Dear Nazaruddin Sinaga

" This wave effect has not been implemented, so far, in the computational fluid dynamic calculations " what do you mean exactly, in DNS, LES, RANS? Are you considering this latter? CFD is too generic....

Dear Mr. Chitrarth Lav, thank you very much for your response. Yes, there has been turbulence transition models. However, all of them have a restricted area of application. In my opinion, we can propose a more general model that can be used to estimates when and where the turbulence set up. And maybe it is not like a turbulence model.

Filippo Maria Denaro. Thank yu very much for your comment. I am considering about implementation of turbulence transition models in RANS.

Dear Mr. Tapan K. Sengupta. Thank you very much for your response.

Could you send me the full reference of your invention, please?

By the way, is your results of STWF just only valid for zero pressure gradient boundary layer flow?

Nazaruddin Sinaga

I don't know what is your idea of a "more general model", however I think that, by definition of RANS formulation, we can never produce for it a universal model for transition

A very fruitful discussion. Dr. Tapan K provide us with more details plz as u r very familiar with the field.

Please refer the followings:

1. https://www.researchgate.net/publication/222125988_The_laminar-turbulent_transition_zone_in_the_boundary_layer

2. https://www.researchgate.net/publication/37181299_Recent_advances_in_the_dynamics_of_the_transition_zone

3. https://www.researchgate.net/publication/24318908_Modelling_the_transitional_boundary_layer

To the original question: For aerodynamic flows with low disturbance background and smooth wall there is the so-called e-to-the-N method which gives integrated amplification factors of instability waves, for instance Tollmien-Schlichting (TS)waves for 2-d boundary layers, or steady or travelling crossflow waves/vortices (CFV) for 3-d boundary layers. If the integrated growth factor is about 9-10, then the laminar flow gets turbulent. This method is based on primary linear (in)stability theory (LST) of laminar flows. Simpler but somewhat related models used in RANS calculations are based on the strength of the maximum-over-y (y-wall-normal distance) products of (i) the spanwise vorticity times wall distance for mainly 2-d boundary layers for TS instability , and (ii) the streamwise vorticity times wall-distance for 3-d boundary layers for CFV instability. Both are indicators of the local flow instability (strong disturbance growth rate) derived from LST and observations. The latter are used in the models suggested by F. Menter (ANSYS/CFX RANS), see for instance AIAA-2015-2474, Langtry & al. that I attach.

I personally am more in the research LST and DNS field, and, of course, we simulated long ago the transition to turbulence induced by TS waves that, if nonlinear amplitudes are reached, cause a rapid amplification of 3-d waves leading to full transition. See for instance on my RG account the work from the early 1990s (also on an adverse-pressure gradient flow) or, for crossflow transition, from 2002 on.

Thank you very much Filippo Maria Denaro, Ridha Djebali, Chitrarth Lav, Tapan K. Sengupta, Mohsen Jahanmiri, and Markus J. Kloker. All your contributions are very helpfull.

If I am not wrong, based on the information you shared, the theory or model of transition flow is specifically be implemented for flow types. My poor question is: Could we make a more general theory (other than TM wave), by combining all the previous results, to estimates the onset of turbulence?

Thank you.

Dear Tapan K. Sengupta .

Yes, the aim of my question is clear. And I hope a lot of think we can do if we have a simple and general model for the transition flow. As simple as how to make a criteria of laminar/turbulence flow by using Reynolds number, hopefully. In this case, we just compare the effect of inertia to viscous force.

So, please share me your Conference Paper: Comparison of RANS and DNS for Transitional Flow Over WTEA-TE1 Airfoil. I'd like to read it.

Thank you.

