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Old   February 19, 2022, 07:14
Question Question of this paper.
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Sangho Ko
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Hello everyone.
I'm reading paper and I don't understand some part.
So I want to ask you.

Link of this paper is below.
https://www.researchgate.net/publica...bulence_Models

I'm not good at English so there can be difficulty to communicate.
Also cause of this, there is a confusion of nomenclature and it is hard to understand meaning of sentence from paper.
So please understand me.

In addition there are many questions.
Cause of many questions, it can be annoying.
Sorry. But I really need your help.
Please understand me.
Thanks



1. In page 1,
"Finally, further from the impingement point the flow does revert to a thin shear flow but by no means to a simple one, with the maximum shear stress occurring outside the wall region and the flow thus retaining a significant memory of its upstream history. "

* Actually I'm not sure that I understand the correct meaning of this sentence because my English is not good.
But I've written qustions to extent that I understand.
If I misundertand the meaning of sentence, let me know.

A. Thin shear flow
What is thin shear flow?
I guess it means flow in viscous sublayer because viscous sublayer is very thin compared with outer region.
Is it right?
B. Wall region
What is wall region? I've uploaded figure that describe what I understand(wall jet region).
Is it right?
And also what does 'Outside wall region' indicate?
Where is the 'outside the wall region'?
C. Retaining a significant memory of its upstream history
What does it mean?
Does it mean that we can get information of upstream by using the information of thin shear flow?
If it is right, how can we get information of upstream by using the information of thin shear flow?
How it can be possible?


2. In page 6, 3\nu _{T}(\frac{\partial V}{\partial y})^2

A. How it can be derived?
I don't know how it is derived?
I've guessed that it is derived from Boussinesq's hypothesis(\overline{u'v'}=\nu _{T}(\frac{\partial U}{\partial y}+\frac{\partial V}{\partial x})), but I'm not sure.
How it is derived?


3. In page 6,
"In a simple shear flow the action of \phi _{ij2} is to transfer a proportion of the energy generated in streamwise fluctuations to those in the plane orthogonal to the mean velocity"


A. Transfer a proportion of the energy generated in streamwise fluctuations to those in the plane orthogonal to the mean velocity
I don't undertstand this situation.
How 'proportion of the energy generated in streamwise fluctuations' are transferred to 'those in the plane orthogonal to the mean velocity'?
I've guessed this situaiton like as follow.

Fluctuations(u') are caused by mean velocity gradient(Boussinesq's hypothesis) and it is expressed to Reynolds Stress.(Refer to uploaded pictures)
\overline{u_{i}'u_{j}'}=\nu _{T}(\frac{\partial U_{j}}{\partial x_{i}}+\frac{\partial U_{i}}{\partial x_{j}})-\frac{2}{3}k\delta _{ij}
Shear stress acts parallel to streamwise.
But in this case, this fluctuation is converted into deformation of plane orthogonal to streamline.

Is it right?
But I have one doubt point.
This sentence is treating basic Reynolds Stress Model.
Actually I don't know Reynold Stess Model well, but what I know is in Reynolds Stress Model, there is another assumption with Boussinesq's hypothesis.(Is it right? I'm not sure.)
I've heard Reynolds Stress Model is different with Eddy viscosity Model.
So I'm not sure whether I can reflect Boussinesq's hypothesis or not.
If I'm wrong, then what is proper situation?


4. In page 6,
"thus the intervention of \phi _{ij2}^{w} reduces the effective generation rate of \overline{v'v'}."


A. Reduction of generation rate of \overline{v'v'}

Why generation of \overline{v'v'} is reduced?
I guess this is transferred to deformation of plane to u direction and it is same context with 3rd question.

"In a simple shear flow the action of \phi _{ij2} is to transfer a proportion of the energy generated in streamwise fluctuations to those in the plane orthogonal to the mean velocity"

Is it right?


4. In page 6,
"Thus, in a stagnation flow the wall ‘damping’ term \phi _{ij2}^{w} actually leads to an augmentation of the turbulent velocity normal to the wall. "


A. Damping term '\phi _{ij2}^{w}' and 'augmentation of the turbulent velocity normal to the wall'
In question 2 and 3, we've seen \overline{v'v'}(that is same with turbulence velocity normal to the wall) is reduced by conversion into deformation.
But here is a inconsistency.
In this sentence, why this paper claims turbulence velocity normal to the wall is increased?
What does this sentence mean?


