Static pressure correction in high Reynolds number fully developed turbulent pipe flow

Abstract

Measurements are reported of the error in wall static pressure reading due to the finite size of the pressure tapping. The experiments were performed in incompressible turbulent pipe flow over a wide range of Reynolds numbers, and the results indicate that the correction term (as a fraction of the wall stress) continues to increase as the hole Reynolds number d + = u τ d/ν increases, contrary to previous studies. For small holes relative to the pipe diameter the results follow a single curve, but for larger holes the data diverge from this universal behaviour at a point that depends on the ratio of the hole diameter to the pipe diameter.

Pitot probe corrections in fully developed turbulent pipe flow

“…The Pitot tubes had outer diameters of 0.30, 0.51, 0.90 and 1.83 mm, with an inner to outer diameter ratio of 0.6. The pressure tapping correction of McKeon and Smits (2002) was applied to the static pressure measurements for all Reynolds numbers. A single normal constant-temperature hot-wire probe was also used, employing a 2.5 µm diameter tungsten wire with an active length of 0.5 mm, mounted on a Dantec P01 body and powered by a Dantec M10 series anemometer.…”

Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes

“…McKeon et al (2003) identified a low Reynolds number correction (also called the viscous correction), a shear correction (otherwise known as the velocity gradient correction), a near-wall correction, a turbulence correction, and, if the static pressure is measured using a wall tapping, a Reynolds-number-dependent correction for the static pressure reading may be necessary. For the experiments reported here the static tap correction was found to be unnecessary, since the tap diameter remained sufficiently small relative to the viscous scale in all cases; see McKeon & Smits (2002) for a static tap correction used in high Reynolds number pipe flow.…”

Further observations on the mean velocity distribution in fully developed pipe flow

“…A new static pressure correction (McKeon & Smits 2002) is used in analysing all data and leads to significant differences from the Zagarola & Smits conclusions. The results confirm the presence of a power-law region near the wall and, for Reynolds numbers greater than 230 × 10 3 (R + > 5 × 10 3 ), a logarithmic region further out, but the limits of these regions and some of the constants differ from those reported by Zagarola & Smits. In particular, the log law is found for 600 < y + < 0.12R + (instead of 600 < y + < 0.07R + ), and the von Kármán constant κ, the additive constant B for the log law using inner flow scaling, and the additive constant B * for the log law using outer scaling are found to be 0.421 ± 0.002, 5.60 ± 0.08 and 1.20 ± 0.10, respectively, with 95% confidence level (compared with 0.436 ± 0.002, 6.15 ± 0.08, and 1.51 ± 0.03 found by Zagarola & Smits).…”