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

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.