![Themodynamics (MU) 8-2
Compreees
nt. Due to
positive
(a)
displacement ofairby the piston in the cylinder, the air iscompressed and.
vessel called receiver.] These are capable of producing
Volume flowraesorWithTowmassflowratC3
The reciprocating compressors are considered as
ppen steady flow systems Tti
the rate of heat and work transfers are at uniform rate..
Reciprocating compressors may by single acting compressor or douhla
A reciprocating compressor uses the piston cylinder arrangement. De
delivered tos
large pressure ratios
pliesthat
ouble actingM
compressor.
A single acting reciprocating compressor hasonedeliverystrokeperrevolution
of t
two delivery strokester
crankshaft, while the doubleacting reciprocatingcompressorhastwo deliverystrol
revolution ofthecrankshai
Inpositivedisplacementrotary compressor the positive displacement of air or fluid :.
low.
to a rotating part causingcompression offluid. These compressors rotateat hiph
thereforethey can handldlarge volumeormassflowrate )butthe pressureratiosare
etc.
Examples of positive displacement rotary compressors are root blower, vane blowereto
are
Non-positive orsteadyflow compressors :
Non-positive displacement compressor
(b)
also called as
steady flow compressors e.g.lcentritugal compressors and axial
COnpresSOTS. Lnese are rotary compressors.
In these compressors, the fluid is not contained in a confined space (i.e. by so
boundaries like piston cylinder arrangement of a
reciprocating compressor), but t
moves at steady rate through the machine..
In rotary compressors the dynamic head imparted to a fluid of solid boundar
(e.g. impeller of centrifugal compressor ) causes the pressure rise of the fluid.
Based on number ofstages:Compressors based on number of stages are
classifiedas:
) Single stage compressor
Multistage compressor
i)
The Single stage compressors are either air cooled (small size) or water cooled
compressors (big sizes). Normally a single stage compressor is employed when the
pressure ratio is limited upto 5.
Multistagecompressorsareused to achieve higher pressure ratios exceeding the
(ü)
compression ratio more than 5. Generally, the reciprocating compressors can deliver the
following maximum pressures
Keciprocatmg compressor aximum delivery pressures
Upto 5 bar
Single stage compressor
5 bar to 35 bar
Twostagecompressor
Three stagecompressor 35 bar to 80 bar
Four stage compressor More than 80 bar
Based on
pressure limits
Depending uponthe discharge pressures, the compressors are also classified as
Low
pressurecompressors:Delivery pressure upto 1.1 bar
Medium pressure compressors: Delivery pressure upto 7 bar
ii) High pressure compressors: Delivery pressure more than 7 bar.
()](https://image.slidesharecdn.com/compressornotes-220406111558/85/compressor-notes-pdf-2-320.jpg)
![7Themodynamics (MU)
8-5 Cornpressors
Usual
lly the compressors are
high speed machines due to which the ratc of hcat transre
be negligible, thus the process is essentiallyfadiabaticl If friction is ncgccld
cess becomes reversible adiabatic or
isentropic andfollows the law pV=
shows the thermodynamic cycle involved in compression. In this (a-1) shows the
aSSued
the
compressio
Fig. 8.4.2(a)
sess at constant pressure, followed by reversible adiabatic compression
suctoue Dressure and temperatures rise to P2» T2 due to work supplied from external source and finally
on process (1-2) during
w h i c h
the
airis
deli
elivered in process 2-b) at constant pressure, P2
Fig. 8.4.2(c)
8.4.2(c) represents the workdone required during the cycle on (p-V) diagram. In case the
in kinetic and potential energies are neglected then the work, W = [- V. dp. This work
c h a n g e s
bythearea under the
compression processontheordinateic
e p r e s
ented by the
Work done, W = V dp =
area (a- 1 -2-b)J
The heat transter dunng polytropic the process of a (1 -2) cooled compressor is shown in
8.
s42(d) on (T-S) diagram. The area under the compression process curveon abscissa represenis the
Fig.
heat transfer during the processi.e.area(1-2-c-d).
