The Research Of Newton Fluid Doing The Eccentric Annulus Flow Which Is Based On Potential Superposition Principle

In the drilling construction process, the drill strings drilling rotated ceaselessly under the action of drilling pump. They are easy to instability and cause deviation because of the drilling fluid soak and rotary torque generated by the bucking and vortex dynamics. The role of drilling fluid flow field that close to the drill strings is not to be ignored. The flow of the drilling fluid is the spiral flow in the eccentric annulus air. In order to facilitate the research, we assume it for the Newtonian fluid. Now the most available method of solving the problem of Newtonian fluid in eccentric annulus flow in the air is that through the fluid mechanics equations. But the general solution of the equation set is very difficult so that nobody has solved it. Therefore, solving the problem is not only has theory value but also has a lot of engineering practice significance.A new method is presented to solve the problem of the eccentric annulus flow field. it is the potential energy superposition principle. This principle is by breaking the complex of eccentric annulus flow field into four kinds of simple flow state which are homogeneous linear flow, dipole, rotation circulation and revolution of circulation, and then solving the potential function and stream function of them. During the process of solving, I got the revolution of the point vortex velocity distribution by simplified the N-S equation. And then I deduced the expression of homogeneous linear flow, and started out the method of the rotation point vortex ring from the definition of circulation. I used the circle theorem to solve the boundary problem at the same time, finally superimposed them to acquire the potential function and stream function of the eccentric annulus flow field.This paper not only gave the final eccentric annulus flow mathematical model, but also used the Matlab to solve the model and drew the motion pattern, compared with the flow field simulated by the Fluent, and obtained that the flow field intension didn’t change with the transform of the heart position of the small circle when the eccentric distance is immobilization. Also determined the accuracy of the mathematic model, and proved the feasibility and correctness of the theory.