In this numerical study, an original approach to simulate non-isothermal viscoelastic fluid flows at high Weissenberg numbers is presented. Stable computations over a wide range of Weissenberg numbers are assured by using the root conformation approach in a finite volume framework on general unstructured meshes. The numerical stabilization framework is extended to consider thermo-rheological properties in Oldroyd-B type viscoelastic fluids.

The temperature dependence of the viscoelastic fluid is modeled with the time–temperature superposition principle. Both Arrhenius and WLF shift factors can be chosen, depending on the flow characteristics. The internal energy balance takes into account both energy and entropy elasticity. Partitioning is achieved by a constant split factor.

An analytical solution of the balance equations in planar channel flow is derived to verify the results of the main field variables and to estimate the numerical error. The more complex entry flow of a polyisobutylene-based polymer solution in an axisymmetric 4:1 contraction is studied and compared to experimental data from the literature. We demonstrate the stability of the method in the experimentally relevant range of high Weissenberg numbers. The results at different imposed wall temperatures, as well as Weissenberg numbers, are found to be in good agreement with experimental data.

在此数值研究中，提出了一种模拟高Weissenberg数下非等温粘弹性流体流动的原始方法。通过在普通非结构化网格上的有限体积框架中使用根构象方法，可以确保在广泛的魏森伯格数范围内进行稳定的计算。扩展了数值稳定框架，以考虑Oldroyd-B型粘弹性流体的热流变性。

粘弹性流体的温度依赖性是用时间-温度叠加原理建模的。可以根据流量特性选择Arrhenius和WLF偏移因子。内部能量平衡考虑了能量和熵弹性。通过恒定的拆分因子实现分区。

推导了平面通道流动平衡方程的解析解，以验证主场变量的结果并估计数值误差。研究了在轴对称4：1收缩中更复杂的聚异丁烯基聚合物溶液的进入流，并将其与文献中的实验数据进行了比较。我们在高Weissenberg数的实验相关范围内证明了该方法的稳定性。发现在不同施加的壁温以及魏森伯格数下的结果与实验数据非常吻合。