Study On Elastic Turbulence In 3D Kolmogorov Flow Of Viscoelastic Fluid Based On Direct Numerical Simulation

Elastic turbulence in viscoelastic fluids can occur at an arbitary low Reynolds number, Re, i.e. the inertial effect can be neglected (under this condition the Newtonian fluid flow must be in laminar regime), and is induced completely by the elaticity of the fluids. The flow in elastic turbulence regime exhibits features of developed inertial turbulence such as sharp growth of flow resistance and significant increase in the rates of momentum and mass transfer and a broad range of spatial and temporal scales of random fluctuations with an algebraic decay. Nonetheless, it still exihibits its own unique properties, such as faster decay rate, random in time and smooth in space. Besides, the underlying physical mechanism of elastic turbulence shows completely different as compared with inertial turbulence which corresponds to large Reynolds stress.To further understand the characteristics and the following mechanism of elastic turbulence, direct numerical simulations in a three-dimensional Kolmogorov flow with very simple geometric setup were carried out for both inertial turbulence in Newtonian fluids and elastic turbulence in viscoelastic fluids. Based on the numerical results, velocity field, vortical structures, polymer conformation field as well as the underlying physical mechanism of inertial turbulence and elastic turbulence were studied. It is obtained that (I) smaller critical Weissenberg numer is got, which indicates the flow is more unstable to the perturbations in the simulations of three-dimensional flow as compared with two-dimentional flow; (II) when the flow becomes elastically turbulent, the polymer molecules contained in the flow are statistically intensely stretched, and above the coil-stretch transition, which indicates the polymers have a strong feedback on the flow; (III) different from inertial turbulence, in elastic turbulence it is the elastic stress fluctuations which through velocity fluctuations injects energy to the flow structures at each scale so as to counteract the viscous dissipation and maintain the turbulent intensity; (IV) in elastic turbulence the vortical structures are generated in the region where elastic stress is apparent or the polymers are intensely stretched, and due to the narrow strong shear region, the vortical structures observed in the simulation are flat; (V) when the elastic turbulence is induced, the elastic energy contained by the polymers are much larger than kinetic energy contained by the flow elements, which indicates the flow is full of elasticity, and from the instantaneous energetic viewpoint, the additional force mainly supports the dissipation by viscositiy, elasticity and numerical methods to sustain the instantaneous kinetic energy, elastic energy, enstrophy and the strain of the whole system; (VI) from the fluctuating energetic viewpoint, in elastic turbulence the main source of turbulent fluctuations is the ineraction between the fluctuations of elastic stress and velocity, fuctuating vortex tubes are stretched by the interaction between the fluctuations between vorticity and polymer comformation (not the flow strain), and the strain generation and energy cascade between different scales are also caused by the interaction between polymer conformation and the flow strain, not by the strain self-amplification.