粘弹性流体各向同性湍流特性研究
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摘要
添加剂湍流减阻技术对流体输送系统的节能及输送效率的提高有重要的应用价值。自Toms湍流减阻效应被发现至今60多年来,国内外学者开展了大量的研究工作,但仍存在很多亟需解决的问题,如粘弹性流体湍流减阻机理和高雷诺数下粘弹性流体流动大涡数值模拟等。
目前,粘弹性流体湍流减阻的研究工作主要集中在具有壁面效应的槽道、管道及边界层流动。壁面的存在使得流动具有不均匀性,因此不利于分析粘弹性流体分子微观结构与湍流结构之间的相互作用。然而,粘弹性流体各向同性湍流的研究却能很好地解决上述问题,这主要是因为在该流动中不存在流动剪切应力,粘弹性流体的存在并不能改变流动系统的动量输运,但能够改变从大尺度到小尺度间的能量传递规律。因此对粘性流体各向同性湍流的研究具有重要的理论意义和学术价值。
本文首先基于粘弹性流体各向同性湍流模型推导了其动力学方程,通过对方程中各项分析研究了粘弹性流体的作用,并建立了粘弹性流体各向同性湍流直接数值模拟(DNS)程序。采用伪谱方法对粘弹性流体弹性应力修正的Navier-Stokes方程进行求解,而对于具有双曲型特性的粘弹性流体分子变形率张量输运方程(FENE-P模型)的求解采用有限差分方法,并基于KT格式离散其对流项,从而保证了粘弹性流体分子变形率张量的对称正定特性。
其次,对粘弹性流体衰减各向同性湍流DNS结果进行分析,主要从能量输运方程,分析流体粘弹性对流动的影响,发现流体粘弹性的存在改变了经典的湍动能输运模式。基于粘弹性流体分子微观结构与湍流结构之间的能量转换谱很好地解释了这一现象,提出了粘弹性流体衰减各向同性湍流的减阻定义表达式,并阐述了其物理意义。从涡结构、拟涡能和变形能输运方程中的生成项与粘弹性流体的作用项之间的联合概率密度函数,发现流体粘弹性的存在抑制了流动中的涡结构(尤其是小尺度涡结构)。通过速度梯度偏斜因子解释了粘弹性流体对流动非线性及耗散率的影响,并基于不同尺度下的平坦因子和速度结构函数的高阶平坦因子解释了小尺度间歇性受抑制的现象。根据速度梯度张量的Galilean不变量特性分析了流动中的几何特性,即涡量场、流动变形场和粘弹性流体分子变形场之间的关系。基于涡量、变形能和弹性能采样平均拟涡能生成项等物理量,分析了流动的非线性及拟涡能生成项等物理量和弹性能之间的关系。
最后,对粘弹性流体强迫各向同性湍流DNS结果进行分析,根据速度梯度平坦因子及湍动能等物理量随时间的演化规律,可知本文外力场的施加方式是可行的。根据粘弹性流体分子微观结构与湍流结构之间的能量转换谱及二阶径向结构函数,很好地解释了流体粘弹性的存在改变了经典的湍动能输运模式的现象,提出了粘弹性流体强迫各向同性湍流的减阻定义表达式,解释了其物理意义。同时,通过对涡结构和速度场本征正交分解结果的分析,发现流体粘弹性抑制了小尺度涡结构且使流动更加规则,进一步解释了粘弹性流体的湍流减阻效果。速度偏导数的平坦因子和高阶统计量的分析结果表明,流体粘弹性的存在抑制了小尺度间歇性,且拟涡能场(或涡量场)比变形场(或耗散率场)具有更强的间歇性。基于速度梯度张量的Galilean不变量特性,分析了拟涡能和变形能的分布规律,并研究了流动拓扑动力学特性。
The turbulent drag-reducing technique by additives has important application value for energy-saving and increasing transport efficiency for liquid transportation system. Since the discovery of Toms effect (turbulent drag reduction) more than sixty years ago, there have been a large amount of foreign and domestic researchers being engaged in the investigation of this phenomenon. But there still exist many problems to be solved immediately, for example, the drag-reducing mechanism for viscoelastic fluid flow and large eddy simulation for viscoelastic fluid flow at high Reynolds number.
