Modeling of an Upper-Convected-Maxwell Fluid Hammer Phenomenon in Pipe System

In this paper, the occurrence of water hammer phenomenon is examined in a situation that instead of water, an upper-convected-Maxwell fluid flows in a pipe system. This phenomenon is called an upper-convected-Maxwell fluid hammer. This expression relates to transients of Maxwell fluid caused by the sudden alteration in the conditions of flow. Upper-convected-Maxwell fluids are a kind of non-Newtonian viscoelastic fluids. The system studied is a valve-horizontal pipe and reservoir. The equations representing the conservation of mass and momentum govern the transitional flow in the pipe system. The numerical method used is a two-step variant of the Lax-Friedrichs method. Firstly, the nondimensional form of governing equations is defined, then, the effect of Deborah and Reynolds numbers on pressure historic is investigated. The results revealed that increasing Deborah number, indicating the elasticity of the polymer, increases the oscillation height and consequently attenuation time of the transient flow becomes longer. It was also found that in low Reynolds, in a Newtonian fluid, line packing phenomenon effect is observed only at the first time period but in upper convected Maxwell fluid the effect of this phenomenon continues to more time periods and damping time becomes longer.