Based on the above discussion the work transfer and heat transfer in various processes can be
marized with the help of Fig. 8.4.2(a) and Fig. 8.4.2(b) respectively as follows:
Sr. No. ProcesSS Work transfer,W
Refer Fig.8.4.2a)1 Refer Fig,84.2(6]
Heat transfer,Q
1. Adiabatic process,p . V=C Area (a-1-2-b) Zero
2. Polytropic process,p V =C Area (a-1-2'-b) Area (1-2-d-c)
Isothermal process, p . Area (a-1-2"-b)Area (1-21 e - c)|
3.
It is evident from above table that the work required is maximum with adiabaric process and
work required isminimum with isothermal process.
As a designer our aim issupply minimumenefgyinput during compression process.
Therefore, isothermal compression process is considered as an ideal process because the
work input required is minimum. Thus the best value of index of compression isn = 1. m
However, the isothermal compression is not possible in practice since the heat needs to be
dissipated corresponding to infinitesimal temperature rise during infinitesimal compression process.
This heat transfer will require sufficient time. In other words, an air compressor needs to be run at an
extremely slow speed to achieve approximately an isothermal process. It will reduce the mass flow rate
of air which can be compressed. Whereas, the practical requirement is to compress the air with high
mass flow rate.
Generally, compressors run at sufficient high speed to obtain sufficient mass flow rate of
compressed air, the process of compression will be nearly adiabatic with index n = y.
However toapproachtheisothermalcompressionprocess,theairorwatercoolingisdone during
pression processorcoldwateris sprayedduringcompression,so thatthe adiabaticcompression
gesto polytropic compression withindex n <y.Thevalueofindexn varies between 1.25 to1.35.
chang
Due to continuous cooling of compressed air, it's specific volume reduces. It results in decrease
d work input which equals to area (1 -2-2)asshown in Fig. 8.4.2(a) and Fig. 84.2(b) in
polytropic process and area (1 - 2-2") in case of isothermal process.](https://image.slidesharecdn.com/compressornotes-220406111558/85/compressor-notes-pdf-5-320.jpg)
compressor notes.pdf
- 1. Module 5 C H A P T E R 8 Compressors Syllabus Reciprocating Air Compressor, Single stage compressor - computation of work done, isothermal efficiency, effect of clearance volume, volumetric efficiency, free air delivery, Theoretical and actual indicator diagram. Multistage compressors-Constructionaldetails ofmultistage compressors, Need of multistage, Computation of work done, Volumetric efficiency, Condition for maximum efficiency, Inter cooling and after cooling (numerical), Theoretical and actual indicator diagram for multi stage compressors. Rotary Air Compressors Classification, Difference between compressors and blowers, Working and constructional details of roots blower, screw type and vane type compressors. Compressor andtheirClassification 8.1 Definition ofa Compressor Thecompressors are work absorbing devices. They can be defined as follows Compressor: A compressor is a device which is used to increase the pressure ofafluid on the expense of work energy supplied. Usually, the compressors are driven by motors, I.C. engines or gas turbines. Air compressor: A compressor with workingfluid as air is called an air compressor. 8.2 ClassificationofCompressors 8.2 Compressors can be classified in thefollowing ways: Based on design and principle of operations : Based on the principle of operations . compressors can be classifiedas: Positive displacement Compressors, and i) Non-positive or Steady flow compressors ) ositive displacementcompressors:These compressors are further divided into: (a) Reciprocating compressors (b) Rotary compressors
