非等温黏弹性流动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具有重要的应用价值。光滑粒子流体动力学(Smoothed Particle Hydrodynamics, SPH)方法作为一种典型的拉格朗日型无网格方法，能够避免网格类方法中的网格畸变、网格缠结等问题，适用于具有自由表面、大变形等复杂流动的求解。本文应用改进SPH方法对非等温黏弹性流体进行数值模拟，主要工作内容如下：

      (1)应用改进SPH方法对等温黏弹性泊肃叶流进行数值模拟，其中流体的黏弹特性通过Oldroyd-B本构模型来表征。为了提高模拟结果的精度，采用了改进的核梯度修正技术；为了灵活地施加边界条件，提出了改进的固壁边界处理方法。通过将改进SPH结果与传统SPH结果和解析解进行比较，表明了采用改进的核梯度修正技术具有更高的计算精度；随后将模拟扩展到非等温流动，通过将改进SPH方法模拟的数值结果与有限体积方法的结果进行比较，验证了本文提出的改进固壁边界处理方法的有效性。讨论了等温流动与非等温流动的不同流动特征，深入分析了温度依赖系数、Péclet数等热流变参数对黏弹性流动过程的影响。

      (2)为了更合理地描述黏弹性流体的剪切稀化行为，将Oldroyd-B本构模型扩展到由支化聚合物分子理论推导得出的eXtended Pom-Pom(XPP)本构模型，并对非等温XPP库埃特流动进行数值模拟。首先，模拟了等温情况下基于XPP模型的黏弹性库埃特流动；然后，将其扩展到非等温流动进行模拟，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改进SPH方法模拟非等温XPP黏弹性流动问题的有效性和准确性，并在此基础上，探讨了XPP黏弹流变参数对流动过程的影响。

      (3)为了更好地理解和预测流体在复杂流动中的行为，将模拟由泊肃叶流和库埃特流扩展到自由表面流，运用改进SPH方法对非等温黏弹性自由表面流问题进行数值模拟。为了消除流动过程中的拉伸不稳定性，施加了改进的粒子迁移技术。首先，以非等温Oldroyd-B液滴撞击固壁问题作为研究对象，给出了运用改进SPH方法的模拟结果，并将其与传统SPH结果进行比较，结果表明本文改进的粒子迁移技术可有效解决拉伸不稳定性问题；随后，应用改进SPH方法模拟非等温XPP注塑成型问题，深入分析了温度依赖系数、熔体与冷壁的温差、Weissenberg数等流变参数对黏弹性自由表面流动过程的影响。数值结果表明，本文改进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。

      Non-isothermal viscoelastic flows widely exist in nature and industrial productions. It is important to accurately predict the non-isothermal flow mechanism and complex rheological properties of viscoelastic fluids. As a typical Lagrangian meshless method, Smoothed Particle Hydrodynamics (SPH) can avoid mesh distortion and entanglement problems in mesh-like methods, and is suitable for solving complex flows with free surfaces and large deformations. In this paper, the improved SPH method is applied to numerical simulation of non-isothermal viscoelastic fluids. The main work is as follows:

      (1) The improved SPH method is used to simulate isothermal viscoelastic poiseuille flow. The viscoelastic properties of the fluid are characterized by the Oldroyd-B constitutive model. In order to improve the accuracy of simulation results, an improved kernel gradient correction technique is used. In order to enforce the boundary conditions flexibly, an improved solid wall boundary treatment method is proposed. By comparing the improved SPH results with the traditional SPH results and analytical solutions, it is shown that the improved kernel gradient correction technique has higher calculation accuracy; then the simulation is extended to non-isothermal flow, and the numerical results of the improved SPH method are compared with those of the finite volume method, and the effectiveness of the improved solid boundary treatment method is verified. The different flow characteristics of isothermal flow and non-isothermal flow are discussed, and the influence of heat rheological parameters such as temperature dependence coefficient and Péclet number on viscoelastic flow process is analyzed.

      (2) In order to better describe the shear thinning behavior of viscoelastic fluids, the Oldroyd-B constitutive model is extended to the eXtended Pom-Pom(XPP) constitutive model derived from the branched polymer molecular theory, and the non-isothermal XPP couette flow is numerically simulated. Firstly, the viscoelastic couette flow based on XPP model is simulated under isothermal conditions. Then, it is extended to non-isothermal flow simulation, and the effectiveness and accuracy of the improved SPH method in simulating non-isothermal XPP viscoelastic flow are verified by comparing the solution with the finite volume method and evaluating the numerical convergence. On this basis, the influence of XPP viscoelastic rheological parameters on the flow process was discussed.

      (3) In order to better understand and predict the behavior of fluid in complex flows, the simulation is extended from poiseuille flow and couette flow to free surface flow. The improved SPH method is used to simulate the non-isothermal viscoelastic free surface flow. In order to eliminate the tensile instability in the flow process, an improved particle shifting technique is applied. Firstly, the problem of non-isothermal Oldroyd-B droplet impact on the solid wall is taken as the research object, and the simulation results using the improved SPH method are given, and the results are compared with the traditional SPH results. The results show that the improved particle shifting technique introduced in this paper can effectively solve the problem of tensile instability. Then, the improved SPH method was used to simulate the non-isothermal XPP injection molding, and the influence of rheological parameters such as temperature dependence coefficient, temperature difference between melt and cold wall, Weissenberg number on the viscoelastic free surface flow were analyzed. The numerical results show that the improved SPH method can stably and accurately describe the heat transfer mechanism, complex rheological properties and free surface variation characteristics of non-isothermal viscoelastic complex flows.

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