Up to now, the main efforts of turbulent drag-reducing flow of viscoelastic fluid have been focused on the wall-bounded turbulent flows where the wall plays an important role, such as channel, pipe and boundary layer flows. The existence of the wall makes the flow inhomogeneous, so it is hard to investigate the interaction between the micro-molecular structures of viscoelastic fluid and turbulent vortex structures. However, the study on isotropic turbulence in viscoelastic flud can solve well the above problems. This is because there is no mean shear stress in the flow; the existence of viscoelastic fluid can not change the momentum transportation of flow system, but it can change the turbulent kinetic energy cascading from large-scale to small-scale. So the study of isotropic turbulence in viscoelastic fluid has important theoretic meaning and scientific value.
Firstly, the dynamics equations based on isotropic turbulence in viscoelastic fluid were deduced in this thesis, and the effect of viscoelastic fluid was investigated through analyzing each term of the equations, and then a direct numerical simulation (DNS) program of isotropic turbulence in viscoelastic fluid was built. The pseudo-spectral method and the finite different method were used to numerically simulate the modified Navier-Stokes equation with elastic stress of viscoelastic fluid and the rate-of-strain tensor transportation equation of viscoelastic fluid molecules with hyperbolic charactericstics. The Kurganov-Tadmor (KT) scheme was used to discrete the convection term so as to assure the symmetric and positive definite characteristics of the rate-of-strain tensor of viscoelastic fluid molecules.
Then, the DNS results of decaying homogeneous isotropic turbulence (DHIT) in viscoelastic fluid were analyzed in the thesis. It investigated the effect of viscoelastic fluid on flow through budget-analyzing the energy transportation equations. The results showed that the existence of viscoelastic fluid changes the classical turbulent kinetic energy cascading. This phenomenon could be well explained based on the energy transformation spectra between the micro-molecular structures of viscoelastic fluid and turbulent vortex structures. A definition of drag-reduction rate for DHIT in viscoelastic fluid was proposed and its physical meaning was expatiated. Through investigating the vortex structures and the joint probability density function between the production terms and the effective terms of viscoelastic fluid in the enstrophy and strain transportation equations, it was found that the existence of viscoelasticity in the fluid inhibits the vortex structures, especially for small-scale votex structures. It explained the effect of viscolasticity on dissipation based on the skewness of the velocity gradient and explained the inhibition of small-scale intermittency based on the flatness of different scales and the high-order flatness of velocity structure function. According to the Galilean characteristics of velocity gradient tensor, it studied the geometrical characteristics of the flow, such as, the relationship among vorticity, strain of the flow and molecules strain of viscoelastic fluid. Then it investigated the flow nonlinearity and the relationships between the important parameters (such as the enstrophy production term) and elastic energy through conditionally-averaging some important parameters based on vorticity, strain energy and elastic energy.
Finally, the DNS results of forcing homogeneous isotropic turbulence (FHIT) in viscoelastic fluid were analyzed in the thesis. Accroding to the skewness of velocity gradient and the elovement of the important parameters, such as turbulent kinetic energy, it showed that the method of force field in our simulations is reasonable. The existence of viscoelastic fluid changes the classical turbulent kinetic energy cascading in FHIT also. This phenomenon was explained well based on the energy transformation spectra between the micro-molecular structures of viscoelastic fluid and turbulent vortex structures and second-order longitudinal structure function. Then the definition of drag-reduction rate for FHIT in viscoelastic fluid was proposed and its physical meaning was expatiated. Meanwhile, the analyses results for vortex structures and the proper orthogonal decomposition of velocity field showed that the small-scale vortex structures are inhibited and the flow is more regular, which further explains the turbulent drag-reducing effect of viscoelastic fluid. The results of the skewness of velocity partial derivative and high-order statistical parameters suggested that the small-scale intermittency is inhibited due to the existence of viscoelasticity and the intermittency of enstrophy field (or vorticity field) is stronger than that of strain field (or dissipation field). Based on the Galilean characteristics of velocity gradient tensor, it studied the distribution of enstrophy and strain, and investigated the characteristics of flow topological dynamics.
