Exploratory Study By Finite Difference Method Of High Precision And Much Difference On Tran-sformation Of Flow State In A Two-dimensional Diffuser

A pipe having diverging boundaries is widespread used in hydraulic engineering field such as pumped storage power station and water supply and drainage pipe system and other engineering field. During the application of engineering, it is found that the change of flow state is quite complex. These changes include fluctuation, backflow vortex and bias current. They are adverse to the application of pipes having diverging boundaries.A two-dimensioned pipe having diverging boundaries is chosen in this paper to build a numerical model based on the parametric polynomial method. Several measures such as numerical discrete, linearisation of equations, control of error are taken to make the model reliable. According to related mathematical theory and method, the conditioned number of coefficient matrix is used as a reference to simulate the development of flow field from a small flow to a mass flow.During the research, it is found that a significant change of flow field often occurred at the jump point of conditioned number of coefficient matrix. It is claimed that change of flow field in the pipe having diverging boundaries is quite relevant with related mathematical mechanism. The divergence angle of the pipe has an appreciable influence to the change of flow field. The change in a pipe with a lager angle appears earlier and more complex. Flow state after change often consists of backflow, vortex and bias current which is similar to the phenomenon observed in the engineering. At the same time, viscosity of the fluid also has an influence to the change of flow state. With a big viscosity, the change of flow state will not occur until the rate of flow is very large. But under the several different viscosities, Reynolds numbers at the change point is very close. It is claimed that Reynolds number is one of the most important factor to control the change of flow state.