T-S disturbances without noise/turbulence in airfoil boundary layer?

kepler123 · November 25, 2020, 11:04

I have noticed a typical streamwise velocity fluctuation (urms) double peak in my inflection profile, with the first peak being very close to the wall (related to total boundary layer height). Both of these, the double peak and the low critical layer height correspond to the presence of T-S disturbances according to the literature I have been reading. Furthermore, the magnitude being around 1% of the free-stream velocity gives me more confidence that this is in fact a T-S disturbance.

Image below: Delta star refers to the boundary layer height determined by the location where spanwise vorticity goes close to zero. 'y' is the wall-normal axis and the absolute value of the fluctuating streamwise velocity is shown on the horizontal axis.

Simulation case: Wall-resolved LES around an airfoil. It does not however include any kind of added turbulence or noise. It is a base case with 0% TI.

My question(s) is/are:

Is it possible for T-S disturbances to form within the boundary layer in such a scenario? I am of the impression that T-S disturbances are caused after the receptivity of some disturbances by the boundary layer. which in my case do not exist.

Is an adverse pressure gradient sufficient to cause the growth of T-S disturbances?

If the above are not possible, are my T-S disturbances caused by numerical noise? If this is the case, how do I determine the "level" of noise? What does this really mean? It is a question posed to me by a reviewer.

I have spent a few days looking for literature on the topic, but could not find any case where T-S disturbances are observed in the absence of some kind of added noise to the flow.

duri · November 25, 2020, 22:59

It is interesting to see such a profile when there is no inlet turbulence or disturbance. Where does it occurs on the airfoil. Does the location of TS wave consistent with the theory.
Some perturbation is required for flow instability. But it is interesting to think that numerical perturbations as source of flow instability. This may unlikely to occur, if the perturbation starts to grow and influence the solution then the it leads to numerical instability.
Numerical noise may be an issue. But in my opinion, the numerical noise is the result of mixing the waves of different scales at different time levels which is possible only in steady state solution. It should not occur in unsteady as the time levels are consistent. Are you using dual time stepping, will it lead to numerical noise due to steady state behavior of inner iteration.

kepler123 · November 26, 2020, 04:12

Quote:

Originally Posted by duri

It is interesting to see such a profile when there is no inlet turbulence or disturbance. Where does it occurs on the airfoil. Does the location of TS wave consistent with the theory.
Some perturbation is required for flow instability. But it is interesting to think that numerical perturbations as source of flow instability. This may unlikely to occur, if the perturbation starts to grow and influence the solution then the it leads to numerical instability.
Numerical noise may be an issue. But in my opinion, the numerical noise is the result of mixing the waves of different scales at different time levels which is possible only in steady state solution. It should not occur in unsteady as the time levels are consistent. Are you using dual time stepping, will it lead to numerical noise due to steady state behavior of inner iteration.

Hi Duri,

First of all thanks for taking the time to read and comment. It was very helpful. Here are some replies to the questions you asked.

1. The T-S waves begin to grow just as we reach the adverse pressure gradient of the suction side. They are not very strong in the sense that transition occurs through a separation bubble on this profile through a Kevin-Helmholtz instability (shear on the edge of the boundary layer).

2. I am not sure how to test it out and compare with linear stability theory. I do not have access to any code and I could not find literature to help me out with this when it comes to the algorithms needed. I could come up with the algorithms if I knew the theory required. In all cases, I have seen you begin by assuming two of the four parameters (time formulation and not space) of the Orr-Sommerfeld equation.

3. I cannot remember the paper, but there was one where I read that they used numerical instability as the source of "noise". But, other than that there was nothing else remarkable in the paper from what I recall.

4. No, I am not using dual time-stepping, I did not know about this method until I looked it up. A low storage Range Kutta scheme which is second-order accurate is used. The corrector step is the usual pressure-correction method.

FMDenaro · November 26, 2020, 04:14

Could you provide details about your numerical method?

kepler123 · November 26, 2020, 04:23

Quote:

Originally Posted by FMDenaro

Could you provide details about your numerical method?

Sure, here are some details, let me know if there is anything else that you need, Prof. Denaro:

Wall-resolved LES with a no-slip condition, the first cell height is at a y+ of 0.5 with a wall-normal expansion using a geometrical progression of 1.05. The spanwise delta z+ is less than 25 and streamwise delta x+ is less than 30, so in line with well-resolved requirements by Piomelli et al.

The SGS model used is the dynamic Smagorinsky model.

Accuracy in space: 2nd order accurate
Accuracy in time: 2nd order accurate
Solution scheme: predictor-corrector time marching scheme
Predictor: low-storage Range Kutta
Corrector: Pressure correction method
Pressure Velocity Coupling: Momentum interpolation technique

Just for the sake of being complete, here are other details:
Variable arrangement: cell-centered, non-staggered.
The discretization of integrals is done using a mid-point rule and the interpolation scheme is linear interpolation.

FMDenaro · November 26, 2020, 05:03

1) I do not fully understand the profile you posted. Could you show in terms of y+? The first cell at y+=0.5 means you have very few node to describe the viscous sublayer. That is a first problem inducing numerical errors
2) The second order central discretization introduces a dispersive character of the local truncation error, that should be somehow mitigated by the action of the dynamic eddy viscosity. Check the eddy viscosity profile along the vertical direction.
3) The non-staggered arrangement with second order discretization can introduce spurious mode. How do you manage this issue, using R-C interpolation?

kepler123 · November 26, 2020, 10:36

Quote:

Originally Posted by FMDenaro

1) I do not fully understand the profile you posted. Could you show in terms of y+? The first cell at y+=0.5 means you have very few node to describe the viscous sublayer. That is a first problem inducing numerical errors
2) The second order central discretization introduces a dispersive character of the local truncation error, that should be somehow mitigated by the action of the dynamic eddy viscosity. Check the eddy viscosity profile along the vertical direction.
3) The non-staggered arrangement with second order discretization can introduce spurious mode. How do you manage this issue, using R-C interpolation?

