Dear sir:

I would like to simulate the compressible microchannel flow(1.2 micrometer heigh, 3000 micrometer long, gas constant=296.7, absolute viscosity=1.85e-5, ratio of specific heats=1.4, the working fluida are nitrogen). The outlet Knudsen number and outlet pressure are 0.055 and 100.8kpa, respectively(experimental data by Pong). The numerically result are compare with Numerical(Chen et. al and Dr. Raju) and experimental data(Pong et. al). But after several tests I found that the outlet Knudsen number seems not equal 0.055.

The outlet density can be solved by using eos: p=rho*R*Tout==>rho=1.082

so, kn=mu*sqrt(pi)/sqrt(2*R*Tout*rho^2)/H==>0.0585

I don't know what's the problem. Has anyone calculated this problem? Please help me. Thank you very much!!

Best regard

Sally Yu

Dear Sally,
if I am right, the Knudsen number is the length of the mean free path of a molecule. You did not measure it directly, right? All exprimental data will contain some error, maybe 5 % (if they are excellent).
0.0585/0.055 is 1.064, only 6 % difference. Why do you worry? Did I understand your problem correctly?

Greetings,


Marc

Dear Dr. Marc:

Thank you so much for your reply. Actually, two engineers has calculated this case before. They clear said "outlet Knudsen" is equal to 0.055, and the numerical result seems very similar to each other. So, I'm worry about different outlet Knudsen number may cause large numerical error (such as pressure distribution and slip velocity). Am I using wrong equation for calculating outlet density? Please help me. Thank you very much!!

Best regard

Sally Yu

I think that Kn=sqrt(pi)/sqrt(2*R*Tout*rho^2)*1/H.? It may be helpful to review the article "The fluid mechanics of microdevices-The freeman scholar lecture"-Journal of Fluid engineering, Vol. 121, pp. 5-33, 1999. The difference is due to the fact that a few thermodynamic properties you used is different from those of previous articles, I guess. These are empirical constants and therefore can have slightly different values corresponding to the referencing chart.

Dear Dr. Choi:

Thank you for your help!! Sorry to disturb you again. Did you ever calculated this case (microchannel flow)? If I want to calculate wall slip velocity (u=Kn*du/dy). Which Knudsen number I should use(centerline Kn or not?)? Please help me!!

Best regard

Slly Yu

Centerline Kn number is appropriate. If the flow is near equilibrium in the bulk flow region(slip flow), this value(Kn) is easily obtained. I'm not a PhD, now. The degree will be obtained February, 2003.

Regards.

H. Choi

Dear Choi:

Thank you for your kindness!!! Thanks!!

Best Regard

Sally Yu