Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows

The behavior of unsteady velocity profiles in laminar and turbulent water hammer flows is numerically investigated. In this way, the governing equations for the quasitwo-dimensional equations of transient flow in pipe are solved by using the modified implicit characteristics method. A $k-ω$ turbulence model which is accurate for two-dimensional boundary layers under adverse and favorable pressure gradients is applied. The numerical results for both steady and unsteady turbulent pipe flows are in good agreement with the experimental data. The results indicate that both decelerating and accelerating flows are produced in a wave cycle of water hammer. During deceleration of the flow, a region of reverse flows and also strong gradients is formed near to the pipe wall. In case of the turbulent water hammer, this region is very close to the pipe wall compared with the laminar water hammer. Moreover, point of inflection and also point of zero velocity are formed in the unsteady velocity profile due to the water hammer problem. The results show that the point of zero velocity does not move very far from its initial location, while the point of inflection moves rapidly from the wall.