Numerical Simulation of Transient Non-Isothermal Viscoelastic Couette Flows Based on the SPH Method
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摘要: 基于光滑粒子流体动力学(smoothed particle hydrodynamics，SPH)方法对瞬态非等温黏弹性流动问题进行了数值模拟.首先，模拟了等温情况下基于Oldroyd-B模型的黏弹性Couette流动；随后，将其扩展到非等温情况下进行模拟，其中选用Reynolds指数模型来评估黏度和松弛时间的温度依赖.通过与有限体积方法解的比较和对数值收敛性的评价，验证了SPH方法模拟非等温黏弹性流动问题的准确性和有效性.讨论了非等温流动相较于等温流动的不同流动特征，分析了温度依赖系数、Péclet数等对黏弹性流动过程的影响.数值结果表明，SPH方法可准确有效地模拟非等温黏弹性流动问题.
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关键词:
- 光滑粒子流体动力学 /
- 非等温 /
- 黏弹性 /
- Oldroyd-B模型 /
- Couette流
Abstract: Based on the smoothed particle hydrodynamics (SPH) method, the transient non-isothermal viscoelastic flows were numerically simulated. First, the viscoelastic Couette flow based on the Oldroyd-B model under isothermal condition was simulated. Then, the simulation was extended to the non-isothermal case, in which the Reynolds exponential model was adopted to evaluate the dependence of the viscosity and the relaxation time on the temperature. The accuracy and effectiveness of the SPH method for simulating transient non-isothermal viscoelastic flows were verified through comparison with the finite volume method and evaluation of numerical convergence. The different flow characteristics of the non-isothermal flow compared with those of the isothermal flow were discussed. The effects of the temperature dependence coefficient and the Péclet number on the flow physics were analyzed. The numerical results demonstrate that, the SPH method can accurately and effectively simulate transient non-isothermal viscoelastic flow problems.-
Key words:
- smoothed particle hydrodynamics /
- non-isothermal /
- viscoelastic /
- Oldroyd-B model /
- Couette flow
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图 3 等温黏弹性Couette流动在t=1时刻的粒子分布和速度分布
Figure 3. The particle distribution and the velocity distribution of the isothermal viscoelastic Couette flow at t=1
图 4 等温黏弹性Couette流动A, B, C三点处的速度u和弹性剪切应力τxy随时间的变化：SPH数值解与解析解的对比
Figure 4. Isothermal viscoelastic Couette flows at 3 points A, B and C: a comparison of SPH and analytical solutions for velocity u and elastic shear stress τxy
图 5 Re= 1和10时，等温黏弹性Couette流动的SPH模拟：点B处的速度u和弹性剪切应力τxy随时间的变化
Figure 5. SPH simulations of isothermal viscoelastic Couette flows with Re= 1 and 10: the time changes of velocity u and elastic shear stress τxy at point B
图 6 非等温黏弹性Couette流的SPH模拟：φ对点B处速度u和弹性剪切应力τxy随时间变化的影响
Figure 6. The SPH simulation of the non-isothermal viscoelastic Couette flow: the effect of temperature dependent parameter φ on the time changes of velocity u and elastic shear stress τxy at point B
图 7 非等温黏弹性Couette流的SPH模拟：Pe对点B处速度u和弹性剪切应力τxy随时间变化的影响
Figure 7. The SPH simulation of the non-isothermal viscoelastic Couette flow: the effect of Pe on the time changes of velocity u and elastic shear stress τxy at point B
图 8 非等温黏弹性Couette流的SPH模拟(Pe=1, φ=0.01)：6个不同时刻的温度关于y的分布
Figure 8. The SPH simulation of the non-isothermal viscoelastic Couette flow (Pe=1, φ=0.01): the temperature distribution vs. y at 6 different moments
图 9 利用SPH得到的温度分布图的收敛性分析及其与FVM解的比较
Figure 9. Convergence analysis of the temperature distribution obtained with the SPH and the comparison with the FVM solution
图 10 非等温黏弹性Couette流的SPH模拟：β对点B处速度u和弹性剪切应力τxy随时间变化的影响
Figure 10. The SPH simulation of the non-isothermal viscoelastic Couette flow: the effect of β on the time changes of velocity u and elastic shear stress τxy at point B
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