- 2. Themodynamics (MU) 8-2 Compreees nt. Due to positive (a) displacement ofairby the piston in the cylinder, the air iscompressed and. vessel called receiver.] These are capable of producing Volume flowraesorWithTowmassflowratC3 The reciprocating compressors are considered as ppen steady flow systems Tti the rate of heat and work transfers are at uniform rate.. Reciprocating compressors may by single acting compressor or douhla A reciprocating compressor uses the piston cylinder arrangement. De delivered tos large pressure ratios pliesthat ouble actingM compressor. A single acting reciprocating compressor hasonedeliverystrokeperrevolution of t two delivery strokester crankshaft, while the doubleacting reciprocatingcompressorhastwo deliverystrol revolution ofthecrankshai Inpositivedisplacementrotary compressor the positive displacement of air or fluid :. low. to a rotating part causingcompression offluid. These compressors rotateat hiph thereforethey can handldlarge volumeormassflowrate )butthe pressureratiosare etc. Examples of positive displacement rotary compressors are root blower, vane blowereto are Non-positive orsteadyflow compressors : Non-positive displacement compressor (b) also called as steady flow compressors e.g.lcentritugal compressors and axial COnpresSOTS. Lnese are rotary compressors. In these compressors, the fluid is not contained in a confined space (i.e. by so boundaries like piston cylinder arrangement of a reciprocating compressor), but t moves at steady rate through the machine.. In rotary compressors the dynamic head imparted to a fluid of solid boundar (e.g. impeller of centrifugal compressor ) causes the pressure rise of the fluid. Based on number ofstages:Compressors based on number of stages are classifiedas: ) Single stage compressor Multistage compressor i) The Single stage compressors are either air cooled (small size) or water cooled compressors (big sizes). Normally a single stage compressor is employed when the pressure ratio is limited upto 5. Multistagecompressorsareused to achieve higher pressure ratios exceeding the (ü) compression ratio more than 5. Generally, the reciprocating compressors can deliver the following maximum pressures Keciprocatmg compressor aximum delivery pressures Upto 5 bar Single stage compressor 5 bar to 35 bar Twostagecompressor Three stagecompressor 35 bar to 80 bar Four stage compressor More than 80 bar Based on pressure limits Depending uponthe discharge pressures, the compressors are also classified as Low pressurecompressors:Delivery pressure upto 1.1 bar Medium pressure compressors: Delivery pressure upto 7 bar ii) High pressure compressors: Delivery pressure more than 7 bar. ()
- 3. Thermodynamics (MU) Cornpressors Base on capacity of compressors ) (i) Low capacity compressors: Volume flow ratio upto 10 m/min or less Medium capacity compressors:Volumeflow rates 10 m to 300 m per minute. High capacity compressors: Volume flow rates above 300 m'/min. (Gi) 8.2.1 Classification between Fan, Blower and Compressors per American Society of Mechanical Engineers (ASME), the fans, blowers and compressors As pe a r e c l a s s i f i e c fied according to pressure ratios achieved. These are as follows Fans: Pressureratioupto 1.1 Blower: Pressure ratio from 1.1 to 2.5 A () Pressure ratio above 2.5 Compressors: (i) 8.2.2 Air Pumps Compressors used for creating vacuum are called air pumps or exhausters. Applicationsof Compressors 8.3 Applications / Practicaluses of Compressed Air MU May 12 University Question Enumeratethevarioususes ofaircompressor (May12) The compressed air finds its use in many industrial applications. Some of its uses are To operate pneumatic tools like drill, hammers, riveting machine etc. i) Driving a compressed air engine () Spray painting (iv) Refrigeration and air conditioning industry. Gas turbine power plants (vi) Supercharging of LC. engines, (V1) Conveying the materials like sand and concrete along a pipe line Vii) Pumping of water. ix) Driving mining machinery where fire risks are too many. () In blast furnaces and boiler furnaces. (xi) Cleaning the surfaces by air blast. Basic Concept of Thermodynamic Cycle for Compressors and Efficiencies 8.4 Representation of Thermodynamic cycle of compressors on (p-V) and (T-S) diagrams for compressors ueneral: Schematic representation ofa compressor is shown inFig. 8.4.1.
