空间分数阶非Newton流体本构及圆管流动规律研究

杨旭; 梁英杰; 孙洪广; 陈文

doi:10.21656/1000-0887.390153

空间分数阶非Newton流体本构及圆管流动规律研究

doi: 10.21656/1000-0887.390153

河海大学力学与材料学院, 南京 211100

基金项目: 国家杰出青年科学基金（11125208）;国家自然科学基金（11572112;41628202;11528205）;111引智计划(B12032);中央高校基本科研业务费(2018B687X14);江苏省研究生科研与实践创新计划(KYCX18_0532)

详细信息

作者简介:
杨旭（1990—），男，博士生（E-mail: darrenyang366@gmail.com）;梁英杰（1989—），男，讲师（E-mail: liangyj@hhu.edu.cn）;孙洪广（1982—），男，教授，博士生导师（E-mail: shg@hhu.edu.cn）;陈文（1967—）男，教授，博士生导师（通讯作者. E-mail: chenwen@hhu.edu.cn).

中图分类号: O232;O172;O373
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出版历程
- 收稿日期: 2018-05-25
- 修回日期: 2018-09-26
- 刊出日期: 2018-11-01

A Study on the Constitutive Relation and the Flow of Spatial Fractional NonNewtonian Fluid in Circular Pipes

College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R.China

Funds: The National Science Fund for Distinguished Young Scholars of China（11125208）;The National Natural Science Foundation of China（11572112; 41628202; 11528205）

摘要

摘要: 对非Newton流体的本构及流动规律进行研究是分析、预测和控制非Newton流体在管道中流动的关键.实验表明非Newton流体在流动过程中具有历史记忆性，基于空间分数阶微积分方法，建立了分数阶非Newton流体本构模型；并推导了该模型在圆管中的流速分布、流量、平均流速、压降、平均Reynolds数等管道流动参数；提出了分数阶非Newton流体圆管流态判别准则.研究表明非Newton流体的圆管流层间的切应力可以通过流速的轴向分布大小来描述.对于不含屈服切应力的分数阶非Newton流体，分数阶的阶数越大，断面流速分布越均匀，记忆能力越强.分数阶的阶数大小反映了流体对全域空间的记忆性强弱；而对于含有屈服切应力的分数阶非Newton流体，分数阶的阶数越大，速梯区流速分布越均匀，流核区速度越小.分数阶的阶数大小反映了局部空间记忆性强弱.该研究为非Newton流体的记忆特征提供了一种新的建模方法.
- 分数阶算子 /
- 圆管流动 /
- 流态判别 /
- 数学力学建模
Abstract: A thorough understanding of the flow behavior of non-Newtonian fluid is the first step for analyzing, predicting and controlling of pipe flow. Experiments indicate that non-Newtonian fluid is historically dependent on the procedure of shear flow. The constitutive model for fractional non-Newtonian fluid was established via the spatial fractional calculus approach. The velocity profile, the flux, the mean velocity, the pressure drop and the mean Reynolds number of the proposed model were also derived. In addition, a novel criterion for the flow state of fractional non-Newtonian fluid was proposed. The results show that, the shear stress of the non-Newtonian fluid can be described by the axial velocity distribution. For the fractional non-Newtonian fluid without yield shear stress, the larger the fractional order is, the more uniform the velocity distribution will be and the stronger the memory of the fluid will be. The magnitude of the fractional order reflects the memory of the fluid with respect to the global space. For the fractional non-Newtonian fluid with yield shear stress, the larger the fractional order is, the more uniform the velocity distribution in the velocity gradient region will be, and the smaller of the velocity in the core region will be. In this case, the magnitude of the fractional order reflects the memory of the fluid with respect to the local region. This study offers a new method for the modeling of memory characteristics of non-Newtonian fluid.
- fractional operator /
- pipe flow /
- criterion for flow state /
- mathematical and physical modeling

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