I do not have access to the data and will be able to get back to you about point number 1 either tomorrow evening or on the weekend. Corona schedules

2. Sadly, I do not have the output dynamic eddy viscosity directly from my code and to run it again is too expensive.

I definitely need to do some reading about this, but do you think if I plotted the eddy viscosity calculated from the grid size and velocity gradients as proposed by Smagorinsky it would suffice? By reading I mean, I need to see how the dynamic eddy viscosity is actually calculated, I know the principle behind it, not the actual equations, yet.

$\nu_t = \Delta x \Delta y \sqrt{\left(\frac{\partial u}{\partial x}\right)^2 + \left(\frac{\partial v}{\partial y}\right)^2 + \frac{1}{2}\left(\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}\right)^2}$

3. Yes, in order to avoid the decoupling of pressure and velocity on the non-staggered grid, the R-C momentum interpolation technique is used. I had to go through the literature of the code I am using and the subroutine to make sure this was done. This was something I learned today about the differences between a staggered and non-staggered grid, thank you for that.

FMDenaro · November 26, 2020, 10:53

Quote:

Originally Posted by kepler123

I do not have access to the data and will be able to get back to you about point number 1 either tomorrow evening or on the weekend. Corona schedules

2. Sadly, I do not have the output dynamic eddy viscosity directly from my code and to run it again is too expensive.

I definitely need to do some reading about this, but do you think if I plotted the eddy viscosity calculated from the grid size and velocity gradients as proposed by Smagorinsky it would suffice? By reading I mean, I need to see how the dynamic eddy viscosity is actually calculated, I know the principle behind it, not the actual equations, yet.

$\nu_t = \Delta x \Delta y \sqrt{\left(\frac{\partial u}{\partial x}\right)^2 + \left(\frac{\partial v}{\partial y}\right)^2 + \frac{1}{2}\left(\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}\right)^2}$

3. Yes, in order to avoid the decoupling of pressure and velocity on the non-staggered grid, the R-C momentum interpolation technique is used. I had to go through the literature of the code I am using and the subroutine to make sure this was done. This was something I learned today about the differences between a staggered and non-staggered grid, thank you for that.

You have to manage exactly the eddy viscosity variable as computed from the code.

November 25, 2020, 11:04	T-S disturbances without noise/turbulence in airfoil boundary layer?	#1
kepler123 Member Brandon Join Date: Jun 2018 Location: Germany Posts: 46 Rep Power: 7	I have noticed a typical streamwise velocity fluctuation (urms) double peak in my inflection profile, with the first peak being very close to the wall (related to total boundary layer height). Both of these, the double peak and the low critical layer height correspond to the presence of T-S disturbances according to the literature I have been reading. Furthermore, the magnitude being around 1% of the free-stream velocity gives me more confidence that this is in fact a T-S disturbance. Image below: Delta star refers to the boundary layer height determined by the location where spanwise vorticity goes close to zero. 'y' is the wall-normal axis and the absolute value of the fluctuating streamwise velocity is shown on the horizontal axis. Simulation case: Wall-resolved LES around an airfoil. It does not however include any kind of added turbulence or noise. It is a base case with 0% TI. My question(s) is/are: Is it possible for T-S disturbances to form within the boundary layer in such a scenario? I am of the impression that T-S disturbances are caused after the receptivity of some disturbances by the boundary layer. which in my case do not exist. Is an adverse pressure gradient sufficient to cause the growth of T-S disturbances? If the above are not possible, are my T-S disturbances caused by numerical noise? If this is the case, how do I determine the "level" of noise? What does this really mean? It is a question posed to me by a reviewer. I have spent a few days looking for literature on the topic, but could not find any case where T-S disturbances are observed in the absence of some kind of added noise to the flow.

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November 25, 2020, 22:59		#2
duri Senior Member duri Join Date: May 2010 Posts: 245 Rep Power: 16	It is interesting to see such a profile when there is no inlet turbulence or disturbance. Where does it occurs on the airfoil. Does the location of TS wave consistent with the theory. Some perturbation is required for flow instability. But it is interesting to think that numerical perturbations as source of flow instability. This may unlikely to occur, if the perturbation starts to grow and influence the solution then the it leads to numerical instability. Numerical noise may be an issue. But in my opinion, the numerical noise is the result of mixing the waves of different scales at different time levels which is possible only in steady state solution. It should not occur in unsteady as the time levels are consistent. Are you using dual time stepping, will it lead to numerical noise due to steady state behavior of inner iteration.

November 26, 2020, 04:14		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	Could you provide details about your numerical method?

November 26, 2020, 05:03		#6
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	1) I do not fully understand the profile you posted. Could you show in terms of y+? The first cell at y+=0.5 means you have very few node to describe the viscous sublayer. That is a first problem inducing numerical errors 2) The second order central discretization introduces a dispersive character of the local truncation error, that should be somehow mitigated by the action of the dynamic eddy viscosity. Check the eddy viscosity profile along the vertical direction. 3) The non-staggered arrangement with second order discretization can introduce spurious mode. How do you manage this issue, using R-C interpolation?