5. In page 6,
We note, however, that if (as proposed in ref. [13]) the recorded mean velocity of the single hot wire on the axis is interpreted as
\sqrt{V^{2}+\overline{v'^{2}}+\overline{u'^{2}}}
, Fig. 3, the predicted profile with Model 3 for H/D = 6 accords quite well with the experimental data with, in particular, the strongly non-linear variation very close to the wall being well captured.


A. Mean velocity and fluctuation

Though fluctuations(\overline{v'^{2}} and \overline{u'^{2}}) are summed, why it is called MEAN velocity gradient?
And if it represents the velocity at every each time, I think below is more accurate.

\sqrt{(V+\sqrt{\overline{v'^{2}}})^2+\overline{u'^{2}}}

But why it doesn't write it like upper?


6. In page 6,
"Model 1 and, to a lesser extent, Model 2 produce too high near-wall velocities because the turbulence levels they predict are excessive."

"Model 4 gives too low velocities because of the excessive mixing of the jet before coming under the influence of the wall."


A. Excessive mixing
In my opinion, I think I understand first sentence properly.
I think model 2 produces too much turbulence cause of damping function '\phi _{ij2}^{w}'.
But I can't understand why there is excessive mixing in model 4?
How can we know that?
I think I know the meaning of mixing properly.
Mixing is the process caused by drag of near air from jet right?
But why there is excessive mixing in model 4 especially?


7. In page 8,
"Models 3 and 4 achieve close correspondence with the measurements whereas Models 1 and 2 produce too rapid mixing as would be expected from the excessive predicted levels of shear stress shown in Fig. 6. "


A. Damping function '\phi _{ij2}^{w}' and too rapid mixing

We have seen there is too much turbulence in model 2 because of damping fucntion, not rapid mixing.

"thus the intervention of \phi _{ij2}^{w} reduces the effective generation rate of \overline{v'v'}."

But why this sentence says rapid mixing, not damping function?


8. In page 9,
"The reason for this apparent inconsistency is that, unlike the case of a thin shear layer, the normal stress terms make a substantial contribution to the mean momentum budget for r/D < 1.5"

A. Normal stress term and Mean momentum
What does it mean?
I guess, to mix(fluctuate, normal stress), flow need to spend energy.
So energy that is going to be used to make normal stress(fluctuation, mixing) is derived from mean momentum.(ex: Transport equation for mean momentum).
So to make normal stress, it should spend some energy from mean momentum.
Then, cause of reduced mean momentum by making normal stress, there is effect to Reynolds shear stress.
Because to make Reynolds shear stress, it should spend some energy also.
Is it right?




Thanks for reading this long questions.
I'm not good at English so please excuse my bad English.
I'm not professional about turbulence.
But I'm interested in that field.
So help me please
Thanks
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Old   February 19, 2022, 12:31
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1A. Simple shear flows are your elementary flows like Couette flows and the the boundary layer that develops between parallel layers of fluid with different velocities. It is not the viscous sublayer. The point is, even though far from the point of stagnation, a wall boundary layer develops, thi wall boundary layer is still rather complex and not an elementary boundary layer that you find over a flat plate.
1B. The wall region of a jet impingement flow is the region away from the stagnation point where the wall boundary layer is developing and the flow is mostly parallel with the wall (instead of normal to the wall). There's a lot of pictures like so that demonstrate this.

1C. It means the correlation time and length scales are larger than in simple shear flows. The correlation is the information.

2A. The production term is the product of the Reynolds stress with the deformation. I forget how to derive exactly 3 but the square of the gradient should be there. The production is exact if you know the Reynolds stresses. Maybe the wiki gives you some hints.

3. What you have written down is the stress-strain correlation. The mechanism being discussed is the pressure-strain correlation.
4. This is again the influence of the pressure-strain and how it acts differently here compared to simple shear flows.
5. This requires a lesson in how hot-wires work and hot to correct them in practical scenarios. A single wire hotwire has a strong sensitivity flow perpendicular to its axis but it can't differentiate which velocity is which. In other words, single-wire HWA doesn't actually measure V even if you orient the hot-wire perfectly.


(to be continued)
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Old   February 19, 2022, 15:00
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A further note on the damping term that I think will help you understand your remaining questions. The damping term in ordinary shear flows steals energy from streamwise fluctuations transfers them orthogonal to the flow direction. In other words, it mixes them out.

