非等温eXtended Pom-Pom泊肃叶流动的光滑粒子流体动力学方法模拟

doi:10.19596/j.cnki.1001-246x.8685

摘要/Abstract

摘要：

开展非等温黏弹性泊肃叶流动的光滑粒子流体动力学(SPH)方法模拟，其中流体的黏弹特性依据eXtended Pom-Pom(XPP)本构模型进行建模和计算。推导温度方程的SPH离散格式，并依据时温等效原理考量流体的黏弹特性对温度的依赖。将SPH模拟结果与利用有限体积方法得到的结果进行比较，验证SPH方法模拟非等温XPP泊肃叶流动的准确性和有效性。利用4个不同粒子初始间距进行模拟，讨论SPH方法的数值收敛性。研究温度方程的引入对泊肃叶流动带来的影响。深入分析不同物理参数对流动过程的影响。

关键词: 光滑粒子流体动力学, eXtended Pom-Pom模型, 非等温, 泊肃叶流动

Abstract:

Smoothed particle hydrodynamics (SPH) simulation of non-isothermal viscoelastic poiseuille flow is carried out, in which the viscoelastic properties of the fluid are modeled and calculated according to the eXtended Pom-Pom (XPP) constitutive model. The SPH discrete format of the temperature equation is derived, and the temperature dependence of viscoelastic properties of fluid is considered based on the principle of time temperature equivalence. The accuracy and effectiveness of the SPH method for simulating non-isothermal XPP poiseuille flow are verified by comparing the SPH results with those obtained by the finite volume method. The numerical convergence of the SPH method is discussed by performing simulations with four different initial particle spacings. The influence of the introduction of the temperature equation on poiseuille flow is studied. The influence of different physical parameters on the flow process is deeply analyzed.

Key words: smoothed particle hydrodynamics, eXtended Pom-Pom model, non-isothermal, poiseuille flow

中图分类号:

O242

许晓阳, 赵雨婷. 非等温eXtended Pom-Pom泊肃叶流动的光滑粒子流体动力学方法模拟[J]. 计算物理, 2024, 41(2): 161-171.

Xiaoyang XU, Yuting ZHAO. Smoothed Particle Hydrodynamics Simulation of Non-isothermal eXtended Pom-Pom Poiseuille Flow[J]. Chinese Journal of Computational Physics, 2024, 41(2): 161-171.

图/表 7

图1 黏弹性泊肃叶流的几何区域

Fig.1 The geometric region of viscoelastic Poiseuille flow

图2 SPH解与FVM数值解和稳态解析解

Fig.2 Comparison of SPH solutions with FVM numerical solutions and steady analytical solution

图3 SPH解的收敛性分析和FVM的解

Fig.3 Convergence analysis of SPH solutions and comparison with FVM solution

图4 非等温流动与等温流动的比较及温度依赖系数φ对点A处的速度u随时间变化的影响

Fig.4 Comparison between non-isothermal flows and isothermal flow and effect of φ on velocity u at point A with time

图5 Péclet数对点A处的速度u随时间变化的影响

Fig.5 Effect of Péclet number on velocity u at point A with time

图6 7个不同时刻的温度关于y的分布

Fig.6 Temperature distribution with respect to y at seven different times

图7 不同流变参数对点A处的速度u随时间变化的影响(a) Re；(b) Wi；(c) β；(d) α；(e) γ；(f) Q

Fig.7 Effect of different rheological parameters on velocity u at point A with time (a) Re; (b) Wi; (c) β; (d) α; (e) γ; (f) Q

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