Construction of Pitot Corrections for the Zagarola & Smits Superpipe Data

The original turbulent pipe flow experiments in the Princeton “Superpipe” by Zagarola & Smits (PRL 1997) at unprecedented laboratory Reynolds numbers R⁺ have started an ongoing debate on the logarithmic law in the mean velocity profile U⁺(y⁺) and the question of Pitot probe corrections for shear, viscous effects and turbulence level. Considering that the Pitot probe diameter d⁺ exceeded 7000 wall units at the highest R⁺, the various corrections had to be extended into uncharted territory. In this contribution, the inverse approach is adopted, where the result of the corrections is taken to be the model for U⁺ developed by Monkewitz in PRFluids 2, 2017. The latter has an inner part identical, up to higher order corrections, to the zero-pressure-gradient turbulent boundary layer profile and switches around y⁺ ≈ 500 to a pipe-specific logarithmic overlap layer. The simplicity of the resulting global Pitot correction proportional to d⁺(R⁺)^-1/2, with only two fitting parameters, indirectly supports this model. In addition, the higher order correction for the overlap layer, originally proposed by Afzal & Yajnik (J. Fluid Mech. 1973) and tied to the pressure gradient by Luchini (PRL 2017), is extended to the entire profile and shown to provide an excellent fit to the data.