INLE.T

Fig. 4·11. Liquid piston rotary compressor.

4·9. RECIPROCATING vs. ROTARY POSITIVE DIS- PLACEMENT COMPRESSORS

Tlw reciprocating romp•cssor due to its low speed and high inertia tends to lie hulky. Hmwv1·r, it consumes les~-power due to its high efficiFncy It has a lnw initial cost. Recicrncati·•g comprFss,r3 are capable of develnping very high nressurc rati:,s and the maximum cap.1city is limited tn ahout 300 m"/miqute. Recipr.1nting com- prrs,ors an, cithtr wate,· or air c·i,lled while the rotarv compr,:,s·:irs are oil cr,ol(·d. hi rotary comm·e,sws s;vne oil i, uspd for luhric::ction

;is well as for cooling th~ air,";, special <frtergent oil and that t0) in large q11an!i1ie-s, is nef'ded. Due tn hnt oil being mrd in main·

bfaring, leakage is a problem. This i5 s~ecially- so for IJ1dian tr ,pica] c0nditiom where oil takes relativdy hnger ti one to cool.

Rotary compressors re-quire mnre power than rcci;ir,xating c,-mpressors for same mass flow as sh·1wn in Table 4·1 and this . extra p:iwer manifests itself in high~r 011tlet te·rl[)eratures. Rotary compressors have outlet temperatures about 35° to 45°C higher than their reci prorating counterparts.

136 GAS TURBINE AND JET'AND ROOKET PROPULSION TABLE 4·1

POWER REQUIRED FOR VARIOUS COMPRESSORS Air delivery, FAD, m3/min

I

^3·5

^I

^4'5/5

l

⁶

I

⁷

I

^10'5

Positive displacement rotary

1---;-

⁵⁰

1--;-1-~-,

⁹⁶

1--- l--1----1

Reciprocating, h.p. ^I 26 38 88

I I

^{49 I 62}

Rotary compressors are used for delivering large air quantities at relalively low pressures upto 8 kgf/cm^{2 •} Rotary compressors are high speed machines and can be directly coupled to turbines and are smalier in size and have a uniform delivery without a large receiver between the compressors and the air main as provided in reciprocating types.

ILLUSTRATIVE EXAMPLES 4·.i. H.ecipro-.:adng compressor: power required

A reciprocating compressor delivers 5 kg of air per minute at a pressure of 7·5 kgf/cm". The pressure and temperature of the air before compression are 1 kgf /cm² and 16°0, respectively, and the compression rprocess may be assumed to follow the law pvl·' =constant. If the rate of heat transfer from the cylinder is estimated to be J·6 h.p., calculate the power required/or the compression. Take Cr,=0·24.

I

!'·"

_pv

"'=c

., "vfJ•u

- ~ ,£:c,v n 1 - - - - f L.~~~~~~-

I

=288x\

V

I'OSIHVE DISPLACEMENT COMPRESSOR 137 Total power required=mass ratexcp(T2-T1)+heat transferred

_ 5x0·24(403-288) +l·"

- 10·54

°

=13·1+1·6=14·7 h.p. Ans.

(Note 10·54 kcal/min= l h.p.)

{2. Two-stage co:m.pressor : h.p.; "l)iso, F.A.D. ; heat transfer A single-acting two stage compressor with complete intercooling delivers· 5 kg/min of air at 15 kgj/cm2 • Assuming an intake state of 1 kgj /cm² and 15°0, and that the compression and expansion processes are reversible a-nd polytropic with n=1·3. Calculate the power required, the isothermal efficiency and the free air delivery. Also calculate the net heat transferred in each cylinder and in the intercooler.

If the clearance ratios for the low and high pressure cylinders are 0·0-1 and 0·06 respectively, calculate the swept and clearance vol·umes

J

or earJ1, cylinder. The speed is 420 rev/min.

V

Final pressure P3=15 kg/cm2 ; Initial pressure P1=1 kg/cm2 Pres8'11,re. ratio

P.ressnre at the end of first stage of compression,

Work detut in. compression

Total v,rork done per cyk is given by

W =2m~RTr( Pi)?!

_{n--1 L P1} n-1 ^-1

l

.,J

2x5 1·3 M-1

-,r

=--x---x29·27x288[f3·88) 60 · I ·3-1 ' ¹ -11 • Ans.

