The Basic k-ϵ Model and a New Model Based on General Statistical Descriptions of Anisotropic Inhomogeneous Turbulence Compared with DNS of Channel Flow at High Reynolds Number

Round 1

Reviewer 1 Report

The work is an important step toward models based on a fundamental basis that does not require empirical models. The work is limited to replacing expressions for turbulent momentum diffusion and conservative scalars with general expressions.  Non-conservative terms are still modeled.

Although the paper is clearly written and its undoubted merit is the systematic physical interpretation of the terms appearing in the equations, the results presented are of some concern. Comparisons of the classical k-eps model with the proposed fundamental model lead to rather unexpected conclusions.

The graphs shown in Fig. 1 and especially in Fig. 2, do not so much testify to the incorrect results of calculations according to the classical k-eps model, but rather to the poor selection of the empirical parameters of this model for the analyzed flow case.

 The variable x, used in part of the text, is not very happily chosen, once appearing in the clear form xi, and once replacing the variable y (distance from the wall) in the Cartesian system. Although the author explains this in the text, but without catching this detail, analysis of the graphs is a bit cumbersome.

This quantity first appears in line 150 - "To provide boundary conditions at the wall the viscous layer is surpassed by applying the solutions of the log layer at x = 0 : [5,6].", and the explanation "...the subscript 2 of x2 will be dropped" appears later in line 200.

 At the same time, there is a dominant assumption that the viscous layer does not play a role in prediction the parameters of the fully developed part of the turbulent layer.

The author tries to physically interpret the terms appearing in the equations which is a great advantage of the paper.

 The presented results show the advantages of the new proposed k-eps turbulence model, but still do not solve its main drawback which is its restriction to the area outside the viscous layer and the necessity to model nonconservative terms remains.

 The paper can be published in its current form, although I would suggest changing the x-variable to another one that is easier to interpret when viewing the graphs.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

In the current manuscript, the authors attempted to verify the predictions of mean values of statistical variables of large scale turbulent flow by the widely used basic k-e model and a new fundamentally based model against published results of Direct Numerical Simulations DNS of the Navier-Stokes equations. The verification is related to turbulent channel flow at shear Reynolds numbers of 950, 2000 and 10⁴. The values obtained with the new method related to important output variables like turbulent viscosity, diffusivity of passive admixture, temperature, and fluid velocities yielded good comparison with DNS. On the other hand, the basic k-e model yields significant differences.

The topic of the paper is interesting and worthy of investigation. It would be of interest to the research community in this field of work. However, some major improvements are stil needed:

- The author should reconsider the usage of the term “fundamentally based”. A synonym for “fundament” would be base, basis. Hence, the meaning could be interpreted as “basically based”.

- Please clearly explain the “diffusion hypothesis” as well as its relevance to turbulent fluxes in detail.

- The direct application of the considered model in real-world industries should be mentioned.

- It is suggested, if applicable, to introduce different elements of diffusion tensor Dij.

- The authors should clearly express the assumptions and limitations of their models and methods.

- Abbreviations should be properly introduced when used for the first time.

- What is the superiority of the proposed model compared to the other ones in the literature?

- The title of Fig. 1: “DNS are represented by the solid line, from the fundamental model by dashdot line and from the basic k-e model by dashed line.”. Such information is not needed in the figure title, the legend is clear enough. The same comment pertains to all the figures.

- The literature overview needs to be improved. It contains 21 references, which is on the borderline. However, a relatively large number of references are old, and even extremely old (one of them nearly 150 years old). The newest reference is from 2022 (practically 2 years old), and there are only a couple of such references. A great majority is more than 10 years old. This is not a proper way of representing the state of the art in the field. A suggested reference:

Brkić, D.; Stajić, Z. Excel VBA-based user defined functions for highly precise Colebrook’s pipe flow friction approximations: a comparative overview. Facta Universitatis-Series Mechanical Engineering, 2021, 19(2), 253-269. doi:https://doi.org/10.22190/FUME210111044B

- Conclusions are too long, should be more concise and represent the major findings. Numerous references are used in conclusions, which is not usual. There is even a table. All of that belongs to discussions, rather than conclusions. Conclusions should summarize in a few sentences what has been done, what the main findings are, what the limitations are and what the directions of future work related to the topic would be.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The manuscript has been suitably revised. It is recommended for publishing as it is.