Experimental study and mathematical modeling of a vapor ... · diagram or the temperature-enthalpy diagram and ... R290,R600a,R1270 as well as their blend mixtures in various ratios

1

Experimental study and mathematical modeling of a vapor compression refrigeration system

Dr Shurooq Talib Remedhan Al-Hemeri

Abstract Vapor compression refrigeration systems are regularly utilized to give a cool atmosphere to space thermal condition control purposes in commercial and industrial applications especially in dehydration of gases and application of refrigeration in the petroleum industry including lubricating-oil purification in addition to the separation of volatile hydrocarbons Keeping in mind to outline good-performance that can be implemented for a wide range of operation mathematical modeling which allows the simulation of its behavior for changing input conditions necessary to be developed In this work we changed the volumetric flow rate of secondary fluid (water) in the condenser in the range of (16-40) literhr to study the experimental and mathematical analysis of condenser and evaporator of the cycle Experimental analysis was conducted using a test rig for a vapor compression refrigeration system with R-134a as a refrigerant The theoretical model is based on the mathematical formulation of the refrigerant side and water side in the condenser and air side of the evaporator and the simulation program is based on the steady state mathematical model of vapor compression refrigeration cycle components solved using Mat-lab program that is used to solve the algebraic equations The model requires input parameters of mass flow rate of the secondary fluid (water) to obtain the model prediction of the outlet temperature of the secondary fluids at the condenser and evaporator the condenser and evaporator thermal capacities the power consumed by the compressor and the coefficient of performance The experimental validation of the model has been carried out using R-134a as a working fluid concluding that the model can predict the performance of the cycle with an error lower than plusmn10

Keyword Refrigeration COP heat exchanger R134a refrigerant

I Introduction

Refrigeration processes are important in a variety of applications where the refrigeration is used in large scale industries especially in the manufacture of ice dehydration of gases domestic commercial refrigerators and other commercial industrial services The applications of refrigerants in the oil industry include the separation of Light components in the reactions required low temperature and for the purification of lubricating-oil The refrigeration system design depends on the properties of the E-mail 80024uotechnologyeduiq salhemeri2004yahoocom Chemical engineering department University of Technology Baghdad Iraq

refrigerants because evaporation and condensation processes in refrigeration systems are achieved in consider a result of the energy transfer from refrigerants and change its phase from the vapor into the liquid [1] Due to the amount of energy required by the refrigeration sector which is estimated to be around 15 of total energy consumption in the world the scientific community is working hard to optimize the operation of refrigeration plants To do so mathematical models constitute one of the best tools both for analyzing and for controlling systems [2]There are two types of mathematical models slated to the behavior of vapor compression refrigeration system empirical or statistical models and physical models Empirical models are based on mathematical routines which obtain the formulation of the system from experimental data but these were only valid for a particular system or specific conditions The physical models were based on detailed data of parts in the system and their modeling using equation derived from the physics laws [3] Vapor compression refrigeration systems which are frequently utilized to give chilled media to space warm condition control purposes in domestics commercial and industrial applications mainly comprise a compressor a fixed-orifice expansion device two of heat exchangers such as (condenser and evaporator) and the light secondary fluid known as (refrigerant) which evaporates and condenses readily And the one since for the system was closed to never the refrigerant leaves the system [4] The ratio of the cooling heat capacity of the compression work called as a coefficient of performance for refrigeration system therefore COP can be increased by increasing the refrigerating effect or by decreasing the compression work For a vapor compression refrigeration cycle it is important to study how much heat is extracted and how little energy is spent The ratio of heat absorbed to the work input is called the coefficient of performance The ratio should be as high as possible [5] COP= =

minus (1)

Theoretical COP is the ratio of (theoretical refrigerating effect) to (the theoretical compressor work or isentropic compressor work) Theoretical refrigerating effect calculated from enthalpies about evaporator is found from the pressure-enthalpy diagram or the temperature-enthalpy diagram and isentropic compressor work is calculated from enthalpies about compressor was also got from the

The Eighth Jordan International Chemical Engineering Conference (JIChEC 2017)

November 7-9 2017

2

diagram Whenever define the actual coefficient of

performance COPrdquoas a ratio of actual refrigeration

effect to the actual work supplied to the compressor

[6]

There are a many literature which deals with the

mathematical statements of the vapor compression

refrigeration systems such as Arora and Kanshik [7]

who presented the theoretical analysis and the

exergy analysis in detail to the real vapor

compression refrigeration cycle for highest

condensing efficiency in a condenser Viabhav et

al[8] studied the property of the refrigerant that

dependent a thermodynamic model for the simple

vapor compression refrigeration system using

various refrigerants that simulate the performance of

actual system used for a higher efficiency Gustavo

[9] studied the theoretical and experimental analysis

of the effect of condenser sub-cooling on the

performance of vapor compression refrigeration

system using various refrigerants Belman et al[10]

the analyst of the refrigeration cycle such as vapor

compression refrigeration cycle by artificial neural

network using a mathematical model which

depended on the operation of a biological neural

networks where the analysis and experimental

results provided ideas to clarify the linkage between

the input and output parameters in vapor

compression refrigeration cycle and at the end of

the model actually predicted the performance of the

cycle Maruthi et al [11] performed the

experimental analysis of vapor compression

refrigeration system by using R134a and R404a

which also evaluated the performance of the cycle

Mitesh et al[12] predicated a theoretical


system and refrigerating effect with alternative

hydrocarbon refrigerants such as

R290R600aR1270 as well as their blend mixtures

in various ratios Kedarnath and Patil [13] studied

the performance enhancement of vapor compression

refrigeration system using nano-fluids which

increased the area available for exchanging heat and

efficiency

The experimental study of any refrigeration

framework generally is considered complicated

essentially because of the cost and the vast number

of factors included The utilization of numerical

models can lessen the costs and furthermore

encourage understanding the phenomena related to

the issue Refrigeration systems models are

partitioned into two wide classes steady ndashstate

models and dynamic models [14]

