黏弹性液滴广泛存在于自然界和工业生产中，研究其与固壁面碰撞对深化液滴动力学机理的理解具有重要的学术意义，并对指导相关工业过程具有潜在的应用价值。光滑粒子流体动力学(Smoothed Particle Hydrodynamics, SPH)方法是一种Lagrangian型的无网格数值方法，适用于含自由面的黏弹性流动模拟，但传统的SPH方法在模拟黏弹性液滴撞击固壁面问题时会出现张力不稳定问题，这种张力不稳定性会使粒子在运动过程中形成团块并最终导致模拟的中断，因此，有必要对传统的SPH算法进行改进。本文提出了一种改进的SPH算法，随后对改进的SPH算法进行了准确性和有效性验证，并在此基础上通过降低Reyonlds数捕捉到了黏弹性液滴撞击固壁面后的弹跳行为。最后，利用改进SPH算法模拟了各模型下黏弹性液滴撞击固壁面后的铺展和弹跳行为，并详细分析了相关动力学机理。本论文的主要内容如下：

(1) 针对传统SPH方法模拟黏弹性液滴撞击固壁面后出现的张力不稳定问题，本文提出了改进算法：为了防止粒子穿透固壁，提出了一种增强型的边界处理技术；为了消除张力不稳定性，发展了粒子迁移技术。通过黏弹性Poiseuille流验证本文改进SPH方法的准确性，实验结果表明本文改进的SPH方法具有良好的准确性和收敛性。随后利用本文改进SPH方法数值模拟了基于Oldroyd-B模型的黏弹性液滴撞击固壁面后的铺展行为，通过与解析解或有限差分方法解的比较和对数值收敛性的评价进一步验证了本文改进SPH方法的有效性和优势。

    (2) 在液滴撞击固壁面后发生铺展行为的基础上，通过降低Reyonlds数捕捉到了液滴弹跳现象，随后，深入分析了Reyonlds数、Weissenberg数、溶剂黏度比对黏弹性液滴撞击固壁面后动力学行为的影响。同时将本文改进的SPH方法扩展到基于PHan-Thien-Tanner(PTT)模型、Giesekus模型和eXtended Pom-Pom(XPP)模型的黏弹性液滴撞击固壁面的数值模拟中，详细分析了PTT模型下的拉伸参数ε、Giesekus模型下的流变参数α和XPP模型下的各向异性流变参数α、分子链拉抻量γ、分子链臂数Q等流变参数对液滴撞击固壁后的最大铺展宽度和弹跳高度的影响。

本文提出了增强型边界处理技术，通过发展粒子迁移技术对传统SPH方法进行了改进，捕捉到了液滴的弹跳行为，数值模拟并分析了不同模型下各流变参数对液滴撞击固壁面后动力学行为的影响，为深化液滴动力学机理的理解提供了重要的学术意义，并对指导相关工业过程提供了潜在的应用价值。

Viscoelastic droplets are widely present in nature and industrial production, studying their collision with solid walls is of great academic significance for deepening the understanding of droplet dynamics mechanisms, and has practical application value in guiding related industrial processes. The Smooth Particle Hydrodynamics (SPH) method is a Lagrangian type meshless numerical method suitable for simulating viscoelastic flows with free surfaces, however, the traditional SPH method may encounter tension instability when simulating the impact of viscoelastic droplets on a solid wall, this tension instability can cause particles to form clumps during motion and ultimately lead to simulation interruptions. Therefore, it is necessary to improve the traditional SPH algorithm. In this paper, an improved SPH method is proposed, and then the accuracy and effectiveness of the improved SPH algorithm are verified, based on this, the bouncing behavior of viscoelastic droplets after impacting a solid wall is captured by reducing the Reynolds number. Finally, the improved SPH method was used to simulate the spreading and bouncing behavior of viscoelastic droplets after impacting a solid wall in various models, and the relevant dynamic mechanisms were analyzed in detail. The main content of this paper is as follows:

(1) To solve the problem of tension instability arising from viscoelastic droplet impact on solid wall simulated by traditional SPH method, this paper proposes an improved algorithm: In order to prevent particles from penetrating solid wall, an enhanced boundary processing technique is proposed; in order to eliminate tension instability, particle transport technology has been developed. The accuracy of the improved SPH method is verified by viscoelastic Poiseuille flow, the experimental results show that the improved SPH method has good accuracy and convergence. Then, the improved SPH method is used to numerically simulate the spreading behavior of viscoelastic droplet upon impact on a solid wall based on Oldroyd-B model, the effectiveness and advantages of the improved SPH method are further verified by comparing with analytical solutions or finite difference solutions and evaluating the numerical convergence.

(2) Based on the spreading behavior of droplet after impact on solid wall, the droplet bounce phenomenon was captured by reducing the Reyonlds number, and then, the influence of Reyonlds number, Weissenberg number and solvent viscosity ratio on the dynamic behavior of viscoelastic droplet after impact on solid wall was deeply analyzed. The improved SPH method is extended to the numerical simulation of viscoelastic droplet impact on solid walls based on PHan-Thien-Tanner(PTT) model, Giesekus model and eXtended Pom-Pom(XPP) model, the effects of the rheological parameters ε of PTT model, α of Giesekus model, α of anisotropic rheological parameter of XPP model, γ of molecular chain stretch and molecular chain arm number Q on the maximum spreading width and bouncing height of droplet impacting the solid wall are analyzed in detail.

In this paper, the enhanced boundary processing technology is proposed, and the traditional SPH method is improved by developing particle migration technology, captures the bouncing behavior of droplets, numerically simulates and analyzes the influence of various rheological parameters on the dynamic behavior of droplets after impacting a solid wall under different models, providing important academic significance for deepening the understanding of droplet dynamic mechanism, and also providing potential application value for guiding related industrial processes.

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