广义二阶流体管内轴向流动

General Second Order Fluid Flow in a Pipe

1.
Department of Petroleum Engineering, Xi'an Petroleum Institute, Xi'an 710061;
2.
Department of Resources and Environmental Sciences, Beijing Normal University, Beijing 100875;
3.
Institute of Porous Flow and Fluid Mechanics, Academia Langfang 102801

摘要: 在流体的本构关系中引入分数阶导数运算,对于介于粘性与弹性之间的流体的描述更具有合理性。本文将这种关系引入二阶流体,研究其管内轴向流动。我们先求出了1/2阶导数的解析解,用以验证Laplace数值反演的CRUMP方法的有效性。然后用CRUMP法分析二阶流体管内轴向流动的特征。分析表明粘弹性特征越明显的流体,其速度与应力对分数导数的阶数越具有敏感性。
- 二阶流体 /
- 轴向流动 /
- 积分变换
Abstract: It is more satisfactory for fluid materials between viscous and elastic to introducethe fractional calculus approach into the constitutive relationship. This paper employsthe fractional calculus approach to study second fluid flow in a paper. First, we derivethe analytical solution which the derivate order is half and then with the analytical solution we verify the reliability of Laplace numerical inversion based on Crumpalgouithm for the problem, and finally we analyze the characteristics of second order fluid flow in a pipe by using Crump method. The results indicate that the more obviousthe viscoelastic properties of fluid is, the more sensitive the dependence of velocity andstress on fractional derivative order is.
- second order fluids /
- axial flow in a pipe /
- integral transforrnation

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