Knudsen numbers

[Hangaround]

Now just after I felt I was getting a grip on the Reynolds number concept, I found a reference to the "Knudsen number" and them I can't find good information about anywhere. Can anybody share information about them? What is it, why is it, and do we have to consider them at our low Reynolds ?

Regards

[raptor22]

THe knudsen number is a number relating the ratio of cottage cheese volume to curd amount.

It was invented by Mr. Knudsen for his cottage cheese company. He rated knudsen numbers as the following:
1-5: giant curd
6-10:large curd
10-15:medium curd
15-20: small curd.

The importance is that only small curd cheese can be painted onto a wing and dried to make an effective turbulator. ANd turbulator are useful to improve low reynolds number section performance.

--Alex

[Hangaround]

No thats's just cheesy ..

A little more googling and I found:
From http://roland.lerc.nasa.gov/~dglover/dictionary/k.html

"A number used to describe the flow of a low density gas, equal to the ratio λ/l where λ is the mean free path of the gas molecule and l is a characteristic length, such as boundary layer thickness, or apparatus dimension."

I don't get it, "free path of the gas molecule" this got something to do with density in the boundary layer ? Perhaps is it more interesting for high velocity flight where compression is a bigger issue ?

Regards

[peejay]

Hi

This is a measurement of how valid the approximation of continuity is for a gas - for Knudsen numbers greater than one, a gas molecule will on average travel further than the characteristic length before it scatters from another molecule. It's the limit at which the usual approximations of fluid mechanics stop working reliably - and you need to treat the gas as a bunch of particles instead of a continuous fluid.

The mean free path of a gas molecule at atmospheric pressure and room temperature is really small (measured in fractions of a micron) so I wouldn't expect this to be relevant for the type of conditions an aerofoil normally lives in. As its proportional to Temp / Pressure, it might be important in space where pressures are really low - hence the mention on NASA site I guess.

Just found this section - I've been trying to find a use for my PhD in Physics for the past 5 years - maybe this is it ;)

Phil

[peejay]

Just been doing some more trawling around on this subject... whetted my appetite.

From what I've found on various sites on aerodynamics, this stuff matters for hypersonic flight... breaking the sound barrier in a big way. Still looks like it's not likely to be important for model flight.. or have you read differently?

Phil