# Estimating drag using only a temperature profile

1. Apr 27, 2016

### OrangeDog

I was reading this thread on Reddit about estimating drag using only a temperature profile. I was reading the responses, and I feel like most of them are missing something. Since this forum is more science-focused, what do you guys think?

In theory, if you could measure the temperature field perfectly, you would have enough information to know some of the terms in the energy portion of the N-S equation. NASA provides a good picture:
https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html So essentially, you'd be able to know the E terms (using cp*T), the q terms (the heat flux), but you could not determine the shear stress, or the velocity components, u,v,w, and the pressure field unless you assumed P=rho*R*T.

This leaves a few cases:
If you had a body with no separation, you might be able to measure the heat generated in the boundary layer and compute the velocity profile. For simple cases like the flat plate you can even find exact solutions. From this information you could compute the viscous drag

If you assume P=rho*R*T and neglect viscosity You can figure out the magnitude of the velocity field, since you simply have the advective acceleration of the flow at that point equaling the pressure gradient.

If you a assume 1 or 2 dimensional flow
There might be some special cases where you can get an exact solution.

So overall:
It isn't practical
It can be done only in limited cases
Off the top of my head, I can't think of any way this would work. There are still too many variables involved. It seems to me that the level of complexity required to use a temperature field as the initial conditions required to solve for the flow around a body essentially boils doing to doing a full DNS on the problem, and that is not currently an economical option for vehicle-sized problems (computational time scales with $Re^3$). Trying to find a simpler way to convert temperature into drag other than through the governing equations doesn't seem feasible to me.