Dear Tapan Sengupta,

Please see my papers in Researchgate:

1. ON INTERACTION OF T-S WAVES AND 3-D LOCALIZED DISTURBANCE IN A DIVERGENT FLOW UNDER ZERO PRESSURE GRADIENT

2. Experimental studies of a distorted turbulent spot in a three-dimensional flow

3. Laminar-turbulent transition modelling at IISc

I hope these papers may answer your query.

https://www.researchgate.net/publication/235428279_ON_INTERACTION_OF_T-S_WAVES_AND_3-DLOCALIZED_DISTURBANCE_IN_A_DIVERGENT_FLOWUNDER_ZERO_PRESSURE_GRADIENT

https://www.researchgate.net/publication/231952164_Experimental_studies_of_a_distorted_turbulent_spot_in_a_three-dimensional_flow

https://www.researchgate.net/publication/235339612_Laminar-turbulent_transition_modelling_at_IISc

Hi Nazaruddin Sinaga ,

There is a 1-eqn turbulence model called KDO (turbulent Kinetic energy Dependent Only). The model does not include specific transition mechanisms, but It can capture the transition onset locations of various types of transition. The model is established based on phenomenological theory and the model's framework is flow-structure adaptive. Along with the evolution of the k equation, transition naturally appears. The model has only 2 empirical coefficients which remain fixed for any types of transition. In other words, the users need not to adjust the coefficients. You may have a try:)

https://www.researchgate.net/publication/329602896_Capturing_transition_with_flow-structure-adaptive_KDO_RANS_model

Mathematics will be easy after you get the physics right. Turbulence is a crack in Fluid, and therefore it's collision and friction after it's broken. No continuity is possible.

After realizing this, the math was pretty straight forward. And it even fit's perfectly on observations.

Yes Afraa, the turbulence flow is a complicated phenomena. And currently, we have a lot of questions about this. But I believe someday we will find a better understanding to describe the turbulence flow mystery. So, everybody in this field should always think and rethinking from the basic theory. Maybe, we have to think out of the box.....

Wow, now I am little bit lost. My initial thoughts were that TS waves were necessary for transition. Whereas bypass terminology is used when high turbulence intensity is used to drive or force the transition.

Professot Tapan statement "We also do not agree that the disturbance field only travels in the downstream direction and we stay away from parabolized stability equation." agrees with Babinsky's observation for compressible flows too.

Hi Julio,

I think that a a fundamental issue in comparing experimental and theoretical results is the fact that in any real experiment we have possible interference with acustic waves (and not only...) that propagate in any directions at a finite velocity. Assumptions on the mathematical model to study transition in a theoretical framework could prevent the appearence of some transition mechanism simply because the type of PDE does not allow to fully describe the possible physics. I am not an expert on theory of transition but I would take care in this difficult field.

Hello Tapan K. Sengupta

I think that the long hystorical tradition in this field has given somehow a sort of barrier in the last decades. I see a tendency to a mathematical approach that required many assuptions which, on the other hand, have not always a real correspondence in the experiments that other researchers performed. The matching of the conclusions in some cases and the conflicts in other cases has never been clearly explained in my opinion. That happens since I was a student. But this is not exactly my field and could be just a personal opinion.

Dependency of transitional flow on presence of TS waves relates to the flow turbulence intensity and Reynolds number which could follow either classical transition, or bypass transition process.

Dear @ Filippo Maria Denaro

" I see a tendency to a mathematical approach that required many assumptions which, on the other hand, have not always a real correspondence in the experiments that other researchers performed. The matching of the conclusions in some cases and the conflicts in other cases has never been clearly explained in my opinion".

In my opinion, maybe, we have to rethink the concept of the fluid, especially the term of viscosity.....

Tapan K. Sengupta

It is just a random hunch. I just think that a viscosity is a property of fluid. For a Newtonian fluids, the shear stress t = mu. du/dy. But when the flow is turbulent, we can not use this equation. So, the viscosity is the fluid property? Maybe it is just a hunch.......

Hi Tapan K. Sengupta

I've done some definitive work around this issue.

https://www.youtube.com/watch?v=Itkf0cZxzG8

I was able to change the "noisiest turbomachine ever" (contra-rotating propellers of TU-95) to a peaceful high efficiency turbine and this even in Incompressible media. (water)

This turbine actually has a efficiency-world record in low Head. My whole idea about this construction was to maintain the continuity inside the turbine, so that the fluid is not "broken" because of too sudden velocity and pressure changes.

