Cross-validation of numerical and experimental data in turbulent pipe flow with new scaling correlations

Abstract

The dependence of turbulence statistics and wall friction on Reynolds number in fully developed turbulent pipe flow remains a fundamental subject in fluid mechanics. This paper cross-validates experimental and numerical results, focusing on the scaling of turbulence statistics at the pipe centerline and across the inner-outer flow region. Pipe flow experiments were reviewed for friction Reynolds numbers 810 ≤ Reτ ≤ 55 × 103, where Reτ = uτ R/ν, uτ is the wall friction velocity, R the pipe radius, and ν the kinematic viscosity. Complementary DNS data for 180 ≤ Reτ ≤ 2880 provide detailed insight into near-wall turbulence. A novel friction correlation, Reτ = 0.048 × Re0.923 c is introduced, predicting pipe-wall friction across a wide range of Rec with accuracy better than ±2.06%, where Rec is the Reynolds number based on the centerline velocity Uzc. This correlation enables reliable friction estimates from centerline single-point measurements or DNS data without requiring near-wall or pressure-gradient information and is validated by consistent agreement with both experiments and DNS. The monotonic decrease in centerline turbulence intensity $\langle u^{\prime 2}_z\rangle^{1/2}/Uzc$ with increasing Rec is explained using the streamwise mean momentum equation. Finally, azimuthal spatial filtering of DNS data highlights the limitations of hot-wire resolution near the wall. For Reτ ≥ 2880, higher-order experimental statistics agree well with DNS for y+ ≥ 30 and into the logarithmic region, with both datasets equally well described by logarithmic or power-law correlations, while near-wall discrepancies remain due to resolution limits.