目前,粘弹性流体湍流减阻的研究工作主要集中在具有壁面效应的槽道、管道及边界层流动。壁面的存在使得流动具有不均匀性,因此不利于分析粘弹性流体分子微观结构与湍流结构之间的相互作用。然而,粘弹性流体各向同性湍流的研究却能很好地解决上述问题,这主要是因为在该流动中不存在流动剪切应力,粘弹性流体的存在并不能改变流动系统的动量输运,但能够改变从大尺度到小尺度间的能量传递规律。因此对粘性流体各向同性湍流的研究具有重要的理论意义和学术价值。
本文首先基于粘弹性流体各向同性湍流模型推导了其动力学方程,通过对方程中各项分析研究了粘弹性流体的作用,并建立了粘弹性流体各向同性湍流直接数值模拟(DNS)程序。采用伪谱方法对粘弹性流体弹性应力修正的Navier-Stokes方程进行求解,而对于具有双曲型特性的粘弹性流体分子变形率张量输运方程(FENE-P模型)的求解采用有限差分方法,并基于KT格式离散其对流项,从而保证了粘弹性流体分子变形率张量的对称正定特性。
其次,对粘弹性流体衰减各向同性湍流DNS结果进行分析,主要从能量输运方程,分析流体粘弹性对流动的影响,发现流体粘弹性的存在改变了经典的湍动能输运模式。基于粘弹性流体分子微观结构与湍流结构之间的能量转换谱很好地解释了这一现象,提出了粘弹性流体衰减各向同性湍流的减阻定义表达式,并阐述了其物理意义。从涡结构、拟涡能和变形能输运方程中的生成项与粘弹性流体的作用项之间的联合概率密度函数,发现流体粘弹性的存在抑制了流动中的涡结构(尤其是小尺度涡结构)。通过速度梯度偏斜因子解释了粘弹性流体对流动非线性及耗散率的影响,并基于不同尺度下的平坦因子和速度结构函数的高阶平坦因子解释了小尺度间歇性受抑制的现象。根据速度梯度张量的Galilean不变量特性分析了流动中的几何特性,即涡量场、流动变形场和粘弹性流体分子变形场之间的关系。基于涡量、变形能和弹性能采样平均拟涡能生成项等物理量,分析了流动的非线性及拟涡能生成项等物理量和弹性能之间的关系。
最后,对粘弹性流体强迫各向同性湍流DNS结果进行分析,根据速度梯度平坦因子及湍动能等物理量随时间的演化规律,可知本文外力场的施加方式是可行的。根据粘弹性流体分子微观结构与湍流结构之间的能量转换谱及二阶径向结构函数,很好地解释了流体粘弹性的存在改变了经典的湍动能输运模式的现象,提出了粘弹性流体强迫各向同性湍流的减阻定义表达式,解释了其物理意义。同时,通过对涡结构和速度场本征正交分解结果的分析,发现流体粘弹性抑制了小尺度涡结构且使流动更加规则,进一步解释了粘弹性流体的湍流减阻效果。速度偏导数的平坦因子和高阶统计量的分析结果表明,流体粘弹性的存在抑制了小尺度间歇性,且拟涡能场(或涡量场)比变形场(或耗散率场)具有更强的间歇性。基于速度梯度张量的Galilean不变量特性,分析了拟涡能和变形能的分布规律,并研究了流动拓扑动力学特性。
The turbulent drag-reducing technique by additives has important application value for energy-saving and increasing transport efficiency for liquid transportation system. Since the discovery of Toms effect (turbulent drag reduction) more than sixty years ago, there have been a large amount of foreign and domestic researchers being engaged in the investigation of this phenomenon. But there still exist many problems to be solved immediately, for example, the drag-reducing mechanism for viscoelastic fluid flow and large eddy simulation for viscoelastic fluid flow at high Reynolds number.
