On the Prediction of Boundary Layer Quantities at High Reynolds Numbers
Round 1
Reviewer 1 Report
This work derives a new formula for the calculation of boundary layer quantities including boundary layer thickness, friction coefficients and the boundary layer profile for the flat plate. The formula is obtained based on the power-law method and give a better prediction accuracy in a wider range of Reynolds number than the typical 1/7 power-law. The paper is suggested to be accepted after the following minor problems are solved.
- line 90, the figure 4 is cited directly after the figure 1 is mentioned, which is not quite reasonable. This should be modified properly.
- The nomenclature is suggested to add.
Author Response
1. line 90, the figure 4 is cited directly after the figure 1 is mentioned, which is not quite reasonable. This should be modified properly.
The sentence was rephrased and the link to Figure 4 was removed from the text flow
2. The nomenclature is suggested to add.
From the author's point of view, a nomenclature is not necessary, as all quantities are explained in detail the first time they are mentioned.
Reviewer 2 Report
An improved formula, developed based on the power-law approach, has been proposed to evaluate the boundary layer quantities of a flat plate. This approach generalises the 1/7 power-law to a wider range of Reynolds numbers, and the analytical result compares well with the experimental measurement.
The paper is well written with clear logic. I recommend this paper be published with minor revision. Please find my comment below:
- The author mentioned the current so-call 1/7 power law might not be valid for the high Reynolds number region. And your previous study demonstrates a better agreement of 1/n power-law with n>7. Is there any other variant of power-law or other research related to the development based on power-law to address those issues?
- Missing definitions of C_pow in Equation 1.
- Figure 1, what are those solid red and grey lines?
- Some equations are ended with a period whereas others are not, any reason for that?
Author Response
1. The author mentioned the current so-call 1/7 power law might not be valid for the high Reynolds number region. And your previous study demonstrates a better agreement of 1/n power-law with n>7. Is there any other variant of power-law or other research related to the development based on power-law to address those issues?
The cited work by Barenblatt also deals in detail with the topic of a powerlaw approach, although no specific boundary layer quantities such as the boundary layer thickness are derived here.
2. Missing definitions of C_pow in Equation 1.
The definitions were added in line 46
3. Figure 1, what are those solid red and grey lines?
An explanation was added to the caption
4. Some equations are ended with a period whereas others are not, any reason for that?
Formulas were considered as part of the sentences. At the end of each sentence stands a period.
Reviewer 3 Report
The paper presents an aspect of compiling experimental data of turbulent boundary layers into empirical formulae. The author covers a wide range of existing discussion relevant to the topic and makes a fair comparison between them. The conclusions drawn are reasonable and there is nothing to debate on the findings, hence the manuscript can be accepted for publication in Fluids.
The reviewer has a minor concern about the significant figures of numbers proposed in the paper. Some numbers have five digits while others only three. These should better be revisited and more homogeneous set of numbers should be proposed, with the experimental accuracy taken into account.
Author Response
The differences resulted from omitting zeros after the decimal point. However, the point about accuracy with regard to the measurement data is very valid. The data has now been rounded to 3 decimal places to reflect a good balance between the accuracy of the formulas and the underlying data.
