Bài giảng chapter 4 single stage cycle

CARNOT REFRIGERATION CYCLE CARNOT REFRIGERATION CYCLE STANDARD VAPOUR COMPRESSION REFRIGERATION SYSTEM VCRS SUBCOOLING AND SUPERHEATING CYCLE LIQUID – SUCTION HEAT EXCHANGER... Standard

CHAPTER 4:

SINGLE STAGE CYCLE

Aft thi h t t d t

After this charpter, student can :

- Analyze and perform cyclic calculations for

C t f i ti l d th

Carnot refrigeration cycle and others

- Analyze and perform cyclic calculations for

CARNOT REFRIGERATION CYCLE

CARNOT REFRIGERATION CYCLE

STANDARD VAPOUR COMPRESSION

REFRIGERATION SYSTEM (VCRS)

SUBCOOLING AND SUPERHEATING CYCLE

LIQUID – SUCTION HEAT EXCHANGER

ACTUAL STANDARD VAPOUR COMPRESSION ACTUAL STANDARD VAPOUR COMPRESSION REFRIGERATION SYSTEM

Institute of Technology (IIT)

[2] Kỹ thuật lạnh cơ sở - Nguyễn Đức Lợi

CARNOT REFRIGERATION CYCLE

1 Definition:

Carnot refrigeration cycle is a completelyreversible cycle, hence is used as a model ofy ,perfection for a refrigeration cycle operatingbetween a constant temperature heat source andpsink It is used as reference against which the realcycles arey comparedp

CARNOT REFRIGERATION CYCLE

CARNOT REFRIGERATION CYCLE

qc − qe = wnet

qc qe net

CARNOT REFRIGERATION CYCLE

Refer (page 155, [1]) :(p g , [ ])

CARNOT REFRIGERATION CYCLE

The Coefficient of Performance (COP) is given by:( ) g y

- The COP of Carnot refrigeration cycle is ag yfunction of evaporator and condenser temperaturesonly and is independent of the nature of the workingy p gsubstance

- From Carnot’s theorems, for the same heat,source and sink temperatures, no irreversible cyclecan have COP higher than that of Carnot COP.g

CARNOT REFRIGERATION CYCLE

3 Practical difficulties with Carnot refrigerationgsystem:

- During process 1-2, a mixture consisting of liquid g p , g qand vapour have to be compressed isentropically in the compressor -> compressor will be damagedp p g

- Using a turbine and extracting work from thesystem during the isentropic expansion of liquidy g p p qrefrigerant is not economically feasible, particularly

in case of small capacity systems.p y y

CARNOT REFRIGERATION CYCLE

- This is due to the fact that the specific workpoutput (per kilogram of refrigerant) from the turbine

is given by:g y

- The specific volume of liquid isp q much smaller

compared to the specific volume of a vapour/gas,the work output from the turbine in case of the liquidp qwill be small In addition, the inefficiencies of theturbine -> then the net output will be furtherpreduced

Standard Vapour Compression Refrigeration System (VCRS)

In practicalp considerations,, the Carnotrefrigeration system need to be modified:

- Dry compression with a single compressor isy p g p

possible if the isothermal heat rejection process isreplaced by isobaric heat rejection processp y j p

-The isentropic expansion process can bereplaced by an isenthalpic throttling process.p y p g p

Standard Vapour Compression Refrigeration System (VCRS)

This is the theoretical cycle on which the actualyvapour compression refrigeration systems arebased

Standard Vapour Compression Refrigeration System (VCRS)

Due to these irreversibilities, the cooling effect, greduces and work input increases, thus reducing thesystem COP This can be explained easily with the y p yhelp of the cycle diagrams on T-s charts

Standard Vapour Compression Refrigeration System (VCRS)

- There is a reduction in refrigeration effect whengthe isentropic expansion process of Carnot cycle isreplaced by isenthalpic throttling process of VCRSp y p g pcycle, this reduction is equal to the area d-4-4’-c-d(area A2) and is known as throttling loss.