There is a large number of researchers who studied a

steady state condition for refrigeration system type

of vapor compression for example Koury et

al[15]Jong et al[16] and Sivak and Hroncova[17]

suggested a refrigeration system model related to

parameters for condenser and evaporator and

simulated the compressor and expansion device

using the refrigerant R134a

The main objective of this work is to study the

experimental data and present the mathematical

analysis for the two heat exchanger ldquocondenser and

the evaporatorrdquo used in the test rig of the vapor

compression refrigeration system A vapor

compression refrigeration system is simulated at

steady state conditions A Mat-lab programming

version 2013a was used in analyzing the heat

transfer for evaporator and condenser in addition to

thermodynamic properties for the refrigerant The

simulation was performed with the eco-friendly

1112-tetrafluoroethane or known as hydro-

fluorocarbon (HFC) refrigerant R134a

II Description of physical system

A simple vapor compression refrigeration cycle is

shown in Figure 1 which comprises of the four

fundamental parts evaporator compressor

condenser and expansion valve The refrigerant is

the primary working fluid in the cycle In the

evaporator the refrigerant takes heat from the low-

temperature primary fluid by vaporization The

refrigerant in the evaporator is superheated and

vapor is then moved to compressor To get on the

highest level of energy done by adding the

mechanical work On the discharge side of the

compressor the vapor at higher pressure and

temperature is condensed in the condenser

In the condenser the refrigerant vapor gives the heat

to the secondary fluid and then it condenses The

condensation is done in horizontal tubes which

involves total condensation of the vapor Close to

the outlet of the horizontal level tubes the vapor

lessens to zero and the flow in the tube becomes

liquid stream

The condensed refrigerant then passed through an

expansion valve which is lowering the pressure and

control of the mass-flow rate of the refrigerant The

refrigerant leaving the extension gadget enters the

evaporator in which the refrigerant absorbs heat and

boils The refrigerant at that point comes back to the

compressor and the cycle is returned again The

ideal vapor compression refrigeration cycle is shown

on the pressure ndash enthalpy and temperature-entropy

diagrams in Figures 23 also the refrigeration cycle

of vapor compression at actual state is shown in

Figure 4 [141819]

Fig 1 Schematic diagram of simple vapor

compression refrigeration system [14]

3

Process 1 ndash 2 Isentropic compression in the compressor

Process 2 ndash3 Constant pressure heat rejection in the condenser Process 3 ndash 4 Isenthalpic expansion in the expansion device

Process 4 ndash1 Constant pressure heat absorption in the evaporator

Fig 3 T-S diagram for the ideal vapor

compression refrigeration cycle [19]

Fig 4 P-h diagram for the actual vapor


Fig 2 P-h diagram of ideal vapor compression refrigeration cycle [19]

me

ter

119824119815 119830119842119847

Saturated

vapor

Saturated

liquid 2

3

4rsquo

4 1

119824119819

4

III Experimental work

Experimental rig

Test rig of refrigeration system was used to perform

the experimental tests as shown in Figure 5 which

consist of the following components compressor

condenser capillary tube evaporator and

accessories like ( Pressure gages thermocouples

and readers flow meters and sight glasses)

Compressor A single 370W capacity hermetic

compressor (Panasonic model QB77C16GAX5) was

selected in the current work The compressor was

designed to work at a speed 2990rpm and R134a

was used as a refrigerant

Condenser The water condenser used in this cycle

is wire and tube type with exchange surface area

equal to 600 m2

Expansion Device In this cycle the capillary tube

consists of a single copper tube with (2800 mm)

length and (15 mm) diameter is located before the

evaporator to make a pressure drop and control on

the mass flow rate of refrigerant that enters the

evaporator

Evaporator In order to get variable load on the

evaporator a shell and coil evaporator has been

used where the flow of refrigerant in the tube and

air in a shell with exchange surface area equal to 600

m2

Sight Glass Sight glasses are used for viewing the

phase of refrigerant through the refrigeration system

and to view the liquid refrigerant level through tubes

and other vessels in the system It is used also as

refrigerant moisture indicator to ensure that the

refrigerant contains less moisture

Pressure Gauges Pressure gaugesare used to

measure the pressures at different locations in the

cycle Pressure gauge with a range of (0 to 20) bars

is used to measure the low side pressure and the

high side pressure

Temperature Sensors Temperatures at different

points in the test rig were measured by

thermocouples connected to the temperature readers

Temperatures were measured by K-type

thermocouple operating in the range of (-200 to

1250 ordmC)

Flow Meters Two flow meters were used in the

present work the first one was used for measure the

volumetric flow rate of the liquid refrigerant in the

refrigeration cycle model (10C- R134a) with a

range of (003 ndash 03) Lmin The second flow meter

was used to measure the volumetric flow rate of the

inlet water to the condenser model (Z-3002-liquid

water) with a range of (14 ndash40) Lhr

Experimental procedure

The main object of this work is to estimate and

analyze the performance of the vapor compression

refrigeration system with R134a as a refrigerant by

using refrigeration rig that is shown in Figure 5

1- The test rig system was turned on and

operated without a thermal load in the

evaporator for 5 min to ensure a proper

operation

2- Set the float in the water volumetric rot meter

to any flow in the range (16-40) L hr

3- Turn on the compressor and the fan

4- Check the system has reached to steady state

by selecting the temperature and pressure

measurements every minute until no further

change is observed should be (10 to 15 )min

5- At steady state take the readings of the

refrigerant flow rate four pressures and eight

temperatures This step was repeated for each

thermal load applied to the evaporator

6- For shutdown stop the compressor wait for 5

minutes then close the water valve Then

switch off the main power supply and thermo-

couple device (to save batteries)

IV Thermodynamic model for vapor

compression refrigeration performance

The mathematical models of the parts for the

refrigeration circuit including the compressor heat

exchangers expansion valve at steady state was

include it in simulation program To simulate a

refrigeration system we ought to be joined the parts

models into a general model as indicated by the

relationship for ingredients parameters Figure 6 is a

simplified flow chart for the vapor compression

refrigeration system with assuming the pressure

losses in condenser and evaporator are ignored

Considering the operation of the cyclic system at

steady-state using refrigerant R134a vapor outlet

from evaporator at point 1 and compression through

the compressor to point 2The sub-cooled refrigerant

exits the condenser at point 3 then flows through the

expansion valve to the evaporator inlet at point 4

The analysis of the cycle in Figure 6 in terms of

1) Cooling capacity

2) Condenser heat capacity

3) Compressor power consumption

4) Mass flow rate of refrigerant

5) Coefficient of performance

6) Efficiency of vapor compression refrigeration

cycle

Independent variables Uncertainty

interval

Pressure gauge plusmn 02 ( bar )

Temperature readers plusmn 1 ( ordmC )

Thermometer plusmn 1 ( ordmC )

Flow meter plusmn 0014 ( kgsec )

Table 1 Accuracy for the experimental

measurements

5

In the present work developed assumptions to

specify thermodynamic analysis in the refrigeration

system

Pressure losses in the pipelines are neglected

Kinetic and potential energy are not considered

Heat transfer from the system or to the system is

not considered

By applying the first law of thermodynamics with

the change in internal energy for a cyclic process is

zero we get [8]

(QcondndashQ

evap)ndashW=0 (2) Where Q

cond is the rate of heat rejection in the

condenser (kW)Qevap is the rate of heat absorbed by

the evaporator (kW) W is the power input to the

compressor (kW)

The heat absorbed through the evaporator and

exothermic from the condenser occurs by the

working fluid ldquorefrigerantrdquo streams with mass flow

rates and specific heats Therefore the heat-transfer

rate to the cycle in the heat exchanger (evaporator)

ie cooling capacity becomes

)8T ndash7(T air)pC m( ) =1h ndash 4(h refm = evap

Q (3)

Where Cp is the heat capacity for the external fluid

(air) (kJkgK)T7 is the external fluid (air) inlet

temperature (K) T8 is the external fluid (air) outlet

temperature (K) mref is the mass flow rate of

refrigerant (kgs) and h is the specific enthalpy of the

refrigerant at state point (kJkg)

