Hello folks, I have been studying transonic flows for some time now but there is one question that's always puzzled me. In a transonic flow over an airfoil, say, why does the shockwave occur?

I understand why the flow speeds up as it passes over the airfoil and that the flow eventually exceeds the speed of sound but have never understood WHY a shock is formed.

I know that the supersonic "bubble" will terminate with a shock, across which we have a jump in our flow variables but have never understood the physical reasons for this.

If someone could please point me to some references (preferrably online - I don't have library access at the momemt) then I'd be very grateful,

Many thanks F

Dear Frank,

Shock waves are a result of a balance bewteen non-linear wave steepening and physical diffusion processes. To make the statement clear, note that if you worked with a linear convective equation you would not get a shock. Shocks occur only if the governing equations are non-linear. This can be understood quite easily by taking up the characteristics. For a LCE, these characteristics would be simply parallel straight lines. If the convective velocity is a non-linear function, the characteristics would be non-parallel. At the point of intersection, you would have a graduient catastrophe. There is a steepening of the gradients, and the point where the charcteristics intersect we have multiple solutions which is physcially impossible. Physically translated, there is a series of compression waves, each following wave travelling faster than the other which coalesce and results in a jump in quantities. For an initial smooth distribution, this would amount to the waveform becoming more and more vertical, but cannot overturn. What prevents the overturning and opposes the steepening are the physical diffusion processes existing in nature. Whenever there is a steepening, viscosity tends to smoothen it out and a natural balnce is struck between the non-linear wave steepening, which tries to make the waveform vertical and the diffusive phenomena which tries to smoothen this out. The balance resulst in a high gradient region over a small distance, which is nothing but a shock wave. It is only mathematically that the shock is a discontinuity, physcially it is a high gradient region. This aspect of shock formation is clearly reflected in numerics, when the schemes with low dissipation fails for transonic flow problems.

P.S.: You could refer to Randall LeVeque's book for a nice description.

Hope this helps

Regards,

Ganesh

And here are the pictures

http://selair.selkirk.bc.ca/aerodyna...ed/Page2c.html

http://selair.selkirk.bc.ca/aerodyna...Speed/fish.htm

RoM

I think it is to satisfy downstream conditions, not quite sure

Ganesh gave an excellent response. To add to it, I have a more phenomenological explanation to offer, in form of an analogy.

Imagine cars driving on a freeway with three lanes, and somewhere down the road two of the lanes are merging. If everyone drives reasonably slowly and looks far ahead, they will see the bottle-neck coming way before they get there, and will slow down accordingly. In this situation traffic flow will be smooth. Now, instead, imagine everyone going at insanely high speed, and imagine they are all inexperienced drivers who typically focus their view on a spot right in front of their cars instead of looking far ahead. They won't see the bottle-neck coming until they get there! Consequently, they'll have to step on the brakes to decelerate very quickly, creating the equivalence of a compression shock.

The important thing here is a difference of two speed: The speed at which particles (cars, fluid particles) travel downstream, and the speed at which information travels upstream (how far the car drivers look ahead). Fluid particles in supersonic flow do not feel what's coming up until it's almost too late, because information travels upstream only at the speed of sound, i.e. there is essentially (*) no information traveling upstream in supersonic flow. However, to satisfy the freestream or exit conditions, pressure has to rise at some point, and that happens almost instantaneously just in time (to satisfy the governing equations).

(*) Of course, a particle in a real supersonic flow is not 'completely' detached from everything downstream. It does receive some delayed information creeping upstream inside the boundary layers.

Guys, I have a naive doubt about this thread. I haven't studied Euler problems in depth, so, I will leave here my doubt and let you guide me if my assumptions make sense of not.

we know that if we rise the pressure of the air contained in a bottle, it will reach a state when the air will condense (because the molecules, or fluid particles which get closer). Now, imagine the air flowing at very high speed. In this case, there will be some regions (probably near to some obstacle) where the air will start to compress itself up to some point when it'll start to condense (or at least the fluid particles will get closer and closer). In these regions the density will become much higher than in other ones originating a high gradient in this parameter. Furthermore, in these regions the fluid will disturb itself since it will be modifying the flow path (as it was creating or modifying obstacles to itself). Sometimes it can be witnessed, for example, racing cars and airplanes travelling in regions where the air has high humidity. There are some vapour clouds, or sprays (I don't know the more proper word in English for it) near to airfoils edges.

Is it an example of shock wave being formed? The fluid "compressing itself" while flowing at some high speed.

Would it be a kind of shock wave "in situ" visualization?

p.s.: I know that shock waves are not restricted to these regions that I tried to describe (where we can see the air condensation). It was an example of extreme case but I think that the phenomenon of shock wave formation can be physically described in a similar way.

Renato.

The condensation you're talking about is not necessarily indicative of a shockwave, as it can certainly occur in conditions where the flow is not approaching the speed of sound, rather just undergoing extreme pressure gradients, such as at aircraft wingtips under certain conditions. The condensation effects do occur in sufficiently humid air when aircraft go supersonic... see any of the widely available videos of an F-14 or F-18 going supersonic at low altitude ( like http://www.youtube.com/watch?v=z7SEr1-hy-M ).

lots of people running in the road.the second is faster than te first(but can's be No.1),and the sthird is faster than the second,,,,and you can image that for minutes all people are at a line,we can say this is a shock. OK,come back here, if we take pertabation people disturbed waves as people in air,that's shock!! Good luck F.B.Tian

I think we have to distinguish between some things mentioned in the previous posts: condensation of air, condensation of water, and compression of air.

