Expert: Mark Janus - 8/24/2004

Question
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Followup To
Question -
I have been modeling various geometries that will be exposed to speeds of 550 knots, at 49°C ambient temperatures near sea level.  This is approximately .79 Mach and therefore I expect to have some degree of viscous heating.  I do not have any prior empirical experience in this flight profile and therefore am looking for a closed form formula that I could use to ballpark what the rise might be.  I am using a CFD tool for my overall 3D geometry study.  Can you suggest a litmus test approach for this?

Thanks
Mike
Answer -
The adiabatic wall temperature for such a case is approximately (this would be true for a Prandtl number 1 flow)...  

taw = tinf + rc*uinf^2/(2*c)      

note: the Prandtl number (Pr) for air is ~.72

taw - adiabatic wall temp (no heat transfer at the wall)
tinf - static temperature of fluid
uinf - velocity of fluid
c - specific heat of fluid (constant pressure)
rc - recovery factor ~ Pr^.333  (for turbulent flow)

hope this helps,
mj
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Followup To
Answer –

Interesting…  I would have thought that the viscosity of the fluid would have played a part.  In addition, I see that both the reference temperature “tinf” and the reference velocity “uinf” are taken at the free stream conditions and do not take localized Mach into account.  I realize that I was only looking for a litmus test, I was only hoping that it would reflect more of the in situ conditions.

Thanks again,
md


Answer
The fluid viscosity does play a part (in the recovery factor)....

The Prandtl number is the ratio of viscous dissipation to thermal conduction....  so for standard air that is nearly .72

Your Mach number is not that high for heating "problems"

mj