Author(s): M. Zhao; M.S. Ghidaoui; A.A. Kolyshkin

Linked Author(s):

Keywords: Water hammer; linear stability analysis; transient growth; initial value problem

Abstract: Existing transient pipe flow models assume that the flow field is stable and axisymmetric. Recent experimental and theoretical researches show that water hammer flows can become unstable and these instabilities lead to the breakdown of the axisymmetric assumption and to significant changes to the flow held and the magnitude and distribution of wall shear stresses. In addition, previous experiments revealed that in some cases the flow asymmetry developed in a time scale smaller than the water hammer time scale (ratio of pipe length to wavespeed) and in other cases the instability developed in a time scale of the order of the water hammer time scale. The current stability analysis is consistent with previous experimental observations. In particular, it is shown that there are two distinct mechanisms of instability, namely, a transient growth mechanism which develops in time scale shorter than the water hammer time scale and an exponential growth mechanism which develops in time scale of the order of the water hammer time scale; and the instability is indeed of asymmetric nature. Perturbations with large streamwise length scale (i.e. large streamwise wavelength) are more susceptible to the transient instability while perturbations with small streamwise length scale are more susceptible to exponential instability. The exponential instability may become active only if ihe flow “survives” the instability associated with the transient growth. The transient flow instability (sometimes referred to as bypass instability) can arise even when the flow is deemed to be stable by the traditional modal stability analysis. Such instability is known to occur in other Hows and lands support to the experimental finding that instabilities can occur shortly after the passage of the first water hammer wave. Physically. Ihe bypass instability is associated with the tilting of base flow vortices by the velocity fluctuations. Plots of the flow lield clearly show the breakdown of the axisymmetric assumption and produce asymmetric velocity profiles consistent with those observed in water hammer experiments.

DOI: https://doi.org/10.1080/00221686.2004.9628318

Year: 2004