- 4. 8-4 Themodynamics (MU) Heat loss to - Compressed air (p,V,.T,) surToundings (air/cooling water) Work supplied, W (Ether by motor or IC engines) Compressor Air in surroundings (PV,T) Fig. 84.1: Schematie representatlon ofan alr compressor As shown in Fig. 8.4.1, the air is taken into compressor from the surroundings P. V, T). It is compressed to pressure p, upto state 2 (P, V2, T,) on the expense of work oled mlate compreson During the compression, heat may be rejected cither to surrounding air in case of air cooled e having fins or to cooling water in cylinder jacket in casc of watcr cooled compressors. 8.4.1 Representation of Compresslon Processes on (p-V) and (T-S) Diagrams and Work Input The theoretical air compression cycle is shown in Fig. 8.4.2 on (p-V) and (T-S) diagrams representation ofwork and heat transfers. with Delivery pressure T 2 2 Adiabatic, p.v=C p.V=C p.v Polytropic, p.v-c T T2 Isothermal p(pV=C a Suction pressure P.V C d s a) (p-V) diagram (b) (T-S) diagram P Compression process V.dp Compression V (C)Work,W= area (a-1-2-b) (d) Heat transfer Q area (c-1-2,d) Fig. 8.4.2: Representation of compressionprocesses on (p-V) and (1-S) diagram with work and heat transfers
- 5. 7Themodynamics (MU) 8-5 Cornpressors Usual lly the compressors are high speed machines due to which the ratc of hcat transre be negligible, thus the process is essentiallyfadiabaticl If friction is ncgccld cess becomes reversible adiabatic or isentropic andfollows the law pV= shows the thermodynamic cycle involved in compression. In this (a-1) shows the aSSued the compressio Fig. 8.4.2(a) sess at constant pressure, followed by reversible adiabatic compression suctoue Dressure and temperatures rise to P2» T2 due to work supplied from external source and finally on process (1-2) during w h i c h the airis deli elivered in process 2-b) at constant pressure, P2 Fig. 8.4.2(c) 8.4.2(c) represents the workdone required during the cycle on (p-V) diagram. In case the in kinetic and potential energies are neglected then the work, W = [- V. dp. This work c h a n g e s bythearea under the compression processontheordinateic e p r e s ented by the Work done, W = V dp = area (a- 1 -2-b)J The heat transter dunng polytropic the process of a (1 -2) cooled compressor is shown in 8. s42(d) on (T-S) diagram. The area under the compression process curveon abscissa represenis the Fig. heat transfer during the processi.e.area(1-2-c-d). Based on the above discussion the work transfer and heat transfer in various processes can be marized with the help of Fig. 8.4.2(a) and Fig. 8.4.2(b) respectively as follows: Sr. No. ProcesSS Work transfer,W Refer Fig.8.4.2a)1 Refer Fig,84.2(6] Heat transfer,Q 1. Adiabatic process,p . V=C Area (a-1-2-b) Zero 2. Polytropic process,p V =C Area (a-1-2'-b) Area (1-2-d-c) Isothermal process, p . Area (a-1-2"-b)Area (1-21 e - c)| 3. It is evident from above table that the work required is maximum with adiabaric process and work required isminimum with isothermal process. As a designer our aim issupply minimumenefgyinput during compression process. Therefore, isothermal compression process is considered as an ideal process because the work input required is minimum. Thus the best value of index of compression isn = 1. m However, the isothermal compression is not possible in practice since the heat needs to be dissipated corresponding to infinitesimal temperature rise during infinitesimal compression process. This heat transfer will require sufficient time. In other words, an air compressor needs to be run at an extremely slow speed to achieve approximately an isothermal process. It will reduce the mass flow rate of air which can be compressed. Whereas, the practical requirement is to compress the air with high mass flow rate. Generally, compressors run at sufficient high speed to obtain sufficient mass flow rate of compressed air, the process of compression will be nearly adiabatic with index n = y. However toapproachtheisothermalcompressionprocess,theairorwatercoolingisdone during pression processorcoldwateris sprayedduringcompression,so thatthe adiabaticcompression gesto polytropic compression withindex n <y.Thevalueofindexn varies between 1.25 to1.35. chang Due to continuous cooling of compressed air, it's specific volume reduces. It results in decrease d work input which equals to area (1 -2-2)asshown in Fig. 8.4.2(a) and Fig. 84.2(b) in polytropic process and area (1 - 2-2") in case of isothermal process.
