Applied Heat and mass transfer

8/10/2019 Applied Heat and mass transfer

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Mechanical Engineering Dept. CEME NUST 1

Ch-2:Vapor Compression Cycle

Book:

Refrigeration & Air-Conditioning by Wilbert F.

Stoecker / Jerold W. Jones


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Vapor Compression cycle

The Carnot Cycle

Ideal thermodynamically Reversible Cycle, first investigated by Sadi Carnotin 1824

A measure of the maximum possible conversion of heat energy into

mechanical energy

Heat rejected to low

temperature sink

Cool Liquid

Compressor

2 3

41

Turbine

Heat from high

temperature source

WorkWork

2 3

41Temperature

T1=T4

T2=T3

SA SBEntropy

Process 4-1: isothermal rejection of heat

Process 1-2: Adiabatic Compression

Process 2-3: isothermal addition of heat

Process 3-4: adiabatic expansion


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2 3

41Temperature

T1=T4

T2=T3

SA SBEntropy

Process 1-2: adiabatic compression

Process 2-3: isothermal addition of heat

Process 3-4: adiabatic expansion

Process 4-1: isothermal rejection of heat

Heat supplied during isothermal expansion (2-3)= T

2(S

B- S

A)


The Carnot Cycle

work done = Heat supplied Heat rejected

= T2(SBSA) T1(SBSA)

= (SBSA)(T2T1)

Heat rejected during isothermal compression

(4-1) = T1(S

BS

A)

=

=

=

=

Efficiency increases as T2is increased and T1is decreased

Heat should be taken in, at as high temperature as possible and rejected

at as low a temperature as possible.


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A measure of the maximum performance to be obtained from a refrigeratingmachine


Reversed Carnot Cycle (i.e. Carnot Cycle for Refrigeration Cycle)

Heat from low

temperature sink

Cool Liquid

Turbine

3 2

14

Compressor

Heat to high

temperature source

Work

Entropy

Net Work

23

4 1Temper

ature

1-2: Adiabatic compression

2-3: Isothermal heat rejection

3-4: Adiabatic expansion

4-1: Isothermal addition of heat or isothermal

expansion


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Carnot Cycle:

o A standard of comparison,

o A convenient guide to the temperatures

that should be maintained to achieve

maximum effectiveness

Heat absorbed from the low temperature source

in process 4-1 is the Refrigeration Step


Reversed Carnot Cycle (i.e. Carnot Cycle for Refrigeration Cycle)

Entropy

Net Work

23

4 1Temperature




4-1: Isothermal addition of heat or

isothermal expansion


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Ratio of out put to input would be misleading for

a refrigeration system as the o/p in process 2-3 is

usually wasted


Coefficient of Performance (COP)

=

Entropy

Net Work

23

4 1Temperature




4-1: Isothermal addition of heat

or isothermal expansion

=

=


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Area underline 2-3 represents the Heat

Rejectedfrom the cycle

Useful Refrigeration is the heat transferred inprocess 4-1, or the area beneath the line 4-1


Conditions for Highest Coefficient of Performance

23

4 1Temperature

Entropy (S)

KJ / Kg.K

Refrigeration

Net Work

Area enclosed in rectangle 1-2-3-4 represents

the Net Work

Work done = Heat Rejected Heat Supplied

= T2(S2S3) T1(S1S4)

= (T2T1) (S1S4)= Area of rectangle

=

=


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Coefficient of Performance (COP)




4-1: Isothermal addition of heat

or isothermal expansion

COP of the Reversed Carnot Cycle is entirely a

function of the temperature limits and can varyfrom zero to infinity

To obtain maximum possible COP

oCold body temperature T1should be as high as possibleoHot body temperature T2should be as low as possible

COP indicates that a given amount of

refrigeration requires only a small amount of

work

23

4 1

T

emperature

Entropy (S)

KJ / Kg.K

Refrigeration

Net Work


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All refrigeration works against certain temperature limitations

Temperature Limitations

t

t

S

T

-20 oC = 253 K

30o

C = 303 K

2

1

3

4

Cold Room

Atmosphere

oCold room to be maintained at -20 oC or 253 K

oReject heat to the atmosphere at 30oC or 303 K

During Heat Rejection Process,refrigerant temperature must be

higher than 303 K

During the Refrigeration Process, refrigeranttemperature must be lower than 253 K

Q. Do we have the control over the temperature?


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To decrease tto zero, eitherUorAwould have to be infinite

Reduction of t can be accomplished by

increasing A or U in the heat exchange

equation:

we can keep the tas small as possible

Infinite values ofU andAwould also require an infinite cost


Temperature Limitations

t

t

S

T

2

1

3

4

Cold Room

Atmosphere

Q = U A t


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Carnot Heat Pump

Heat Pump rejects heat at a high

temperature

Refrigeration cycle absorbs heat at a

low temperature

Heat PumpRefrigeration system operates

for the purpose of delivering heat at a highlevel of temperature


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COP of Refrigeration Cycle with the same

temperatures would be: T1/(T2- T1).

