Kinetic Theory And Numerical Simulation Of Non-newtonian Fluid-particle Flow

Most of the existing kinetic models for granular flow are established for gas-solid flow.The inertial effect of particles in the liquid phase is significantly weakened,and the tendency of turbulent diffusion is enhanced.It is of great significance to develop a kinetic model for dense liquid-solid two-phase flow,in which both particle-turbulence interactions and interparticle collisions should be integrated into the solid phase constitutive relations based on KTGF.In addition,most industrial liquids exhibit typical non-Newtonian rheological characteristics.It is necessary to study the effects of rheological parameters of non-Newtonian fluids on the flow characteristics of particles.The liquid-solid fluidized bed and the cuttings transportation during well drilling are typical industrial applications of non-Newtonian fluid-particle flow,and it is of practical significance to study the characteristics of the two-phase mixing and the suspension and deposition of particles in the liquid phase.The liquid turbulence-particle interaction is considered,and the structure of the collision component from dense gas molecular kinetics is used to solve the collision component of solid stress and fluctuation kinetic energy.The explicit expressions for the particle transport coefficients such as solid shear viscosity,bulk viscosity,granular pressure,and conductivity of fluctuation energy are obtained,and a kinetic theory of granular flow for dense liquid-solid flow is established.The particle transport coefficients in the liquid-solid flow calculated by the present model are higher than those from the original kinetic model.While in the gas-solid flow with high particle inertia,the solid transport coefficients obtained are very close to the original kinetic model,and the difference between the two is only reflected in the fluid turbulence fluctuation contribution at lower particle concentration.For the non-Newtonian fluid-particle flow,a new drag model considering effects of rheological properties is developed.At high particle concentrations the apparent rheological parameters of the non-Newtonian fluid at the surface of the particles are corrected based on the Ergun equation,and at low particle concentrations the modified Reynolds number and the C_d-Re_n correlation considering the effect of flow behavior index are adopted based on the Wen-Yu model.In Newtonian fluids,the non-Newtonian drag model can be degraded to the Gidaspow model.In the simulation of liquid-solid bubbling fluidized bed,the average solid concentration and particle velocity predicted by the kinetic model proposed in this paper is in better agreement with the experiment.When the liquid velocity is higher than 2.5u_mf,the solid viscosity is dominated by its kinetic component.When the solid concentration is higher than 0.25,the collision component is dominant in its viscosity.In the simulation of the liquid-solid circulating fluidized bed,the distribution of particle concentration and velocity along the radial direction of the riser predicted by the present kinetic model is also in better agreement with the experiment.In addition,the simulation of the power law fluid-particle fluidized bed using the kinetic model combined with the non-Newtonian drag model developed in this paper shows that the new drag model predicts better void fraction under different rheological parameters,particle diameters,and liquid velocities.The transport mechanism of cuttings particles carried by non-Newtonian drilling fluids in the wellbore annulus is studied numerically.Swaying phenomena of cuttings concentration and velocity distribution along the direction of drill pipe rotation and the three-layer flow pattern of cuttings including suspended region,moving bed region and fixed bed region are obtained.When the inclination angle of the well is low,the movement of cuttings is dominated by the suspension flow.With the increase of the inclination angle,the flow pattern of the rolling movement of cuttings particles gradually becomes prominent.When the inclination angle is between 35°and 65°,the cuttings transport ratio is the lowest and the pressure drop is the highest.The embedded sliding mesh method is used to realize the planetary rotation of the drill pipe during the cuttings transportation process.The orbital revolution of drill pipe periodically scrapes the cuttings bed at the bottom of the annulus,and more cuttings particles enter the suspension region from the fixed bed and are transported out of the wellbore.When the direction of self-rotation of the drill pipe is opposite to the revolution,a significant secondary flow occurs in the annulus.With the increase of the drill pipe rotation speed and the radius of revolution,the cuttings transport has been improved to a certain extent,but this significantly increases the torque exerted by the liquid-solid mixture on the drill rod.In addition,a pulsed drilling scheme for wellbore cleaning is proposed and its effect on improving cuttings transportation is numerically simulated.Results show that the pulsed drilling fluids significantly reduce the cuttings concentration in the moving bed region and increase the axial velocities in the fixed bed region.Increasing the amplitude and frequency of drilling fluid velocity pulses increases the cuttings transport ratio.Aiming at effects of the rheological characteristics of non-Newtonian fluids,the effects of rheological parameters on the plastic Herschel-Bulkley fluid-cuttings flow in the drilling annulus are numerically simulated.Increasing the yield stress,consistency coefficient,and flow behavior index of the drilling fluid with Herschel-Bulkley characteristics enhances the axial flow of cuttings at the bottom of the annulus and expands the tangential flow area,and improves the transportation of cuttings.As the yield stress of drilling fluid increases,the axial flow of cuttings at the bottom of the annulus increases,while the axial flow of cuttings in the upper part of the annulus weakens slightly.When both the consistency coefficient and the flow behavior index of drilling fluids are low,the movement of cuttings in the wellbore is an unsteadily pulsating process.