Up to now, the main efforts of turbulent drag-reducing flow of viscoelastic fluid have been focused on the wall-bounded turbulent flows where the wall plays an important role, such as channel, pipe and boundary layer flows. The existence of the wall makes the flow inhomogeneous, so it is hard to investigate the interaction between the micro-molecular structures of viscoelastic fluid and turbulent vortex structures. However, the study on isotropic turbulence in viscoelastic flud can solve well the above problems. This is because there is no mean shear stress in the flow; the existence of viscoelastic fluid can not change the momentum transportation of flow system, but it can change the turbulent kinetic energy cascading from large-scale to small-scale. So the study of isotropic turbulence in viscoelastic fluid has important theoretic meaning and scientific value.
Firstly, the dynamics equations based on isotropic turbulence in viscoelastic fluid were deduced in this thesis, and the effect of viscoelastic fluid was investigated through analyzing each term of the equations, and then a direct numerical simulation (DNS) program of isotropic turbulence in viscoelastic fluid was built. The pseudo-spectral method and the finite different method were used to numerically simulate the modified Navier-Stokes equation with elastic stress of viscoelastic fluid and the rate-of-strain tensor transportation equation of viscoelastic fluid molecules with hyperbolic charactericstics. The Kurganov-Tadmor (KT) scheme was used to discrete the convection term so as to assure the symmetric and positive definite characteristics of the rate-of-strain tensor of viscoelastic fluid molecules.
Then, the DNS results of decaying homogeneous isotropic turbulence (DHIT) in viscoelastic fluid were analyzed in the thesis. It investigated the effect of viscoelastic fluid on flow through budget-analyzing the energy transportation equations. The results showed that the existence of viscoelastic fluid changes the classical turbulent kinetic energy cascading. This phenomenon could be well explained based on the energy transformation spectra between the micro-molecular structures of viscoelastic fluid and turbulent vortex structures. A definition of drag-reduction rate for DHIT in viscoelastic fluid was proposed and its physical meaning was expatiated. Through investigating the vortex structures and the joint probability density function between the production terms and the effective terms of viscoelastic fluid in the enstrophy and strain transportation equations, it was found that the existence of viscoelasticity in the fluid inhibits the vortex structures, especially for small-scale votex structures. It explained the effect of viscolasticity on dissipation based on the skewness of the velocity gradient and explained the inhibition of small-scale intermittency based on the flatness of different scales and the high-order flatness of velocity structure function. According to the Galilean characteristics of velocity gradient tensor, it studied the geometrical characteristics of the flow, such as, the relationship among vorticity, strain of the flow and molecules strain of viscoelastic fluid. Then it investigated the flow nonlinearity and the relationships between the important parameters (such as the enstrophy production term) and elastic energy through conditionally-averaging some important parameters based on vorticity, strain energy and elastic energy.
Finally, the DNS results of forcing homogeneous isotropic turbulence (FHIT) in viscoelastic fluid were analyzed in the thesis. Accroding to the skewness of velocity gradient and the elovement of the important parameters, such as turbulent kinetic energy, it showed that the method of force field in our simulations is reasonable. The existence of viscoelastic fluid changes the classical turbulent kinetic energy cascading in FHIT also. This phenomenon was explained well based on the energy transformation spectra between the micro-molecular structures of viscoelastic fluid and turbulent vortex structures and second-order longitudinal structure function. Then the definition of drag-reduction rate for FHIT in viscoelastic fluid was proposed and its physical meaning was expatiated. Meanwhile, the analyses results for vortex structures and the proper orthogonal decomposition of velocity field showed that the small-scale vortex structures are inhibited and the flow is more regular, which further explains the turbulent drag-reducing effect of viscoelastic fluid. The results of the skewness of velocity partial derivative and high-order statistical parameters suggested that the small-scale intermittency is inhibited due to the existence of viscoelasticity and the intermittency of enstrophy field (or vorticity field) is stronger than that of strain field (or dissipation field). Based on the Galilean characteristics of velocity gradient tensor, it studied the distribution of enstrophy and strain, and investigated the characteristics of flow topological dynamics.
引文
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