IMPROVED METHOD FOR SIMULATING FRICTIONAL LOSSES IN LAMINAR TRANSIENT LIQUID PIPE FLOW

Abstract

This paper is devoted to the problem of energy dissipation and it concerns unsteady friction modeling of the liquid flow in hydraulic lines. One dimensional (1D) quasi-steady model of energy dissipation is in common use. It means that the loss of energy is estimated by the Darcy-Weisbach formulae. Such an approximation is close to reality only for slow changes of the velocity field in the pipe cross section. In case of fast changes, like fast transients, e.g. water hammer, it fails. In this work the wall shear stress τ (defined as an effect of unsteady fluid friction) is presented as a sum of quasi-steady and unsteady components. The unsteady component of the wall shear stress is modeled as an convolution of the local fluid acceleration and a weighting function w(t). The weighting function, in general, makes an allowance for a relation of the historic velocity changes and the unsteady component of the wall shear stress. Primitive weighting functions have usually very complicated structures, and what is more, they make it impossible to perform an efficient simulation of dynamical runs. In this paper, a new weighting function is presented as a sum of exponential components in order to enable efficient calculation of the unsteady component wall shear stress. A few examples of the new effective method of unsteady wall shear stress simulations, in case of the water hammer, are presented. The results of the calculations are compared with experiments known in literature and satisfying results are obtained.