As the same the heat-transfer rate between the

refrigeration cycle and the sink in the condenser ie

condenser heat capacity is

Qcond = m

ref (h2 ndash h3) = (m Cp)w (T5ndash T6) (4)

Where T5 is the external fluid (water) inlet

temperature (K) and T6 is the external fluid (water)

outlet temperature (K)

And the power required by the compressor at

isentropic efficiency is given by

W = mref (h1 ndash h2) (5)

We then calculate the circulation rate of refrigerant

mmiddotref which is determined from the rate of heat

absorption in the evaporator by the equation

mmiddotref = Qevap

h1 minus h4

(6)

The COP is defined as the refrigerating effect over

the net work input ie

COPrdquoactualrdquo = Qevap W =

(h1 ndash h4)

(h2 ndash h1) (7)

Fig 5 Refrigeration Unit

6

Performance of coefficient for Carnot ideal cycle

ω =COPcarnot = 119879119888

119879ℎminus119879119888

(8)

Where Tc = T1sat is the saturated temperature of

refrigerant in (K) at evaporator pressure and Th= T3

sat is the refrigerant saturated temperature in (K) at

condenser pressure

Efficiency of vapor compression cycle ( ɳ )

ɳ=COPrdquoactualrdquoω (9)

Requirements for calculation the

thermodynamic properties of R134a

refrigerant in simulation of the refrigeration

cycle To analysis the refrigeration system the following

requirements must be availability to calculate the

refrigerant thermodynamic properties [20-21]

Temperature Symbols Define

T1 Refrigerant inlet compressor temperature T2 Refrigerant discharge compressor

temperature T3 Refrigerant outlet condenser temperature T4 Refrigerant inlet evaporator temperature T5 Water inlet condenser temperature T6 Water outlet condenser temperature T7 Air inlet evaporator temperature T8 Air outlet evaporator temperature

Fig 6 Schematic diagram of the vapor compression refrigeration system

Compressor

119827120789

Evaporator

T4

119827120786

Refrigerant

turbine

flow

119827120783

119827120788

119827120785119827120787

119827120784

Water flow

meter

Water

Out

Water

In

Condenser

Throttling

Device

119827120790

Fan

Cooling Mode

Diagram

7

The quick calculation Because occur many

calculations that related to the simulation field of

thermodynamic properties for refrigerant

therefore the quick calculation of refrigerant

thermodynamic properties consider an important

factor for simulation and it has an effect on the

selection of component model in the system

Higher stability Since there are many attempts

for the calculation of refrigerant thermodynamic

properties the dissimilarity in calculation has

happened regardless of the possibility that

likelihood is low in a solitary estimation so the

requirement on the stability must be achieved

The reversibility There are a large number of

refrigerant thermodynamic properties in the

simulation of refrigeration systems which need to

be converted to each other In spite of the

deviation is almost very little in a solitary

conversion process however will lead to a large

difference in the last figured outcomes due to a

numerous iterations that required

The continuity and simplify The result of

convergence is achieved only when there is

iteration for continuous functions And because

of some refrigerant thermodynamic properties

are used the differential coefficients therefore

the differential coefficients must be also

continuous and its function curve should be

smooth

Cleland [22] and Wang etal [23] presented a quick

method to calculate the refrigerant thermodynamic

properties in addition they gave the correlations for

R134a for the saturation temperature of _40 to70 oC For a reversible calculation the formula of saturation

pressure and temperature is presented in a simple

and practical model consumes less computation

time The estimations of polynomial curve- fit

equations for thermodynamic properties of

refrigerant R134a are easy and computationally

quick for usually refrigeration conditions

anticipated properties generally a large concur with

the source information to about plusmn04

For the saturated temperature of the saturated

pressure relationship Antoine equation was adopted

Tsat = (

120784120784120782120782120791120790120782

120784120783120787120783120784minus119819119847119823119852119834119853 ) -24661 (10)

Where temperature in (0C) and the pressure in(KPa) At point (3) outlet from condenser The extend of

liquid sub-cooling found by

∆Tb = T3sat

ndashTL (11)

Where TL= T3 and T3sat is calculated from

eq(10) at high pressure ldquoPcondrdquo

hL3 =50952+133529 T3 +170650T2

3 +76741

10-3T33 (12)

hL3enthalpy of sub-cooled liquid (kJkg) at ∆Tb gt 0

and is enthalpy of saturated liquid at ∆Tb= 0

At point (4) since the expansion is the throttling

valve

h4=hL3 (13)

h4 enthalpy of refrigerant at outlet from throttling

valve (kJkg)b ~gt 0 then b ~gt 0 then Provided AT

At point (1) outlet from evaporator if vapor

superheat that is given by

∆Ts=Tsup ndash T1sat (14)

Where Tsup= T1 and T1

sat is calculated from

eq(10) at low pressure rdquoPevaprdquo hv =249455+606163 T1

sat -105644 T21

sat -

18242610-2T31sat (15)

hv enthalpy of saturated vapor at ∆Ts=0 in(kJkg)

h1= hv (1+34818610-3 ∆Ts +1688610-6 ∆T2s

+9264210-6∆Ts T1sat -769810-8 ∆T2

s T1sat

+

1707010-7∆TsT21

sat-1213010-9∆T2sT2

1sat (16)

h1 enthalpy of superheated vapor at ∆Ts gt0 that

inlet to compressor (kJkg) At point (2) outlet from compressor the vapor is

superheat therefore we need another parameter to

determine h2 that is the specific volume of saturated

vapor (ῦv ) in (m3kg)

ῦv=exp(-124539+2669

27315+T1sat )(101357+

10673610-3T1sat-9253210-6 T2

1sat -32192

10-7 T31sat ) (17)

then convert ῦv to superheated specific volume V1

sup at point (1) in (m3kg)

s 2T∆6-396510- sT∆3-(1+4788110 vῦ= sup

1V

)sat1

2T s2T∆9-540110- sat1

2T sT∆7-+8573910(18)

∆Tc= T3sat ndash T1

sat (19) C1=106469-1690710-3 T1

sat -856010-6 T21sat

-213510-5 T1sat∆Tc -6173010-7 T2

1sat∆Tc

+2074010-7 T1sat∆T2

c +772010-9 T21

sat∆T2c -

610310-4∆Tc (20)

C=C1(1+1175710-3∆Ts-181410-5∆T2s+

412110-5∆TsT1sat-809310-7∆T2

sT1sat) (21)

Where C is the curve fit equation Calculate ∆hmacr enthalpy change in isentropic

compression for R134a

∆hmacr = 119862

119862minus1 P1 V1

sup(1198752

1198751

119862minus1

119862 - 1) (22)

∆h119938119940119957 = ∆119841macr

ɳcomp (23)

ɳcomp actual efficiency of compressor and equal

80

h2 = ∆hact + h1 (24)

