# A new mathematical approach to turbulence modeling

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November 2, 2021, 13:15
A new mathematical approach to turbulence modeling
#1
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Bekhzod
Join Date: Nov 2021
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Dear CFD experts, many of you know that in the framework of the Reynolds approach, it is impossible to build a correct mathematical model of turbulence! The Reynolds approach is based on two hypotheses:
1) the velocity in a turbulent flow consists of averaged and fluctuating velocities;
2) the applicability of the Navier-Stokes equation for the description of turbulent flow. These conditions are not sufficient to obtain a closed system of equations. Therefore, a different approach is needed, which leads to a closed system of equations.
This approach is presented in the Mathematical Model of Turbulence Based on the Dynamics of Two Fluids.
The work can be found here: https://www.sciencedirect.com/scienc...470?via%3Dihub
(if you need the original article, I can throw it in a personal)

Thus, I would like to know your opinions on this turbulence model, and I would also like you to test it on your problems in the calculations of aerodynamics.
Thank you!
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 November 2, 2021, 19:35 #2 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,246 Rep Power: 63 I'm not here to discredit anyone that attempts to develop a new turbulence model but: Any turbulence modeling approach that utilizes a transport equation to provide an eddy viscosity can be conceptually re-imagined as the flow of a homogeneous mixture of two fluids. This not-so-novel two-fluid approach that you are really excited about is therefore equivalent to a typical one-equation turbulence model. Nothing is being overturned. Let's say this is the one model that will rule them all. It will go down in history as the one equation Malikov model. That is, not Spalart-Almaras or Prandtl, but a one equation turbulence model nonetheless. FMDenaro, fportela and aero_head like this.

 November 3, 2021, 01:33 #3 Senior Member   Joern Beilke Join Date: Mar 2009 Location: Dresden Posts: 453 Rep Power: 19 You might try to present the work at the ISPRAS-open conference, which will be in December in Moscow. https://www.isprasopen.ru/en/cfd.html#Intro Bekish likes this.

 November 4, 2021, 03:07 #4 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,092 Blog Entries: 29 Rep Power: 38 There are some technical aspects of the paper that, in my opinion, signal some warning. Besides this, however, it seems to be a 3 eq. model. I was not aware of this class of models, nor I had time to look at the references, so I can't say anything of its novelty. My main concern, however, is about implementation details. If I am ever going to implement a model I need to know exactly how bcs (including wall functions) and implicit source term treatment work. But none of these are treated in a sufficiently clear manner (or at all). Actually, the employed numerical method seems pretty specific for this model instead of, say, a classical cell centered unstructured fv approach. In addition, if I understood correctly, there is a 3x3 eigenvalue problem to be solved at each cell and iteration. This, with the 3 eqs, makes it really costy. Finally, there is not much comparison with other models (like at all) that could trigger any will to actually implement it. Probably, a comparison with other 3 eq. models would be more appropriate. aero_head likes this.

November 4, 2021, 12:25
#5
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by Bekish Dear CFD experts, many of you know that in the framework of the Reynolds approach, it is impossible to build a correct mathematical model of turbulence! The Reynolds approach is based on two hypotheses: 1) the velocity in a turbulent flow consists of averaged and fluctuating velocities; 2) the applicability of the Navier-Stokes equation for the description of turbulent flow. These conditions are not sufficient to obtain a closed system of equations. Therefore, a different approach is needed, which leads to a closed system of equations. This approach is presented in the Mathematical Model of Turbulence Based on the Dynamics of Two Fluids. The work can be found here: https://www.sciencedirect.com/scienc...470?via%3Dihub (if you need the original article, I can throw it in a personal) Thus, I would like to know your opinions on this turbulence model, and I would also like you to test it on your problems in the calculations of aerodynamics. Thank you!

This proposal, as well as some new ideas, were discussed here

https://www.researchgate.net/post/Is...lence-possible

November 5, 2021, 06:53
#6
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Bekhzod
Join Date: Nov 2021
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Quote:
 Originally Posted by sbaffini There are some technical aspects of the paper that, in my opinion, signal some warning. Besides this, however, it seems to be a 3 eq. model. I was not aware of this class of models, nor I had time to look at the references, so I can't say anything of its novelty. My main concern, however, is about implementation details. If I am ever going to implement a model I need to know exactly how bcs (including wall functions) and implicit source term treatment work. But none of these are treated in a sufficiently clear manner (or at all). Actually, the employed numerical method seems pretty specific for this model instead of, say, a classical cell centered unstructured fv approach. In addition, if I understood correctly, there is a 3x3 eigenvalue problem to be solved at each cell and iteration. This, with the 3 eqs, makes it really costy. Finally, there is not much comparison with other models (like at all) that could trigger any will to actually implement it. Probably, a comparison with other 3 eq. models would be more appropriate.

