The Flow Of Power-Law Fluid In A Helical Pipe

It is a quite hotspoted problem for the research of the flow in a curved pipe in the hydrodynamics domain. Whether the research of the time independent flow in a curved pipe or the research of the time independent flow in a helical pipe, both are the research of viscous flow for the viscous fluid. It has not been reported for the research of the flow of power-law fluid in a helical pipe, perturbation method is one of the basic tools of studying non-linearity problems. It can give a sententious and approximate analytic solution. Which can be use to discuss problem qualitatively or quantitatively. The fist term of perturbation method can post the hypostasis of physics problem. Along with the development of the computer industry, numerical calculation is widely used in the computation hydrodynamics. Among the numerous numerical calculation method, the finite volume method is often used, because its conception is conciseness and the implement process is convenient. The isothermal time independent flow for power-law fluid in a helical pipe with circular section is studied with theoretic method (perturbation method) and numerical method (finite volume method) in the paper. The result of the research is important both in theory and in practice. The research contents are as follows:1. The operation of governing equations in orthogonal coordinate system. The Navier-Strokes equation has been educed with tensor analysis theory in helical curved coordinate system. The mathematic model for fully developed flow of power-law fluid in the a helical pipe is obtained.2. The flow of power-law fluid in a helical pipe with circular section has been studied using perturbation method. The second order perturbation solution for the flow of power-law fluid in stillness a helical pipe is obtained with curvature and torsion as small parameter. The effect of curvature, torsion and Dean number on secondary flow is discussed.3. The flow of power-law fluid in a helical pipe with circular section has also been studied using numerical method (finite volume method). The triangle mesh is used to proceed to numerical calculation and the compares with perturbation solution and the results in the article is conducted. The effect of curvature, torsion and Dean number on secondary flow, the isoline of stream function, the distribution of axial speed and wall friction is discussed in detail. The relation between flow flux and pressure gradient in different curvature and torsion a helical pipe is studied with practical calculation.The creative research contents are as follows:1. The study of the flow of power-law fluid in a helical pipe with circular section with perturbation method. With curvature and torsion as small parameter, the second order perturbation solution for the flow of power-law fluid in a helical pipe with circular section is obtained using double parametric perturbation method.2. The study of the flow of power-law fluid in a helical pipe with circular section with numerical method (finite volume method). The triangle mesh is used to proceed to numerical calculation. The functional value on the interface of the control volume is calculated using the QUICK scheme with upwind style.3. The practical parameter of a helical pipe was used to proceed to calculation. The relation between flow flux and pressure gradient in different curvature and torsion a helical pipe is studied. The research results can be used for the design of a helical pipe.4. It is discovered that the shape of the secondary flow is changed from one vortex to two vortexes with the increment of Dean number. But the appear of the second vortex of power-law fluid is later than that of Newtonian fluid.The shape of the secondary flow is changed from two almost symmetrical vortexes to one vortex with the increment of torsion of a helical pipe. But the disappear of the second vortex of NewtonianIIfluid is later than that of power-law fluid.