Total temperature, static temperature or recovery temperature as drivi

[novis76]

Hello, I doing a thermal expansion analysis on a nitrogen supply line for a expansion tank. I am doing two calculations. One in hot conditions and one in cold conditions. The hot temperature is known and is no problem. The problem is the cold case.

The system consists of a nitrogen tank of approx. 6 bar(a) / 10 deg C. After this there is a valve that is followed by a DN100 outlet pipe that connects to the expansion tank. If the valve is fully open and the expansion tank exit valve (large compared to the first valve) is also fully opened the first valve is choked and there is a flow of approx. 1.78 kg/s through the pipes (valve = ball valve is approximated with nozzle of D=40mm). Assuming neglible pressure loss in the outlet part this corresponds to about 189.83 m/s. With no change in total temperature the static temperature in the pipe should be

(273.15 + 10) - 189.83^2/ (2 * 1041) = 265.84 K = -7.31 deg C

My first thought was to use this temperature. However then I came across this page

http://me.queensu.ca/courses/MECH448/documents/MECH448_AerodynamicHeating_Sept_2010.pdf

that says that the temperature on the surface will be heated up due to the no slip (aerodynamic heating) of the surface to almost the total temperature (recovery factor = 0.89). My intuition says that i should use the static temperature (cold) but I am not sure. Can somebody please help me? Should I use the static temperature or the total temperature in my calculations?

Thanks

 

[ione]

You should always consider the actual temperature, which will be something between stagnation temperature and static temperature. Now the recovery effect, due to aerodynamic heating, increases as velocity increases (for subsonic flow aerodynamic heating won’t have such an impact). In conclusion and following a conservative approach I would go with the static (the lower) temperature.

 

[novis76]

@ ione

Thank you for the reply. However, I am also interested in this question beside my task at hand (so the conservative value isn't "good enough" ). If the recovery factor is 0.89 then the wall temperature, assuming isolation on the outside, is:

(273.15 + 10) - (1 - 0.89)*189.83/(2 * 1041) = 281.26 K = 8.11 deg C

Is this a more correct value? I have always thought that the pipe would be cool when exanding it through the valve but (10 - 8.11) = 1.89 deg C isn't that much. I also came across this question that says that as long that the pipe is adiabatic the static temperature is measured if the temp gauge is mounted flush with the pipe. Is this incorrect?

http://en.allexperts.com/q/Aeronautical-Engineering-1809/Temperature-measurement.htm

Thanks

 

[ione]

You’re mixing up things. Whether the temperature of a gas stream after an expansion increases or decreases depends on the Joule-Thompson coefficient of the gas.

The temperature increase due to aerodynamic heating is another matter, as it is related to viscous forces which act on the pipe surface producing a skin friction effect, which does not implies the temperature of the bulk of the stream is the same as that at the pipe surface.

To measure the static temperature of a gas stream, the sensor should move at the same velocity of the gas stream (no relative velocity between the stream and the sensor). Practically it’s not possible to carry out direct measures of the static temperature, so it is necessary to make indirect measures.

A temperature probe will measure a recovery temperature which is higher than the static temperature because of boundary layer effect.

A final note. Usually for subsonic flow (V<0.3 M) the difference between the total (or stagnation) temperature and the static temperature is of scarce relevance.