efficincy calcs. for recip. comp.

[upm]

gents,
Any hint how can i calculate the volumatric eff. for a multi stages recip. compressor? it is 3 stages comp. pumping pure ethylene from 0.95 bara to 37bara (-90 deg c to 150 deg c). i know the calcs will not be accutrate as we need the detailed dimensions and clearances but as an estimate only.
upm

 

[pmover]

the equation for volumetric efficiency is in the compressor chapter of the gpsa. if you do not have the gpsa, i recommend obtaining a copy.
without accurate cylinder clearances, it is difficult to determine volumetric efficiency.
to determine VE, you will need: compression ratio (at cylinder flange), specific heat ratio, and cylinder clearance.

VE = 1 - Clr% [Rc^(1/k) - 1]

check this website:

http://www.vairex.com/pdf/Efficiency-0523.pdf

good luck!
-pmover

 

[pmover]

by the way, this calc will need to be done for each cylinder for each stage! for double acting cylinders, you will need to consider both sides of the piston.
-pmover

 

[25362]

Don't forget to use the clearance as a decimal, i.e., 5% would be 0.05. For ethylene the n value changes from suction to dicharge; an average for a ballpark estimate would be 0.2.

The formula given by pmover is correct; however, sometimes expert books prefer to substitute 0.97 for 1:

VE₁=0.97-[clea.(PR^1/n-1)].
PR is the pressure ratio.

As an example, assume PR per stage is 3.4, i.e.,(37/0.95)^0.333, and an effective clearance of 10%,

VE₁=0.97-0.1(3.4^1/1.2-1)=0.792=79.2% per stage.

A second step would correct (slightly improve) the VE for high-pressure supercompressibility:

VE₂= 1+clea.-[(1+clea.-VE₁)Z_s/Z_d]

where Z_s, Z_d are the compressibility values at suction and discharge, respectively.

 

[upm]

Gents,
Thanks alot for the great support. i will calculate the VE based on the design clearances (max. limit) then i already planned for piston/cylinder inspection soon to measure the actual clearances and to check up the piston conditions. once i measured the actual, i will re-calculate the VE to check for the deviation.

pmover
what is the "gpsa" book, and how can i get it?
thans again for the help
upm

 

[TD2K]

http://www.gasprocessors.com/gpsa_book.html

 

[upm]

25362 ,
sorry but i could not understand what did you mean by %clearance ?? normally the cylinder to piston clearance is between 0.5 to 1 mm? can i use these numbers in the equasion ?could you pls. explain me? for n , k values do i need to coorect for the actual temp. or the change will be minor?
thanks the help
upm

 

[25362]

Clearance is %, but in the formula it is taken as a decimal. For example, 5% is taken as 0.05.
"n" values change with T,P. That's the reason I took 1.2 as an average for ballpark estimates. Values for ethylene are given in the technical literature.
For each stage they wouldn't change too much, and an average of "in and out" for each stage would suffice. There are other factors such as leakages, friction drops, changes in temperature, losses due to imperfect valve action, that decrease the real efficiency. By splitting the total compression into three stages you actually improve the VE, the first stage would have a higher VE than that of a single-stage. See the formula. I've seen a graph showing actual values of VE for air compression estimated for one-stage units as function of PR and % clearance that includes the other factors.

Since I cannot reproduce the graph, I'll give some values that will enable your own plotting of VE% as f(PR) the straight lines are the % clearances:

VE,% PR clea.,%
0.96 3 0
0.945 4 0
94 3 2
90.5 3 4
88 3 6
91 4 2
87 4 4
82.5 4 6

One notices that even for 0% clearance the VEs are not 100%.
n in a piston compressor is always lower than Cp/Cv. For example, for air the conventional Cp/Cv=1.4, however, actual polytropic values are 1.3-1.35.

 

[balu1]

Sir 25362 Chemical hasn't taken into account that we "dumb" mechanical engineers need a strate forward explanation.

Percentage clearance means that a relative clearance is used in that equation (I assume). If my interpretation is correct than:

If a clearance is 1mm and cylinder bore is 100mm, the relative clearance is 1/100=0.01

Having the same clearance but half the bore size the relative clearance is 1/50=0.02

 

[upm]

man this is why my calcs is not correct

 

[ephraimike]

Hi Guys,

I would like to know how to calculate the Coefficient of performance for a vapor compression refrigeration cycle.

ephraimike.