- 6. Themodynamics (MU) 8-6 Compreseo The actual work supplied at the shaft called shaft work or motor work will he. compression work if the mechanical friction is considered. be more than 8.4.2 Isothermal, Polytroplc and Isentroplc Efflclencles Isothermalworkinput Isothermal eficiency,Tr Actual work input 84) Polytr pic workinput Polytropic efficiency, n, Actual workinput 842) Adiabatic workinput Adiabatic or Isentropic efficiency, n,= Actual work input .(843 8.5 UncooledRotaryCompressors In case of uncooled rotary compressors, the ideal T process is isentropic process (1 - 2) and actual process is represented by polytropic compression process (1 - 2) with index n >y after considering the fluid friction. Thermodynamic cycle is represented in Fig. 8.5.1 on (T-S) diagram. Adiabatic, p.VC -p.V=C (n 2 Note that cooling of rotary compressors cannot be carried out due to inherent practical difficulties. The additional work needs to be supplied to overcome the friction. Since friction work converts into heat, as a result the specific volume Fig. 8.5.1:Uncooledcompressorcycle during compression process increases. The additional work required in uncooled compression will be the sum of -V dp workequalto area (1 2 2) due to increased specific (c 1-2 -d) volume of air and the frictional work equal to area Isentopicworkdone Ideal or Isentropic efficiency, n Actual work done ...(8.5.1) Syllabus Topic: Reciprocating Air Compressor- Single Stage Compressor and Computation of Workdone, Isothermal Efficiency 8.6 ReciprocatingAir Compressor MU-Dec. 16 University Questions Define followingtermsforreciprocatingcompressors. (1) Mechanicalefficiency (2) Indicatedpower Explain construction and working of single-state, double-actingreciprocatingair compressor neat labelleddiagram (Dec.16) (Dec.16
- 7. Themoaynamics (MU) 8-7 Cornpressors D e s c r i p t i o n Fig. 6.1 shows the sketch of a I- intet Vat reciprocating air consists of a piston D Ootvery Vatre conventona/ 1npressor. Oyflinder jch r e c i p r o c a t e s in a cylinder and it d n v e iven through the connecting rod a n d c r a n k The rankshaft is driven h a prime mover. The inlet O Connecting- Piston rod the delivery valve (D) are alue(I). nted in the cylinder head. The Cranik casa mounted F a / T e s a aves are plate type and spring loaded called presure differential type i.e. Crank the valves are automatically opened and ciosed depending upon the sSure diiference across the valves Crank-Shaf c e n outside and cylinder P T e s s u r e s . )Assumptions Foliowing are the assumptionsmade in consideing the cycle of operation: 6) There is no clearance. ) Working fluid is a perfectgas. Fig. 8.6.1:Reciprocatingaircompressor (i) There are no friction losses. iv) There are no wire-drawing effects in the valvesorpipe line. (v) The cylinder is well insulated. (o) Working An ideal (p-V) diagram for a single stage reciprocating aircompressoris shown in Fig. 8.62 Reversilble.x adiabatic (pV'=C) -pv"- Poyropio) Isothemal (pV=C) Stroke Volume (a) (b) Fig. 8.6.2: (p-V) and(T-S) diagrams for single stage air compressor
- 8. 8-8 Themodynamics (MU) Comptenaa The air is sucked inside the cylinder at pressure p When the inlet valve conditions as represented by the process (a-b). The air is then compressed adiabatically and reversibly upto pressure pa lve opens al atmosphed epresented by Curve (b-c), thelawofcompression beingp V= Constant. Now the dclivery valve opens and the compressed air of the cylinder is dischar a at constant pressure, p, represented by the process (c - d). The anca (a be d) ropresents the work required to compress the air from pregeq discharged to a roueve pressure p, to p,h cquals to -V dp work. (d) Calculations for work of compresslon and efficlencles 6) Reversible adiabatic work Workdone on the air per cycle, PVa+ PVPp, V, =(T V,-P, V) . W Area (a bcd)= Area(odce)+Area(ec b)-Area(o a bf But, PV = p2 V, , forcompressionprocess (b-c) - ( or, - - From Equations (i) and (i) we get, W "- 8.6.1) Also, p V, = mRT, 1 mR 1 gan .8.6.) Isothermal and polytropic work ofcompression However the slope of an isothermal compression curve is less than the adiabatic curve. Theretor in case the air is compressed isothermally it would follow curve (be"). The area (a b c" d woad represent the work of compression which is less than the reversible adiabatic compression workbya amount equal to the area (bc c'). In other words the isothermal process would be themostd process but such a process is difficult to achieve in practice because it would need the compressor run at an extremely slow speed consequently reducing the massflow-rate ofthe air compressed In order to save the work of compression, the practice is to reduce the index ofcompression high speeds by coolingthe cylinder. This is done either by spraying water on it or by waterjacketing cylinder in case of single stage compressors so that the law of compression becomes, pV= Constant Where the value of index 'n' is less than . It is represented by the curve (bc). In tnis work of compression per cycle with the help of Equation (8.6.1) can be written as, ase tne A
