How cold can you make a supersonic stream of air?

Factual Questions
1

Inspired by the thread about holding an ice cream bar in front of an air conditioning vent. My first thought reading that thread was that whatever cooling benefit there was of the cool airstream, it would eventually be overcome if the air velocity got high enough. Think of spacecraft re-entry, or high speed planes like the SR-71 needing to cool down after being heated by a supersonic airflow around their frames.

But could the air conditioner be really ramped up? Or how much could it be ramped up? Perhaps the work of accelerating air to high speed necessitates heating that air to above ambient air temperature?

So, if you want to make something like an combination of air conditioner and jet engine, what are the limits of how cold you can make the exhaust and how fast you can blast it out?

2

The first thing I thought of when I read your post was a vortex cooler. They can get pretty frikken cold. We use them for spot cooling in industrial processes. The downside of them is that they are annoyingly loud.

I couldn’t remember off the top of my head exactly how cool they can get (other than really cold). Wikipedia says -50 °C, which sounds about right to me.

3

What heats the air during reentry and with the SR-71 is friction. I’m not sure the velocity of the air matters in an ideal situation. In the real world things get quite complicated.

4

So what? I imagine there would be a lot of friction in a machine forcing air through an ejection port at very high speed.

5

I see velocity as a factor in a formula, but I don’t see any way to isolate it in a way that would determine there was any limit to it, or any limit to the temperature (excepting of course Absolute Zero) if the velocity was unlimited.

6

No. Compression of the air is what heats it during reentry.

7

Assuming you can produce a supersonic stream of air in a vacuum it shouldn’t get hotter once it’s ejected from whatever device is propelling it. Using a nozzle for this purpose should actually lower the air temperature from whatever it was entering the nozzle. I’m guessing the minimum temperature is limited only by the means of accelerating the air in the first place.

8

This.

You can calculate the stagnation pressure for a given velocity as density * V[sup]2[/sup]/2. If density is in kg/m^3 (1.2 for air), and velocity is in meters per second, then your stagnation pressure is in Pa.

You can then calculate the stagnation temperature using the thermodynamic relations for an adiabatic process:

P1[sup]1-gamma[/sup]*T1[sup]gamma[/sup] = P2[sup]1-gamma[/sup]*T2[sup]gamma[/sup] (for air, gamma = 1.4)

subscript 1 denotes ambient conditions, subscript 2 denotes stagnation. Use absolute values for pressure and temperature.

The air is really only in stagnation near the leading edges of an object, which is why things like the nose cone and wing leading edges on the shuttle (and the blunt bottom of the Apollo capsule) had to tolerate the highest temperatures.

If you do the math, you find that you need to get to pretty high speeds before you achieve significant temperature rise. ISTR from the recent eco-cooler thread that a temperature change of a few degrees requires a velocity on the order of a couple hundred MPH. The exponential relationships involved mean that as you get up toward the speed of sound (or multiples of it), you start getting into temperatures that can fry things.

9

Yes, the reality of this scenario is the coldest temperature of super-sonic air depends on the machine that makes the air super-sonic.

Compression is a one of the many forms of friction in this situation. Add in viscosity and boundary layer frictions and it all adds up.

The ideal I’m thinking of is 100 K air at 2,000 km/hr in an environment of 100 K air at 2,000 km/hr. Here we would have no compression or boundary layers and a fairly low viscosity, at least until the air’s components start to liquify.

“My first thought reading that thread was that whatever cooling benefit there was of the cool airstream, it would eventually be overcome if the air velocity got high enough.”

The water molecules absorb the heat energy, and it can be said that the water molecules “contain” the energy. The air flow drives these water molecule away, with the energy contained in them. This is the cooling effect of our ice cream, pretty much the same as humans sweating on a hot day, the human is cooler in a breeze because the energy is driven off with the water molecules. The stronger the breeze, the better this cooling effect. I don’t believe there’s an upper bound to this, ideally, however in a super sonic air stream I would think the ice cream and cone would be driven off no matter the state it’s in.

10

Actually it is the other way around, the supersonic air gets extremely cold. I spent much of my life working in NASA wind tunnels. Gratuitous self promotion: I’m on page 54 of “Wind Tunnels of NASA”. Not because I did anything special, the photo just happened to make the book.

Anyhoo, to accelerate air (or other gases, as we shall see) beyond the speed of sound, it is necessary to first constrict the flow. Every SS wind tunnel has a point of the smallest cross sectional area, called the throat. No matter how much pressure you give to the air upstream of it, the throat remains at exactly the speed of sound, and has a shock wave across it. As the air expands downstream of the throat, it accelerates and cools.

For an example, the 10 foot by 10 foot tunnel I worked in the most has a throat that is barely constricted at low speeds, but is only 16 inches wide at the full speed of Mach 4.

http://turbo.mech.iwate-u.ac.jp/Fel/turbomachines/stanford/images/tunnel_schematic.gif

Scientists always want higher testing speeds, especially in the era of orbital flight and beyond. Alas, we cannot generate such velocities (continuously), it is physically impossible. Why?

If we use air for the wind tunnel, it cools down so much it liquefies. So, we preheat the air with a pebble bed heater. Now the velocity is higher, but it still liquefies.

Using a gas with the lowest condensation temperature (helium), heating it to the point of material failure of the structure and expanding as much as possible, the velocity is still not as high as rockets achieve in the upper atmosphere.

So we start with 3000 degree F helium and end up with -450 degree helium. And even this design is a “blow down” tunnel with a test time of less than a second.

There are higher speed tunnels, but they only give a fraction of a second testing time. Some fire the tiny test vehicle counterflow to the air stream using a gun. Others, like LENS-X are “burst tunnels”, pressurized to extreme temperatures and pressures and accelerating after a diaphragm is ruptured.

LENS-X can hit Mach 25, maybe 30. It starts with hot helium and generates 20,000 psi by a series of diaphragms. It cost hundreds of thousands of dollars for a test series.

The ultra fast wind tunnels actually use an explosion to generate a millisecond shock wave. Then the tunnel is destroyed and a new one built.

Dennis

11

I have never used experimental set ups this large- instead, my experiments with enormous pressure differential were for another purpose: freezing of molecules in low energy states such that their electronic states and geometries could be studied. The set up was a high pressure solution/liquid that has a single pore opening into a vaccum, the molecules go through one at a time and their rotational and vibrational degrees of freedom are partially (ideally, entirely) converted to translational energy. The goal is to achieve as close to 0K as possible to simplify the light absorption spectra. Similarly, the jet of molecules would go from room temperature to -273˚C in the stream/jet.