When turbulence encounters a wall, something entirely different happens. Due to the kinematic blocking effect of the wall (i.e. the flow encounters a wall) the wall-normal gradients are zero. Keep in mind that wall-normal is also streamwise with respect to the impinging jet (i.e. wall-normal and jet-axis are the same direction). The kinematic constraint is dV/dy and dv'/dy=0. This means that v' tends towards a maximum at the wall. This isn't merely a claim of the authors, it's basic physics guaranteed to occur (unless the fluid somehow teleports itself through the wall). The pressure-strain correlation is one of the mechanisms that allows this transfer of energy (augmenting the v') to take place. This phenomenon would actually correspond to a negative turbulence viscosity in ordinary mixing length models. In simple shear flows, the damping term steals energy from the v' fluctuations (and mixes them down); in the case of impinging jets it can do the opposite and amplify them, but it does so only near the stagnation region where the impinging effect occurs.


6. In simple shear layers, streamwise (i.e. wall parallel) fluctuations are larger than normal ones. For impinging jets, wall-normal fluctuations (which is streamwise-jet) can become large. Again, be very careful with the meaning of streamwise for a shear layer versus an impinging jet. In a wall-bounded shear layer, the wall is parallel with the mean flow. In an impinging jet, the wall is normal to the jet axis.
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Old   February 19, 2022, 23:01
Question I have a question about your answer.
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Quote:
Originally Posted by LuckyTran View Post
A further note on the damping term that I think will help you understand your remaining questions. The damping term in ordinary shear flows steals energy from streamwise fluctuations transfers them orthogonal to the flow direction. In other words, it mixes them out.

When turbulence encounters a wall, something entirely different happens. Due to the kinematic blocking effect of the wall (i.e. the flow encounters a wall) the wall-normal gradients are zero. Keep in mind that wall-normal is also streamwise with respect to the impinging jet (i.e. wall-normal and jet-axis are the same direction). The kinematic constraint is dV/dy and dv'/dy=0. This means that v' tends towards a maximum at the wall. This isn't merely a claim of the authors, it's basic physics guaranteed to occur (unless the fluid somehow teleports itself through the wall). The pressure-strain correlation is one of the mechanisms that allows this transfer of energy (augmenting the v') to take place. This phenomenon would actually correspond to a negative turbulence viscosity in ordinary mixing length models. In simple shear flows, the damping term steals energy from the v' fluctuations (and mixes them down); in the case of impinging jets it can do the opposite and amplify them, but it does so only near the stagnation region where the impinging effect occurs.


6. In simple shear layers, streamwise (i.e. wall parallel) fluctuations are larger than normal ones. For impinging jets, wall-normal fluctuations (which is streamwise-jet) can become large. Again, be very careful with the meaning of streamwise for a shear layer versus an impinging jet. In a wall-bounded shear layer, the wall is parallel with the mean flow. In an impinging jet, the wall is normal to the jet axis.
Actually I think I should study pressure-strain correlation.

But apart from that, I don't understand why dV/dy and dv'/dy must be zero on the wall when jet impinges to the wall?
I think if jet is shot to the wall, jet must approach stagnation point.
Then mean normal velocity(V) becomes zero in stagnation point.(V=0)
There is no flow rate that towards to wall.
Flow never penetrates into the wall.
So I think as jet approaches to the wall, mean velocity of jet(V) should be decreased.
It means there is a Mean velocity gradient(dV/dy).

But why dV/dy must be zero on the wall for jet impingement?

And also why v' must be maximum on the wall?
If dv'/dy must be zero on the wall, v' can be maximum or minimum.
But how can we decide whether v' must be maximum or minimum?
I've guessed it in terms of Boussinesq's hyptothesis to grasp approximate trend
because I think both Boussinesq's hypothesis and Reynolds Stress model have similar concept although there can be difference of quantification.
(Mixing: Boussinesq's hypothesis \approx Reynolds Stress Model: "Damping term steals energy from streamwise fluctuations then transfers them orthogonal to the flow direction.")
(Is upper convincing? I want to be confirmed whether I understand properly or not.)

I think dV/dy becomes maximum on the wall when jet impinges to the wall.(as I've told you in upper)
Because it approaches to the stagnation point, velocity of jet is decreased extreamly.
Cause of this high fluctuation(v') occurs.