- 9. 8-9 Cornpressors Themodynamics (MU) (n1yn Polytropic work, W,= .v. ..(8.5 In case of i s o t h e r m a isothermal compression the work ofcompression reauired per cycle would be gv y by. 1sathermal work, WP Vlog. v PV,logmRT,log.D | P2 Isothermal work, ...(8.6.4) P Indicated power(L.P.) asairpower.required to drive the compressor i5 Thereforethe indicated power (L.P.), also known a given by the e q u a t i o n , Wn LP.60x1000 60000 W KW 8.6.5) n Number of strokes/min. completedby the compressor N Speed of compressor in r.p.m. n N, for single acting compressor n 2N,for double acting compressor where Let, o)Isothermal efficiency Isothermal workinput Actual work input Isothermalefficiency, n .(8.6.6) (o)Polytropicefficiency,n Itis defined as the ratio of polytropic work to actual work input. Polytropicefficiency, n Polytropic work input ..8.6.6(A)) Actual work input Note: InEquations (8.6.6 and(8.6.6(A),theactualworkinputmaybetakenasisentropicworkinput in casetheactualworkinputisnotgivenina problem a () Mechanical efficiency: It is defined as the ratio ofindicatedpower to the power required torun the compressor)The power required to drive the compressor is called the brake power(B.P.) or shaft power or the motor power which, in case of compressors, is more than the indicated power (1.P.) because of the extra power requiredto overcome the friction and other losses of the compressor. L.P Mechanical efficiency B.P. 8.6.7) Adiabatic efficiency = o Adiabatic power B.P. .(8.6.8) 86.1 Methods of Improving Isothermal Efficiency T A Use of fins over cylinder for faster heat dissipation from inside ofcompressor to outside. 0By providing waterjacket around compressor cylinder and cireulating the cooling water through waler jacket. Thus it cools the air during compression. By spraying water at the end of injection process. However this method is not used since ) Alr gets mixed with water which has to be separated before use. ) It contaminates the lubricant film on cylinder surface which may cause corosion. un Special arrangements need to be made in compressor.
- 10. gpThermodynamics (MU) 8-14 Cornpke 0.88 0.885.8305 kw Isothermal powe 0.7103 or 71.03% Actual power, P 5.1309 Actual power5.8305 U.7103or71.03% (it) Cylinder dimensions (D and L) V, = V, xN =% D'LN; I = D x 1.8 Dx240 D = 0.1434 m and L= 1.8 D = 0.258 m (iii) Raiing of drive = Actual power = 5.8305 kW Syllabus Topic : Effect of Clearance Volume, Volumetric Efficie Air Delivery (F.A.D) ,Fre 8.7 EffectofClearanceVolumeinCompressors MU Dec.1 University Question Define following termsforreciprocatingcompressors (1)Volunmetricefficiency (2) Free AirDelivery (Dec. 18 Practically speaking, a certain amount of clearance has to be provided between the piston nd on cylinder so that the piston does not strike with the cylinder head. Also, a certain space between nit and cylinder has to be provided to accommodate valves. The ideal (p- V) diagram for a single stage air compressor is shown in Fig. 8.7.1 with clearance volume A small quantity of air in clearance at delivery pressure P2 of volume V. expands polytropically along the curve (3-4) till its pressure becomes equal to the suction P2 pv =c pressure. At point-4 the inlet valve opens and the air is drawn into cylinder at atmospheric pressure represented by the process (4-1). Therefore, the volunme of air drawn (V, - V) is less than, the stroke volume(V,-V). It follows that the handling capacity of the compressor is reduced due to the clearance space between the piston and cylinder head. For this reason in case ofcompressors the clearance volunme is kept asSmall-as possible The measure of handling capacity in case of compressors, is defined as the vO efficiency. P -.. Effective volume Total volume b d Fig. 8.7.1: Air compressor cycle with clearance UMIMluM Fu
