Unsteady friction in transient vertical-pipe flow with trapped air

Existing pipe-filling models have primarily considered steady friction alone, tending to underestimate pressure attenuation. Various popular unsteady friction models are considered here to simulate pressures within a rapidly filling vertical pipe. Numerical predictions are compared to each other and to experimental results. The models considering unsteady friction better reproduce measured pressure oscillations. The greatest errors in predicted pressures neglecting unsteady friction occur after the first period, but numerical errors are markedly greater for cases with smaller initial air volumes and higher inlet pressures. Significantly, the largest errors in the prediction of maximum air pressure when ignoring unsteady friction effects occur near the critical value of initial air volume (here around 2-3% of pipe volume). Compared to accurate but computationally demanding convolution models, the Trikha-Vardy-Brown simplified model is shown to be indistinguishable in terms of accuracy; however, the improved Brunone model is even more computationally efficient and retains excellent numerical accuracy.