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Purdue University

Purdue e-Pubs

International Compressor EngineeringConference

School of Mechanical Engineering

1974

Application of Basic Thermodynamics toCompressor Cycle Analysis

R. G. KentAllis Chalmers Corporation

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Kent, R. G., "Application of Basic Thermodynamics to Compressor Cycle Analysis" (1974).International Compressor EngineeringConference. Paper 135.http://docs.lib.purdue.edu/icec/135

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1. Total work of compression 172 610 - 500)18.9 BTU

2. Work supplied by atmospheric air in the crankcase.Work (BTU) PSIA x Piston Area x Piston Travel xSq. In.

144 Sq. Ft.Ft. Lb,778 BTU= PSIA x (Init ial ft . 3 - Final rt.3)'14.7 X 12.613.4 BTU

7.68) X 144TIE3. Thus, work supplied by crankshaft, to compressthe air:

Total Compression Work- Work Provided bv Atmos. AirCrankshaft Workc. Work to push the air out of the cylinder.1. Total work PSIA x (Init ial - Final volume) x

X 144m29.4 X 7.68 - 0) X 144

8"' 41.8 BTU

2. Work supplied by atmospheric air in the crankcase.Work (BTU) 14.7 X 7.68 - 0) X 144

8"' 20.9 BTU

3. Work supplied by crankshaft to push the air outof the cylinder.41.8 - 20.9 "' 20.9

d. Summing up the work supplied by the crankshaftfor one complete revolution.Work during: Suction

Compression+ DischargeNet crankshaft worko)5.5)~ 2 0 . 926.4 BTU)

rather than on the air. Starting with air in theinlet l ine, we' l l review the same fundamental stepsof compressor operation.a. Total energy or enthalpy (h) in the intake l ine

h '_internal energy and potential energyh (BTU) "' CvT + pv x 144

TIE= .172 X 500 + 14.7 X 144 X 12.6778"' 120.3 BTU

b. Work done by the air during suction stroke.The minus sign-will show that work was done by,rather than on, the air.

PSIA (Init ial volume - Final volume x14477814.7 X 0-12.6) X 144778-34.3 BTU

c. Work done on the air during compressionWork (BTU) = .172 610 - 500)

= 18.9 BTUd. Work done the air during discharge

= 29.4 X 7.68 X 144m= 41.8 BTU

e. Total energy or enthalpy in the discharge lineh at inlet the net work on the air = h at dischar

120.3 - 34.3 18.9 41.8 = 146.7 BTUCheck:h = .172 X 610 + 144 29.4 X 7.68)778And : Change in EnthalFY :

146.7 BTU

Now the Textbook Way 146.7- 120.3 = 26.4 BTUConsider the same problem with the thermodynamictextbook heat balance approach where changes inenthalpy ( i .e . , the sum of internal and potentialenergy) are calculated, Calculations can be considerably simpler than the previous example byomitting the effect of crankcase pressure, providing we t reat the suction stroke as work done by,

292

Therefore, the compressor has increased the air stotal energy by 26.4 BTU which is equal to thenet work done by the crankshaft in our f i r s t approach. This is obvious, for when there is nofr iction or heat flow into, or out of the air, a l lthe work done by the crankshaft must be absorbedby the air. Accordingly when we summarize and

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= 5 ~ 1.4 - 11 .4 .715

h. 1 .4 -1 ]144 X 14.7X 12 .6X 1 .4 X .715 4 7 ~ Xm :4385 TU per poun

The resulting work of38.5 BTU per pound. th usagrees with Moll ie rch arts showing ent hal py changes38. 5 BTU perpound wi th a temperature change from 500R to660R.

Conclusioncompressor des igner re ading this outline would

no doubt wish to ampl ify many ofthe general sta te-m ents and in clu de additional Side issues w hichenter into the picture . Converselya plant engi ne ermay believetha tdayto day shop problems do no tnecessitate a w ork ing know ledge of entropy, en -th alpy, etcetera.hewri te r rec og nizes validi tyin bo th of th esepositions. However, i t is hoped that a fundamentalkn owledge of what occurs between compres sor suctionand discharge flanges will be a usefulstart ing

point for the sho p man when problems of compressorselection or operationarise.

Re ferences1. Wal te rKidde Co, Moll ier Char t for Air, April19532. U. S. Naval Institu te, Energy Analysi s ofNaval Machinery .3. A J . Ste pan off , Turbo Blowers, Wiley Sons,

1955.

296

NOMENCLATUREP Absolutepre ssurep Absolutepre ssureT Absolute te mpe ra tur eV =Volum ev = Volum eR = The gas const an tCv Specificheat at con st ant volume

CP Specific heat at consta ntpress ure

1 Conversion facto rmk Ratio fo rspecificheats

U Internalen ergyorth em easure ofgas's kineticen ergyPV Potentialenergy of a gasmh En thalpyor total en ergyS Entropy

a = energyNp =Polytr opic Efficiency

1bs/ft2lb s /in 20 R ankinecu . f tcu. f tf t perBTU per

per lb.oFlb. perde gree, .172 fodry a ir

BTU per lb. perdegree, .241 fodryairBTU per f t lb .

14 fordr yair BTU per lb .

BTU per lb.

BTU perlb .BTU per lb .per 0 FBTU per lb .