Performance Factor


Carnot Heat Pump

S

T

2

1

3

4

Net Work

HeatRejected

=

=

=

Performance

Factor

=

=

+

=

+ = +


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Cycle differs from the Carnot cycle by the

addition of areas xand y

If vapor/gas such as air is used as the refrigerant, cycle would differ from thefamiliar rectangle of the Carnot cycle.

Effect of area xis to increase the work required,

which decreases the COP.

Effect of area y is to increase the work required

and in addition reduce the amount of refrigeration


Both these effects of areas xand yreduce the COP

Carnot Refrigeration Cycle for Vapor as Refrigerant

23

4

1

T

S

x

y

Atmosphere

Cold Room


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o liquid refrigerant may be trapped in the head of the

cylinder by the rising piston and may damage the

compression valves and the cylinder itself

With a reciprocating compressor, the wetcompressoris not suitable

Wet Compression versus Dry Compression

The Compression process 1-2 is called wet

compression


Revision of the Carnot Cycle

T

S

23

4 1

Atmosphere

Cold Room

Saturated

Liquid

Saturated

Vapor

o Another possible danger of wet compression is that the droplets of liquid may wash

the lubricating oil from the valve of the cylinder thus increasing wear


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If the refrigerant entering the compressor is saturated vapor as point 1, the

compression from point 1-2 is called Dry Compression

Compression of a dry vapor results in atemperature at point 2 which is higher than

the condensing temperature.

Area of that part of the cycle which is above

the condensing temperature is called the

Super Heated Horn

Super Heated Horn represents additional work required by dry compression

Wet Compression versus Dry Compression



2

3

4 1

Super

Heated Horn

T

S


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Expansion Engine is not found suitable

oWork derived from the expansion engine is a small

fraction of that to be supplied to the compressor

Carnot cycle demands that the expansion 3-4takes place Isentropically and

that the resulting work be used to help drive the compressor

o Difficulties such as lubrication intrude when a fluid

of two phases drives the engine

o Economics of the Power Recovery has not justified the cost of the expansion process

Expansion Process



2

3

41

T

S


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Expansion Process



2

3

41

T

S

A Throttling Device such as a valve or other

restrictions is almost universally used for this

purpose

No change in potential and kinetic energy andwith no transfer of heat, constant enthalpy

process i.e. h3 = h4i.e. process is Isenthalpic

Constant enthalpy throttling process is Irreversibleand during the process

entropy increases

o Friction is one of the biggest reasons for any process to be irreversible


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Simple/Standard Vapor Compression System

