Effect of fluid elasticity and shear-thinning viscosity on the chaotic mixing between two alternately rotating cylinders has been studied. The h-p finite element method is used to obtain high accurate solutions of the...Effect of fluid elasticity and shear-thinning viscosity on the chaotic mixing between two alternately rotating cylinders has been studied. The h-p finite element method is used to obtain high accurate solutions of the steady flow. The unsteady, periodic flow is simulated using the piecewise-steady approximation. Characteristics of the chaotic mixing are analyzed by examining the asymptotic coverage of a passive tracer and the lineal stretching of the fluid elements in the annulus. For the viscoelastic fluids modeled by the upper-convected Maxwell constitutive equation (UCM), our computation predicts little effect of the fluid elasticity on the mixing patterns. On the other hand, the shear-thinning viscosity, modeled by the Carreau equation, has a large impact on the advection of a passive tracer and the distribution of lineal stretching. We find that the zones of the lowest stretching match remarkably well with the regular zones in the tracer-coverage plotting. Our study reveals the vital importance of reducing the discretization errors of the velocity field in the numerical simulation of chaotic flews.展开更多
This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approx...This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approximation to this model and the L~∞-truncation method, one can establish the existence theorem of weak solutions for p-potential flow with p ∈(8/5, 2] provided that large initial are regular enough.展开更多
基金Supported by the National Natural Science Foundation of China (No. 29776039), Skloche PRE Laboratory of China and Cao Guangbiao Science Foundation of Zhejiang University.
文摘Effect of fluid elasticity and shear-thinning viscosity on the chaotic mixing between two alternately rotating cylinders has been studied. The h-p finite element method is used to obtain high accurate solutions of the steady flow. The unsteady, periodic flow is simulated using the piecewise-steady approximation. Characteristics of the chaotic mixing are analyzed by examining the asymptotic coverage of a passive tracer and the lineal stretching of the fluid elements in the annulus. For the viscoelastic fluids modeled by the upper-convected Maxwell constitutive equation (UCM), our computation predicts little effect of the fluid elasticity on the mixing patterns. On the other hand, the shear-thinning viscosity, modeled by the Carreau equation, has a large impact on the advection of a passive tracer and the distribution of lineal stretching. We find that the zones of the lowest stretching match remarkably well with the regular zones in the tracer-coverage plotting. Our study reveals the vital importance of reducing the discretization errors of the velocity field in the numerical simulation of chaotic flews.
基金supported by National Natural Science Foundation of China (Grant No. 11571279)Education Department of Jiangxi Province (Grant No. GJJ151036)Youth Innovation Group of Applied Mathematics in Yichun University (Grant No. 2012TD006)
文摘This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approximation to this model and the L~∞-truncation method, one can establish the existence theorem of weak solutions for p-potential flow with p ∈(8/5, 2] provided that large initial are regular enough.
