Talk:Busemann's Biplane

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[edit] About the diagram

About the diagram. The waves emanating from the wedge peak and its reflection at the symmetry plane, they are expansion waves, not shock waves. Butakun 12:00, 31 December 2006 (UTC)

As far as I know (and I'm not an expert) expansion fans consist of shock waves.WolfKeeper 21:56, 31 December 2006 (UTC)

No, expansion fans are not discontinuities (though often depicted as a fan of discrete lines) and isentropic, unlike shock waves. Across shock waves, static pressure rises and total pressure decreases (thus increase in entropy), whereas across expansion waves, static pressure decreases and total pressure remains constant.--Butakun 00:52, 1 January 2007 (UTC)

Some comments,

1. The waves emanating from the edges of the vehicle are oblique shock waves and not expansion waves. They are formed because the flow is being turned into itself. Other way to look at is, since the area is decreasing from front to middle, there has to be a rise in pressure, which is accomplished by shock waves. If the vehicle is moving too fast slow, the shock waves will become more and more normal to the flow till they form a normal shock.
2. How the waves get reflected is a different matter. If the vehicle is flying at design speed (as indicated in the caption of the figure), and the shock waves are incident precisely on the throat, they will get reflected as expansion waves and one will see an expansion fan. The figure needs to be corrected for this. At other speeds depending on where the shocks waves hit the vehicle, they may get reflected as shock waves or expansion fan.
3. One may look at an expansion fan as a collection of infinite number of shock waves. They are very weak shock waves and are referred to as Mach waves. Thinking of these waves as shock waves can lead to confusion and should be avoided, but is not incorrect. Across a Mach wave the stagnation properties do not change, the static properties change by small extent and may increase or decrease. A collection of many Mach wave at one point will lead to a normal or oblique shock (this will happen is the Mach wave converge). If the Mach waves diverge they will form an expansion fan.

I hope this helps. Myth (Talk) 08:47, 30 January 2007 (UTC)

1) The first part I agree with. What I was referring to was not the leading edge shocks. However, as for the second part, I do not agree completely. If the throat area is sufficient enough to swallow the mass flow, the oblique L.E. shocks will be weak shocks, meaning that the shock angle will decrease as Mach number increases. 3) I agree also, but I used the word "shock" simply to mean compression discontinuity, but yes, Mach wave is an infinitesimally weak shock of which Prandtl-Meyer fan is made.--Butakun 11:37, 30 January 2007 (UTC)

I agree, I meant to say slow for as Mach number decreases, the shock will become more normal to the flow. I have made the appropriate corrections. Thank you. Myth (Talk) 12:05, 30 January 2007 (UTC)

I've updated the file slightly, it's possibly an improvement. Ideally we would replace it with a still or something from the Japanese groups simulation; but we would need to negotiate a license- I haven't tried that as yet. Mostly my aims for this picture are so that people get atleast a vague idea what's happening, how the cancelation occurs, but it's still very half-arsed.WolfKeeper 08:59, 30 January 2007 (UTC)

If anyone has a better diagram, feel totally free to replace it.WolfKeeper 08:59, 30 January 2007 (UTC)

[edit] No wave drag!

I am not sure if it is correct to say that the vehicle produces no wave drag. Any vehicle traveling at supersonic speed will produce a wave drag (unless it is straight line, which aligns itself with the streamlines). The reason we observe wave drag is because across a shock wave (both normal and oblique shock) there is drop in the stagnation pressure. This loss can be related to the wave drag that a vehicle produces. Myth (Talk) 10:07, 30 January 2007 (UTC)

Busemann's biplane only works if you align it with the stream. The theory says that there is no wave drag, and the theory and the biplane have been successfully tested in a wind tunnel.WolfKeeper 16:25, 30 January 2007 (UTC)

The external link provided in the article mentions that the configurations they tested had lower wave drag. They also say that the wave drag is minimized for particular operating conditions. These claims I can agree with. Note that it never says that the wave drag is reduced to zero. The presence of oblique shock is enough to ensure that there will always be some amount of wave drag (maybe small but not zero). Myth (Talk) 21:34, 30 January 2007 (UTC)

You may well be right, but we need a reference I think. Zero is a good minimum(!) They can't show that it does or does not zero out in a simulation anyway.WolfKeeper 21:46, 30 January 2007 (UTC)

The pressure plot shows the variation in pressure on the lower "wing" if we follow the dashed line.

I will see if I can find any references. I didn't know the concept of Busemann's biplane till yesterday. btw even if they had infinite-precision computations, they won't be able to show that the wave drag is zero.

Here are few google results that I found, this and this go to page 59 of the pdf file. Both these references say that there will be no wave drag, however I am not able to understand why. I made the following sketch to show what I understand is happening. Clearly the pressure is higher on the surface BC than on surface CE. If we add up the pressure on the top and bottom "wings", the net component of the pressure will be in the flow direction (i.e. a drag on the vehicle).

The reason as to why the other references are not correct is because they are representing the expansion fan by a single wave, which, IMO, is not correct (unless the "wing" is thin and there is no significant spread in the fan before it reaches the other side). I may be wrong here or maybe making too much fuss about concepts like . Sorry about that, but just a doubt I wanted to get clarified. Thanks. Myth (Talk) 23:30, 30 January 2007 (UTC)

It is not possible to design a vehicle traveling at supersonic speeds to not form shock waves. Myth (Talk) 10:07, 30 January 2007 (UTC)

Well, if you shape it as the biplane then you could. But the shape is highly restricting and gives no lift. Rumour has it that this shape has been tested as a way to silence weird-shaped bullets though.WolfKeeper 16:25, 30 January 2007 (UTC)

I agree, I hadn't though long enough about that earlier. I can think of geometries where you do not have shock waves. But they will require isentropic compression and expansion using Mach waves and also that the compression waves do not converge to a point to form a shock wave. But this is not the case here, where we have oblique shocks from the leading edges of the vehicle, getting reflected as expansion waves. Myth (Talk) 21:34, 30 January 2007 (UTC)