6

1

2

3

4

5

7

8

1- Evaporator

to produce a heat transfer surface

through which heat can pass from

the refrigerant space into the

vaporizing refrigerant

2- Suction Line

carries the low pressure vapor from

the evaporator to the suction inletof the compressor


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6

1

2

3

4

5

7

8

3- Compressor

To draw refrigerant vapor from the

evaporator and then it rises its

temperature and pressure to such a

point so that it may be easily

condensed with normally available

condensing media

4- Discharge Line or Hot Gas Line

delivers the high temperature, high

pressure vapor from the discharge

of the compressor to the condenser


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6

1

2

3

4

5

7

8

5- Condenser

to provide a heat transfer surface

through which heat passes from

the hot refrigerant vapor to the

condensing medium, which is

either air or water

Energy rejected by the Condenser

comprises the heat energy removed by

each kilogram of refrigerant passing

through the Evaporator and the heat

energy added to each kilogram of

refrigerant passing through the

Compressor


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6

1

2

3

4

5

7

8

6- Receiver Tank Reservoir which stores the liquid

refrigerant coming from the

condenser and supplies it to the

evaporator according to the

requirement

7- Liquid Line

carries the liquid refrigerant from

the receiver tank to the

refrigerant flow control valve

8- Refrigerant Flow Control or

Expansion Valve

to supply a proper amount of refrigerant to

the evaporator after reducing its pressure

considerably so that the refrigerant may

take sufficient amount of heat from the

refrigerant space during evaporation


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Introduction to PH-Charts

The properties of the refrigerants can be listed in tables or they can be shown

on a graph

Most useful and commonly used in refrigeration work is called the Pressure

Enthalpy (P-h) or Mollier diagram

Condition of the refrigerant in any

thermodynamic state can berepresented as a point in the P-h chart

that represents the condition of the

refrigerant in any one particular

thermodynamic state

Once the state point has been located on

the chart, other properties of the

refrigerant for that state can be

determined directly from the chart

P

h

Saturated

Vapor Curve

Saturated

Liquid Curve

2 31


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Introduction to PH-Charts

Property Lines on the Pressure

Enthalpy Diagram

P

h

Iso-ThermalLine

Iso-Pressure

Line

Iso-Quality Line

Iso-Entropy Line

Iso-Specific

Volume Line

Iso-Enthalpy

Line

Saturated Vapor Curve

Saturated Liquid

Curve


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Performance of standard vapor compression cycle

P

(kPa)

h, kJ/kg

23

1

Evaporation4

Condensation

Expansion

Condenser

Compressor

Evaporator1

Expansion

Valve

23

4

oWork of compression

oHeat rejection rate

oRefrigeration effect

oCOP

o Volume flow rate per

KW of refrigeration

With the help of ph-diagram, significant

quantities of the vapor compression

cycle will be determined:


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P

(kPa)

h, kJ/kg

23

1

Evaporation4

Condensation

Expansion

Work of compression

Change in enthalpy in process 1-2

W = ( h1 - h2)

Knowledge of the work of compression isimportant this term may be one of the largest

operating costs of the system

Heat rejection

KJ/kg

Change in enthalpy in process 2-3, ( h3 - h2) KJ/kg

This heat rejection value is used in sizing the condenser and calculating the required flow

quantities of the condenser cooling fluid


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P

(kPa)

h, kJ/kg

23

1

Evaporation4

Condensation

Expansion

Refrigerating Effect

Change in enthalpy in process 4-1

( h1 h4) KJ/kg

Knowledge of the magnitude of this term is

necessary because performing this process is

the ultimate purpose of the entire systemCOP

=

Volume flow rate per kW is usually expressed in cubic meter per second per kW

(m3/sec.kW).

Volume Flow Rate is rough indication of the physical size of the compressor Greater

the value of the term, greater must be the displacement of the compressor in m3/sec

Efficient refrigeration system has a low value of power per kW, but a high COP


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A standard vapor-compression cycle developing 50 kW of refrigeration using

refrigerant 22 operates with a condensing temperature of 35 oC and an

evaporating temperature of -10 oC. Calculate :

(a) the refrigerating effect in Kj/kg,

(b)the circulation rate of refrigerant in kg/s,

(c) the power required by the compressor in kW,

(d)the COP,

(e) the volume flow rate measured at the compressor suction,

(f) the power per kW of refrigeration

(g) the compressor discharge temperature.


Example


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l


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Vapor Compression Cycle

PH-Diagram of superheated R-22 Vapor

C i l


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Heat Exchangers

Condenser

Compressor

Evaporator6

Heat

Exchanger

23

45

1

P

h

23

1

Evaporation

5/

Condensation

Expan

sion

6

4

5

Sub Cooling

Super Heating

Heat exchanger sub cools the liquid from the

condenser with suction vapor coming from

the evaporator

h3 - h4= h1 h6


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V C i l


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Actual Vapor Compression Cycle

P

h

23

14

Pressure Drop

Pressure Drop

Sub Cooling

Super Heating

Actual Cycle

Standard Cycle

Difference b/w actual and Standard cycle can be shown by superimposing the

actual cycle on the Ph-diagram of the standard cycle

Essential Differences between the actual and the standard cycle appear:

o In the pressure drops in the

condenser and evaporator

o In the sub cooling of the liquid

leaving the condenser

o in the superheating of the

vapor leaving the evaporator

V C i l


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Mechanical Engineering Dept CEME NUST 35


Example

In the vapor compression cycle a throttling device is used almost universally to

reduce the pressure of the liquid refrigerant.

(a) Determine the percent saving in net work of the cycle per kg of refrigerant if

an expansion engine could be used to expand saturated liquid refrigerant 22

isentropically from 35 oC to the evaporator temperature of 0 oC . Assume

that compression is isentropic from saturated vapor at 0 oC to a condenser

pressure corresponding to 35 oC.

(b) Calculate the increase in refrigerating effect in kJ/kg resulting from use of

the expansion engine.

Applied Heat and mass transfer

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