Unsteady friction model modified with compression–expansion effects in transient pipe flow

Abstract

This paper aims to modify the conventional one-coefficient instantaneous acceleration-based (IAB) model for better prediction of unsteady friction behavior. In this work, the energy dissipation caused by viscous stress during fluid volume compression–expansion (CE) was derived from the compressible Navier–Stokes equation. It is found that the energy dissipation term can be expressed by the product of the second-order partial derivative of velocity in space and the second viscosity coefficient. On this basis, a modified IAB-CE model was developed with the energy dissipation term and solved by the method of characteristic (MOC). The numerical results obtained from the modified model showed a good agreement with the four test cases, where the relative errors are improved by 0.26, 2.03, 9.56, and 36.67%, compared with the results from the original IAB model. The estimation for wave peak and valley is improved as well. Furthermore, the Bradley equation can be applied to establish the relationship between the dissipation coefficient and the Reynolds number. The modified model developed in this study takes into account the fluid CE effects and improves the prediction accuracy of wave amplitude of unsteady flow.

A thermodynamically consistent model for hydraulic transients in metallic pipes undergoing elasto-viscoplastic deformations

“…The employment of the assumption of inviscid or laminar flows is also clearly limited. A diverse range of quasione-dimensional and quasi-two-dimensional fluid models that better capture unsteady flow mechanics can be found in the literature [23][24][25][26] In addition to this limited description of the fluid flow, the constitutive choice that the metallic material deforms elasto-plastically loses its accuracy when the pipe is subjected to high-temperature environments, i.e., around one-third of the melting temperature of the material under consideration [27]. Even though the viscous characteristics of metallic materials are already present at room temperature [28], at high temperatures, such a feature is prominent.…”

Numerical Analysis of Transient Pressure Damping in Viscoelastic Pipes at Different Water Temperatures

“…With respect to viscoelasticity, the Kelvin–Voigt (K–V) model has been used to describe the viscoelastic behavior of the pipe wall [ 7 ]. As for friction, one-dimensional (1D) quasi-steady and unsteady friction models [ 8 , 9 , 10 , 11 ] and two-dimensional friction models [ 12 , 13 , 14 , 15 ] have been used to describe the wall shear stress in transient flows. Generally, the classic transient flow model with a quasi-steady friction model is capable of accurately simulating the maximum value in terms of the pressure fluctuation in elastic pipes; however, it cannot accurately describe the peak pressure damping in most instances [ 1 ].…”

“…Generally, the classic transient flow model with a quasi-steady friction model is capable of accurately simulating the maximum value in terms of the pressure fluctuation in elastic pipes; however, it cannot accurately describe the peak pressure damping in most instances [ 1 ]. Cao et al [ 8 ] modified the 1D instantaneous acceleration-based (IAB) model to better predict the wave peak and valley. Urbanowicz [ 9 ] improved the 1D model with a weighting function to calculate the unsteady-state component.…”