From the previous equations the procedure of flow

chart for the saving simulation is shown in Figure 7

8

Start

Input (mwater)

Read PhldquoPcondrdquo PLrdquoPevaprdquoT1 T2 T3 T4 T5 T6 T7 T8mref

measured from experimental work

Calculation at point 3

Calculate Tsat3 from eq(10)

Calculate ∆Tb from eq(11)

Calculate hL3 from eq(12)


h4=hL3


Calculate T1sat from eq(10)

Calculate ∆TS from eq(14)

Calculate hv from eq(15)

Calculate h1from eq(16)


Calculate ῦv from eq(17)

Calculate V1sup from eq(18)

Calculate ∆Tc from eq(19) C1from eq(20) and C from eq(21)

Calculate ∆hmacr from eq(22) Calculate ∆h119938119940119957 from eq(23)


Outputs

cooling capacity eq(3)

condenser heat capacity eq(4)

compressor power consumption eq(5)

COP eq(7)

ω eq(8)

Efficiency of vapor compression refrigeration cycle eq(9)

End

Fig 7 Schematic diagram describing the overall model for simple

vapor compression refrigeration system with R134a

9

V Results and Discussion

In this area thermodynamic performance parameters

are computed from the experimental data using

refrigerant R134a by utilizing the different equations

(2-24) and discussed The outcomes acquired from

this research may vary slightly relying on the

refrigerant charge experimental and the

environmental conditions Performance parameters

of the vapor compression refrigeration system for

example genuine work of compressor coefficient

of performance cooling capacity and condenser

capacity were analysis for various volumetric flow

rate of water inlet to the condenser that using R134a

Many investigations are executed into performance

analysis of the vapor compression refrigeration

system But a limited research is implemented for

effect of volumetric or mass flow rate of the

secondary fluid in condenser on the refrigeration

system Some researchers such as Dalkilic and

Wongwises [24] and Elsayed and Hariri [25]

studied the effect of air mass flow rate in shell

evaporator on the heat pump system

The numerical results of the obtained simulation are

presented in a graphical form as shown in Figures

8-14

It was seen that for the same inlet temperature

(Tincond) of water which the condenser secondary

fluid as the water mass flow rate (mw) increases the

condenser heat capacity (Qcond) increased due to

increase water mass flow rate as seen from Figure 8

Figure 9 shows the COP (coefficient of

performance) variation with respect to the condenser

heat capacity As the cooling capacity (Qevap) was

the constant It was observed that as the condenser

heat capacity increases coefficient of performance

increased as studied by Maruthi et al [11] Bhatkar

et al[18]and Saidur et al[26] Figure 10 and

Figure 11 show the effect of variation of condenser

heat capacity on system temperatures Tincond(T5)

Tinevap(T7) Toutcond(T6) and Toutevap(T8) data are

independent of refrigerant temperature in two heat

exchangers The temperature (T6) gradient outlet

from condenser increases with increases in

condenser heat capacity as shown in Figure 10 But

there is a slight change in temperature of air outlet

from evaporator (T8 ) with variation for condenser

heat capacity as shown in Figure 11 Variation of

condenser pressure (Ph) and evaporator pressure (PL)

with condenser heat capacity is shown in Figure

12The condenser pressure decreases whereas

evaporator pressure increases with increase in

condenser heat capacity The results show the same

trend as obtained by Akintunde et al[27] Figure 13

pointed out that as the pressure drop between

condenser and evaporator increases for same cooling

capacity (Qevap) of the system the work of

compression increases due to decreased condenser

heat capacity (refer Figure 12) Figure 14 shows the

COP variation with respect to the rate of heat

transfer in (kW)As the compressor work

consumption reduced thus COP increases And when

condenser heat capacity increases COP increases

too But cooling capacity is nearly the same at

obtained increased in COP as studied by

Yeunyongkul et al[28] Therefore in this case

when consider in (equation 7) it was found that the

compressor work decreases resulting in the increase

in COP with remaining the cooling capacity nearly

constant

20

205

21

215

22

225

23

235

24

245

0 0005 001 0015

Q˙ c

on

d(k

W)

m˙water(kgsec)

Fig 8 Variation of condenser heat capacity at

different water mass flow rate

4

45

5

55

6

65

7

75

8

20 21 22 23 24 25

CO

P

Qcond (KW)

Fig 9 Variation of coefficient of performance

at different condenser heat capacity

10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)

Fig10 Variation of water inlet ampoutlet

temperatures about condenser vs condenser

heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)

Fig11 Variation of air inlet ampoutlet

temperatures about evaporator vs condenser

heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)

Fig12 Variation of condenser pressure amp

evaporator pressure vs condenser heat

capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)

