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Characteristics of unsteady Poiseuille flow of Newtonian fluid in circular pipe
CHEN Lei1,2, TANG Yuannan3, LIU Gang1,2, LU Xingguo1,2
(1.College of Pipeline and Civil Engineering in China University of Petroleum(East China), Qingdao 266580,China;2.Shandong Key Laboratory of Oil & Gas Storage and Transport Safety Engineering, Qingdao 266580, China;3.SINOPEC Sales Company Limited South China Branch, Guangzhou 510000, China)
Abstract:
At the initial stage of Hagen-Poiseuille flow, there is an unsteady process for the velocity developing which will cause deviation on the results of measurement. In order to analyze the deviation caused by the unsteady Poiseuille flow for the viscosity measurement, studies were carried out through a numerical model. Taking the incompressible Newtonian fluid as an example, we studied the unsteady Poiseuille flow process at a constant flow rate and unsteady flow rate boundary conditions. The dimensionless viscosity and dimensionless time were used to reflect the unsteady process and a numerical model was built. The variation rules of the dimensionless viscosity under the boundaries of the constant average velocity, the average velocity which increases linearly from 0, and the constant pressure drop were given via numerical calculations. It was found that dimensionless viscosity falls to 1 with the time increasing and the non-dimensional time is a constant when the flow attains the stable state under different boundary conditions. When the types of boundary conditions are decided, the dimensionless viscosity can be viewed as a function only with respect to the dimensionless time in the unsteady process. For different types of boundary conditions, the unsteady processes reduce corresponding to the boundary conditions of the constant average velocity, the constant pressure drop, and the average velocity which increases linearly from 0.
Key words:  rheology  unsteady Poiseuille flow  numerical model  boundary conditions  dimensionless viscosity  dimensionless time.