[MachZero]

I have a sort of canonical problem and am looking for some guidance from the heat transfer community.

I have a model involving a wing where the surface of the wing is maintained at a temperature above ambient conditions. It is a constant temperature. When I run my simulation I post process and look at heat flux. My mechanical engineering colleagues indicate that the heat flux should ALWAYS be maximized at the exact same location as the stagnation point because the boundary layer is thinnest. I was initially thinking that it would not be maximized at this point because the air velocity is slow (zero to be exact).

I ran the simulation at various angles of attack from -7 to 7 deg. In some cases the max heat transfer is at the stagnation point where as in others it is not.

Are there any experts out there who can shed light on this? It appears both my colleagues and my intuition were wrong and I want to understand.

Please advise!

[agd]

I don't consider myself an expert but I will share what I can. First, the fluid temperature at the stagnation point will be higher than anywhere else in the flow, so the thermal gradient between the fluid and the constant temperature surface will be the largest. Additionally, the convective velocity in the fluid is not very large near the stagnation point, meaning that more energy will flow into the structure at the stagnation point than anywhere else. Second, surface heat transfer calculations using CFD typically require finer grids than those used for lift/drag calculations. If your y+ is not on the order of 0.1 then I would be concerned that your heat flux calculations may not be accurate enough. That number is just based on experience of coworkers who have done significant heat transfer work. That's what I have learned over the years. Make of it what you will.

[FMDenaro]

Just as my curiosity, you are solving viscous flow, I suppose, how do you define the "stagnation point" in such case?

[LuckyTran]

Originally Posted by MachZero

...that the heat flux should ALWAYS be maximized at the exact same location as the stagnation point because the boundary layer is thinnest. I was initially thinking that it would not be maximized at this point because the air velocity is slow (zero to be exact).

Indeed the heat transfer tends to be the highest when the boundary layer is thinnest. The velocity is zero on all solid surfaces due to no-slip... The reason higher air velocity tends to higher heat transfer is because you are talking about the velocity not on the wall but away from the wall, and a higher velocity means the BL is thinner for the same freestream conditions.

It is quite easy to verify empirically that the heat transfer is highest near the stagnation point. Just get in a hot tub.

Originally Posted by MachZero

I ran the simulation at various angles of attack from -7 to 7 deg. In some cases the max heat transfer is at the stagnation point where as in others it is not.

Did you check where the new stagnation point is when you changed the angle of attack? It can also move. The stagnation point is not necessarily the tip of the nose.

[MachZero]

Thanks for the advice. Not sure why my stagnation location and peak heat transfer are not matching. My stagnation point isn't changing when I switch turbulence models but my convective heat transfer does, as well as the location of peak values. Very weird.

Currently using low y+ mesh but not quite down to 0.1.

[FMDenaro]

Originally Posted by MachZero

Thanks for the advice. Not sure why my stagnation location and peak heat transfer are not matching. My stagnation point isn't changing when I switch turbulence models but my convective heat transfer does, as well as the location of peak values. Very weird.

Currently using low y+ mesh but not quite down to 0.1.

Again, how do you compute the stagnation point?

[MachZero]

I actually missed two of the responses when I replied. My mistake.

Stagnation point does seem to move with aoa. I am locating the stagnation point by looking at where the velocity in freestream goes to zero and where the shear on the surface is zero.

And yes I agree for the hot tub and an impinging jet that stagnating the flow will increase temp but the question here is specifically to do with an airfoil. Do they have to align. I know as flow hits the wing and stagnates, especially at any appreciable aoa, it has to really accelerate around the leading edge. Therefore locally the velocity spikes and the temperature drops. The question is, is it a hard rule that they must be co located or can these local increase in velocity and decrease in temp cause the max heat transfer to not be co located.

[FMDenaro]

Originally Posted by MachZero

I actually missed two of the responses when I replied. My mistake.

Stagnation point does seem to move with aoa. I am locating the stagnation point by looking at where the velocity in freestream goes to zero and where the shear on the surface is zero.

And yes I agree for the hot tub and an impinging jet that stagnating the flow will increase temp but the question here is specifically to do with an airfoil. Do they have to align. I know as flow hits the wing and stagnates, especially at any appreciable aoa, it has to really accelerate around the leading edge. Therefore locally the velocity spikes and the temperature drops. The question is, is it a hard rule that they must be co located or can these local increase in velocity and decrease in temp cause the max heat transfer to not be co located.

Obviously, the first issue is to give care to the grid refinement. But I think you should consider better the definition of stagnation point as it cannot be defined on the airfoil but on the inner of the BL. It could be a cause of error.

[MachZero]

It cannot be defined on the airfoil? That's a new one for me. I thought if I looked at shear and found where it is zero or where pressure is maximized. Perhaps fundamentally I can see what you are saying but for practical purposes?

I'll reexamine my grids today however I remember something like 20 cells around the wrap between the stagnation and the max heat flux. So I believe that is fine.

I also found this same trend in two different cfd codes now. With different meshes.

[FMDenaro]

Originally Posted by MachZero

It cannot be defined on the airfoil? That's a new one for me. I thought if I looked at shear and found where it is zero or where pressure is maximized. Perhaps fundamentally I can see what you are saying but for practical purposes?

I'll reexamine my grids today however I remember something like 20 cells around the wrap between the stagnation and the max heat flux. So I believe that is fine.

I also found this same trend in two different cfd codes now. With different meshes.

Over an airfoil, the velocity is zero (for fixed airfoil) everywhere by definition of no-slip condition for viscous flows. And to define a stagnation point where a stagnation pressure is reached by the static pressure, you should invoke the Bernoulli equation that is not valid in the BL. Therefore, to define a "stagnation point" in the fluid, that is the inner region of the BL, you should be careful.