polytropic head in a centrifugal compressor 1

[Rotaryeqpt]

Can any one explain in simple terms ( as understood by a mechanical Engineer) about Polytropic Head in a Centrifugal Compressor?

 

[pmover]

good grief!

not being sarcastic or such...

this subject is reviewed in theory in most thermodynamic textbooks, plus other engineering references.

investigate these websites for further reading:

http://www.rplpe.com/

http://www.dresser-rand.com/e-tech/turbo.asp

good luck!
-pmover

 

[iainuts]

Here's a link to a previous post:

http://www.eng-tips.com/viewthread.cfm?spid=469&newpid=469&sqid=68363

Also for a definition: Head, polytropic. The energy in foot pounds required to compress polytropically and to transfer one pound of a given gas from one pressure level to another.

I'm not sure if it would help or not but perhaps a discussion of a polytropic process would help.

A polytropic process is one in which PV^n = constant.

For isothermal compression, the exponent n = 1
For isentropic compression, the exponent n = k (ratio of specific heats)
For compression where the isentropic efficiency is LESS than 100%, (ie: heat is added to the gas) the exponent n > k

Note that as the exponent, n, increases, the amount of power required by a compressor for any given inlet and outlet pressure and any given flow rate also increases. The extra energy goes into the gas as an increase in temperature.

For values of n less than k, there is heat being removed during the compression process. Note that an isentropic process is not the most efficient in terms of power required. An isothermal process is much more efficient because energy is being removed during the compression process.

For values of n greater than k, there is heat being added during the compression process. This heat is generally due to inefficiencies (esp. for recips) and results in higher levels of power being required for compression as compared to isentropic.

An isentropic process is also adiabatic, thus has no heat added or removed during the process.

Hope that helps,
Dave.

 

[1969grad]

Agree with pmover that this is a subject every mechanical engineer should know that works with compressible fluid flow and heat transfer. Suggest you hit the books starting with your thermo book and educate yourself. Just because you got a degree does not mean the education process stops.

 

[fredt]

There is another angle on this:

In the fan world basic calculations are carried out assuming incompressible fluid. When estimating the performance of a high pressure machine using "fan laws" the calculated pressure would fall short of the actual pressure. A correction is then necessary to account for the fact that the fluid is compressible and the compression polytropic. The resultant (true) pressure (polytropic head?) will be significantly higher than the incompressible calculation.

 

[25362]

Little can be added to iainuts' comments. A polytropic curve is the graphical relationship between pressure p and volume V for various values of n in the compression formula pV ⁿ = C.
Let us say that being the work of compression W=integral of p dV between two points, and since pV ⁿ = C, the work (area in the graph) increases with n.

Since most machines tend to work along a polytropic path nearing the adiabatic, most compressor estimations are done based on an adiabatic curve. In these cases one substitutes k for n. Where k =C_p/ C_v the ratio of the specific heat at constant pressure to the specific heat at constant volume.

The adiabatic head, in m, is estimated from

[k/(k -1)](847.8/MW)T₁[(p₂/ p₁)^{(k -1)/ k} -1]​

MW is molecular weight of the gas being compressed.
847.8=8,314/9.806
T₁ is the inlet absolute temperature, degrees K

Multiplying the above head by the mass flow rate, kg/s, times 9,806 N/kg we obtain the compression work in 1000 N.m/s= kW.