RECIPROCATING COMPRESSORS

Transcription

1 RECIPROCATING COMPRESSORS There are various compressor desigs: Rotary vae; Cetrifugal & Axial flow (typically used o gas turbies); Lobe (Roots blowers), ad Reciprocatig. The mai advatages of the reciprocatig compressor are that it ca achieve high pressure ratios (but at comparatively low mass flow rates) ad is relatively cheap. It is a pisto ad cylider device with (automatic) sprig cotrolled ilet ad exhaust valves. Delivery is usually to a receiver. The receiver is effectively a store of eergy used to drive (eg) compressed air tools. Ilet TDC Swept vol. BDC Delivery Clearace vol. Receiver

2 Reciprocatig compressors usually compress air but are also used i refrigeratio where they compress a superheated vapour (to which the gas laws strictly do ot apply). I order to be practical there is a clearace betwee the pisto crow ad the top of the cylider. Air 'trapped' i this clearace volume is ever delivered, it expads as the pisto moves back ad limits the volume of fresh air which ca be iduced to a value less tha the swept volume. The iduced volume flow is a importat purchasig parameter. It is called the "Free Air Delivery" (FAD), ad it measures the capacity of a compressor i terms of the air flow it ca hadle. It is ormally measured at stadard sea level (SSL) atmospheric coditios ad allows the capacities (size) of compressors to be compared. N.B. The iduced mass per cycle must equal the delivered mass per cycle (cotiuity!), although the iduced ad delivered volumes will be differet. 2

3 Cycle Aalysis The cycle may be aalysed as two o-flow (compressio ad expasio) processes ad two flow processes (delivery ad iductio) PROCESS GROSS WORK 2 Compressio 2 3 Delivery 3 4 Expasio 4 Iductio p2v2 - pv p2(v2-v3) p4v4 - p3v3 p(v4-v) Note that we assume polytropic compressio ad expasio. This is because some degree of coolig is usually attempted for reasos we shall see later. If o coolig were attempted becomes g. O p-v co-ordiates: pressure (kpa) Volume (litres) 3

4 The work per cycle is give by: å gross work p2v2 - pv work per cycle + p2(v2-v3) + + p(v4-v) p4v4 - p3v3 but pp4 & p2p3 p4v4 - pv p2v2 - p3v3 + p(v4-v) + + p2(v2-v3) p(v4-v) p(v4-v) p2(v2-v3) work per cycle p2(v2-v3) but \ p(v4-v) {+ } + p2(v2-v3){+ } mass delivered mass iduced p2(v2-v3) p(v-v4) RT2 RT p2(v2-v3) p(v-v4) T2 T work per cycle p(v-v4) { T2 } [ -] T for a polytropic process : T2 T p2 p ( ) rp Notig that (V-V4) is the iduced volume (Vid), ad p is the ilet pressure (pi) we may re-arrage ad write: work per cycle pi Vid { rp -} NB Power required work per cycle x cycles per sec 4

5 Volumetric Efficiecy We have already oted that the iduced volume is less tha the swept volume. To eable this effect to be evaluated we defie volumetric efficiecy (hvol) as: hvol Iduced volume Swept volume but p3v3 p4v4 V-V4 Vs \ V4 V3 rp V3 is the clearace volume (Vc), ad V Vc + Vs \ hvol Vc + Vs - Vc rp The referece coditios (p & T) at which the volumetric efficiecy is measured should always be quoted (it would ormally be SSL coditios). Vc [The cocept of hvol applies also to reciprocatig egies.] Vs hvol - ( rp - ) Vs hvol Vc Vs rp 50 5

6 Volumetric Efficiecy referred to SSL coditios. I testig a compressor, the measured iduced volume flow will be that of the actual test ilet coditios. It is ulikely that these ilet coditios will be SSL. We therefore eed to refer our results to SSL coditios. (Measured) SSL Ilet >>. Vi Ts Ps Ti Pi The mass flow of gas must be the same both at SSL (s) coditios ad at Ilet (i) coditios... ms mi psvs RTs Vs.. pivi RTi.. pi Ts Vi ps Ti dividig both.. sides by Vswept hvol(ssl) pi Ts ps Ti hvol(ilet) 6

7 Compressor Efficiecy If we plot the specific work (kj/kg delivered) agaist the polytropic idex we obtai: 250 w RTi { rp -} w kj/kg rp8 rp Isothermal compressio Polytropic Adiabatic compressio It is clear that the closer the compressio is to isothermal the less work is required. The savigs are greater at higher pressure ratios (eg above rp4 ad rp8) It is also apparet that isothermal compressio represets the ideal miimum work iput for a compressio process (where coolig is feasible). 7

8 We ca therefore defie compressor efficiecy as: hiso Isothermal work per cycle Actual work per cycle If we recalculate the work iput assumig isothermal compressio [ W2 pv l(p/p2) etc] it is foud that: hiso l rp { rp -} Note that this efficiecy is kow as the isothermal efficiecy. The degree of coolig possible durig a sigle stage compressio process teds to be limited. It improves at low speeds but this limits compressor capacity. Oe way of improvig efficiecy, especially at higher compressio ratios ad speeds, is to go to multistage compressio with coolig of the gas betwee each stage. 8

9 Multistage compressio To avoid uacceptable reductios i compressor capacity (RPM ad volumetric efficiecy) ad to miimise power iput with high compressio ratios, multistagig with iter-coolig is used. The umber of stages will ormally be betwee two ad four. itercoolers i > > out Stage Stage 2 Stage 3 Each stage may be treated as a separate compressor, however, with multistagig, all will ormally rotate at the same speed. The volumetric efficiecy of the compressor as a whole is determied by the first stage. If the iter-coolig is such that the ilet temperature to the followig stage(s) is the same as the ilet temperature to the first stage we have ideal (or perfect) iter-coolig. Sice the work iput to ay stage is depedet o the pressure ratio across it, it should be possible to miimise the total work iput by the correct choice of compressio ratio across each stage. 9

10 Optimum stage pressure ratio Assume we have two stages of compressio with ideal itercoolig ad the same idex of compressio (ad expasio) '' i each stage. Total Work per cycle é pi Vid { rp -} + p2i V2id { rp2 -} ù ë û Sice the mass iduced by the first stage must be equal to the mass iduced by the secod stage: pi Vid R Ti p2i V2id R Ti \ Total Work per cycle pi Vid é { rp -} + { rp2 -} ù ë û If p is the ilet pressure ad p2 the fial delivery pressure, let pi the iter-stage pressure: the rp pi p & rp2 p2 pi If we substitute the above i the expressio for Total Work ad differetiate wrt pi, we ca fid pi for miimum Total Work. whece pi [p p2] ½ or rp rp2 ( p2 ) ½ p We could exted the same method to N stages with the result that, for miimum work iput, the pressure ratio across each stage must be the same ad equal to the Nth root of the overall pressure ratio. rp(opt) rp(overall) N 0