Air motor: temperature of exhaust

[elektrinis]

I have an industrial application where 20kW of heat is being wasted, which is painful to watch. I have learned already that low temperature turbines just don't work, so would like to check some ideas and better understand how air motors/turbines work. I have also learned so far that η=1-(Tout/Tin), however I don't think this takes pressure into account. This is where I am lost.

Let's say I have a closed system with air or other refrigerant:
* input at 1000 kPa, 50ºC, 1kg/sec
* scroll motor with expansion rate of 1:10
* output pressure at 100kPa

How do I go about calculating:
* input power?
* output temperature?
* mechanical power produced?

Is there anything missing?

 

[JRMichler]

The best way to find the power needed to compress air, and power produced from air motors, is to get it directly from the manufacturers catalogs. You will need to contact one of their sales engineers to find exhaust air temperature.

An air compressor needs 400 to 450 hp to produce 1 kg/sec of air at 1000 kPa: https://www.ingersollrandproducts.c...age-Oil-Flooded-Rotary-Screw-Compressors.html. Other manufacturers include Quincy and Sullair.

A rule of thumb from my plant engineering days is that it takes four horsepower of air compressor to produce one horsepower of work from an air motor. That does not include the power for the air dryer. Parker makes an air motor rated at 18 kW, or 24 hp. That motor needs 700 SCFM at full load, but at maximum 7 bar air pressure. Two of these motors would use the full output of a two stage 250 hp Ingersoll Rand air compressor, which is not that far off from the rule of thumb. http://www.parker.com/portal/site/P...t=EN&vgnextcatid=6147890&vgnextcat=AIR MOTORS

What is the source of this waste heat? Maybe there is a way to reduce waste heat by improving the process efficiency. That would be a far better approach than trying to reclaim that heat.

 

[OCR]

Parker makes an air motor...

That reminds me... of this . . I love that camera 'jerk'... I rather doubt I could hold it steady either. .

 

[Mech_Engineer]

A good approach would be to consider the process using a thermodynamic process analysis.

It sounds like you're describing an Isentropic Expansion process, in which case the analysis technique is well-established. Given your input state (Air, 1000 kPa @ 50 ºC) you can calculate the final state properties because you know the final pressure (100 kPa).

Some equations for isentropic compression/expansion are given on NASA's Beginner's Guide to Aeronautics, so this might be a good starting point. You can calculate the exit temperature using the following equations (red arrow indicates the one you need):

I think you'll find the exit temperature is going to be very low, so this might be a problem for the design of your system.

 

[Mech_Engineer]

For some more information regarding calculating power output, you'll need to find the Enthalpy of air at State 1 and State 2. Once you've found the properties of State 2 (temperature and pressure) you can use the enthalpy difference (Δh, kJ/kg) multiplied by your mass flow rate (M_dot, kg/s) to estimate the isentropic power output for the system.

Some more information is given here: OU Thermodynamics E-Book

For an adiabatic turbine which undergoes a steady-flow process, its inlet and exit pressures are fixed. Hence, the idealized process for turbine is anisentropic process between the inlet and exit pressures. The desired output from a turbine is the work output. Hence, the definition of isentropic efficiency of turbine is the ratio of the actual work output of the turbine to the work output of the turbine if the turbine undergoes an isentropic process between the same inlet and exit pressures.

ηT = Actual turbine work/Isentropic turbine work
= wa/ws

wa and ws can be obtained from the energy balance of the turbine. Usually the kinetic and potential energies associated with a process through a turbine is negligible compared with the enthalpy change of the process. In this case, the energy balance of the turbine is reduced to

The isentropic efficiency of turbine can then be written as

ηT

(h2a - h1)/(h2s - h1)

where
h1 = enthalpy at the inlet
h2a = enthalpy of actual process at the exit
h2s = enthalpy of isentropic process at the exit