Comparative study on numerical performances of log-conformation representation and standard conformation representation in the simulation of viscoelastic fluid turbulent drag-reducing channel flow
Comparative study on numerical performances of log-conformation representation and standard conformation representation in the simulation of viscoelastic fluid turbulent drag-reducing channel flow
复制标题
粘弹性流体湍流减阻通道流模拟中对数构象表示与标准构象表示数值性能对比研究
DOI：
10.1063/5.0034589
复制
发表时间：
2021
影响因子：
4.6
通讯作者：
Li Fengchen
中科院分区：
文献类型：
--
作者：
Zhang Wen-Hua;Li Jingfa;Wang Qiankun;Ma Yu;Zhang Hong-Na;Yu Bo;Li Fengchen
本文利用矩阵对数的泰勒级数定义，给出了粘弹性流体流动的对数构象控制方程的一种新的推导过程。基于对数构象表示法（LCR）和标准构象表示法（CR），采用有限差分法对Oldrophil-B本构模型描述的粘弹性流体湍流减阻槽道流动进行了数值模拟。结果表明，CR方法可以成功地再现低Weissenberg数（Wi = 1）或中等Weissenberg数（Wi = 5）条件下的湍流减阻效果，而LCR方法在相同网格分辨率下很难获得，如果在计算域中采用常用的插值方法（即，日志域）。进一步的研究表明，对数构象张量的插值方法是导致LCR方法不能获得湍流DR效应的主要原因之一。如果在物理域中进行插值，则可以使用LCR方法再现湍流DR效应。如果CR方法中的插值在对数域中进行，则仍然可以模拟湍流DR现象，但DR效应减弱。总之，这项研究表明，在对数域中常用的插值方法应该负责LCR方法的性能差。
In this paper, a new derivation process of the log-conformation governing equation for viscoelastic fluid flows is presented by using the Taylor series definition of the matrix logarithm. Based on the log-conformation representation (LCR) and standard conformation representation (CR) methods, the turbulent drag-reducing channel flow of viscoelastic fluid described by the Oldroyd-B constitutive model is simulated by the finite difference method. The comparison illustrates that the turbulent drag reduction (DR) effect under the condition of a low Weissenberg number (Wi = 1) or moderate Weissenberg number (Wi = 5) can be successfully reproduced by the CR method but is very difficult to be obtained by the LCR method at the same grid resolution if the commonly used interpolation approaches in the computing domain (i.e., log domain) are employed. Further research reveals that the interpolation method of log-conformation tensor involved is one of the dominant reasons responsible for the disability to obtain a turbulent DR effect by using the LCR method. If the interpolation is performed in a physical domain, the turbulent DR effect can be reproduced by using the LCR method. If the interpolation involved in the CR method is carried out in a log domain, the turbulent DR phenomenon can still be simulated but with a weakened DR effect. In sum, this study demonstrates that the commonly used interpolation approaches in the log domain should be responsible for the poor performance of the LCR method.