Isothermal Work And Polytropic Workdone 4d5d3o

TOPIC : RECIPROCATING COMPRESSOR

Introduction to compressors 

The machine which takes in air or any other gas at low pressure and compresses it to high pressure is called compressor. The compressor is power consuming machine in which mechanical work is converted into pressure energy of fluid. They are also considered as reversed heat engine.

Uses of compressed air  To

compress the refrigerant and to create pressure difference in system.  Operating pneumatic tools.  To operate air motor in mines where fire risks are more.  To compress air in gas turbine power plant.  Spray painting.  For sand blasting.  Operating blast furnaces.

Classification of compressors The compressors are classified as follows: According to design and principle of operation:  Positive displacement type compressor: In this type, air/gas is compressed by positive displacement of air by piston or rotating elements.  Examples: Reciprocating compressor, Rotary compressor, etc. 

Reciprocating

Rotary

 Roto

dynamic compressors: In this type, compression is carried out by a rotating element imparting velocity to the flowing gas and develops desired pressure, and compression is achieved by dynamic action of rotor.  Examples: Centrifugal compressor

Axial flow

Mixed flow

 According to number of stages:  Single stage compressor – Low delivery

pressure(≤10

bar)  Multi stage compressor – High delivery pressure(≥10 bar)

 According to final(delivery) pressure of gas  Low pressure compressors : final pressure < 10 bar  Medium pressure compressors : final pressure between

10 bar to 80 bar  High pressure compressors : final pressure between 80 bar to 1000 bar  According to pressure ratio:  Fan : pressure ratio <1.1  Blower : pressure ratio >1.1 and <2.3  Compressors : pressure ratio >2.3

 According

to quantity of air delivered

(capacity):  Low

capacity : volume flow rate<10  Medium capacity : volume flow rate between 10 to 300  High capacity : volume flow rate >300  According to number of cylinders:  Single

cylinder

 Multi

cylinder

According

to type of fluid to be compressed  Air compressor  Gas compressor  Vapor compressor

According

to action of piston:  Single acting compressors: They are the reciprocating compressor which has piston working only in one direction. There is one suction and delivery stroke per revolution of crank.

 Double

acting compressors: As from its name it uses its

both sides to compress the air. These types of compressors have two sets of suction/intake and delivery/exhaust valve on both sides of the piston .As the piston moves up and down, both sides of the piston is utilized in compressing the air. The intake and exhaust valve operates corresponding to the movement of the piston or with the stroke of the compressor. The air is compressed accordingly and delivered continuously as compared to single-acting air compressor. Here both of sides are effectively used for compressing the air.

According

to methods of cooling:  Water cooled air compressors  Air cooled air compressors According to arrangements of cylinders:  Vertical  Horizontal  V – type

W – type

According to types of drives: Motor driven I.C. engine driven Turbine driven

Radial

COMPRESSORS

POSTIVE DISPLACEMENT

ROTO--DYNAMIC

TURBO COMPRESSOR RECIPROCATING

SINGLE STAGE

SINGLE ACTING

EJECTOR

ROTARY

MULTI STAGE

RADIALFLOW (CENTRIFUGAL)

DOUBLE ACTING

MIXED FLOW

AXIAL FLOW

Reciprocating compressor  Reciprocating

compressors are widely used for compressing air and it is satisfactory for all ranges of pressures. The number of cylinders may be more than one. In single stage reciprocating compressor pressure ratio is kept 5 to 8, and the speed varies from 100 to 1500 rpm.

 Reciprocating

compressors are driven by electric motors, or I.C. engine. It is not driven by gas turbines because turbines have high rotational speed. The air/gas coming from reciprocating compressor is not continuous but intermittent. So the air/gas is stored in receiver from where continuous flow of air/gas can be supplied. Reciprocating compressor generally seen where there is requirement of high pressure and low flow. Mostly where the air is used for hand-tools, cleaning dust, small paint jobs, commercial uses, etc.

Construction and working



The single stage, single cylinder, single acting compressors consists of piston, cylinder, cylinder head, connecting rod, crank shaft, flywheel, crank case, water jacket, suction valve and delivery valve as shown in fig.

 The

compressor takes inside successive amount of volume of air from intake valve and confined it in closed surface at that time piston moves downward with the closure of intake valve. Then there is compression of air by reducing its volume .Now the piston moves upward and compress the air and then displace the compressed air through exhaust valve. And then again intake take place and cycle repeat itself.

These types of compressor also called positive displacement machines. They are available in both as lubricated and oil-free.  The reciprocating compressor is single acting when the compressing is accomplished using only one side of piston and double acting when both the sides of piston used. 