There was no direct observation for Turbulence / Laminarity, but indirectly it was easy to observe that the flow remained very Laminar inside the turbine. We even got an insident where the 3-hole pitot-pipe broke because of this laminar-alike flow. I warned about this when I noticed that it started to vibrate because of Vortex-shedding behind the turbine. But those with experience said me that it's impossible to have this kind of Vortex shedding behind of turbine because the flow is so Turbulent. But the fact is that this pitot pipe broke, and it made noise and vibration which was really Vortex-shedding alike.

Nazaruddin Sinaga

what do you mean for " . For a Newtonian fluids, the shear stress t = mu. du/dy. But when the flow is turbulent, we can not use this equation. So, the viscosity is the fluid property? "

The physical viscosity does not change depending on the laminar, transitional or turbulent regime of the flow....It is a state property built-in in the continuum model.

Filippo Maria Denaro

"For a Newtonian fluids, the shear stress t = mu. du/dy. But when the flow is turbulent, we can not use this equation. So, the viscosity is the fluid property? "

It means that the physical viscosity of the fluid can only be used to calculate the shear stress for only laminar flow, and not for turbulent flow. We have to add something like or "appearance viscosity" to calculate the turbulence shear stress. The appearance viscosity is not a physical property of the fluids. So we calculate the total shear stress by using both physical and not physical parameters. With this condition, in my opinion, the physical viscosity is not the property of the fluid in turbulence flow......

You are wrong, the stress due to the molecular action does not depend on the flow regime

Dear Nazaruddin Sinaga and Filippo Maria Denaro

You are both right, pls. dont fight & keep talking. I understand the point of Mr. Sinaga perfectly. As he is simply saying that as the Observation doesn't support the equation, the equation is wrong. (Must be; Scientific method!) But I also agree with Mr. Denaro as he points out, the viscosity of a fluid (= measure of its resistance to deformation at a given rate) does not depend on the flow regime.

As I don't want to predict my own thoughts continuously, I rather ask a question;

"Why this deformation suddenly just isn't there anymore?" Any ideas?

Thanks Jouni Jokela

I like and enjoy this discussion. I will keep talking with Prof. Filippo Maria Denaro .

Dear Prof. Filippo Maria Denaro

I agree with you that the stress due to the molecular action does not depend on the flow regime.

But my point is about the question: Why we can't compute the total shear stress, in turbulent flow, employing a simple relationship like we calculate the shear stress in laminar flow, that is: tau = mu. du/dy ?

Is something wrong?

Nazaruddin Sinaga Who told you you cannot?? Take a DNS database and compute all the components of the Newtonian stress tensor you want...

Jouni Jokela

deformation of a volume of fluid is intrinsically measured by the gradient of the velocity. That fact that we link this gradient multiplied by the viscosity to the stress tensor is a modelling implied by the introduction of the Newton law

Thanks Filippo Maria Denaro

"Take a DNS database and compute all the components of the Newtonian stress tensor you want... "

Do you mean that we can compute the total shear stress, for turbulent flow, by using the relation tau = mu. du/dy ?

Please advice me.

Thank you

Nazaruddin Sinaga

exactly, that is what is commonly done in DNS of wall turbulence (and, in some extent, also in LES)

Filippo Maria Denaro

"DNS database"... like;

https://www.fdy.tu-darmstadt.de/fdy/fdyresearch/dns/dns_plane_couette/dns_couette.en.jsp

Ok, I opened ie:

https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/turbulent-plane-couette-flow-at-moderately-high-reynolds-number/83EA4FC2028E534781D9182C4DE47A82

and then I read -again- from abstract;

"It is confirmed that the fluctuation intensities in the streamwise and spanwise directions do not scale well in wall units. The scaling failure occurs both near to and away from the wall. "

So, we have statistics from measured data, and we can use these to correct our calculations, but I believe this is not the point here. We don't have an equation without these correcting factors. This means our present equations are wrong.

Something is wrong! But I do agree that it's not the Newton's law or viscosity stress tensor.

The "scaling failure" is a consideration that doing a DNS solution we observe a discrepancy from theoretically expected scaling law. Maybe the framework in which the theory was hystorically based must be reviewed? Otherwise we should suppose that the DNS solution is wrong just because the NSE are wrong...

