Fluid Dynamics - Spanwise Vorticity of Turbulent Boundary Layer

[pobatso]

Hi all,

Am reading a few papers for a Uni case study about structures in Turbulent Boundary Layers over a Flat Plate (water), particularly low-speed streaks.

I'm confused over what mechanism causes the span wise variations in velocity that seems to cause low speed streaks.

Would anyone know an easy to get explanation for this?

Regards,
pobatso

 

[boneh3ad]

Generally it is streamwise vorticity that would lead to streaks. Imagine a vortex propagating downstream. One side will have an upward motion while the other will have a downward motion. These tend to drag low momentum fluid higher into the boundary layer and high momentum fluid lower into the boundary layer respectively. That means that at some given height off of the surface, you will see spanwise streaks in velocity.

 

[MrMatt2532]

The simple answer for spanwise variation is that turbulent flow in inherently unsteady and 3 dimensional even if you would like to view it as a 2-dimensional problem.

As to the streaky nature, it is unclear if you are referring to fully developed turbulent flow or laminar flow transitioning to turbulence.

I'm guessing you are referring to transition. This streaky nature can be viewed as turbulent streaks. The flow in transition can be modeled as laminar flow except for for immediately downstream of one of these turbulent streaks.

 

[boneh3ad]

I'm guessing you are referring to transition. This streaky nature can be viewed as turbulent streaks. The flow in transition can be modeled as laminar flow except for for immediately downstream of one of these turbulent streaks.

True, though the nature of these phenomena depends somewhat on the specific type of boundary-layer instability causing the question. However, even once the flow is fully turbulent, there are still various large-scale structures, one of the main types of which is streamwise vorticity. That often leads to the spanwise streaks in the fully turbulent region.

 

[pobatso]

Sorry for the delay in reply all, and thank you for your reply's!

What I believe I've read and understood is that these low speed streaks that occur due to span wise variations in velocity actually have a pattern to them. When readings are taken over a long enough time period, a pattern emerges that actually gives these streaks a visual mean spacing across the span wise direction. In the paper we're studying they refer to vortex stretching as the main mechanism for causing these low speed streaks.

Perhaps I should of been more specific in saying that the specific phenomena we're investigating are born out of the laminar sub region of a turbulent flow. They then tend to become more unstable further down the flow and get ejected vertically out into the turbulent regions of the flow.

If anyone's curious as to the basis of the case study we're doing, we were told to read a paper by Kline, Reynolds, Schraub and Runstadler titled "The Structure of Turbulent Boundary Layers" (1967).

What I gather from vortex stretching, is that if you take a circular flow of material and cause it to speed up, the radius of its flow is going to decrease to maintain angular momentum: just like the kid spinning on an office chair pulling his legs into spin faster.

Is it then the gaps that would be left at either ends of the tube of vortex that cause the span wise velocity, due to other material trying to fill its place?

 

[Vadar2012]

This is a pretty interesting topic. I did a Masters thesis on simulating the onset of vorticity inside a scramjet combustion chamber. The explanations given here of what cause this are pretty well explained. Some interesting points to add are that the Reynods number at which these vortices start to occur can be predicted by laminar 2D calculations, but the extent of their effect on the flow, such as the heat transfer at the wall, can only be predicted by turbulent 3D simulations. This highlights the importance of Matt's comments. Note that for the past 50 years or so, we thought that these effects were cause by the transition of turbulence, not by the creation of vorticies in the flow. If you're interested I can recommend some papers that investigate this. From memory they explain how they are formed quite well.

 

[pobatso]

Hi Vadar, any sources to help demistify the topic would be very much appreciated, as it also looks like I'm steering my final year project towards something in this subject area.

I think one of the things that is drawing me towards this subject matter is the inherent difficulty with which one can try to model these phenomena. After 2 years of subjects reliant on deterministic Newtonian mechanics, its nice to have a topic where it feels like we don't know everything!

Going back to the final year project thing, what thoughts do you chaps have on the feasibility of doing something along the lines of a receptivity study of turbulence forced by sound waves?

I've come across a few papers that investigate this or a variation of it, so I would probably need to do a bit more thinking towards putting my own spin on it, but its an interesting idea.

Cheers

 

[boneh3ad]

Investigating the boundary layer receptivity to acoustic disturbances is an active area of intense research. That's probably too bold for a senior project. I know people who earn a living trying to simulate that, as it's perhaps the biggest remaining hole in the theory of transition to turbulence.

 

[pobatso]

Yeah, my project tutor didn't sound too convinced when I pitched it to him. I'm genuinely struggling here, any suggestions for what might make a good project in this area?

 

[boneh3ad]

I mean, don't get me wrong, regardless of what your tutor thinks it is a great research topic, it is just too advanced to realistically do as a senior project. The problem is that you are venturing pretty close to the current edge of understanding of the topic (and when you talk about receptivity, you are actually at that edge), so most topics are going to require either extensive and very specialized experimental facilities or else a very powerful computer and DNS code.

 

[Vadar2012]

Bonehead is right. I used some specialised exerimental facilities that take a long time to learn. Are also very sensitive and the tiniest thing gives you silly results, which means experiments can take months. Then you have to learn how to use Linux and how to use a command shell to access a supercomputer to actually run the simulations that are required for such analyses. This is PhD level stuff, way too much for an undergrad project.

 

[boneh3ad]

I suppose it would be easier to look at the effect of acoustic disturbances on turbulence that has already developed on the boundary layer, as that would require much less specialized equipment. I am not sure what good a study like that would do or what it would show you. The more interesting problem is the effect of acoustic disturbances on a laminar boundary layer and how that leads to turbulence, and that would require a special low-disturbance wind tunnel (of which there are only a handful in existence) to get any truly useful data. I have some colleagues in the next lab over who have been doing some work in that field.

 

[pobatso]

Yup that does sound all very much out of my league at the moment. And agreed as well that I'm not sure I could see the aim of studying the effect of acoustic disturbance on a turbulent boundary layer - our tutor's been emphisizing how important it is to have a measurable property at the centre of our study, and that just sounds a bit vague.

So is there anything else in the wider fluid mechanics field that could make a good project to study? Any previous topics you've seen other undergrads take on and make a sucesss out of?

Cheers again.