Advantages: Relatively

Cheap. Easy maintenance Suitable for high pressure

Disadvantages: Sounds

too much. One has to arrange a room for it or put it into isolating box. High outlet temperature of compressed air. High oil content in air piping.

Single stage reciprocating compressor :  Let

us consider piston to be at top dead centre (TDC) and move towards bottom dead centre (BDC). Air gets into cylinder during this stroke and is subsequently compressed in next stroke with both inlet valve and exit valve closed. After piston reaching BDC it reverses its motion and compresses the air inducted in previous stroke. Compression is continued till the pressure of air inside becomes sufficient to cause deflection in exit valve.



At the moment when exit valve plate gets lifted the exhaust of compressed air takes place. This piston again reaches TDC from where downward piston movement is again accompanied by suction. This is how reciprocating compressor keeps on working as flow device. Reciprocating compressor described above has suction, compression and discharge as three prominent processes getting completed in two strokes of piston or one revolution of crank shaft.

Work done: Compression of air in compressor may be carried out following number of thermodynamic processes such as isothermal compression, polytropic compressor or adiabatic compressor. Fig. shows the thermodynamic cycle involved in compressor. Theoretical cycle is shown neglecting clearance volume but in actual cycle clearance volume cannot be negligible.  Clearance volume is necessary in order to prevent collision of piston with cylinder head, accommodating valve mechanism etc. 

The compressor is work consuming machine, hence work done is negative.  Let,  pressure of air at inlet of compressor  pressure of air at outlet of compressor  volume of air before compression  volume of air after compression  absolute temperature of air before compression  absolute temperature of air after compression 

Isentropic Compression ,

 1        p  W  p1V1  2   1  1  p1    

polytropic compression n 1   n   p n   W  p1V1  2   1 n 1  p1    

Isothermal compression  p2  W  RT1 ln    p1 

If compression process is isothermal, pV = C, temperature remains constant, the change of internal energy during compression process is zero. Thus as per law of conservation of energy the entire work of compression is related to the cooling medium (surroundings). It is clear from for p-V, the area 1-2”-34 is less than area 1-2-3-4 and area 1-2’-3-4. It means that in isothermal compression no energy is wasted in heating the air or increasing the internal energy. It has been found that work required for compression is minimum when the process is isothermal.

Methods of cooling: Faster heat dissipation from inside of compressor to outside by use of fins over cylinder. Fins facilitate quick heat transfer from air being compressed to atmosphere so that temperature rises during compression can be minimized.  Water jacket may be provided around compressor cylinder so that heat can be picked by cooling water circulating through water jacket. Cooling water circulation around compressor regulates rise in temperature to great extent. 





The water may also be injected at the end of compression process in order to cool the air being compressed. This water injection near the end of compression process requires special arrangement in compressor and also the air gets mixed with water and needs to be separated out before being used. In case of multistage compression in different compressors operating serially, the air leaving one compressor may be cooled up to ambient state or somewhat high temperature before being injected into subsequent compressor. This cooling of fluid being compressed between two consecutive compressors is called intercooling and is frequently used in case of multistage compressors.

Single stage reciprocating compressor with clearance: 

With clearance volume the cycle is represented on Fig. The work done for compression of air polytropically can be given by the area enclosed in cycle 1-2-3-4. Clearance volume in compressors varies from 1.5% to 35% depending upon type of compressor. In the cylinder of reciprocating compressor (V1-V4) shall be the actual volume of air delivered per cycle.Vd = V1 – V4. This (V1 – V4) is actually the volume of air in hated in the cycle and delivered subsequently.

Work done for polytropic : n 1   n   p n   W  p1 V1  V4   2   1 n 1  p1    

Volumetric efficiency:  V4  V3 v  1   1  V1  V3  V3 

The volumetric efficiency decreases with increase pressure ratio . At r = 1 ∴ p2 = p1 and efficiency = 100%. It means that no compression takes place. For given value of C and the delivery pressure is limited due to decrease in in single stage reciprocating compressor. Hence it is necessary to go for multistage compressor to get desired pressure with satisfactory value of .However higher pressure ratio up to 8 in a single stage refrigerating compressor is used as compared to air compressor because n in refrigeration system is lower than that of air.

v

1   p2  n   1 C  C   p1    

    

The efficiency decreases with increase in the clearance ratio C. At C = 0, clearance volume= 0, efficiency= 100%, no clearance is provided. When the value of C and r are constant, efficiency increases with n.