- It is easy to show that the loss in refrigerationeffect increases as the evaporator temperaturep pdecreases and/or condenser temperature increases

A practical consequence of this is a requirement ofp q qhigher refrigerant mass flow rate

Standard Vapour Compression Refrigeration System (VCRS)

The heat rejection in case of VCRS cycle alsoj yincreases when compared to Carnot cycle

- The heat rejection in case of Carnot cycle (1-2’’-3-j y (4’) is given by:

- In case of VCRS cycle, the heat rejection rate isy , jgiven by:

Standard Vapour Compression Refrigeration System (VCRS)

Hence the increase in heat rejection rate ofjVCRS compared to Carnot cycle is equal to the area2’’-2-2’ (area A1) This region is known as superheat( ) g phorn, and is due to the replacement of isothermalheat rejection process of Carnot cycle by isobaricj p y yheat rejection in case of VCRS

Standard Vapour Compression Refrigeration System (VCRS)

Standard Vapour Compression Refrigeration System (VCRS)

The net work input in case of Carnot and VCRSpcycles are given by:

wnetnet,,CarnotCarnot = (q(qcc − qqee ))CarnotCarnot = area 1− 2' '−3 − 4'−1

wnet,VCRS = (qc − qe )VCRS = area 1− 2 − 3 − 4'−c − d

− 4 −1

Standard Vapour Compression Refrigeration System (VCRS)

The COP of VCRS cycle is given by:y g y

Unlike Carnot COP, the cycle efficiency dependsvery much on the shape of T-s diagram, which iny p g ,turn depends on the nature of the working fluid

Standard Vapour Compression Refrigeration System (VCRS)

As mentioned before, the losses due to,superheat (area A1) and throttling (area A2 ≈ A3)

depend very much on the shape of the vapor domep y p p(saturation liquid and vapour curves) on T sdiagram The shape of the saturation curvesg pdepends on the nature of refrigerant

Standard Vapour Compression Refrigeration System (VCRS)

T-s diagrams for three different types ofg yprefrigerants

Standard Vapour Compression Refrigeration System (VCRS)

Type 1 : Refrigerant such as: Amonia, COyp g , 22, H, 22O.Both the superheat and throttling losses (areas A1and A3) are significant) g

Type 2 : Refrigerants such as CFC11, CFC12,HFC134a These refrigerants have small superheatg plosses (area A1) but large throttling losses (area A3)

Type 3 : High molecular weight refrigerantsyp g g gsuch as CFC113, CFC114, CFC115, iso-butane.Having significant throtting loss; do not have anyg g g ; ysuperheat losses, i.e., when the compression inlet

condition is saturated (point 1), then the exit(p ),condition will be in the 2-phase region -> danger

Standard Vapour Compression Refrigeration System (VCRS)

The superheat loss increases only the workp yinput to the compressor, it does not effect therefrigeration effect In heat pumps superheat is not ag p p ploss, but a part of the useful heating effect.However, the process of throttling is inherently, p g yirreversible, and it increases the work input and alsoreduces the refrigeration effect.g

Standard Vapour Compression Refrigeration System (VCRS)

Heat transfer rate at evaporator or refrigeration p gcapacity, is given by:

Qee= mrr.(h( 11 - h44 ), (kW)), ( )Where :

(h1 − h4 ) is known as specific refrigeration effect

or simply refrigeration effect, (kJ/kg)

Power input to the compressor, is given by:p p , g y

Wc= mr.(h2 - h1 ), (kW)(h2−h1) is known as specific work of compression

or simply work of compression, (kJ/kg)

Standard Vapour Compression Refrigeration System (VCRS)

Heat transfer rate at condenser, Q, cc is given by:g y

Qc=mr.(h2- h3 ), (kW)Where:

h3 and h2 are the specific enthalpies (kJ/kg) atthe exit and inlet to the condenser, respectively., p y

The COP of the system is given by:

Standard Vapour Compression Refrigeration System (VCRS)

At any point in the cycle, the mass flow rate ofy p y ,refrigerant can be written in terms of volumetric flowrate and specific volume at that point, i.e.,p p , ,