138 GAS TURBINEJ AND JEr A~D ROCKET fROPULSION

Isothermal work done, W;=mRT1 log-;;

5 .

=

60 x29·27x288xlog. ¹⁵

= 1908 kgf/s or 2.'H h.p.

~ , Wiso

Isothermal etuc1cncy, 'l)iso= - - -

w

Free air delivery

Free air delivery, V=m

1;\

1

Hcai trnn'ferred

Since there is pnfect intrrcooling, temperature at the cT,d of each stage is equal, i.e.

0 ~

=288 ( ~i )FT =394 K

\ l /

r\;Jplyingth~ First Law ofThnmoclyrJarntc~, thehcat t:,,: !.":··

r-d ~ ~ c~1ch cyrndct l:_..i givfn hv

Tlie rnlu:nctric rffi'.:iency is given by

II . I r,rr1=l- ; : {( ; : ) ~- ·- ! }

POSITIVE VlSPLACEMENT COMPRESSORS

For first cylinder volumetric efficiency

0·3

=

1-0·04{(3 88)1'3 -1}=85·2%

For second cylinder

0·3

·r;,.01= l-0·06{(3·8Sf3 -1}=77·92%

Swept volume and clearance volume The swept volume is given by

V ^Tt F.A.n.

b->-a=

NX·IJ,,ot First cylinder

l ._. •

.! J.)

Vb-Fa= ~.AD.

i\ X YJ,,,,z

4·21

4:.::U X U·85L 0·0117:> :m.⁸ Ans Second cy l indtr

T7 - r, - .. F A .JJ

,." ~ d - p 1'.)

v·

A 2/ l X • X 'IJve l

421 --"·''03'2 3A :n:l8x420xo·7792-"" ^.:J m ns.

Clearance volume

Clearance volume =Clt:arancc ratio;< Swrpt volume Pir.,t cylinder

Cleaiance \Olume=O 01179 :<O·Ot=0·000472 m'¹ Ans.

Second (!/i'.nrler

Clearance rnlunw=O 00332 :<0·06=0 000199 m3 . Ans.

4·3. Reciprocating con'lpi·es§or : 1n1~teacy flow ; time to produce a specified pressure

.t reciproca.ti'.ng comprcs8or delfr·ers ai1· to a receiver h1,i,in:7 a

·volume of ;j rn3. The receiver is initially at a pressure of 1 5 kgf/cm2 and temperature 25cc; the pressnre i;; to be ir.creased to 8·5 kgf.'cm2 ,

ihe temperature being maintained const;int, by means of a cooler. If the comprPssor is driven by ^ri 35 h.p. motor and the ratg of heat tran.efcr from the systern i8 1 2 h.p., calculate the time taken to produce the specified pressure rise (Take Cp=0·24 kcal/leg K, Cv=0· 17 kcal/kg K and atmospheric lemper,1ture t1 =l 8°CJ.

140 GAS TURBINE AND JET AND ROOKET FB.Ol"ULSION

Initial ru<1ss of the air in the receiver, 1 ·5 X 5X 104

29·27 X 298 =S·5 kg Final mass of the air in the receiver,

3·5x Sx 10~

ma= 29·27x298

=

43 ·7 kg Increase in mass=48·7-8·6=40·I kg Writing down the energy equation, we have

Q+W =u2m2-u;mi+h1(m2-m;) where Q=heat transferred

W=work done u=internal energy h=enthalpy

Since the temperature remains constant

U;=U2

Q+ W=mi(m2-m,)+h1(m2-mi)

=cvT;(m2-m,)+c:!)T1(m2-m,)

=(m2-m1)(c,T,+cziT1 )

where T1 is the atmospheric temperatures, T1 =291 K.

Q+W=40·1(0·l 7 x298+0·24x291)

=4820 kcal

( 35-- l · 2) X l O· 54 kcal heat input in 60 seconds 4820 kcal input will be in

60x4820

38.8 ^X lO· 54 =708 se~ or 11 ·8 min. Ans.

EXERCISES 4l Section A

4·1. Describe the various applications of compressed air.

4·2. Define fans, blowers, exhausters and boosters.

4·3. In what way the analysis of fans differ from that of blowers and compressors ?

4·4. What are the two main types of compressors? What are the main differences between them ?

4 5. Define isothermai efficiency. Why the efficiency of'. reciprocating compressors is given in terms of isothermal efficiency ?

