Energy loss in compressible flow

[kayjaygee_13]

I have air flowing through a gate valve with lengths of pipe of matching diameter upstream and downstream. At a certain distance from the valve upstream and downstream, I am measuring static temperatures and static and stagnation pressures. I can estimate the Mach numbers at the tapping points using the static and stagnation pressures and using those Mach numbers, I can calculate the stagnation temperatures. Now using the difference in stagnation pressures and temperatures (i.e. delta P0 and delta T0) which would basically have units of N/m² and °K respectively, is it possible convert those quantities into respective energy loss units of kJ/kg. It's been over a decade since I took thermodynamics and I can't for the life of me remember if it's even possible to convert °K to an equivalent kJ/kg.

Please help! I don't expect a readymade solution, but if someone can recommend a good reference book, I would really appreciate it. Thank you in advance.

 

[Q_Goest]

hi kayjaygee. welcome to the board. when you say, "I can estimate the Mach numbers at the tapping points"
do you mean that the velocity of the air through the pipe is actually a significant portion of the speed of sound in the pipe? If the speed of the air is small compared to mach speed (ie: less than ~ hundred feet per second, which is very fast for typical pipe systems) then you can neglect velocity and just measure static pressure and temperature using a simple T off the line. If the velocity really is that high, we can talk about it. Assuming the velocity is 'normal' or just 'very high velocity' for a piping system, we can neglect the energy due to velocity and just apply the first law without including kinetic energy, which is the normal way of approaching this very typical problem. If that's the case, then for an ideal gas, the flow is isenthalpic because the temperature change will be very small and the flow can be modeled as being adiabatic as well. So depending on what 'energy losses' you want to determine, the flow is isenthalpic with dU changing according to:

dH = 0 or U2-U1 = -(p2V2-p1V1)

See this web page:
http://web.mit.edu/16.unified/www/FALL/thermodynamics/chapter_4.htm

But if you're just trying to find the temperature change, that's easy. I'd recommend purchasing a copy of NIST REFPROPS and determining temperature by recognizing that the final state (at low pressure) of the fluid has the same enthalpy as the initial state (at high pressure) and pulling the temperature straight out of the database. It's actually very easy.

 

[kayjaygee_13]

Q_Goest, thank you for replying. Sorry for taking so long to clarify some things. I have an experimental setup with the capability of maintaining an upstream stagnation pressure of up to 210 psi and varying the downstream pressure, so that the flow regime is anywhere from low subsonic to supersonic. As I mentioned in my previous post, I am measuring static and stagnation pressure and static temperature, both upstream and downstream of the valve. Anyway, since I can measure the loss in stagnation pressure (units of N/m²) as well as stagnation temperature (units of °K) across the valve, I was trying to convert those losses into units of kJ/kg. Dividing the stagnation pressure loss by the density (dP/rho) gives units of kJ/kg and I actually used the equation in your post to estimate the energy loss due to loss in stagnation temperature (dT) :

Energy loss associated with loss in stagnation temperature = CvdT + (p2v2 - p1v1)
Energy loss associated with loss in stagnation pressure = dP/rho

Both equations give units of kJ/kg. Anyway, I was just wondering if I was doing it right. Thank you again for the help and I'd really appreciate any suggestions/corrections.