Fig13 Variation of compressor power

consumption with pressure drop between

condenser amp evaporator

11

VI Conclusions This experimental study and the mathematical

model investigated the effect of the changing the

water volumetric flow rate (16-40 )Lhr or by the

mass flow rate (158 to 396 )kghrThe working

fluid in the refrigeration system is R134a From this

study the following conclusion is deduced-

1) The present study is allocated to develop a

physical model that permits clarification the

energy conduct of a vapor compression

system utilizing input parameters that can

be easily acquired from experimental work

2) Based on the simulation of the refrigeration

system it can be said that the refrigeration

system performance is improved by

bringing down the power consumption for

compressor increasing the rejection of

condenser heat capacity or decreasing the

pressure difference amongst condenser and

evaporator

3) The mass flow rate of water which is the

secondary fluid in condenser are need to be

considered in selecting the condenser since

it effect on the condenser heat capacity for

vapor compression refrigeration system

4) Given the requirement for energy

preservation it is desirable to enhance the

execution of vapor compression system

presenting new parameter designs and

additionally applying a proficient operation

In this way a mass flow rate of water of the

refrigeration system can be used at higher

value of the range that used to improve the

condenser heat capacity and coefficient of

performance of the system

5) A validation of the model was carried out

by a comparison between experimental

information and model yields The

outcomes were demonstrating a comparison

between measured mass flow rate values of

refrigerant R134a and those obtained with

the circulation rate of refrigerant that

determined from the rate of heat absorption

in the evaporator It is observed that a good

fit with relative error estimations that differ

withinplusmn10

Acknowledgments

Dr Shurooq T Al-Hemeri thankful to the

department of chemical engineering University of

Technology for providing Laboratory of

thermodynamic and Dr Zaidoon Mohsen Shakor

their help during this study

References

1] CalmJrdquo The next generation of refrigerants-

review and considerationsrdquo International journal of

refrigeration 200831pp1123-1133

2]Liopis R Cabello R Torrella ErdquoA dynamic

model of a shell and tube condenser operating in a

vapor compression refrigeration plantrdquo

International journal of thermal sciences 2008 47

pp 926-934

3]Ye YWeiwei WMengwei HrdquoA state-space

dynamic model for vapor compression refrigeration

system based on moving-boundary formulationrdquo

International journal of refrigeration 201560pp1-

16

4] Suresh B and Satyanarayana V rdquoImproving and

comparing the coefficient of performance of

domestic refrigerator by using refrigerants R134a

and R600ardquo International journal of scientific

research and management studies20148pp267-

277

5]Mishra R rdquoThermodynamic performance

evaluation of multi-evaporators single compressor

in vapor compression refrigeration systems for

reducing ozone depletionrdquo International journal of

advance research and innovation 20142pp325-

332

6]Neeraj U rdquoTo study the effect of sub-cooling and

diffuser on the coefficient of performance of vapor

compression refrigeration systemrdquo International

0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP

Fig14 Comparison of different power Qevap

Qcond W

comp vs coefficient of

performance

12

journal of research in aeronautical and mechanical

engineering 20156pp14-44

7]Arora A and Kanshik S rdquoTheoretical analysis of

vapor compression refrigeration system with

R502R404a and R507ardquo International journal of


8]Vaibhav J Kachhwaha S Mishra R

rdquoComparative performance study of of vapor

compression refrigeration system with

R22R134aR410aR407cM20rdquo International

journal of energy and environment 20112pp297-

310

9]Gustavo P rdquoEffect of condenser sub-cooling on

the performance of vapor compression refrigeration

systems experimental and numerical investigationrdquo

International refrigeration and air conditioning

conference at PuradueJuly16-192012

10]Belman J Ledesma S Garcia J rdquoAnalysis of a

variable speed vapor compression system using

artificial neural networksrdquo Expert systems with

applications2013404362-4369

11]Maruthi G Rajendra P Veeresh G

Experimental analysis of vapor compression

refrigeration system with liquid line suction heat

exchanger by using R134a and R404ardquo

International journal of scientific research and

management studies201412pp382-395

12]Mitesh M Deshmukh K Mali Vrdquo

Performance comparison of R22 refrigerant with

alternative hydrocarbon refrigerantsrdquo International

journal on theoretical and applied research in

mechanical engineering 20152pp17-21

13]Kedarnath B and Patil Urdquo Performance

enhancement of vapor compression refrigeration

system using nano-fluids a reviewrdquo International



14]Santa R and Garbai Lrdquo The mathematical

model and numerical simulation of the heat pump

systemrdquo International journal of engineering-annals

of faculty engineering hunedoara 20134pp271-

280

15]Koury R Machado L Ismail K rdquoNumerical

simulation of a variable speed refrigeration systemrdquo

International journal of refrigeration

201024pp192-200

16]Jong w Gilbong L Min SrdquoNumerical study

on the steady state and transient performance of a

multi-type heat pump systemrdquo International journal

of refrigeration 201434pp1157-1172

17]Sivak P and Hroncova D rdquoState-space model of

a mechanical system in MATLAB Simulinkrdquo

Procedia engineering 201548pp629-635

18]Bhatkar V Kriplani V Awari G

rdquoExperimental performance of R134a and R152a

using microchannel condenserrdquo Journal of thermal


19] Sandip P Chavhan S Mahajan Drdquo

Experimental performance evaluation of R152a to

replace R134a in vapour compression refrigeration

systemrdquo International journal of modern

engineering research 2015 5 pp 37-47

20]Guo L rdquoRecent developments in simulation

techniques for vapor compression refrigeration

systemsrdquo International journal of refrigeration

200730pp1119-1133

21] Lima Rand Seixlack A Modeling of wire-on-

tube condensers for domestic refrigerators 13th

Brazilian congress of thermal sciences and

engineering 2010

22]Cleland A rdquoPolynomial curve-fit for refrigerant

thermodynamic properties extension to include

R134ardquo International journal of refrigeration

200017pp245-249

23]Wang K Ding G Fukaya M rdquoExtension of the

applicable range of the implicit curve-fitting method

for refrigerant thermodynamic properties to critical

pressurerdquo International journal of refrigeration

20073pp418-432

24]Dalkilic A Wongwises SrdquoA performance

comparison of vapor compression refrigeration

system using various alternative refrigerantsrdquo

International communication in heat and mass

transfer 201337pp1340-1349

25]Elsayed A Hariri A rdquoEffect of condenser air

flow on the performance of split air

conditionerrdquoWorld renewable energy congress

Sweden 2011pp2134-2141

26]Saidur H Ahmed J Masjuk H

rdquoThermodynamic performance analysis of R-600

and R-600a as refrigerantrdquo Engineering e-

transaction12015

27]Akintunde M Falade T Bolaji

BrdquoComparative analysis of performance of three

ozone friendly refrigerants in vapor compression

refrigeratorrdquo Journal of sustainable energy and

environment 20152pp61-64

28] Yeunyongkul P Sakulchangsatjatai P

Terdtoon P rdquoMathematical model of the optimum

heat pipe heat exchanger for a condenser of vapor

compression refrigeration cyclerdquo Energy research

Journal 20122pp104-110

13

ShTAl-Hemeri Shurooq

Talib Remedhan Al-Hemeri PhD in

Chemical Engineering - University of

Technology-Baghdad-Iraq Assist professor

ldquolecture ldquo in University of Technology

chemical engineering departmentHer interests

in Thermodynamic engineering rdquoRefrigeration

systemrdquo Phase change of materialsrdquo Extraction

of organic compounds Two-phase in bubble

column and Renewable energy

2

diagram Whenever define the actual coefficient of

performance COPrdquoas a ratio of actual refrigeration

effect to the actual work supplied to the compressor

[6]

There are a many literature which deals with the

mathematical statements of the vapor compression

refrigeration systems such as Arora and Kanshik [7]

who presented the theoretical analysis and the

exergy analysis in detail to the real vapor

compression refrigeration cycle for highest

condensing efficiency in a condenser Viabhav et

al[8] studied the property of the refrigerant that

dependent a thermodynamic model for the simple

vapor compression refrigeration system using

various refrigerants that simulate the performance of

actual system used for a higher efficiency Gustavo

[9] studied the theoretical and experimental analysis

of the effect of condenser sub-cooling on the


system using various refrigerants Belman et al[10]

the analyst of the refrigeration cycle such as vapor

compression refrigeration cycle by artificial neural

network using a mathematical model which

depended on the operation of a biological neural

networks where the analysis and experimental

results provided ideas to clarify the linkage between

the input and output parameters in vapor

compression refrigeration cycle and at the end of

the model actually predicted the performance of the

cycle Maruthi et al [11] performed the

experimental analysis of vapor compression

refrigeration system by using R134a and R404a

which also evaluated the performance of the cycle

Mitesh et al[12] predicated a theoretical


system and refrigerating effect with alternative

hydrocarbon refrigerants such as

R290R600aR1270 as well as their blend mixtures

in various ratios Kedarnath and Patil [13] studied

the performance enhancement of vapor compression

refrigeration system using nano-fluids which

increased the area available for exchanging heat and

efficiency

The experimental study of any refrigeration

framework generally is considered complicated

essentially because of the cost and the vast number

of factors included The utilization of numerical

models can lessen the costs and furthermore

encourage understanding the phenomena related to

the issue Refrigeration systems models are

partitioned into two wide classes steady ndashstate

models and dynamic models [14]

