Study On The Characteristics Of Isotropic Turbulence In Viscoelastic Fluid

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.