Frequency of boundary layer instability

[shreddinglicks]

I've been searching the net but can not find any freely available literature. Can someone give me a quick lesson on boundary layer instability and its frequencies? I have an equation that claims to scale the instability frequency by:

F = U/2*delta

U is leading edge velocity
delta is layer thickness

What information does this give me? Does this tell me the likelihood of transition from laminar to turbulence?

 

[boneh3ad]

This is highly variable and depends on the free-stream and boundary conditions. In many cases, multiple unstable waves coexist associated with different unstable modes, and their frequencies can be very different. So what's the context here?

 

[shreddinglicks]

This is highly variable and depends on the free-stream and boundary conditions. In many cases, multiple unstable waves coexist associated with different unstable modes, and their frequencies can be very different. So what's the context here?

In this case I am using the script mentioned from my other post to obtain properties at the leading edge of a flat plate and cone both at 0 angle of attack. The boundary layer was calculated assuming a constant temperature wall.

 

[boneh3ad]

In this case I am using the script mentioned from my other post to obtain properties at the leading edge of a flat plate and cone both at 0 angle of attack. The boundary layer was calculated assuming a constant temperature wall.

So you are talking about hypersonic/hypervelocity, then?

For hypersonic boundary layers, the estimator $f\approx u_e/(2\delta)$ works for a certain class of instability wherein the boundary layer acts as an acoustic wave guide. Other classes of instability would have different scaling.

The frequency alone does not tell you anything about the likelihood of transition.

 

[shreddinglicks]

So you are talking about hypersonic/hypervelocity, then?

For hypersonic boundary layers, the estimator $f\approx u_e/(2\delta)$ works for a certain class of instability wherein the boundary layer acts as an acoustic wave guide. Other classes of instability would have different scaling.

The frequency alone does not tell you anything about the likelihood of transition.

Yes, hypersonic flow. What does it tell me then? I notice my plate has a larger boundary thickness across the length but the cone has a larger frequency. What can I conclude from this?

 

[boneh3ad]

Yes, hypersonic flow. What does it tell me then? I notice my plate has a larger boundary thickness across the length but the cone has a larger frequency. What can I conclude from this?

Like I said before, essentially nothing. You can conclude that cones have thinner boundary layers for a given size than flat plates, but we knew this already. They're mathematically related by the Mangler transformation.

Also, like I said, the boundary layer doesn't have a characteristic unstable frequency. It has many.

 

[shreddinglicks]

Like I said before, essentially nothing. You can conclude that cones have thinner boundary layers for a given size than flat plates, but we knew this already. They're mathematically related by the Mangler transformation.

Also, like I said, the boundary layer doesn't have a characteristic unstable frequency. It has many.

I wonder why I was given this equation. Thanks for taking the time responding to me.

 

[boneh3ad]

I wonder why I was given this equation. Thanks for taking the time responding to me.

I couldn't tell you. It could have been from someone with only a passing familiarity with high-speed boundary-layer transition (i.e. most people in the high-speed aerodynamics community).

Ultimately, the boundary-layer stability problem can be viewed as a very complex nonlinear dynamic system with a transfer function between the leading edge and some downstream point. It selectively amplifies and attenuates frequencies across the spectrum from 0 to Kolmogorov. If you feed it (via free-stream disturbances interacting with the surface) an input spectrum, the output at a given point is determined by that transfer function that comes out of the stability problem. In many cases, there are multiple separate bands of unstable (amplified) waves, not just one.

This is sounding technical enough at this point that I have to imagine this is either school work or a task assigned to you by a supervisor of some kind.