There is a large number of researchers who studied a

steady state condition for refrigeration system type

of vapor compression for example Koury et

al[15]Jong et al[16] and Sivak and Hroncova[17]

suggested a refrigeration system model related to

parameters for condenser and evaporator and

simulated the compressor and expansion device

using the refrigerant R134a

The main objective of this work is to study the

experimental data and present the mathematical

analysis for the two heat exchanger ldquocondenser and

the evaporatorrdquo used in the test rig of the vapor

compression refrigeration system A vapor

compression refrigeration system is simulated at

steady state conditions A Mat-lab programming

version 2013a was used in analyzing the heat

transfer for evaporator and condenser in addition to

thermodynamic properties for the refrigerant The

simulation was performed with the eco-friendly

1112-tetrafluoroethane or known as hydro-

fluorocarbon (HFC) refrigerant R134a

II Description of physical system

A simple vapor compression refrigeration cycle is

shown in Figure 1 which comprises of the four

fundamental parts evaporator compressor

condenser and expansion valve The refrigerant is

the primary working fluid in the cycle In the

evaporator the refrigerant takes heat from the low-

temperature primary fluid by vaporization The

refrigerant in the evaporator is superheated and

vapor is then moved to compressor To get on the

highest level of energy done by adding the

mechanical work On the discharge side of the

compressor the vapor at higher pressure and

temperature is condensed in the condenser

In the condenser the refrigerant vapor gives the heat

to the secondary fluid and then it condenses The

condensation is done in horizontal tubes which

involves total condensation of the vapor Close to

the outlet of the horizontal level tubes the vapor

lessens to zero and the flow in the tube becomes

liquid stream

The condensed refrigerant then passed through an

expansion valve which is lowering the pressure and

control of the mass-flow rate of the refrigerant The

refrigerant leaving the extension gadget enters the

evaporator in which the refrigerant absorbs heat and

boils The refrigerant at that point comes back to the

compressor and the cycle is returned again The

ideal vapor compression refrigeration cycle is shown

on the pressure ndash enthalpy and temperature-entropy

diagrams in Figures 23 also the refrigeration cycle

of vapor compression at actual state is shown in

Figure 4 [141819]

Fig 1 Schematic diagram of simple vapor

compression refrigeration system [14]

3









me

ter

119824119815 119830119842119847

Saturated

vapor

Saturated

liquid 2

3

4rsquo

4 1

119824119819

4


Experimental rig














equal to 600 m2






evaporator





m2











high side pressure






1250 ordmC)

















operation



































1) Cooling capacity






cycle


interval






measurements

5



system




not considered



zero we get [8]

(QcondndashQ





compressor (kW)








Q (3)










Qcond = m











mmiddotref = Qevap

h1 minus h4

(6)




(h1 ndash h4)

(h2 ndash h1) (7)


6


ω =COPcarnot = 119879119888

119879ℎminus119879119888

(8)




condenser pressure













Compressor

119827120789

Evaporator

T4

119827120786

Refrigerant

turbine

flow

119827120783

119827120788

119827120785119827120787

119827120784

Water flow

meter

Water

Out

Water

In

Condenser

Throttling

Device

119827120790

Fan

Cooling Mode

Diagram

7





























smooth















Tsat = (

120784120784120782120782120791120790120782

120784120783120787120783120784minus119819119847119823119852119834119853 ) -24661 (10)



∆Tb = T3sat

ndashTL (11)



hL3 =50952+133529 T3 +170650T2

3 +76741

10-3T33 (12)




valve

h4=hL3 (13)









sat -105644 T21

sat -

18242610-2T31sat (15)


h1= hv (1+34818610-3 ∆Ts +1688610-6 ∆T2s

+9264210-6∆Ts T1sat -769810-8 ∆T2

s T1sat

+

1707010-7∆TsT21

sat-1213010-9∆T2sT2

1sat (16)






ῦv=exp(-124539+2669

27315+T1sat )(101357+

10673610-3T1sat-9253210-6 T2

1sat -32192

10-7 T31sat ) (17)



s 2T∆6-396510- sT∆3-(1+4788110 vῦ= sup

1V

)sat1

2T s2T∆9-540110- sat1

2T sT∆7-+8573910(18)


sat (19) C1=106469-1690710-3 T1

sat -856010-6 T21sat

-213510-5 T1sat∆Tc -6173010-7 T2

1sat∆Tc

+2074010-7 T1sat∆T2

c +772010-9 T21

sat∆T2c -

610310-4∆Tc (20)

C=C1(1+1175710-3∆Ts-181410-5∆T2s+

412110-5∆TsT1sat-809310-7∆T2

sT1sat) (21)



∆hmacr = 119862

119862minus1 P1 V1

sup(1198752

1198751

119862minus1

119862 - 1) (22)

∆h119938119940119957 = ∆119841macr

ɳcomp (23)


80

h2 = ∆hact + h1 (24)



8

Start

Input (mwater)








h4=hL3












Outputs




COP eq(7)

ω eq(8)


End



9

























8-14












































constant

20

205

21

215

22

225

23

235

24

245

0 0005 001 0015

Q˙ c

on

d(k

W)

m˙water(kgsec)



4

45

5

55

6

65

7

75

8

20 21 22 23 24 25

CO

P

Qcond (KW)



10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)



heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)



heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)



capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)




11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











3









me

ter

119824119815 119830119842119847

Saturated

vapor

Saturated

liquid 2

3

4rsquo

4 1

119824119819

4


Experimental rig














equal to 600 m2






evaporator





m2











high side pressure






1250 ordmC)

















operation



































1) Cooling capacity






cycle


interval






measurements

5



system




not considered



zero we get [8]

(QcondndashQ





compressor (kW)








Q (3)










Qcond = m











mmiddotref = Qevap

h1 minus h4

(6)




(h1 ndash h4)

(h2 ndash h1) (7)


6


ω =COPcarnot = 119879119888

119879ℎminus119879119888

(8)




condenser pressure













Compressor

119827120789

Evaporator

T4

119827120786

Refrigerant

turbine

flow

119827120783

119827120788

119827120785119827120787

119827120784

Water flow

meter

Water

Out

Water

In

Condenser

Throttling

Device

119827120790

Fan

Cooling Mode

Diagram

7





























smooth















Tsat = (

120784120784120782120782120791120790120782

120784120783120787120783120784minus119819119847119823119852119834119853 ) -24661 (10)



∆Tb = T3sat

ndashTL (11)



hL3 =50952+133529 T3 +170650T2

3 +76741

10-3T33 (12)




valve

h4=hL3 (13)









sat -105644 T21

sat -

18242610-2T31sat (15)


h1= hv (1+34818610-3 ∆Ts +1688610-6 ∆T2s

+9264210-6∆Ts T1sat -769810-8 ∆T2

s T1sat

+

1707010-7∆TsT21

sat-1213010-9∆T2sT2

1sat (16)






