Journal of Theoretical
and Applied Mechanics

50, 4, pp. 889-902, Warsaw 2012

Universal weighting function in modeling transient cavitating pipe flow

Kamil Urbanowicz, Zbigniew Zarzycki, Sylwester Kudźma
This work concerns modeling of time-varying resistance during transient cavitating liquid pipe flow. The wall shear stress is presented in the way introduced by Zielke as the integral convolution of liquid local velocity changes and a weighting function.

A new procedure for determination, so-called, a universal laminar-turbulent weighting function, which combines functions of Zielke and Vardy and Brown or Zielke and Zarzycki, is presented. Based on these weighting functions, the method of simulation transients in the pressure lines in a wide range of Reynolds numbers is presented. It eliminates numerical problems associated with the change of laminar flow into turbulent and vice versa. An example application of this method for simulation of water hammer is presented. The calculation results are compared against experiments presented by Bergant and Simpson, and good agreement is found.
Keywords: transient pipe flow; unsteady wall shear stress; weighting function; cavitation