Applying this equation to the inlet condition of the pp y g qcompressor

Standard Vapour Compression Refrigeration System (VCRS)

where V11 is the volumetric flow rate atcompressor inlet, (m3/s) and v1 is the specificvolume at compressor inlet (mp ( 3/kg).g)

We can also write, the refrigeration capacity interms of volumetric flow rate:

is called as volumetric refrigeration effectg(kJ/m3 of refrigerant)

SUBCOOLING AND SUPERHEATING CYCLE

1.Definition : Refer to page 175,[1]p g ,[ ]

In actual refrigeration cycles, the temperature

of the heat sink will be several degrees lower thangthe condensing temperature to facilitate heattransfer Hence it is possible to cool the refrigerantp gliquid in the condenser to a few degrees lower thanthe condensing temperature byg p y adding extra areag

for heat transfer In such a case, the exit condition ofthe condenser will be in the subcooled liquid regionq g

SUBCOOLING AND SUPERHEATING CYCLE

- Similarly, the temperature of heat source willy, p

be a few degrees higher than the evaporatortemperature, hence the vapour at the exit of thep , pevaporator can be superheated by a few degrees

- If the superheating of refrigerant takes placep g g pdue to heat transfer with the refrigerated space (lowtemperature heat source) then it is called asp ) useful

superheating as it increases the refrigeration effect

SUBCOOLING AND SUPERHEATING CYCLE

- It is possible for the refrigerant vapour top g pbecome superheated by exchanging heat with the

surroundings as it flows through the connectingg g gpipelines Such a superheating is called as useless

superheating as itp g does not increase refrigerationgeffect

SUBCOOLING AND SUPERHEATING CYCLE

+ Advantage of subcooling cycle :g g y

SUBCOOLING AND SUPERHEATING CYCLE

- Increases the refrigeration effect by reducing g y gthe throttling loss at no additional specific work

input p

- Without subcooling the throttling loss is equal

to the hatched area b-4’-4-c.

- With subcooling the throttling loss is given by

the area a-4”-4’-b.

-The refrigeration effect increases by an amountequal to (hq ( 44-h4’4 ) = (h) ( 33-h3’3 ).)

- Less vapour at the inlet to the evaporator

SUBCOOLING AND SUPERHEATING CYCLE

+ Advantage of superheating cycle :g p g y

It prevents the entry of liquid droplets into thecompressorp

+ Disadvantage of superheating : In case of

useful superheating increasep g

- Useful superheating increases both therefrigeration effect as well as the work ofgcompression

- The COP (ratio of refrigeration effect and( gwork of compression) may or may not increase withsuperheat, depending mainly upon the nature of the

SUBCOOLING AND SUPERHEATING CYCLE

LIQUID-SUCTION HEAT-EXCHANGER CYCLE

1 Definition :

A LSHX is a counterflow heat exchanger inwhich the warm refrigerant liquid from theg qcondenser exchanges heat with the cool refrigerantvapour from the evaporator.p p

LIQUID-SUCTION HEAT-EXCHANGER CYCLE

LIQUID-SUCTION HEAT-EXCHANGER CYCLE

LIQUID-SUCTION HEAT-EXCHANGER CYCLE

LIQUID-SUCTION HEAT-EXCHANGER CYCLE

2 Refrigeration cycle calculations :g y

If we assume that there is no heat exchangebetween the surroundings and the LSHX andgnegligible kinetic and potential energy changesacross the LSHX, then, the heat transferred, ,between the refrigerant liquid and vapour in theLSHX, QLSHX is given by:, g y

LIQUID-SUCTION HEAT-EXCHANGER CYCLE

If we take average values of specific heats forg pthe vapour and liquid, then we can write the aboveequation as;q ;

cp,l (T3 − T4 ) = cp,v (T1 − T6 )since the specific heat of liquid (cp q ( p lp,l) is larger) gthan that of vapour (cp,v), i.e., cp,l > cp,l, we can write:

(T3 − T4 ) < (T1 − T6 )

( 3 4 ) ( 1 6 )This means that, the degree of subcooling (T3-

T44) will always be) y less than the degree ofgsuperheating, (T1-T6)

