Viscous Heating Problem (reality check)

[dehnemi]

I have been trying to solve several viscous heating problems using a CFD tool. I do not have a lot of wind tunnel experience and therefore do not have any way to “litmus check” the results I have been getting so far. The idea is to prove that one shape is better than another with respect to the skin heating. The only formula I have found so far from Frank Whites text is

taw = tinf + rc*uinf^2/(2*c)

taw: adiabatic wall temp
tinf: free stream static temperature of the air
rc: recovery factor ~ Pr^.333 (for turbulent flow)
uinf: free stream speed of the air
c: specific heat of air

This however is only good for Prandlt numbers of 1 and it does not consider the local Mach numbers or the viscosity changes. I’m really only in the transonic range ~.8 Mach.

1] Does anyone have a rule of thumb calculation so that I can build some confidence in the CFD results.

2] or does anyone have empirical experience of what the ballpark temperature rise would be due to viscous heating for Mach .8, Total Temp 49°C airflow. I’m getting a 7°C rise where as the above equation would indicate a 36°C rise.

Thanks MD

 

[aviat]

This site shows one way to do it, which is finding the total temperature giving the SAT or OAT. It is the stagnation temperature on the leading edges (dry), and would not be the same for other parts of aircraft.

http://web.mit.edu/16.unified/

http://www/FALL/thermodynamics/chapter_6_files/chapter_6_PRS_Questions/Q6.11.html

http://mtp.jpl.nasa.gov/notes/sat/sat.html

TT/T = 1+ (?-1)/2*M^2.
Where TT = Total temperature, TS = SAT or OAT, M = Mach number
If you use ? = 1.4 for air, the formula simplifies to:
TT = T * (1+.2* M^2)
I get a ram rise of 36 with a TT of 49°C (322.15K) with the formula of
TS = TT/(1+.2*M^2) 322.15/(1+.2*.8^2) = 285.6 (12.45°C ), 49-12.45 = 36.55°C