Dear Jouni Jokela and other friends,

I also feel something is wrong, but still do not now how to correct it....

Sorry, I also feel something is wrong, but I still do not know how to correct it....

Hello Tapan K. Sengupta

Please give your comment to our interesting discussion result that said "there is something wrong" with our concept or framework in fluid dynamics.

I know you are the expert of this field.

Thank you

Thanks Tapan K. Sengupta

But I couldn't clearly see your opinion about "there is something wrong" with our concept or framework in fluid dynamics.

If I am not wrong, your statement actually reinforces the statement that "there is something wrong" with our concept or framework in fluid dynamics.

Tapan K. Sengupta

I just created this picture through the ideas (STWF) given in your previous reply;

Data Waves celerity at Froude = sqrt3

It clearly shows how the waves starts to accumulate exactly in Fr=3 so that it system becomes irreversible.

Ps. @ Denaro, I agree that the NSE is "wrong" or rather incomplete.

Dear Tapan K. Sengupta

I do say there is "something wrong" in NSE. It is incomplete; it should at least be clear that in the case of open channel (multiphase) flow, the surface tension is missing, and this is already recogniced ie. here;

Article On the two-phase Navier-Stokes equations with surface tension

and here;

Article Numerical Models of Surface Tension

Where it is added to the NSE .

Now, it can be further asked if this is a common feature of every boundary condition? https://en.wikipedia.org/wiki/Contact_angle

Then, what actually is "flow separation"? ( fluid flow becomes detached from the surface of the object) https://en.wikipedia.org/wiki/Flow_separation

I answer myself; the flow separation has a surface of it's own. There is no viscous interactions over these surfaces, as I have observed ie. here;

https://www.youtube.com/watch?v=BkhaJDDyFtI

It's friction and collision instead of viscosity and surface tension. And also these components are missing from NSE. But I think it will be meaningless to even add these components to NSE for the same reasons as the Kinetic theory of gas is using only statistical methods.

Up to day, even the very simple case of flow through orifice seems to remain unsolvable with NSE, and needs to be investigated experimentally. I took an approach to this issue, according to these ideas;

Data Navier-Stokes existency and smoothness problem, -The Answer (word-txt)

And was able to solve these factors;

http://www.mcnallyinstitute.com/13-html/13-12.htm

accurately without any scaling problem. Some related discussion about the issue can be found here;

https://physics.stackexchange.com/questions/227309/air-core-vortex-physical-explanation-of-the-air-entrainment-hook-at-f-co-0/227333#227333

I will try to produce more papers about this in future, but it depends from my freetime & motivation. If you consider my posts as a "crying foul" just let me know. I have no need for such a behaviour. I see my success in nature, and there is no "news" to me anymore.

Regs,

Jouni Jokela

Jouni Jokela

we are going out of topic... however, as far as the problem of air-liquid flow problem is concerned, I don't see any problem in the formulation of the NSE. The interface where the tension acts is a discontinuity for the properties and must be treated as discontinuity. It is not a lack of presence of surface tension in the NSE as it can be considered as shown by a simple search

https://www.google.com/search?client=firefox-b-d&q=surface+tension+navier+stokes+equation

Filippo Maria Denaro and Tapan K. Sengupta

No it's not of topic / digressing. You are missing my point. At the transition from Laminar to Turbulence the fluid is splitted to parts. The continuity is broken, and on the viscous forces are replaced by surface properties; friction, tension, collision. These discontinuities are missing from the NSE. But it's reasonable and possible to handle these statistically, as the collision and friction are also very similar to viscosity, that's why the equations still work quite satisfyingly, though they actually shouldnt.

Laminar flow is one single continuum where deformation is reversible. Infinite Turbulence is like kinetic gas in high pressure. Just single particle colliding without any viscosity. All deformations are irreversible. Indeed the difference between gas and fluid vanishes in critical point and these are then the same.

Heat is also just velocity.

Jouni Jokela

Sorry, I do not understand you neither in mathematical nor in physical terminology...

- "continuity is broken": continuity of what? Of a mathematical continue field? The validity of the physical continuity equation?