POSITIVE DISPLACEMENT COMPRESSORS 141 4·6. What is free air delivery ? Why capacity of a compressor is given in terms of free air delivery ?

4·7. Define overall volumetric efficiency in terms of (a) mass ratio, (b) volume ratio. Why volumetric efficiency is less than unity? What is absolute volumetric efficiency ?

4·8. Derive the expressions for work done in a single-stage reciprocating compressor if the compression is (a) adiabatic, (b) polytropic, (c) isothermal.

4·9. Define mechanical efficiency of a compressor.

4· 10. What is the effect of clearance volume in a reciprocating com- pressor on (a) work done per kg of cycle, (b) air delivered, (c) volumetric efficiency ?

4·1I. What are the various methods for approximating to the isothermal compression in reciprocating compressors ?

4·12. Prove that in a two-stage reciprocating air compressor, if the ntercool ing is complete, the expression for total work required, W, is g:ven by

n n-1 11-l

W=p1v1n-l (

~)~ii-,+(

f!]_)_n_ -2

\ P1 \. P2

where p1 , p2 ar:d p3 are pressures at inlet to first stage, inlet to second ,tage and outlet from second stage respectively, and v1 is the volume of air entering low pressure cylinder.

Hence prove that in a two-stage compressor, for maximum efficiency the intermediate pressure p2 is the geometric mean of !he initial pressure p₁ and final pre,sure p3.

4·13. What are the conditions for maximum efficiency of a multi-stage reciprocating compressor?

4·14. Show that the temperature rise of1he gas in either cylinder cf an ide;,l two-stage compressor is a minimum wlien the intcrcooler pressure p=( p1p2)0· 5, where Pl and Pz are lo_w pressure -.·y1inder suction and high pressure cylinder delivery pressures respectively. State clearly the assumrticns which are made and explain the low pressure cylinder ratio will in practic;, normally exceed that in the igh pressure cylinder.

4·15. Prove that the volum~tric efficiency of a single-stage reciprocating air compressor having pressure ratio P2IP1 and clearance n.tio C is given by

rii-o,=r-c(i )ii-

1 ^-1.

4·16. What are the 2dvantages of multi-stage compression ?

4·]7. Discuss the typical performance curves of reciprocating ::u:· co:11- prcssors.

4 18. What are the applicatio11:3 of reciprocating compressors?

4· 19. Describe the working of a Root's blower by the help of a neat sketch and pressure ; olume diagram.

4·20. What are the applications of Root's blower?

4·21. Describe the working of a Lysholm compressor with a sketch.

Where Lysholm compressor is used ?

4·22. Describe, with a sketch, the working of a vane type compressor and show its pressure-volume diagram. For what applications it is used?

142 GAS TURBINE AND JET AND ROCKEl' PROPULSION

4·23. Describe with a sketch the liquid piston rotary compressor. What arc its typical applications'!

4 24. Compare the relative merits and demerits of reciprocating vs rotary positive displacement compressvrs.

Section B

4 25. Vane Compressor

A rotary vane compressor has a free air delivery of 10 m3/min when it c-J:·:1;1iesses air from 1 kgf/cm² and 30°C to 2 kgf/cm2. Estimate the power required to drive the compressor when (al the ports are so placed that there is no internal comrression, (b) the ports are so placed that there is a 30 per cent reduc1ion of volume before back-lbw occurs. Assume adiabatic compression.

What is the isentropic efficien~y in each instan~e ?

REFERENCES

4·J. Schmidt, R.: "Turbocompressors i11 the Chenucal Industry", Brown R,•'>eri Review 1967, No. 7.

4·2. Baumann, H. and Nicdermann, E.: Tfie New Brm,·n Boveri Isotherm Con,;,;-essor, Brown Boveri Review, 1963 No. 6/7.

4·3. ''The Use of Turbocompressors in Chemical and Industrial Plants"

Brnsc-Boveri-Sulzer-Turbomachinery Ltd., Uroshore.

4·4. Stoeckicht, A. : The Development of Axial Blowers and Method of Conrro! in Industry, Sulzer Technical Review No. 1, 1961.

4·5. ''Air Compressor Handbook" Caterpillar Tractor Co. 1969.

4·6. Allemann, M. and Walther, R.: Centrifugal Compressors/or Special plications, Sulzer Technical Review. Reprint.

5