Further observations on the mean velocity distribution in fully developed pipe flow
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Citations
On the Blasius correlation for friction factors
Reynolds stress scaling in the near-wall region of wall-bounded flows
Turbulent pipe flow: Statistics, Re-dependence, structures and similarities with channel and boundary layer flows
Density effects on turbulent boundary layer structure: From the atmosphere to hypersonic flow
Direct numerical simulation of turbulent pipe flow up to a Reynolds number of 61,000
References
Boundary layer theory
Boundary Layer Theory
Mean-flow scaling of turbulent pipe flow
A note on the overlap region in turbulent boundary layers
Related Papers (5)
Frequently Asked Questions (14)
Q2. How was the accuracy of the wall distance measured?
to improve the accuracy of the wall distance measurement, a linear encoder with an accuracy of 5 µm per count was used to determine the wall distance (ZS reported an accuracy of 25 µm).
Q3. What is the current study of the flow velocity?
Current studyZS measured 28 velocity profiles over a range of Reynolds numbers from 31 × 103 to 36 × 106 using a 0.9 mm Pitot probe.
Q4. What is the scaling for the mean velocity profile in fully developed turbulent pipe flow?
For high Reynolds numbers, the scaling for the mean velocity profile in fully developed turbulent pipe flow may be expressed in terms of an inner-layer scaling given byU = f ′(y, ui, ν, R) (1.1)†
Q5. What is the value of B at the inverse of the velocity scale?
Ū is used as the velocity scale, the additive constant becomes B∗/ξ (where ξ = (UCL − Ū )/uτ ≈ 4.28, see below) which has a value of 0.280 ± 0.02, and the slope becomes 1/κξ which has a value of 1/(1.798 ± 0.01).
Q6. How much accuracy was the current traverse system compared to ZS?
The accumulated position error of running the present traverse system forward and backward once over a distance of 71 mm was generally less than 30 µm, compared with 50 µm accuracy for ZS.
Q7. What is the dimensionalizing equation for the mean velocity profile in fully developed pipe flow?
Non-dimensionalizing equations (1.1) and (1.2) gives, respectively,U+ = f (y+, R+), (1.3)Uc − U u0 = g(η, R+), (1.4)where U+ = U/uτ and η = y/R. ZS showed that the velocity scaling in the overlap region (where y+ 1 and η 1) can be of two types: complete similarity where u0/uτ is independent of Reynolds number, and incomplete similarity where u0/uτ continues to depend on Reynolds number.
Q8. How much uncertainty is there in the Reynolds numbers?
B∗ has a constant value of 1.20 ± 0.1 (again the majority of the uncertainty lies in the value of κ) for 230 × 103 ReD 13.6 × 106.
Q9. What was the first point taken with the Pitot probe touching the pipe?
The first point was taken with the Pitot probe touching the pipe surface, the 56th point was located at the centre of the pipe, and the 57th point was on the other side of the pipe centre.
Q10. What is the effect of the Pitot correction on the log-law constants?
Since an appropriate Pitot correction must surely collapse data from probes of all diameters, the pipe flow mean velocity measurements were analysed in two different ways to ensure the conclusions were not affected by the Pitot correction.
Q11. How was the position accuracy calculated for the new dataset?
The position accuracy was estimated to be ±1.7% for measuring points close to the pipe surface and ±0.05% for data points taken near the centre of the pipe.
Q12. What is the log law for a boundary layer?
Österlund et al. (2000) in a more recent study of boundary layers found a log law with κ = 0.38 and B =4.1 in the range 200/δ+ < y/δ < 0.15 for Reθ > 6000.
Q13. What is the log law for y+?
Although this log law appears over a rather short region in y+ (200 to about 1000), the authors should note that this includes virtually all boundary layer studies, where few studies have a large enough Reynolds number range to investigate the overlap region with an upper extent where y+ 1000.
Q14. What correction did McKeon et al. use to fit the y 2d data?
The authors will use the correction suggested by McKeon et al. (2003), on the basis that it produces good agreement among different diameter Pitot data sets down to y ≈ d , considerably better than other methods such as MacMillan (1956) and Chue (1975).