- "viscous force are replaced by ...": what do you mean? Viscous forces are present due to the constitutive Newtonian model, you can add further model to take into account other properties into the NSE. That does not substitute the viscous force. Do you think to replace totally the Newtonian model?

- " Laminar flow is one single continuum where deformation is reversible ". Deformation due to the action of viscous stresses due to angular deformation is never reversible, laminar or not the regime in action. This is shown by looking at the fact the any time you have such deformation, the viscosity introduces a conversion of kinetic energy into internal energy with an entropy production. The only part of deformation that does not contribute (at least until the model is valid) to the entropy production is the volume dilatation/contraction due to the action of normal stresses and measured by the Div v term.

- The nature does not like singularity/discontinuity. That appears as a consequence of a model where some effects are disregarded. NSE formally have a mathematical character for which neither the shock wave is a discontinuity. Searching for non regular solution (time-space) in the NSE is a different issue.

I see you are thinking about the fluid in terms of sinlge particles but that happens also in laminar condition. If you like, you can remove any continuum assumption and you can also never introduce the NSE at all. But if you use that set of equations you stay within the continuum and its assumptions. Then the Reynolds transport theorem state a fundamental conservation law for any extensive variable. Newton, Fourier and gas model close the set of equations.

Filippo Maria Denaro

Thanks for asking. I start with the easy one "Laminar flow is one single continuum where deformation is reversible." With this I mean if that if you remain in true laminar state, all movements are reversible so that the order is maintainded. There is no mixing. This is very nicely shown in this video;

https://www.youtube.com/watch?v=p08_KlTKP50&list=PLgUc9kJnDMMExJivT2dWh9dAjdYYUgOFE&index=13&t=0s

After this is accepted it might be already easier to understand what is meant with "continuity is broken" If you have one solid piece, and you push it, the whole piece moves (or receives tension if it's fixed.) This very same happens also in laminar flow. If you break this one solid piece in ie. four pieces, the continuity is broken. even if you place the pieces fitting perfectly to each other, you will notice that the movement is now different.

Because "viscous forces (tension) are replaced by" other things, like collision and friction on the surfaces of the broken pieces.

Yes, I think the fluid as a single particles, but also as a group of particles, and my idea of the broken continuity is relying to the idea, that the velocity between two particles Which are sliding nearby each other without collision is such, that they are either able to interact or not depending on the velocity they are passing by.

This kind of behaviour can be seen ie in this video of "Smarter every day";

https://www.youtube.com/watch?v=KJDEsAy9RyM

(The walking water)

Jouni Jokela , Filippo Maria Denaro and Tapan K. Sengupta

I think our discussion is not digressing according to our big and interesting topic of "there is something wrong" with our concept or framework in fluid dynamics. Because, maybe, it will change our understanding of transition from laminar to turbulent flow, which is our main topic of discussion. But please continue and keep talking.

As I told you before, please ones to rethink the concept of fluid and its dynamics. Mr. Tapan K. Sengupta

Moreover, is this finding can be extended for a non-zero pressure gradient equilibrium flow ?

Even it is a hunch, I ask you to think about the concept of viscosity. First, we can only use the viscosity to compute the shear stress in laminar flow. But when the flow is turbulent we can not use this viscosity to directly compute the shear stress, because there are some fluctuating velocities in this flow regime. And the question arises from this is: How should the relation between shear stress, newtonian fluid viscosity and this fluctuating velocity? Is the relationship the same as for the average velocity?

Secondly, there is a different mechanism to describe and determine the viscosity of liquid and gas. And as a consequence, there is a different effect of temperature to viscosity. Where the higher the temperature, the higher the viscosity of the gas, while its effect on liquids are not like that. The common question aries is: Is there any new theory to describe the same mechanism to determine the viscosity for both the gases and liquids?

I imagine that it would be very beautiful if we can find a simple, easy and straightforward theory that could implemented in the real and practical fluid dynamic applications. Maybe its just a hope......

Please think about it.

Thank you

Have a nice weekend

Again, the stress is modelled by the Newtonian law and is the same boh in laminar and turbulent regime. The velocity fluctuations are within the velocity gradient, not in the molecular viscosity.