The finite volume method for the new model is used in the same way as for all known RANS models. As for the use of the function on the wall, it is discussed in the first original work. The issue is raised that the search for eigenvalues ​​can be expensive. In fact, there is nothing complicated there. In two-dimensional problems for the eigenvalues ​​we will have a quadratic equation, and for three-dimensional problems it is necessary to solve the cubic equation λ3+aλ+b=0, for which there is an analytical solution of Cardano or Vieta. Now the question is about comparing the new model with other well-known RANS models. To date, a comparison has been made for many hydrodynamic problems. Below is a link to the works where these comparisons are made. These works show that the accuracy of the new model is significantly higher than that of other models and is universal. In addition, it is able to adequately describe anisotropic turbulence. Another advantage of the new model is that it has good stability, i.e. acceptable results can be obtained using a coarse computational grid, and it is also possible to integrate the system of equations with significantly larger time steps than using, for example, models such as SA, SST or SSG.

1. Malikov Z.M. “Mathematical Model of Turbulence Based on the Dynamics of Two Fluids”. Applied Mathematical Modeling. V.82, P.409 – 436.
2.Malikov Z.M. “Mathematical model of turbulent heat transfer based on the dynamics of two fluids”. Applied Mathematical Modeling. V.91, P.409 – 43.
3. Malikov Z.M.,*Madaliev M.E. Numerical Simulation of Two-Phase Flow in a Centrifugal Separator // Fluid Dynamics, 2020, 55(8), P. 1012–1028.
4. Madaliev E.,*Madaliev M.,*Adilov, K.,*Pulatov, T. Comparison of turbulence models for two-phase flow in a centrifugal separator // E3S Web of Conferences, 2021, 264, 01009.
5. Mirzoev A.A.,*Madaliev M.,*Sultanbayevich D.Y.,*Habibullo Ugli, A.U. Numerical modeling of non-stationary turbulent flow with double barrier based on two fluid turbulence model // 2020 International Conference on Information Science and Communications Technologies, ICISCT 2020, 2020, 9351403
6. Malikov Z.M.,*Nazarov F.K.,*Omonov Z.J.,*Abdukhamodov S.K. Numerical study of flow in a plane suddenly expanding channel based on Wilcox and two-fluid turbulence models // Journal of Physics: Conference Series, 2021, 1901(1), 012039
7. Nazarov F.Kh. Comparing turbulence models for swirling flows*// Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2021, (2), pp. 25–36
8. Nazarov F.K.,*Malikov Z.M.,*Rakhmanov N.M. Simulation and numerical study of two-phase flow in a centrifugal dust catcher // Journal of Physics: Conference Series, 2020, 1441(1), 012155
9. Malikov Z.M., Madaliev M.E. New two-fluid turbulence model-based numerical simulation of flow in a flat suddenly expanding channel. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2021, no. 4 (97), pp. 24–39 (in Russ.). DOI: https://doi.org/10.18698/1812-3368-2021-4-24-39
10. Malikov Z.M., Navruzov D., Djumayev X. “Models results Comparison of different approaches to turbulence for flow past a heated flat plate” E3S Web of Conferences 264, 01008 (2021) https://doi.org/10.1051/e3sconf/202126401008.

In addition, a new and final third article will be published soon, which lays the final brick in the fundamental foundation of this turbulence model. Title of the article "Modeling a turbulent multicomponent fluid of variable density based on a two-fluid
approach."

 November 5, 2021, 07:51 #7 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,092 Blog Entries: 29 Rep Power: 38 Look, I don't know if you are the author of the model or not. In any case, while I definitely have some issues with the technical side of the papers, it wasn't my intention to express any judgement on that (and indeed I took those issues for myself). Also, I can't speak of the novelty, because I wasn't even aware of this sort of modeling and I should go trough all the references. So, all in all, papers are published and there seem to be some convincing results. So, I'm not judging the merit. But when we go to the personal side and ask me about it (as opposed to provide an objective account of the matter), I can't really change my mind. For example: FV implementation might be the same, but nowhere I saw any closely related description. Unfortunately, you loose me when you write "For the numerical implementation of system (x), introduce the von Mises variables (ξ, ψ)". Maybe my fault, but still. Probably it falls on the personal side, but I still think that solving a cubic equation for each cell and for each iteration, only as part of the source term of a 3 eq. turbulence model is expensive. More expensive than using any 4+ eq. model? Not, but still expensive. While convincing results are there in the papers, I wouldn't certainly put it down with "the accuracy of the new model is significantly higher than that of other models and is universal". I don't think there is such evidence. But neither that it was actually necessary to give merit to the model. Still, there are no comparisons with 3 eq. turbulence models. All in all, when considering things from the personal side, the matter is about: am I willing to spend time implementing this? would be worth it? My answer is: I see some things in the papers that signaled some warnings that some things might have been overlooked, I see no details for implementing it in my code, it's relatively expensive, not for now then. Nothing personal or judgemental, just that. fportela and aero_head like this.

November 10, 2021, 16:52
#8
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Bekhzod
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Quote:
The final fundamental third article has been published, where the idea of using a two-fluid turbulence model for modeling a turbulent multicomponent fluid is being developed.

https://doi.org/10.1016/j.apm.2021.10.045

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