SIMULATIONS OF NON-ISOTHERMAL VISCOELASTIC COMPLEX FLOWS BY IMPROVED SPH METHOD
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摘要: 非等温黏弹性流体广泛存在于自然界和工业生产中, 准确预测黏弹性流体的非等温流动机理和复杂流变特性有着重要的应用价值. 文章提出一种改进的光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)方法对非等温黏弹性复杂流动进行了数值模拟, 其中流体的黏弹特性通过eXtended Pom-Pom本构模型来表征. 为了提高模拟结果的精度, 采用了一种核函数梯度的修正算法; 为了灵活地施加边界条件, 发展了边界粒子和虚拟粒子相联合的边界处理方法; 为了消除流动过程中的拉伸不稳定性, 施加了粒子迁移技术. 运用改进SPH方法数值模拟了液滴撞击固壁和F型腔注塑成型问题, 通过与Basilisk软件得到的结果进行比较验证了改进SPH方法求解非等温黏弹性流体的有效性. 通过利用不同粒子初始间距进行计算, 评价了改进SPH方法的数值收敛性. 研究了非等温流动相较于等温流动的不同流动特征, 深入分析了不同热流变参数对流动过程的影响. 数值结果表明, 文章提出的改进SPH方法可稳定、准确地描述非等温黏弹性复杂流动的传热机理、复杂流变特性和自由面变化特性.Abstract: Non-isothermal viscoelastic fluid flow phenomena widely exist in nature and industrial productions, such as oil reservoir engineering, injection molding, etc. These flows generally exhibit a non-isothermal state. Accurate prediction of non-isothermal flow mechanism and complex rheological properties of viscoelastic fluid has important engineering application value. In this paper, an improved smoothed particle hydrodynamics (SPH) method is proposed for the numerical simulation of non-isothermal viscoelastic complex flow, in which the viscoelastic properties of the fluid are characterized by the eXtended Pom-Pom constitutive model. To improve the accuracy of simulation results, a kernel function gradient correction algorithm is adopted. To enforce the boundary conditions flexibly, a boundary treatment method combining boundary particles and virtual particles is developed. To eliminate the tensile instability in the flow process, the particle migration technology is applied. The improved SPH method is used to numerically simulate the impact of a droplet on the solid wall and injection molding of an F-shaped cavity. The effectiveness of the improved SPH method in solving the non-isothermal viscoelastic fluid is verified by comparing the SPH results with those obtained by the Basilisk software. Good agreement between these two numerical solutions is achieved. The numerical convergence of the improved SPH method is evaluated by using several different initial particle spacings. The different flow characteristics of non-isothermal flow compared with isothermal flow are investigated. It is found that the introduction of temperature leads to stronger contraction behavior of droplet. The influences of some different thermal rheological parameters such as the Péclet number, the Reyonlds number, the Weissenberg number, the solvent viscosity ratio, the anisotropy parameter, the relaxation time ratio and the molecular chain arm number on the flow process are deeply analyzed. The numerical results show that the improved SPH method proposed in this paper can accurately and stably describe the heat transfer mechanism, complex rheological properties, and free surface variation characteristics of non-isothermal viscoelastic fluid.
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图 1 液滴冲击固体表面的计算模型
Figure 1. Computational model of droplet impinging solid wall surface
图 2 运用改进SPH方法模拟得到的液滴冲击固体表面在不同时刻的温度分布
Figure 2. The temperature distribution of droplet impinging solid wall surface at different times obtained by improved SPH method
图 3 利用改进SPH方法和Basilisk软件得到的液滴铺展宽度随时间变化的比较
Figure 3. Comparison of the time changes of the droplet spread width obtained by the improved SPH method and Basilisk software
图 4 利用不同方法得到的液滴在t* = 2.5时刻的模拟结果
Figure 4. The simulation result of droplet at t* = 2.5 obtained by different methods
图 5 温度依赖系数φ对液滴铺展宽度随时间变化的影响
Figure 5. Influence of the temperature dependency coefficient φ on the time change of the droplet spread width
图 6 不同流变参数下液滴铺展宽度随时间的变化
Figure 6. Time change of the droplet spread width under different rheological parameters
图 7 F型腔注塑成型问题的计算模型
Figure 7. Computational model of injection molding process for an F-shaped cavity
图 8 运用改进SPH方法模拟得到的F型腔注塑成型在不同时刻的温度分布
Figure 8. The temperature distribution of F-shaped cavity injection molding at different times obtained by improved SPH method
图 9 Péclet数对F型腔注塑成型在t = 0.6 s时刻的温度分布的影响
Figure 9. Effect of Péclet number on the temperature distribution at t = 0.6 s in F-shaped cavity injection molding
图 10 运用改进SPH方法模拟得到的F型腔注塑成型在不同时刻的第一法向应力差分布
Figure 10. The first normal stress difference distribution of F-shaped cavity injection molding at different times obtained by improved SPH method
图 11 利用不同粒子间距Δx得到的点A处第一法 向应力差N1随时间变化的比较
Figure 11. Comparison of the time change of the first normal stress difference N1 at point A obtained by different particle spacings Δx
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