Analysis Of Plane Flow Field Induced By Eccentric Rotation Of Inner Rod And Outer Cylinder

In oil drilling,the whirl of the lower drill string will lead to the fatigue damage of the drilling tool and increase the drilling cost.The combination of drilling fluid dynamics and drill string dynamics is necessary for the study of the theory of drill string whirl.The flow field analysis under the whirl of drill string is the basis of studying the fluid force of drilling fluid and the whirl law of drill string.Therefore,this paper analyzes the plane flow field induced by the eccentric rotation of inner rod and outer cylinder through three methods,including theoretical and numerical calculation,software simulation and PIV measurement experiment.The dynamic equations of laminar flow in the radial plane of Newtonian fluid induced by the concentric rotation of the inner rod and the outer cylinder under the cylindrical coordinate system are established.Combined with the boundary conditions,the analytical solutions of tangential velocity,pressure and flow function are obtained.The flow function vorticity control equation of Newtonian fluid radial laminar flow induced by the eccentric rotation of the inner rod and the outer cylinder of inertia force in bipolar coordinate system is established.The boundary conditions of velocity,flow function,vorticity and other parameters are given.Based on the finite difference method,the flow function-vorticity control equation is discretized.Lax-Wendroff scheme explicitly advances the solution of the convection term,the fully implicit solution of the diffusion term,and the ultra-relaxation iterative method to obtain the Helmholtz equation.The results show that the critical value of the eccentricity exists in the secondary flow except for the rotation of the inner rod and outer cylinder in the opposite direction;a surface vortex similar to Taylor vortex appears;the vortex center of the secondary flow will deviate shift,mainly due to the inertial force;when only the inner rod rotates eccentrically or only the outer cylinder rotates,the secondary flow area increases with the increase of eccentricity and speed;when the inner rod rotates in the same direction as outer cylinder,the secondary flow area increases with the increase of the eccentricity and the rotation speed of the outer cylinder,and decreases with the increase of the rotation speed of the inner rod;when the inner rod rotates in the opposite direction to the outer cylinder,the secondary flow area increases with eccentricity,the inner rod speedincreases and increases,and decreases as the outer cylinder speed increases.Using Ansys software,the geometric model of the eccentric rotation of the inner rod and the outer cylinder was established and meshed.The grid independence is checked and verified.The eccentric radial plane flow field was simulated by Ansys fluent software,and the change law of the secondary flow was consistent with the numerical analysis results.The dynamic pressure distribution on the inner rod shows that: when only the inner rod rotates eccentrically,the greater the eccentricity and the higher the rotation speed,the more significant the dynamic pressure effect,the dynamic pressure is from the narrowest gap to the widest gap;when the inner rod and the outer cylinder rotate eccentrically,the dynamic pressure caused by the rotation of the outer cylinder causes the flowing fluid to flow from the intermediate position to the side with the narrowest gap toward the side with the widest gap from the intermediate position.An experimental platform for measuring the plane flow field of the fluid induced by rotation of the inner rod and outer cylinder was developed,and the radial plane flow fields of glycerol aqueous solution and water were measured and analyzed by particle image velocimetry technology.The change law of secondary flow is consistent with results of numerical solution and simulation.Experimental results of different fluids show that: only when the inner rod rotates eccentrically,the critical value of eccentricity of the secondary flow of water is greater;when the inner rod rotates in the same direction as the outer cylinder,the fluid is the secondary flow of glycerol aqueous solution,the critical value of eccentricity is greater;other changes are consistent.Finally,the particle image velocimetry experiment results were used to verify the correctness of the numerical solution,and the credibility of the simulation results of the simulation software was also verified.The research in this paper not only lays a theoretical foundation for the analysis of the plane flow field induced by the internal rod whirl considering the inertial force in the moving coordinate system,but also has an important engineering significance for the analysis of the dynamic pressure effect,flow pressure consumption and rock carrying capacity of the drilling fluid under the eccentric rotation of the drill string.