Godunov-type scheme for air–water transient pipe flow considering variable heat transfer and laboratorial validation

Abstract

A robust comprehensive energy dissipation model is developed to investigate the rapid filling process of a T-shaped bifurcated pipeline with entrapped air pocket, while an experimental system is designed to validate the numerical model. In this work, a self-adapting heat transfer model is proposed to describe the energy exchange during transient event, fully considering the heat transfer of entrapped air pocket and hydraulic losses caused by steady friction and unsteady friction in the section of the filling water column. Importantly, the related heat transfer coefficient is variable and determined by mechanism formula of media characteristics, which is obviously different from the constant heat transfer coefficient in conventional model relying on the trial-and-error method and experimental data. Moreover, the second-order Godunov-type scheme is introduced to solve the governing equations of filling water column, while a virtual plug approach is proposed to track the air–water interface. The resulting predictions are compared to those obtained via a conventional empirical polytropic model and constant coefficient heat transfer model, and to experimental data. The proposed model accurately reproduces the experimental pressure oscillations. The results display that when an air pocket content exceeds a certain threshold (>1.7%), the comprehensive model using forced convection can reproduce the pressure fluctuations. When the air content is lower (<0.9%), the comprehensive model using natural convection can simulate pressure changes more accurately. The conventional empirical polytropic model underestimates the pressure damping. The constant coefficient heat transfer model previously cannot be employed if there is no experimental data to calibrate the constant coefficient, but now the constant coefficient can be obtained from the results of the proposed model. Significantly, the comprehensive model can directly and accurately simulate the energy dissipation during the rapid filling process.

Keywords

• Two-phase flow
• entrapped air
• Godunov method
• heat transfer