Refrigeration Cycles محمود/ دعبدالوهاب

The vapor compression refrigeration cycle is a common method for

transferring heat from a low temperature to a high temperature.

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The above figure shows the objectives of refrigerators and heat pumps. The purpose of a refrigerator is the removal of heat, called the cooling load, from a low-temperature medium. The purpose of a heat pump is the transfer of heat to a high-temperature medium, called the heating load. When we are interested in the heat energy removed from a low-temperature space, the device is called a refrigerator. When we are interested in the heat energy supplied to the high-temperature space, the device is called a heat pump. In general, the term heat pump is used to describe the cycle as heat energy is removed from the low-temperature space and rejected to the high-temperature space.

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The performance of refrigerators and heat pumps is expressed in terms of coefficient of performance (COP), defined as

COPQ

W

COPQ

W

RL

net in

HPH

net in

Desired output

Required input

Cooling effect

Work input

Desired output

Required input

Heating effect

Work input

,

,

Both COPR and COPHP can be larger than 1. Under the same operating conditions, the COPs are related by

COP COPHP R 1

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Can you show this to be true?

Refrigerators, air conditioners, and heat pumps are rated with a SEER number or seasonal adjusted energy efficiency ratio. The SEER is defined as the Btu/hr of heat transferred per watt of work energy input. The Btu is the British thermal unit and is equivalent to 778 ft-lbf of work (1 W = 3.4122 Btu/hr). An SEER of 10 yields a COP of 2.9.

SEER = COP * 3.4122Refrigeration systems are also rated in terms of tons of refrigeration. One ton of refrigeration is equivalent to 12,000 Btu/hr or 211 kJ/min. How did the term “ton of cooling” originate?

1 TR = 12000 Btu/hr = 3.517 kW

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Reversed Carnot Refrigerator and Heat Pump

Shown below are the cyclic refrigeration device operating between two constant temperature reservoirs and the T-s diagram for the working fluid when the reversed Carnot cycle is used. Recall that in the Carnot cycle heat transfers take place at constant temperature. If our interest is the cooling load, the cycle is called the Carnot refrigerator. If our interest is the heat load, the cycle is called the Carnot heat pump.

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The standard of comparison for refrigeration cycles is the reversed Carnot cycle. A refrigerator or heat pump that operates on the reversed Carnot cycle is called a Carnot refrigerator or a Carnot heat pump, and their COPs are

COPT T

T

T T

COPT T

T

T T

R CarnotH L

L

H L

HP CarnotL H

H

H L

,

,

/

/

1

1

1

1

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Notice that a turbine is used for the expansion process between the high and low-temperatures. While the work interactions for the cycle are not indicated on the figure, the work produced by the turbine helps supply some of the work required by the compressor from external sources.

Why not use the reversed Carnot refrigeration cycle?•Easier to compress vapor only and not liquid-vapor mixture.•Cheaper to have irreversible expansion through an expansion valve.

What problems result from using the turbine instead of the expansion valve?

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The Vapor-Compression Refrigeration Cycle

The vapor-compression refrigeration cycle has four components: evaporator, compressor, condenser, and expansion (or throttle) valve. The most widely used refrigeration cycle is the vapor-compression refrigeration cycle. In an ideal vapor-compression refrigeration cycle, the refrigerant enters the compressor as a saturated vapor and is cooled to the saturated liquid state in the condenser. It is then throttled to the evaporator pressure and vaporizes as it absorbs heat from the refrigerated space.

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The Vapor-Compression Refrigeration Cycle

The ideal vapor-compression cycle consists of four processes.

Ideal Vapor-Compression Refrigeration Cycle Process Description 1-2 Isentropic compression 2-3 Constant pressure heat rejection in the

condenser3-4 Throttling in an expansion valve4-1 Constant pressure heat addition in the

evaporator

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The following diagrams, show the flow and T-s diagram illustrates the refrigeration cycle.

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The P-h diagram is another convenient diagram often used to illustrate the refrigeration cycle.

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The ordinary household refrigerator is a good example of the application of this cycle.

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COPQ

W

h h

h h

COPQ

W

h h

h h

RL

net in

HPH

net in

,

,

1 4

2 1

2 3

2 1

Thermodynamic analysis of ideal vapor-compression cycle “ SSVCC” “ simple saturation vapor compression refrigeration cycle

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Relative efficiency

Refrigerator relative efficiency is defined as the ratio between the actual refrigeration cycle coefficient of performance and that for Carnot cycle at same heat source and heat sink temperatures.