Compression or expansion is simply air density increasing or decreasing with pressure. Over most of any flow field this occurs smoothly (without discontinuity), so the question "why are there shocks" is really a question on why and how discontinuities (shocks) can appear in compressible flow.

I think it's obvious to anyone that in most aerodynamic situations (including on race cars and fighter planes) we are nowhere near the pressure required for condensation of air!

Water condensation has to do with air temperature. If there's a supersonic flow region present with a temperature low enough for water to condense in humid air, and the temperature behind the shock is large enough to re-vaporize the condensed water, then yes, the sharp downstream border of the "cloud" is a visualization of the shock. However, as Andrew said, not all such condensation clouds are indicators of supersonic flow. Temperature drops in any expansion, below or beyond Mach 1. Those clouds simply show regions of high speed flow and low temperature. If there's a shock or not may be judged by the sharpness of the downstream border of the cloud, indicative of a high temperature gradient.

Actually, for water vapour in air under atmospheric conditions, the region where condensation can be visible is typically supersonic. The (non-equilibrium) condensation process is starts around Mach number unity (it starts ofcourse at a humidity of 100% but is not visible than). These nice pictures of small fog clouds around wings and canopies are a good indication of the supersonic part of the flow.

Bart Prast Twister Supersonic gas solutions

Folks, thanks for the feedback on my question. (and I hope, I'm not disturbing the original question posted by Frank)

Firstly, I'd like to make a slightly correction about my last post:

>> ...it will reach a state when the air will condense ...<

It's not the air that will condense. It should be written that the water molecules in the air (which turns the air humid) that will condense. For chemical computations, anhydrous and clean air is only 21% Oxygen and 79% Nitrogen). Ok... it'll not change our original discussion.

Regarding the condensation, I was not thinking about the temperature influence, I thought about the compression itself. An airplane wing "cutting" the air in a supersonic velocity will surely compress the air at the border of the wing (this is nicely described in that movie posted by Andrew). In this region the water vapour molecules will get closer until they condense. It's also clear that the density will turn higher in these regions, and, of course, the density gradient will get higher accordingly. Moreover, the amount of water in the air (the humidity) will make this phenomena (the condensation) easier or harder to happen in a visible way. It's not hard to imagine also that the water vapour condensation will change the air path in some sense (the phenomenon being propagated). Metaphorically: "A supersonic airplane drags a "wall" of water spray"

In other words, something travelling in a high velocity will compress the fluid in some way that the fluid "doesn't have chance to be uncompressed" (the phenomenon is almost instantaneous and the fluid can't disperse the compression wave), in these regions the air molecules get closer and denser (here, I'm not concerned if they are condensing or not), this phenomenon confined in thin layers will result in regions with high density gradient, which I see as shock wave being formed.

My concern about this phenomenon and the original thread is that if these regions could be, surely, considered as regions where we have shock waves being formed or not.

As I'm not an aerodynamicist, I'm only trying to use my physical sense ;o) (no equations, no theories, only trying to see the nature of the phenomenon)

Does it make sense? If so, I think it's a very intuitive way to understand how the shock waves are formed.

Renato.

>condensation process is starts around Mach number unity

independent of free-stream temperature, free-stream pressure, and humidity? why would that be, i.e. what's the physical mechanism behind it that requires supersonic flow for condensation?

>he air in a supersonic velocity will surely compress the air at the border of the wing (this is nicely described in that movie posted by Andrew). In this region the water vapour molecules will get closer until they condense. It's also clear that the density will turn higher<

Although this may not be your point, I'd like to clear up some misconceptions:

Look at the movie again. What you are seeing is condensation of water in expanded (not compressed) high-speed flow, terminated by a shock. Condensation happens there because the temperature in those regions is low (so are pressure and density). Compressed flow regions are hotter than the free stream, too hot for condensation, regardless of the increased pressure.

>Metaphorically: "A supersonic airplane drags a "wall" of water spray"<

Metaphorically maybe, but not really. It sure looks like that, but the water doesn't follow the airplane around. The flow field around the wing continuously condenses and re-vaporizes "new" water.

Interesting..., It's seems that the shock wave formation really has something related to pressure, temperature and the cloud formation according to this wiki topic http://en.wikipedia.org/wiki/Sonic_boom

paraphrasing the wiki topic

"...When an aircraft is near the sound barrier, *an unusual cloud sometimes forms in its wake*. A Prandtl-Glauert Singularity results from a *drop in pressure*, because of shock wave formation. This pressure change causes a sharp *drop in temperature*, which in humid conditions leads the water vapor in the air to condense into droplets and form the cloud..."

I guess the wiki shock wave topic ( http://en.wikipedia.org/wiki/Shock_wave ) completely answers the Frank's question

Ofcourse it's not idependent of free stream conditions. But around typical (atmospheric) conditions (1 bar, 300K and humidity > 60%) wil result in a VISIBILITY of the condensation around Mach number unity.

Bart

[M MOHSIN]

i want to study cfd analysis of air condensation over the wings at normal flow velocity.
kindly suggest me the appropriate Fluent settings.
Looking Forward
Thanks
Aerospace Engineer

[Antanas]

Originally Posted by M MOHSIN

i want to study cfd analysis of air condensation over the wings at normal flow velocity.
kindly suggest me the appropriate Fluent settings.
Looking Forward
Thanks
Aerospace Engineer

There's ANSYS Fluent forum. You'd better ask there.