Thanks Tapan K. Sengupta

Dear Filippo Maria Denaro

Please show me or proof again that the fluctuating velocity will give shear stress by using the relationship of: Shear stress = mu. du'/dy where u' is the fluctuating velocity. Please mention that u' is not a constant or mean velocity.

Please forgive me....

You have to consider the total velocity not only the fluctuation. The stress tensor is

T= 2 mu S - p I

where S Is the symmetric part of the velocity gradient. This expression is always valid and account for the time-dependent velocity. You can read any fluid dynamic textbook.

T= 2 mu S -p I

This expression is always valid and account for the time-dependent velocity.

That's my question.

Your question is answered. Provided that you accept the continuum assumption and the constitutive Newton law, the above expression is always valid.

I think this is oftopic;

The common question aries is: Is there any new theory to describe the same mechanism to determine the viscosity for both the gases and liquids?

But as I think I can contribute here something, and the interest seems also be present, I just write it here.

The thinking must go all the way.

-What is viscosity? It's electromagnetic propulsion between moving particles.

So why the viscosity-Temperature relation is turned around in fluids/solids and in gas?

Because the electromagnetic interaction is different in freely moving particles and bounded particles. Temperature is particle velocity. In solids/liquids higher temperature causes that the particle are longer time apart each other in distance. This makes the electromagnetic interaction weaker, and lowers the viscosity.

In gas this interaction is just collisions, and here the pressure defines the particle amount in volume, and Temperature mean velocity of these particles. If this velocity (=temperature) is increased, there will be more collisions if the free distance remains the same.

More collisions = more electromagnetic interactions = higher viscosity.

Even more oftopic;

I found this funny, but just yesterday evening I made some basic calculations on this issue cause some conversation provide me new idea to this;

Working Paper STATES OF MATTER defined from The Speed of Light

As if this idea is true, it must also be able to explain the critical points.

And so i took my old excel, and tested this idea, and it was quite amusing to notice that atleast water, oxygen gas and chlorine has the same critical point, if this is defined through the free path-travel time, and this time is approx 2 x eVs so approx 2 x 10^-15 Seconds. Which clearly tells me that at critical point the electrons of single molecules lose more ore less their ability to interact in organised way.

Well, actually this is not quite so oftopic, as can been seen, this sort of explains how two molecules way to interact "viscous-way" depends their own velocities, and this velocity is a construct of temperature, flow velocity, etc.

Thanks Jouni Jokela

Your mind is open for something different....

I hope we can find something new....

Regards

Dear Researchers,

Have a nice weekend with your family....

Dear all distinguished scholars,

Thank you very much for your participation in the discussion. Hope we can make a good friendship and collaboration.

Best regards,

NAzaruddin Sinaga

Dear respected scholars, please join our important and interesting discussion at:

https://www.researchgate.net/post/Do_you_agree_if_we_create_an_international_organization_of_university_lecturers#view=5e3cbc1e2ba3a1a3a972a2d2

We are discussing about creating an international organization of lecturers and researchers for us. I think you would like to be a member or organizer.

Thank you very much.

Best regards.

Yes dear. I agree with your offer.

Thank you dear Mohsen Jahanmiri for your supports.

Theorem 7.4 The necessary and sufficient condition for turbulence generation/ turbulent transition is that the singularity of Navier-Stokes equation (i.e. the

discontinuity of velocity) appears in the flow field.

Reference:

1. Dou, H.-S., Singularity of Navier-Stokes equations leading to turbulence, Adv. Appl. Math. Mech., 13(3), 2021, 527-553.

https://doi.org/10.4208/aamm.OA-2020-0063 ; https://arxiv.org/abs/1805.12053v10

2. Dou, H.-S., No existence and smoothness of solution of the Navier-Stokes equation, Entropy, 2022, 24, 339.

https://doi.org/10.3390/e24030339

3. Dou, H.-S., Origin of Turbulence-Energy Gradient Theory, 2022, Springer.

https://link.springer.com/book/10.1007/978-981-19-0087-7