R =

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Definitions Refrigeration capacity: is the amount of heat transfer to the evaporator in kW; for steady operations the refrigeration capacity equal to the refrigeration loadRefrigeration effect: the amount of heat transfer to the evaporator per one kg of refrigerant mass flow rate through it " kJ/kg"Condenser duty: is the amount of heat transfer from condenser to surroundings in kWCompressor indicated power: is power added to the refrigerant during compression process ;kWCompressor brake power: the power required to brake the compressor kW; compressor brake power greater than the compressor indicate power" defined the compressor mechanical efficiency"

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Example 1

Refrigerant-134a is the working fluid in an ideal compression refrigeration cycle. The refrigerant leaves the evaporator at -20oC and has a condenser pressure of 0.9 MPa. The mass flow rate is 3 kg/min. Find COPR and COPR, Carnot for the same Tmax and Tmin , and the refrigeration capacity in tons of refrigeration.Using the Refrigerant-134a Tables, we have

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12

2 21

1 22 11

3

3

21

238.41278.23

90020

0.9456 43.790.94561.0

3

900

0

s

soo

ss

StateState kJ

kJh Compressor exithCompressor inlet kg

kgP P kPakJT C

s T CkJkg K s sx

kg K

State

Condenser exit

P kPa

x

3 4

44 13

4 3

4101.61 0.358

0.4053200.3738

.0

o

StatekJh x

Throttle exitkgkJ

skJ T T Cs kg K

kg K h h

20

1 4 1 4

, 2 1 2 1

( )

( )

(238.41 101.61)

(278.23 238.41)

3.44

LR

net in

Q m h h h hCOP

W m h h h h

kJkgkJkg

The tons of refrigeration, often called the cooling load or refrigeration effect, are

1 4( )

13 (238.41 101.61)

min 211min

1.94

LQ m h h

kg kJ TonkJkg

Ton

,

( 20 273)

(43.79 ( 20))

3.97

LR Carnot

H L

TCOP

T T

K

K

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Another measure of the effectiveness of the refrigeration cycle is how much input power to the compressor, in horsepower, is required for each ton of cooling.The unit conversion is 4.715 hp per ton of cooling.Find the system SEER?

, 4.715

4.715

3.44

1.37

net in

L R

W

Q COP

hp

Tonhp

Ton

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ACTUAL VAPOR-COMPRESSION REFRIGERATION CYCLE

An actual vapor-compression refrigeration cycle differs from the ideal one in several ways, owing mostly to the irreversibilities that occur in various components, mainly due to fluid friction (causes pressure drops) and heat transfer to or from the surroundings. The COP decreases as a result of irreversibilities.

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Schematic and T-s diagram for the actual vapor-compression refrigeration cycle.

ACTUAL VAPOR-COMPRESSION REFRIGERATION CYCLE

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DIFFERENCE:The difference between actual and simple refrigeration cycles are:1- Non-isentropic compression2- Superheated vapor at evaporator exit3- Sub-cooled liquid at condenser exit4- Pressure drops in condenser and evaporator5- pressure drop in suction and discharge valves.6- refrigerant heating during suction stroke.

ACTUAL VAPOR-COMPRESSION REFRIGERATION CYCLE

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ACTUAL VAPOR-COMPRESSION REFRIGERATION CYCLE

Compressor isentropic efficiencyPolytrophic powerPressure drop in suction and discharge valvesRefrigerant heating during suction process.Actual volumetric efficiency

Reciprocating compressors

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Single acting

Clearance volumetric efficiency=

Apparent “clearance” volumetric efficiency

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• Clearance ratio C = clearance volume/ swept volume

• Clearance volume = volume above the top dead center = Vc

• Swept volume = volume of the cylinder between top and bottom dead centers = volume above the bottom dead center - volume above the top dead center

• PPd

PS

VC V1 V2

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• Actual volume = volume above bottom dead center – volume of residual gages after expansion from discharge to suction pressure = V2 – V1

• Theoretical volume = swept volume = volume above bottom dead center - volume above top dead center = V2 - Vc

• Clearance ratio C = clearance volume / swept volume = Vc / (V2 – V1)

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Volumetric efficiency =

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Compressor powerCompressors are classified into the following

categories from Th.D. point of view

1- isentropic compressors “ Adiabatic + reversible” Q =0 and no internal and external irreversibleness

S = constant IW isent = m ref h isent

2- Adiabatic compressors, Q= 0 and S 0 IW adiab = m ref h act.

Compressor efficiency = compressor isentropic efficiency = IW isent / IW adiab = h isent / h act

Compressor power

• 3- poly-tropic compressors

• During the compression process the refrigerant follows the relation

Pv n = constant = C

Since the indicated work is given as

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Compressor power

• Since,

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Heat transfer to poly-tropic compressor

• Find the rate of heat transfer to the poly-tropic compressor?

•

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Heat Pump Systems