lattice Boltzmann models are established to transform three-dimensional flow problems of non-Newtonian fluid into two-dimensional axisymmetric problems.First,a new axisymmetric LB model is proposed for simulation of exponential flow.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.The validity of the model is confirmed by simulating the flows in simple straight pipe and annulus channel.Numerical predictions for the velocity profiles are presented and shown to be in excellent agreement with analytical results.Then entry flows of exponential fluid in circular contraction is simulated.The velocity profiles and vortex size are compared with the finite element analysis and the results demonstrate that the proposed method is correct.As to viscoelastic fluid,an axisymmetric lattice Boltzmann model with force terms is created.Double distribution functions are adopted to solve the Navier-Stokes equations and Oldroyd-B constitutive equation in this article.Based on this model,viscoelastic fluid flows in straight pipe of is firstly simulated to obtain the flow distribution in the runner and the results verify the the correctness of model.Then the entry flows of in circular contraction is analyzed and the influence of maximum inlet speed,viscosity,and Weissenberg number(Wi)on the flow is studied.The axisymmetric lattice Boltzmann models established in this paper are of great significance for the study of axisymmetric flow of non-newtonian fluid in engineering and provides theoretical basis for axisymmetric flow of other types of fluid.