I'm now doing computations of the viscous flow over airfoil NACA0015, solving laminar Navier-Stokes eqs. The problem is I can't get steady solutions, even at fairly low angles of attack, such as 1.25deg. The freestream Ma is 0.2, and Re based on the airfoil chord is 1,000,000.

Could anyone give me some suggestios about the physical aspects? Do there really exist steady solutions below static stall angle of attack? Would a turbulence model (such as B-L model) be helpful? I also can't find experimental data of CL-ALPHA about airfoils, could you give me some references? Thanks a lot.

In my computaion, the flow always becomes separated at the trailing edge. And once it separates, vortices will form, and shed into the wake. Thus the flow becomes unsteady, whether viewed from the flowfield contours or the CL-t curve.

What's the real physical phenomenon? Are there anyone who also have similar problems as mine? Any advices would be appreciated. Thank you.

Well, you are trying to solve a flow which cannot really exist. At a Re-number of 1 000 000 there will be laminar to turbulent transistions on both surfaces (initially triggered by laminar separation). A turbulence model will help, but none of the mainstream CFD turbulence approaches are going to calculate the transition correctly for you. Experimental data are summarised in the classic work by Abbot & Van Doenhoff, but not at 1e6 Re number.

Really thank you, Charles. Thanks for the discussion ,and thanks for recommending the book. I'll try to find and read it as soon as possible.

As I have worked on this problem for some time, I also considered the effect of Re. In fact, I did another computation using Re=1e4, and still failed to reach a steady solution. My guess, drawn from my computation, is that there might not exist a steady solution with separated zones above the airfoil. That is, once the flow separates, it becomes unsteady. However this is of course contradict to what is described in the textbook, about the static stall process of airfoil. To make things worse, under any Re and angle of attack, the flow computed is separated, thus unsteady, which makes me not able to obtain the CL-ALPHA curve before static stall.

I don't know where I am wrong and how I can work it out. Could you give me more suggestions? Thanks again.

For flows at low angles of attack the flow will always "separate" at the trailing edge...this is what the textbooks mean when they say vorticity is shed into the wake when they are describing problems which are dealt with using potential flow theories. For potential flow problems Kelvin's theory says that the time rate of change in circulation around a close curve consisting of the airfoil an it's wake must be zero...therefore a change in airfoil circulations prompts an equal an opposite circulation shed at the trailing edge into the wake.Eventually,if the flow is a steady one(which for potential flow usually means that the airfoil is not undergoing anytype of time dependent plunging,pitching rolling,etc) this process equilibrizes and the flow becomes steady. Now I don't know much about NS simulations but if you want to make sure that your model itself is ok I would probably turn off any turbulence modelling(if it's possible for you to do this) and attempt to just predict some classical Cl vs alpha curves. For flows at low angles of attack(like 1.25) there shouldn't be any separation over the airfoil surface itself and you should be able to predict the Cl vs alpha curves. If this works then perhaps you have a problem with the turbulence model.