New experiment for the pipe friction factor at high Reynolds numbers and comparisons for the degree of equivalence

Abstract

In this study, pipe friction factors ranging from Re_D ＝ 1.2 × 10⁴–4.0 × 10⁶ were determined at the Gravimetric Thermal Energy Standard (GraTESt) flow facility at the Physikalisch-Technische Bundesanstalt (PTB) in Berlin over a temperature range of 20 °C to 80 °C through measurement of the differential pressure. The bulk velocity was directly obtained from high-precision flow rate measurements, and the upstream length of the test section was 156 D. The results measured at different temperatures show good agreement with each other at the same Reynolds numbers, within the estimated uncertainty. The difference between the present results and previous studies at the Hi-Reff flow facility at the National Metrology Institute of Japan (NMIJ) (Furuichi et al., 2015, Phys. Fluid), is within ± 0.3 % over a wide range of Reynolds numbers from Re_D ＝ 3.3 × 10⁴–1.1 × 10⁶, confirming the consistency between GraTESt and Hi-Reff. At larger Reynolds numbers, the difference between GraTESt and Superpipe (McKeon et al., 2004, J. Fluid Mech.) increases, reaching ± 1.0 % at Re_D ＝ 4.0 × 10⁶. To objectively assess the degree of equivalence of friction factor results in present and previous studies, six data sets are quantitatively compared using an objective indicator, the Key Comparison Reference Value (KCRV). Based on the KCRV, a consensus between friction factors is achieved at Re_D ≈ 3 × 10⁴–3 × 10⁵. However, the degree of equivalence was low at other Reynolds numbers. Further experiments are required to accurately determine the friction factor and its scaling, especially at high Reynolds numbers.