Research On The Fiber's Dispersion Coefficient In Turbulent Fiber Suspension

The rheology and kinetic characteristics of fiber suspension flow are very common in both nature and many industrial processes. Different from spherical particle suspensions, the properties of fiber suspension mostly rely on the orientation distribution of cylindrical particles. The motion of fiber is a combination of translation and rotation. Besides, the motion of particles in a turbulent flow is governed by the mean and fluctuating velocity. The property of fiber in a suspension flow affects the rheology, transport, heat transfer and light scattering behaviors, so it is important to study the particle orientation distribution during flows.In this thesis, the dispersion coefficients of fiber are derived based on motion equation of particles and stochastic theory of turbulent shear flow. The relationship between the effect on macroscopic properties of flow and orientation distribution of particles is investigated.In homogeneous turbulent flow, from the motion equation of particles, considering the virtual mass force due to the acceleration of particles and different velocity between particle and fluid, the relationship between the fluctuating velocity of fiber and fluid is derived. Furthermore, the dispersion coefficient of translation and orientation is also achieved. The results show that decrease as the ratio of fiber length to Lagrangian integral length scale of the turbulence increased.In common nonuniform and inhomogeneous turbulent flows, applied stochastic theory of turbulent shear flow to the equation of fiber orientation, the function of correlation moment between the different fluctuating velocity gradient in a two-dimensional parallel turbulent shear flow. The expression of dispersion coefficient is dependent on the four parameters, i.e., characteristic length, time, velocity and a dimensionless parameter related to the effect of wall. The derived expression can be expanded to three-dimensional turbulent flows and serves for the theoretical basis for solving the turbulent flow of fiber suspension. In the semi-dilute planar turbulent shear flow, based on instantaneous motion equation of fiber suspension and orientation distribution equation(ODE) of fibers, using Reynolds averaging method, the modified Reynolds mean motion equation of turbulent fiber suspension and the equation of probability distribution function for mean fiber orientation are derived. A new successive iteration method is developed to calculate fiber suspension in a turbulent channel flow. The derived equations and successive iteration method are verified by comparing the computational results with the experimental ones. The result reveals that the fibers play a significant role in suppressing the turbulence and reducing the drag. Such role becomes more obvious with increasing of the fiber mass concentration.