Simulation of Heat and Fluid Flow of a Highly Viscoelastic Fluid, Using a Spectral Method

使用谱法模拟高粘弹性流体的热量和流体流动

• 批准号: 04650145
• 负责人: MOCHIMARU Yoshihiro
• 金额: $ 1.34万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04650145/
• 关键词: Viscoelsticity; Spectral Method; Non-Newtonian Fluid; Numerical Analysis; Polymer Solution

Steady-state laminar non-Newtonian fluid flows past an elliptic cylinder or past an ellipsoid of revolution and natural convectin f non-Newtonian fluid filled in the half of an elliptic cylinder are analyzed numericaly to clarify the highly viscoelastic behavior of plymer solutions. A second order fluid model is adopted as a constitutive equation ; in a two-dimensonal flow case the equations of motion lead to a similar, but slightly modified, equation to the vorticity transport equation for an incompressible Newtonian fluid, whereas in a three-dimensional case the situation is different from the two-dimensional case, being supplemented with the stress components. The system f equations in an unsteady form can be split into Fourier components, using Fourier components of a stream function and vorticity in a boundary-fitted conformal coordinate sstem. Then each component is discretized in a finite difference method for doubly-exponential grid spacing in time and space ; the resulting equations can be integrated with respect to time to get a steady-state solution. As a rsult, a large increase of a drag force and a large variation of streamlines due to fluid viscoelastcity is found at moderae Reynolds numbers of Grashf numbers for a variety of shapes.

对非牛顿流体绕椭圆柱和旋转椭球的稳态层流流动以及非牛顿流体在半个椭圆柱内的自然对流进行了数值分析，阐明了非牛顿流体解的高粘弹性行为。采用二阶流体模型作为本构方程;在二维流动情况下，运动方程导致不可压缩牛顿流体的涡量输运方程类似，但略有修改，而在三维情况下，情况不同于二维情况，补充了应力分量。在贴体保形坐标系中，利用流函数和涡量的傅立叶分量，非定常形式的方程组可以分解为傅立叶分量。然后，每个组件在时间和空间上的双指数网格间距的有限差分方法中离散化;所得到的方程可以相对于时间积分以得到稳态解。结果表明，对于各种形状的流体，在中等雷诺数和Grashf数下，由于流体的粘弹性，阻力大幅度增加，流线变化大。

项目成果

Yoshihiro MOCHIMARU: "Numerical Simulation a Viscoelastic Fluid Flow past an Elliptic Cylinder" Theoretical and Applied Rheology/Proc.XIth Int.Congr.on Rheology. 306- (1992)

Yoshihiro MOCHIMARU：“粘弹性流体流经椭圆柱的数值模拟”理论与应用流变学/Proc.XIth Int.Congr.on Rheology。

Yoshihiro MOCHIMARU: "Numerial Simulation of a Viscoelasti Fluid Flow past an Elliptic Cylinder" Theoretcal and Applied Rheology / Proc.Xth Int/. Congr.on Rheology. Vol.1. 306 (1992)

Yoshihiro MOCHIMARU：“粘弹性流体流过椭圆柱的数值模拟”理论与应用流变学/Proc.Xth Int/。

Yoshihiro MOCHIMARU: "Numerical Simulation of a Steady Non-Newtnian Fluid Flow past a Body of Revolution at Moderate Reynolds Numbers, Using a Spectral Method" Proc. 5th Int.Sym.Computational Fluid Dynamis. Vol.2. 273-278 (1993)

Yoshihiro MOCHIMARU：“使用光谱方法对经过中等雷诺数旋转体的稳定非牛顿流体进行数值模拟”Proc。

Yoshihiro MOCHIMARU: "Numerical Simulation of a Viscoelastic Fluid Flow past an Elliptic Cylinder" Theoretical and Applied Rheology/Proc.Xth Int.Congr.on Rheology. 1. 306 (1992)

Yoshihiro MOCHIMARU：“粘弹性流体流过椭圆柱的数值模拟”理论与应用流变学/Proc.Xth Int.Congr.on Rheology。

Yoshihiro MOCHIMARU: "Numerical Simulation of a Steady Non-Newtonian Fluid Flow past a Body of Revolution at Moderate Reynolds Numbers,Using a Spectral Method" Proc.5th Int.Sym.Computational Fluid Dynamics. 2. 273-278 (1993)

Yoshihiro MOCHIMARU：“使用谱法对以中等雷诺数流过旋转体的稳定非牛顿流体进行数值模拟”Proc.5th Int.Sym.Computational Fluid Dynamics。