Transonic flow over a bump in a channel

[AlexNeo]

Hi!!

i am doing a CFD simulation of transonic compressible flow over a small bump in a channel. is there someplace i could find the explanation for the different phsical phenomena associated with this flow? i need to explain the the physics behind the results.

i looked in the books on compressible flow but no luck!

thanks!!

alok

 

[eriksen]

Hi AlexNeo,

Which fenomena are you interested in?
As I used to do research on turbine blades one of the fenomena I recorded was the Von Karman vortex street in 2D subsonic and transonic flows. Due to the pressure and velocity of the trailing flow the vortices were differing in size and frequence. At a fixed velocity and pressure pictures (holograms) were recorded to document the density variation in the centre of the vortices and their development/initiation at the trailing edge.

If these results have your interest please write me and try to include more details on the kind of other fenomema you would like to have described.

Best regards,

Eriksen

 

[AlexNeo]

thanks eriksen!!

air enters the channel at M=0.675 in the first case. there is a bump at the center of the channel. mach number increase over the bump and a shock appears at the bump-top.
so i wated to know the phsysis that leads to this shock. also when air enters the channel at M = 0.5 it accelerates over the bump but does not go to supersonic speeds and there is no shock in the flow. so whats happening there?

so i basiccally want to know the what happens when the air encounters the bump, the physics behind the flow of air over the bump and finally the physics of the shock.
thanks again!!
alex

 

[AlexNeo]

the bump is on the lower wall at the center of the channel

 

[Haf]

When channel flow encounters a "bump" the flow tends to accelerate, as you noted. The degree of acceleration depends on the geometry of the bump. A phenomenon closely related to this is a transonic airfoil. In vehicles that travel at high subsonic speeds, the flow over the wing accelerates to supersonic speeds and a normal shock is formed on the wing. Try doing some research on transonic airfoils; you may have better luck there. I can tell you that there are plenty of articles out there on both transonic flow over bumps and transonic airfoils. Try doing a literature search (text books are a good start, but probably won't have detailed information). The more simple articles will likely be old (I would guess 1960's to 1970's).

In terms of the physics, the phenomenon is relatively simple. When the flow encounters the bump, it accelerates, and depending on the freestream Mach number, the flow may become supersonic at a Mach number slightly higher than unity. Bumps, depending on their geometry, accelerate the flow only slightly, so the Mach number of the incoming flow must be relatively high to lead to supersonic flow. Since transonic flow is relatively unstable, a shock wave forms readily, and it forms at the most stable place: the top of the bump. This makes sense, since the boundary layer is likely to separate at this location (and since the flow will decelerate after the bump as well), thus making it a "preferred" and relatively stable location for the shock wave.

Haf

 

[eriksen]

Hi AlexNeo,

Haf has got a very good explanation there.
When it comes to up-to-date articles on transonic flow try and contact the Von Karman Institute in Belgium. Maybe they even have a reference to documents on their homepage (haven't been there for a while ...)

http://www.vki.ac.be

Address:
Von Karman Institute for Fluid Dynamics
Chaussée de Waterloo 72
1640 Rhode-St. Genese
Belgium

Have fun!
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Eriksen