The Flow Of Incompressible Viscous Fluid In Pipeline

Kinetic study of fluid in pipeline is an important topic in fluid mechanics. Recent decades, it is widely applied to the field of chemical, biological, technology, medicine, transportation and other, therefore the study of such typical model has not only theoretical significance, but also very important value in industrial production.This article studied the viscous incompressible shear-thinning fluid flow in the pipeline. Taking the actual process of industrial production into account, we know that the fluids does not flow in a closed pipeline ordinarily, many of them having an output, typical examples, such as faucet pipe, screw extruder, injection molding machine, ect. In view of what was said above, it is very necessary to go deeply into research the model with inflow and outflow boundary condition. However, natural boundary condition is much more complex than Dirichilet boundary conditions. The possibility of backflow phenomenon inside the fluid may cause the uncontrollable of energy which directly cause concussive of the solution in the outflow boundary. The explanation of this phenomenon is, up till now, the regularity of this typical model remain unclear. Hence, in order to solve the trouble of the outflow boundary brought, in this article, we assume the speed of fluid flow along out of the pipe direction is very slow. Then we do homogeneous processing on boundary of the partial differential equation. We can obtain the local existence of solutions through Galerkin method and then use energy estimate, combine with the truncation method, thus proving the existence of weak solutions of global model, which provides a theoretical basis for experimental and numerical simulation.Further, this paper also studies the heat exchange of the pipeline flow with helical blade rotors. We improve the previous model and research the fluid flow in cross section of the heat exchange tube, pull in the mathematical model that describe the rotation of rigid motion, take angular velocity of helical blade rotors as an unknown quantity, couple fluid flow with rigid motion together to analyze, then the existence and uniqueness of velocity for the mixing unsteady flow are proved. Following, we will discrete the space of the pipe, that is to say, we will slice the pipeline. According to the conclusion of this article that we have got above, we get the conclusion of flow field in pipe cross section, finally through iterative approximation method, thus get solution of the flow field in the whole pipeline.