ῦv=exp(-124539+2669

27315+T1sat )(101357+

10673610-3T1sat-9253210-6 T2

1sat -32192

10-7 T31sat ) (17)



s 2T∆6-396510- sT∆3-(1+4788110 vῦ= sup

1V

)sat1

2T s2T∆9-540110- sat1

2T sT∆7-+8573910(18)


sat (19) C1=106469-1690710-3 T1

sat -856010-6 T21sat

-213510-5 T1sat∆Tc -6173010-7 T2

1sat∆Tc

+2074010-7 T1sat∆T2

c +772010-9 T21

sat∆T2c -

610310-4∆Tc (20)

C=C1(1+1175710-3∆Ts-181410-5∆T2s+

412110-5∆TsT1sat-809310-7∆T2

sT1sat) (21)



∆hmacr = 119862

119862minus1 P1 V1

sup(1198752

1198751

119862minus1

119862 - 1) (22)

∆h119938119940119957 = ∆119841macr

ɳcomp (23)


80

h2 = ∆hact + h1 (24)



8

Start

Input (mwater)








h4=hL3












Outputs




COP eq(7)

ω eq(8)


End



9

























8-14












































constant

20

205

21

215

22

225

23

235

24

245

0 0005 001 0015

Q˙ c

on

d(k

W)

m˙water(kgsec)



4

45

5

55

6

65

7

75

8

20 21 22 23 24 25

CO

P

Qcond (KW)



10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)



heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)



heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)



capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)




11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











4


Experimental rig














equal to 600 m2






evaporator





m2











high side pressure






1250 ordmC)

















operation



































1) Cooling capacity






cycle


interval






measurements

5



system




not considered



zero we get [8]

(QcondndashQ





compressor (kW)








Q (3)










Qcond = m











mmiddotref = Qevap

h1 minus h4

(6)




(h1 ndash h4)

(h2 ndash h1) (7)


6


ω =COPcarnot = 119879119888

119879ℎminus119879119888

(8)




condenser pressure













Compressor

119827120789

Evaporator

T4

119827120786

Refrigerant

turbine

flow

119827120783

119827120788

119827120785119827120787

119827120784

Water flow

meter

Water

Out

Water

In

Condenser

Throttling

Device

119827120790

Fan

Cooling Mode

Diagram

7





























smooth















Tsat = (

120784120784120782120782120791120790120782

120784120783120787120783120784minus119819119847119823119852119834119853 ) -24661 (10)



∆Tb = T3sat

ndashTL (11)



hL3 =50952+133529 T3 +170650T2

3 +76741

10-3T33 (12)




valve

h4=hL3 (13)









sat -105644 T21

sat -

18242610-2T31sat (15)


h1= hv (1+34818610-3 ∆Ts +1688610-6 ∆T2s

+9264210-6∆Ts T1sat -769810-8 ∆T2

s T1sat

+

1707010-7∆TsT21

sat-1213010-9∆T2sT2

1sat (16)






ῦv=exp(-124539+2669

27315+T1sat )(101357+

10673610-3T1sat-9253210-6 T2

1sat -32192

10-7 T31sat ) (17)



s 2T∆6-396510- sT∆3-(1+4788110 vῦ= sup

1V

)sat1

2T s2T∆9-540110- sat1

2T sT∆7-+8573910(18)


sat (19) C1=106469-1690710-3 T1

sat -856010-6 T21sat

-213510-5 T1sat∆Tc -6173010-7 T2

1sat∆Tc

+2074010-7 T1sat∆T2

c +772010-9 T21

sat∆T2c -

610310-4∆Tc (20)

C=C1(1+1175710-3∆Ts-181410-5∆T2s+

412110-5∆TsT1sat-809310-7∆T2

sT1sat) (21)



∆hmacr = 119862

119862minus1 P1 V1

sup(1198752

1198751

119862minus1

119862 - 1) (22)

∆h119938119940119957 = ∆119841macr

ɳcomp (23)


80

h2 = ∆hact + h1 (24)



8

Start

Input (mwater)








h4=hL3












Outputs




COP eq(7)

ω eq(8)


End



9

























8-14












































constant

20

205

21

215

22

225

23

235

24

245

0 0005 001 0015

Q˙ c

on

d(k

W)

m˙water(kgsec)



4

45

5

55

6

65

7

75

8

20 21 22 23 24 25

CO

P

Qcond (KW)



10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)



heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)



heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)



capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)




11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











5



system




not considered



zero we get [8]

(QcondndashQ





compressor (kW)








Q (3)










Qcond = m











mmiddotref = Qevap

h1 minus h4

(6)




(h1 ndash h4)

(h2 ndash h1) (7)


6


ω =COPcarnot = 119879119888

119879ℎminus119879119888

(8)




condenser pressure













Compressor

119827120789

Evaporator

T4

119827120786

Refrigerant

turbine

flow

119827120783

119827120788

119827120785119827120787

119827120784

Water flow

meter

Water

Out

Water

In

Condenser

Throttling

Device

119827120790

Fan

Cooling Mode

Diagram

7





























smooth















Tsat = (

120784120784120782120782120791120790120782

120784120783120787120783120784minus119819119847119823119852119834119853 ) -24661 (10)



∆Tb = T3sat

ndashTL (11)



hL3 =50952+133529 T3 +170650T2

3 +76741

10-3T33 (12)




valve

h4=hL3 (13)









sat -105644 T21

sat -

18242610-2T31sat (15)


h1= hv (1+34818610-3 ∆Ts +1688610-6 ∆T2s

+9264210-6∆Ts T1sat -769810-8 ∆T2

s T1sat

+

1707010-7∆TsT21

sat-1213010-9∆T2sT2

1sat (16)






ῦv=exp(-124539+2669

27315+T1sat )(101357+

10673610-3T1sat-9253210-6 T2

1sat -32192

10-7 T31sat ) (17)



s 2T∆6-396510- sT∆3-(1+4788110 vῦ= sup

1V

)sat1

2T s2T∆9-540110- sat1

2T sT∆7-+8573910(18)


sat (19) C1=106469-1690710-3 T1

sat -856010-6 T21sat

-213510-5 T1sat∆Tc -6173010-7 T2

1sat∆Tc

+2074010-7 T1sat∆T2

c +772010-9 T21

sat∆T2c -

610310-4∆Tc (20)

C=C1(1+1175710-3∆Ts-181410-5∆T2s+

412110-5∆TsT1sat-809310-7∆T2

sT1sat) (21)



∆hmacr = 119862

119862minus1 P1 V1

sup(1198752

1198751

119862minus1

119862 - 1) (22)

∆h119938119940119957 = ∆119841macr

ɳcomp (23)


80

h2 = ∆hact + h1 (24)



8

Start

Input (mwater)








h4=hL3












Outputs




COP eq(7)

ω eq(8)


End



9

























8-14












































constant

20

205

21

215

22

225

23

235

24

245

0 0005 001 0015

Q˙ c

on

d(k

W)

m˙water(kgsec)



