Can Realistic Assumptions Help Design an Efficient Air Acceleration System?

[ReaverKS]

I came up with my own design problem, after completing a refrigeration design problem on the completion of my thermo I class. My design problem is this: I want to accelerate air to 56m/s via a compressor and then a nozzle. I'm trying to do a cost analysis of how much power I would save if the inlet of the nozzle is 0m/s versus 30m/s. Here's the problem, I can't really get enough information to actually do the problem. For example, I'm using a compressor to bring the air up to pressure and then a a nozzle to actually accelerate the air. The object I'm designing would be used in the real world so say the inlet of the compressor is around 21 degrees centigrade so 294K. The compressor brings in air from the atmosphere so say the pressure is 101.3kpa. I can get enough information about state one, the inlet to the compressor but not enough information about state 2 (outlet compressor/inlet nozzle). What sort of real world assumptions can I make here to solve this problem, also I did some google searching to try and find some real world examples of nozzles and compressors isentropic efficiencies and couldn't find them, what are realistic isentropic efficiencies for them?

I'm using air, ideal gas conditions.
State 1 is fixed with T1=294K, P1=101.3Kpa. State 2: I only know that V2=0, state 3: V3=56m/s

Once I get some % figures for real world isentropic efficiencies I know that I can use the definition of isentropic efficiency for the compressor and nozzle, and if I can fix state 2 then I can calculate the ideal state 2, and from that I should be able to get the actual enthalpy at state 2, and then I can use that to interpolate for T. However, from there I'm not quite sure what to do to calculate what the pressure would have to be at state 2, since, if I were to use the ideal gas equation for instance, I would need to know one more piece of information, the specific volume, or volume and mass. So I need to somehow fix state 2, and state 3, what are some realistic assumptions, I know I've got the first law for an open system SSSF at my disposal as well as the 2nd law, but I need to be able to make some general assumptions to get the ball rolling.

Also, I was just wondering how realistic of an assumption it would be to assume the compressor/nozzle to be adiabatic. Keep in mind I've only completed thermodynamics I. It is possible that I may need to complete some more courses to be able to do this. Thanks for all the help,
Kevin

 

[ReaverKS]

Oh cmon, there's got to be somebody that knows! 60 views and no responses :\

 

[boneh3ad]

Do you mind drawing a picture up and posting it including the location of the relevant parameters you have and are seeking? I am having a hard time visualizing based on your description in words.

 

[ReaverKS]

I think part of my difficulty is in deciding relavant parameters. Ultimately what I'm trying to do is accelerate air up to 56ms via a compressor and then a nozzle. Why not a propeller you might ask and a motor, well to be quite frank with you, I haven't yet had any course that introduces a propeller relevant equations. Anyways, I decided that if I were to actually make this, then the compressor would pull in air from the atmosphere, that 1) it would be atmospheric pressure, so 101.3kpa and 2) just pick a roundabout temperature of what it would be outside, so I chose 294K. Both of those decisions seemed like reasonable decisions to me, although I do admit that the temperature will vary, I'll deal with that later. I also made the assumption that there's no pressure loss across the lines between the compressor and the nozzle, as well as whatever the pressure turns out to be, the line can handle it, same goes fro the compressor and nozzle.

Now beyond that I don't know what safe assumptions to make, is an isentropic efficiency for a compressor of 70% achievable in the real world? What about a nozzle with an isentropic efficiency of 90%? I don't know, and my online searches couldn't answer that question. It's almost as if manufacturer's don't really care about isentropic efficiency, or consumers of their products don't.

The other problem I'm encountering is that I don't know enough information about state 2 or state 3 to fix them, solve for important properties such as enthalpy or entropy and then use the isentropic efficiency to calculate for actual pressures and temperatures at those states, which in turn would allow me to calculate the work input necessary for the compressor.

If this is still vague, please let me know, I'll elaborate as best as I can but ultimately I'm trying to design something after I just completed thermo I. For our class we had to design a refrigeration cycle, and he gave us a bunch of parameters such as: isentropic efficiency of the compressor, the total thermal load (heat needing to be removed by the evaporator), the desired temperature of the refrigerator compartment and the ambient temperature of the room. He gave us just enough information that I could use assumptions that I've learned are safe in class so that I could figure out enough information and calculate the COP of the refrigerator based on what refrigerant I chose. Now I'm trying to create a problem for myself to do, partially for good exercise but partially because I'd actually like to see what it would take to build something like this.

 

[ReaverKS]

Bump, anybody know or have more questions about what it is I'm trying to do?

 

[ReaverKS]

One last bump until I give up :p