But why dV/dy must be zero on the wall when jet impinges to the wall?
Thanks
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Old   February 20, 2022, 15:08
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The kinematic blocking condition, the boundary condition for a wall (regardless of slip or non-slip), is that the wall normal gradient is zero. Actually it's not just just V and v' but also U,W, u', and w'. Exactly on the wall the velocity is zero, but in a layer of fluid just above the wall, they approach maximums. This happens actually also for simple shear flows (k is maximum near the wall and 0 exactly on the wall). It may appear that there are two sets of conditions being applied in a small region (near the wall in this case) and that is true. The reconciliation of these two conditions is exactly what leads to boundary layers in physics. See figure 2. You can see that v' abruptly goes to zero in a very small region next to the wall.
You can't interpret maximum/minimum that way for vectors because the flow direction can be the opposite. Furthermore, the rms v' is the same whether positive or negative.

Mixing means I take areas of stuff with high quantities and I send them to areas of with low quantities of stuff. I.e. i.e. if I put sugar in my coffee, I stir it to mix the areas with high sugar concentration with low sugar concentration to get an even drink. If the opposite happens (I stir my coffee and sugar cubes start forming), we don't call it mixing! Eddy viscosity models generally consider energy is transferred from regions of high to low strain and not the opposite.


If you want to understand why v' is a maximum near the wall (but not on the wall) we can continue further but it has nothing to do with what turbulence model you are using.
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Last edited by LuckyTran; February 20, 2022 at 18:25.
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Old   February 20, 2022, 20:26
Question There are 2 questions about your answer.
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Quote:
Originally Posted by LuckyTran View Post
The kinematic blocking condition, the boundary condition for a wall (regardless of slip or non-slip), is that the wall normal gradient is zero. Actually it's not just just V and v' but also U,W, u', and w'. Exactly on the wall the velocity is zero, but in a layer of fluid just above the wall, they approach maximums. This happens actually also for simple shear flows (k is maximum near the wall and 0 exactly on the wall). It may appear that there are two sets of conditions being applied in a small region (near the wall in this case) and that is true. The reconciliation of these two conditions is exactly what leads to boundary layers in physics. See figure 2. You can see that v' abruptly goes to zero in a very small region next to the wall.
You can't interpret maximum/minimum that way for vectors because the flow direction can be the opposite. Furthermore, the rms v' is the same whether positive or negative.

Mixing means I take areas of stuff with high quantities and I send them to areas of with low quantities of stuff. I.e. i.e. if I put sugar in my coffee, I stir it to mix the areas with high sugar concentration with low sugar concentration to get an even drink. If the opposite happens (I stir my coffee and sugar cubes start forming), we don't call it mixing! Eddy viscosity models generally consider energy is transferred from regions of high to low strain and not the opposite.


If you want to understand why v' is a maximum near the wall (but not on the wall) we can continue further but it has nothing to do with what turbulence model you are using.
Thanks
Actually what I want to know is not what model is most appropriate but why that physical situation happens.

1.
I can see v' abruptly goes to zero from figure 2.
But I don't understand how it is related to reason why dv'/dy=0 and v' becomes maximum near the wall.

2.
I can understand the situation that "energy from streamwise fluctuations then transfers them orthogonal to the flow direction."
But I want to know how it can be same context with
"consider energy is transferred from regions of high to low strain and not the opposite"

"streamwise fluctuations=High strain" : Actually I think it can be, cause of fluctuation.
"orthogonal to the flow direction= Low strain": But I don't understand how this can be applied.

Scenario that I've thought about upper is follow.

Let's assume there is a flow on the flat plate like uploaded figure.
From this figure we can see there is a velocity difference in x-direction between upper side and below side because of fluctuation(u')
It means there is a high strain by velocity gradient(difference, du/dy).
But there is No velocity difference in y-direction between left side and right side(blue colored line)
It means there is no strain and velocity gradient(No dv/dx).
So I guess 'transform of energy from high strain to low strain' means energy from streamwise fluctuation(High strain) is trasferred to orthogonal direction(Low strain).
So energy(v') that is orthogonal to the flow direction occurs and it starts to mix.
Is it right?

Thanks
Attached Images
File Type: jpg Flow scenario.jpg (33.6 KB, 4 views)

Last edited by FluidKo; February 21, 2022 at 03:24. Reason: To add some coment
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