Is there vortex shedding after the airfoil ??

In several papers, their results showed that in this case, there was no vortex street. And a paper stated that the critical Reynolds number is 2200.

But the result has vortex street. And I used fluent to simulate this case and set T=300K speed of sound, c = 347.21439 m/s Re = 2000 farfield Mach number 0.85Mach farfield speed, U = 0.85 *c = 295.13223 m/s

constant viscosity mu = density*U*L/Re

= 0.8672 * 295.13223 * 1 / 2000

= 0.12797

There is vortex street!

If the airfoil is to suppose to fly in the air and carry passengers... You are way off the mark!

The FLOW Reynolds Number of an airfoil should be 10^5 to 10^12 or so. (millions/billions, etc.)

First, do a sanity check on your calculations... Your calculations give a viscosity value that is higher than treacle, which tells us that you must be doing something wrong!

Now assuming viscosity of air is 1.8x10^-5 or so... this would actually give you a Reynolds number of 1x10^10 (which is fast but not unreasonable)

I think you are confusing the "2200" Reynolds number figure with either the "critical Reynolds number of pipe flow" (a classically quoted figure in fluid mechanics books), or the "transitional Reynolds number2 which tells you where the flow will become turbulent from the leading edge. (Assuming this to be the second then... the flow becomes turbulent after about 2mm from the leading edge, which sounds plausiable).

Now, flow around a cylinder, gives you a beautiful vortex sheet at a FLOW Reynolds number of 200. Assuming that you are using the chord and not the thickness for your length scale, and that the thickness to chord ratio is around 10:1. Then a FLOW Reynolds number of 2000 would give you very similar flow pattern.

Iain