Free Air Delivery (FAD): The free air delivery is the actual volume of air delivered by the compressor when it reduced to ambient pressure and temperature conditions. It is expressed in and represents the capacity of compressor. Following factors reduce the FAD less than swept volume and volumetric eff.  The presence of clearance volume.  The throttling of the air when it es through the inlet and outlet valves.  Heating of incoming air and  Leakage. 

Actual (indicator) diagram for single stage reciprocating compressor

Mean effective pressure The area of indicated diagram represents the work done per cycle. The average height of the indicator diagram in proper unit of pressure is called the indicated mean effective pressure ( pm ) Area of indicator diagram X spring constant pm  Length of indicator diagram pm

workdone / cycle  sweptvolume / cycle

pm

n 1   n n  p2    p1v   1   n 1  p1    

Indicated power The power consumed inside the cylinder, as mea sured from the indicator diagram is termed as the indicated power. Workdone / min Indicatedpower(IP) = kW 60X1000

But, work done = pm L.A.N(x ×i), Nm p m .L.A.N  IP =  (x × i), in kW 60X1000

x = no. of cylinders per stage i = 1 for single acting i = 2 for double acting

Compressor efficiencies •Mechanical efficiency( m ): It is ratio of Indicated power (IP) to the Brake power (BP) of compressor. The power required to drive the compressor is called the brake power or shaft power of the compressor. 2 NT B.P 

60000

,kW

I .P. m  B.P

It varies from .85 to .96.

•Isothermal efficiency(iso ) : It is the ratio of isothermal work input (minimum work input) to actual work input(polytropic work input). iso

isothermalwork input  actualwork input  p2    p1 

p1 V1ln  

n-1   n   p n   p1 V1  2  - 1 n -1  p1    

It is 100% when compression process is isothermal (best because compressor needs minimum work).

•Adiabatic efficiency(ηad ): It is the ratio of actual work input to adiabatic work input.

ad

Actualwork input  Adiabaticwork input  n  p2 p1V1  n -1  p1  =  γ  p p1V1  2 γ -1  p1 

n-1 n

  -1   γ-1   γ  -1     

  

Multi-stage reciprocating air compressor There are several disadvantages to compress the air at high pressure in single stage reciprocating compressor. To eliminate the limitations of single stage, the air is compressed by more than one stage. As we know, if pressure ratio is increased in single stage reciprocating compressor the volumetric efficiency decrease. The temperature of the air after compression is so high as to cause mechanical problems and the amount of heat is actually the energy loss. so compressor has to handle more volume of air at high temperature.

The increase in temperature needs heavy working parts. With this reasons, in multistage compression the overall compression ratio is divided into two or more stages to have lower compression ratios. An intercooler is used between two stages so that the compressed air from the first stage cools down before it enters second stage with low temperature.

Advantages of multi-stage compression The work done in compressing the air is reduced, thus power can be saved. Prevents mechanical problems as the air temperature is controlled. The suction and delivery valves remain in cleaner condition as the temperature and vaporization of lubricating oil is less The machine is smaller and better balanced Effects from moisture can be handled better, by draining at each stage Compression approaches near isothermal

Disadvantages: A multi-stage compressor is more expensive in initial cost than same capacity single stage reciprocating compressor. This is due to multistage compressor needs more than one cylinder, intercoolers with water supply system.

Two stage- reciprocating air compressor

Condition for minimum work or maximum efficiency The work required per cycle for the above two stage reciprocating compressor without clearance and perfect intercooling is given by: n-1 n-1   n n     p n  p  W= p1 V1  2  + 3  - 2 n -1  p2   p1    

The work input will be minimum when p3 p2  ,pressure ratio per stage is equal p2 p1

 p2 

p3  p1

dW 0 dp2

Minimum work required for two stage compressor Wmin

n-1   2n   p 2n   = p1 V1  3  - 1 n -1  p1    

If there are N numbers of stages, then condition o minimum work required is p N+1 p 2 p3 p 4 = = =____= = z say p1 p 2 p3 pN  p N+1  p2 z = =  p1 p  1  Wmin

1 N

=  pressure ratio through compressor 

n 1   Nn   p Nn    p1V1  N 1   1 n 1  p1    

1 N

Following conditions are necessary for compressing air with minimum work input in a multi-stage compressor with intercooler: •Compression ratio in each stage is equal. •Air is cooled to initial temperature after each stage of compression. •Work required in all stages is equal.

Actual p-V (indicator) diagram for two stage compressor

References: Fluid Power Engineering by J.P.Hadiya, Books India Publications. Images and information from Google.

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