4

45

5

55

6

65

7

75

8

20 21 22 23 24 25

CO

P

Qcond (KW)



10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)



heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)



heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)



capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)




11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











6


ω =COPcarnot = 119879119888

119879ℎminus119879119888

(8)




condenser pressure













Compressor

119827120789

Evaporator

T4

119827120786

Refrigerant

turbine

flow

119827120783

119827120788

119827120785119827120787

119827120784

Water flow

meter

Water

Out

Water

In

Condenser

Throttling

Device

119827120790

Fan

Cooling Mode

Diagram

7





























smooth















Tsat = (

120784120784120782120782120791120790120782

120784120783120787120783120784minus119819119847119823119852119834119853 ) -24661 (10)



∆Tb = T3sat

ndashTL (11)



hL3 =50952+133529 T3 +170650T2

3 +76741

10-3T33 (12)




valve

h4=hL3 (13)









sat -105644 T21

sat -

18242610-2T31sat (15)


h1= hv (1+34818610-3 ∆Ts +1688610-6 ∆T2s

+9264210-6∆Ts T1sat -769810-8 ∆T2

s T1sat

+

1707010-7∆TsT21

sat-1213010-9∆T2sT2

1sat (16)






ῦv=exp(-124539+2669

27315+T1sat )(101357+

10673610-3T1sat-9253210-6 T2

1sat -32192

10-7 T31sat ) (17)



s 2T∆6-396510- sT∆3-(1+4788110 vῦ= sup

1V

)sat1

2T s2T∆9-540110- sat1

2T sT∆7-+8573910(18)


sat (19) C1=106469-1690710-3 T1

sat -856010-6 T21sat

-213510-5 T1sat∆Tc -6173010-7 T2

1sat∆Tc

+2074010-7 T1sat∆T2

c +772010-9 T21

sat∆T2c -

610310-4∆Tc (20)

C=C1(1+1175710-3∆Ts-181410-5∆T2s+

412110-5∆TsT1sat-809310-7∆T2

sT1sat) (21)



∆hmacr = 119862

119862minus1 P1 V1

sup(1198752

1198751

119862minus1

119862 - 1) (22)

∆h119938119940119957 = ∆119841macr

ɳcomp (23)


80

h2 = ∆hact + h1 (24)



8

Start

Input (mwater)








h4=hL3












Outputs




COP eq(7)

ω eq(8)


End



9

























8-14












































constant

20

205

21

215

22

225

23

235

24

245

0 0005 001 0015

Q˙ c

on

d(k

W)

m˙water(kgsec)



4

45

5

55

6

65

7

75

8

20 21 22 23 24 25

CO

P

Qcond (KW)



10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)



heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)



heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)



capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)




11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











7





























smooth















Tsat = (

120784120784120782120782120791120790120782

120784120783120787120783120784minus119819119847119823119852119834119853 ) -24661 (10)



∆Tb = T3sat

ndashTL (11)



hL3 =50952+133529 T3 +170650T2

3 +76741

10-3T33 (12)




valve

h4=hL3 (13)









sat -105644 T21

sat -

18242610-2T31sat (15)


h1= hv (1+34818610-3 ∆Ts +1688610-6 ∆T2s

+9264210-6∆Ts T1sat -769810-8 ∆T2

s T1sat

+

1707010-7∆TsT21

sat-1213010-9∆T2sT2

1sat (16)






ῦv=exp(-124539+2669

27315+T1sat )(101357+

10673610-3T1sat-9253210-6 T2

1sat -32192

10-7 T31sat ) (17)



s 2T∆6-396510- sT∆3-(1+4788110 vῦ= sup

1V

)sat1

2T s2T∆9-540110- sat1

2T sT∆7-+8573910(18)


sat (19) C1=106469-1690710-3 T1

sat -856010-6 T21sat

-213510-5 T1sat∆Tc -6173010-7 T2

1sat∆Tc

+2074010-7 T1sat∆T2

c +772010-9 T21

sat∆T2c -

610310-4∆Tc (20)

C=C1(1+1175710-3∆Ts-181410-5∆T2s+

412110-5∆TsT1sat-809310-7∆T2

sT1sat) (21)



∆hmacr = 119862

119862minus1 P1 V1

sup(1198752

1198751

119862minus1

119862 - 1) (22)

∆h119938119940119957 = ∆119841macr

ɳcomp (23)


80

h2 = ∆hact + h1 (24)



8

Start

Input (mwater)








h4=hL3












Outputs




COP eq(7)

ω eq(8)


End



9

























8-14












































constant

20

205

21

215

22

225

23

235

24

245

0 0005 001 0015

Q˙ c

on

d(k

W)

m˙water(kgsec)



4

45

5

55

6

65

7

75

8

20 21 22 23 24 25

CO

P

Qcond (KW)



10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)



heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)



heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)



capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)




11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











8

Start

Input (mwater)








h4=hL3












Outputs




COP eq(7)

ω eq(8)


End



9

























8-14












































constant

20

205

21

215

22

225

23

235

24

245

0 0005 001 0015

Q˙ c

on

d(k

W)

m˙water(kgsec)



4

45

5

55

6

65

7

75

8

20 21 22 23 24 25

CO

P

Qcond (KW)



10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)



heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)



heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)



capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)




11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











9

























8-14












































constant

20

205

21

215

22

225

23

235

24

245

0 0005 001 0015

Q˙ c

on

d(k

W)

m˙water(kgsec)



4

45

5

55

6

65

7

75

8

20 21 22 23 24 25

CO

P

Qcond (KW)



10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)



heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)



heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)



capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)




11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











10

15

20

25

30

35

40

45

50

20 21 22 23 24 25

T(degC

)

Qmiddotcond (kW)

T in (0C)

T cond(0C)



heat capacity

13

15

17

19

21

23

25

20 21 22 23 24 25

T (

degC)

Qmiddotcond (kW)

T in evap(0C)

Tevap(0C)



heat capacity

0

2

4

6

8

10

12

14

16

18

20

20 21 22 23 24 25

P (

bar

)

Qmiddot cond (kW)

evappress(bar)

condpress(bar)



capacity

3

35

4

45

5

55

6

5 10 15 20

Wmiddot c

om

p(k

W)

∆P (bar)




11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











11



















evaporator


























withinplusmn10

Acknowledgments






References








pp 926-934





16






277






332




0

5

10

15

20

25

30

5 6 7 8

Qmiddot (

kW)

COP

QEVAP

QCOND

WCOMP


Qcond W


performance

12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











12












310






























280




201024pp192-200




















200730pp1119-1133




engineering 2010




200017pp245-249





20073pp418-432





transfer 201337pp1340-1349




Sweden 2011pp2134-2141




transaction12015











13











13











Documents

Experimental study and mathematical modeling of a vapor ... · diagram or the temperature-enthalpy diagram and ... R290,R600a,R1270 as well as their blend mixtures in various ratios