Viscous Heating Problem (reality check)
Viscous Heating Problem (reality check)
(OP)
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
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
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RE: Viscous Heating Problem (reality check)
http://web.mit.edu/16.unified/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