LIQUID-SUCTION HEAT-EXCHANGER CYCLE

If we define the effectiveness of the LSHX, ε, LSHXLSHX

as the ratio of actual heat transfer rate in the LSHX

to maximum possible heat transfer ratep

If we have a perfect LSHX with 100 percenteffectiveness (ε( LSHXLSHX = 1.0), the temperature of the), prefrigerant vapour at the exit of LSHX will be equal

to the condensing temperature, Tc, i.e., (T1 =T3 = Tc )

g p , c, , ( 1 3 c )

Chapter 4 : Single stage cylce

LIQUID-SUCTION HEAT-EXCHANGER CYCLE

3 Effect of superheat on system COP:p y

- When the refrigerant is superheated usefully(either in the LSHX or the evaporator itself), the

refrigeration effect increases

- The work of compression also increases,p ,primarily due to increase in specific volume of therefrigerant due to superheatg p

Actual Standard Vapour Compression Refrigeration System

The cycles considered so far are internallyy y

reversible and no change of refrigerant state takesplace in the connecting pipelines However, in actual

- Heat transfer in compressor

- Pressure drop and heat transfer in connecting

Actual Standard Vapour Compression Refrigeration System

The cycles considered so far are internallyy y

reversible and no change of refrigerant state takesplace in the connecting pipelines However, in actual

- Heat transfer in compressor

- Pressure drop and heat transfer in connectingp gpipe lines

Actual Standard Vapour Compression Refrigeration System

- The pressure drop in the evaporator, in thep p p ,suction line and across the suction valve has asignificant effect on system performance becauseg y psuction side pressure drop increases the specificvolume at suction, compression ratio and discharge, p gtemperature increase -> reduction in systemcapacity, increase in power input and also affect thep y, p plife of the compressor due to higher dischargetemperature -> this pressure drop should be asp p psmall as possible for good performance

Actual Standard Vapour Compression Refrigeration System

- The pressure drop depends on the refrigerantp p p gvelocity, length of refrigerant tubing and layout(bends, joints etc.) Pressure drop can be reduced

by reducing refrigerant velocity (e.g by increasingthe inner diameter of the refrigerant tubes).g )However, this affects the heat transfer coefficient inevaporator andp the carring of the lubricating oilg gback to the compressor

- Pressure drops across the valves of thepcompressor increase the work of compression andreduce the volumetric efficiency of the compressor.y pHence they should be as small as possible

Actual Standard Vapour Compression Refrigeration System

- Heat transfer in the suction line is detrimental

as it reduces the density of refrigerant vapour andincreases the dischargeg temperaturep of thecompressor Hence, the suction lines are normallyinsulated to minimize heat transfer

- Actual systems there are the presence offoreign matter : lubricating oil, water, air, particulateg g , , , pmatter inside the system

- We can’t avoid the presence of oil in systemp ybut we must return oil to compressor properly

Actual Standard Vapour Compression Refrigeration System

Actual Standard Vapour Compression Refrigeration System

Exercise :

In a R22 based refrigeration system, a suction heat exchangerg (LSHX)( ) with aneffectiveness of 0.65 is used The evaporating andcondensing temperatures are 7.2g p oC and 54.4oCrespectively Assuming the compression process to

liquid-to-be isentropic, find:p ,

a) Specific refrigeration effect,

b) Volumic refrigeration effect,) g ,

c) Specific work of compression

d) COP of the system,

Chapter 4 : Single stage cylce

Actual Standard Vapour Compression Refrigeration System

e) Temperature of vapour at the exit of the) p pcompressor

Comment on the use of LSHX by comparing they p gperformance of the system with a SSS cycleoperating between the same evaporator andp g pcondensing temperatures

Actual Standard Vapour Compression Refrigeration System

Actual Standard Vapour Compression Refrigeration System

e) Temperature of vapour at the exit of the) p pcompressor

Comment on the use of LSHX by comparing they p gperformance of the system with a SSS cycleoperating between the same evaporator andp g pcondensing temperatures