粘弹性湍流减阻流动的POD低阶模型研究

Viscoelastic turbulent drag reduction is an important technology for energy saving in fluid transporting systems, with apparent economic and social benefits. It has broad potential applications in oil and gas gathering and transporting systems and long-distant pipelines etc. Proper orthogonal decomposition (POD) method has been proved to be an efficient way for high-precision and fast prediction method by numerical practice so that it is helpful for large-scale industrial applications of drag reduction. Thus, this project will aim to the viscoelastic drag reduction problem described by Giesekus constitutive relation, and establish a POD projection model that can accurate and fast predict the dynamic characteristics of drag reducing flow. Direct numerical simulation will be applied to obtain samples for modelling; POD will be used to extract eigenfunctions from the samples; optimization theory will be introduced to search the optimal combination of eigenfunctions to solve the problem that the optimal truncated location of the reduced order model was hard to fixed. Galerkin projection for multi-field coupling will be considered to solve the problem coupling the momentum equation and the constitutive equation so that the existed problem that the model results for viscoelastic conformation had too low accuracy by projecting the two equations separately. It is expected that the research outcomes will provide theoretical basis and technical support for the design and operation of viscoelastic turbulent drag reducing flow system.

粘弹性湍流减阻是流体输送系统中的一种重要的节能降耗技术，其经济和社会效益明显，在油气集输系统和长输管道等场合有广泛的应用前景。特征正交分解(POD)方法已被数值实践证明是流动传热问题的高精度快速预测方法，有利于推动减阻技术的大规模产业化应用。因此，本项目拟针对由Giesekus本构关系描述的粘弹性减阻流动问题，建立能准确快速描述减阻流动系统动力学特征的POD低阶投影模型，采用直接数值模拟获得建模所需样本数据，采用特征正交分解从样本中获取基函数，引入最优化理论在基函数集合中寻求最优的基函数组合以解决低阶模型最佳截断位置难以确定的问题，考虑多场耦合条件下的Galerkin投影，解决动量方程与本构方程的耦合投影难题，克服以往对这两组方程依次分离建模造成的粘弹性附加应力模拟结果精度过低的问题。研究成果将为粘弹性湍流减阻节能系统的设计运行提供理论依据和技术支持。

粘弹性湍流减阻是流体输送系统中的一种重要的节能降耗技术，其经济和社会效益明显，在油气集输系统和长输管道等场合有广泛的应用前景。特征正交分解(POD)方法已被数值实践证明是流动传热问题的高精度快速预测方法，有利于推动减阻技术的大规模产业化应用。因此，本项目针对由Giesekus本构方程描述的粘弹性减阻流动问题，采用直接数值模拟获得了建模所需样本数据，采用特征正交分解从样本中获取基函数，建立了描述减阻流动系统动力学特征的高精度POD低阶投影模型。对低阶模型的取样密度、基函数个数、对流项和强非线性项的处理等关系到精度和效率的关键因素进行了深入研究，优化了POD低阶模型。基于POD计算结果，详细分析了粘弹性减阻流动的速度场和附加变形场的特征结构，解释了减阻流动结构与附加变形结构之间的内在联系和相互作用机制，深化了对减阻机理的认识。在数值模拟对粘弹性减阻流动特征及机理分析的基础上，进行了粘弹性湍流减阻流动特征实验研究，对形成减阻主要特征结构的机理进行了有益的补充。