- 11. MU) 8-15 Thermodnamics(M Compressors J s a d d ctually compressedand deliveredattheinletpressureandtemperature Therelore. freeairactuall Volumc of Piston displacement A.D) represents the rate of volume of surrounding airwhich is sucked by delivered (FA.D) N o t o : the c o m p r e s s o r and deliveredatdischargeepre Ahernatively Mase equivalentprsten-dspiaccmentaýinketpressureandtermperature 1lvol. Mass ofactuallycompressedairand delivered air ed that the workdone on the air delivered is not affected by the cleararnce ) asthe worke q u i r e epans ansion from point 4 to point 1. should be noted that t d to c o m p r e s s the 82) of air in clearance volume is theoretically regained during its Volumetric Efficiency 87.1 alculations for Eauation (8.7.1), the volumetric efficiency is given by, (Vs +Vo) V where the stroke volumeand V.represents the clearance volume. For ihe polytropic process (3-4) we have, PaxV = P4x V or, V,= Vs Also,PPa PP1 and V= Ve (Refer Fig. 8.7.1) 1/n xVo P1 Substituting for V, from Equation (ii) in Equation (i), ..(ti) v- Pi - =1+V, V, -) .8.7.3) V Let C = Clearance volume ratio =V () Tp Pressureratio= Pi ASndoo TheEquation (8.7.3) can be rewritten as: 1, = 1-IG,-11C P e seen from the Equation (8.7.4) that thevolunetricefficiency reduceswiththeincrease Sure ratio, T, and the clearance volume ratio, C. ...(8.7.4) odvallg onnrebd on
- 12. 8-16 Compress Thermodynamics (MU) 8.7.2 Other Factors Affecting the Reduction in Volumetric Efficieney Apart from reduction in volumetric efficiency due to increased pressure ratio. volume ratio, C, other factors affecting the reduction in volumetric efficiency eeclea compressorsare: aranoe Teciprocaling (a) Increase in temperature of free air drawn from atmosphere due to the heat transter Pressure drop in the inlet passages and across the inlet valve. b) cylinder walls. Due to this heating the specific volume of air increases, hence,them actually present in the cylinder compared to the conditions of free air is reduced, Leakage through the valves or past the piston because this decreases the mass of air delive. livered. (c) (d) Inertia effects in opening the inlet valves. ee At 8.7.3 Volumetric Efficiency Referred to Surrounding Conditions or on Frea Deliveredd Sincethe condition of air at point-1 does not represent the conditions of free air delivered FA n (at atmospheric pressure and temperature) due to heat transfer between the cylinder walls andD and due to pressure drop past the valves, it is necessary to apply the correction factor in theexpr intake air esion ofvolumetricefficiency as follows Let, Vo= Volume offree air delivered at surrounding pressure po and temperatureT PoV m RTo Mass of free air delivered, PiV-V4 RT But, m Since mass of air sucked remains constant, it implies from above, PooP (V-V RT RT PoT (V-V) Hence the volumetric efficiency of Equation () expression referred to surrounding conditions can be modified as, PT PoT ..) (V-V V, Substituting the value of from Equation (8.7.4) in Equation (iv), the modified expression for volumetric efficiency based on free air delivered becomes: ..(8.7.5) - c Note: Expression given byEquation (8.7.5) should not be used forcalculatingthedimenslons or on cylinder Only the expression of volumetric efficiency given by Equation (1.74 bas suctionconditionsshouldbe used for calculation ofcylinderdimensions.
- 13. Themodynamics (MU) 8-17 Compressors Workdone 8.7.4 Workdone per cycle, W Area (1 -2-3-4) = Area (a-1-2- b) - Area (3-4-a-b) n-1y1 w () ) -J-()»v In case the index of expansion and compression is same. -1/1 (n-1n W( ()»-V|)- (n-1/n 8.7.6) For a single stage single acting reciprocating air compressor, actual volume of air taken in is 10 m/min. Initial intake pressure is 1.013 bar and initial temperature is 27 C. Final pressure is 900 kPa clearance is 6% of stroke. Example8.7.1 Compressor runs at 400 rpm. Assume: LD = 1.25 and index ofcompression 1.3 Determine: (1) Volumetric efficiency (2) Cylinder dimensions (3) Indicated power PA Solution: Refer Fig. P. 8.7.1 (V-V.) = 10m/min, P2Pa - p.v=c P 1013 bar= 101.3 kPa T = 27°C = 300 K, P2 900 kPa C 0.06=V -1.25, P1P Vs n = 1.3, N= 400 rpm Fig. P. 8.7.1 ) Volumetric efficiency, n» 1=1-0.06T01.3 1|=0.738or73.8% Ans. 1 - i) Cylinder dimensions, D and L V,=D'LN 10 = Dx 1.25Dx400; V, = V, x N D = 0.3256 m Ans. 0.738 L = 1.25 x D = 1.25 x 0.3256 = 0.407 m ..Ans. ndicated power (L. P.) I.P. = ( v-v.) (v,-v.)( (-y