simulation of an optimized vapour compression ... · simulation of an optimized vapour compression...

Journal of Advanced & Applied Sciences Volume 03, Issue 06, Pages 216-230, 2015

ISSN: 2289-6260

Simulation of an Optimized Vapour Compression Refrigeration System

T. S. Mogaji*

* Department of Mechanical Engineering, Federal University Of Technology Akure, School of Engineering and Engineering

Technology, P M B 704, Ondo State, Nigeria.

* Corresponding author. Tel.: +2348143181937;

E-mail address: [email protected]

A b s t r a c t

Keywords:

Simulation data,

Vapor compression

Refrigeration system,

Sub-cooling, condenser, Coefficient of performance,

Performance improvement.

This paper presents reports on simulation of an optimized vapor compression refrigeration system using a dedicated mechanical sub-cooling cycle in the system. The study aims at

validating a developed double stage vapour compression refrigeration system using numerical

investigation approach. A mathematical model was devised by applying the concept of energy balance in the thermodynamic cycle to the components of the vapour compression refrigeration

system. The developed model implemented in MATLAB software was used to perform the

numerical analysis using Hydrocarbons, R134a as working fluid. Simulation data was

generated to observe the performance of the double stage vapor compression refrigeration system for an important parameters such as condensation (35 to 55°C) and evaporation

temperatures (-5 to 15°C). Performance evaluation of the system was characterized in terms of

cooling capacity and coefficient of performance (COP). The model results compared with the

experimental result from literature revealing good agreement with the later. For the vapour compression refrigeration system being validated, simulated data showed that the performance

of the VCR system with subcooling cycle improves from 3.3% to 11.4% and 3.1% to 12.2%, as

the evaporation and condensation temperature increases and decreases respectively. Statistical

analysis of the comparison results revealed that 80% of the experimental data obtained were successfully predicted within an error band of ±10% and the absolute mean error of 25.2%.

This shows that the model predicts the system performance to a reasonable accuracy.

Accepted:30 December 2015 © Academic Research Online Publisher. All rights reserved.

I. Introduction

Performance of a vapor compression refrigeration

system can be improved in a number of ways, other

than by testing the system in a controlled

environment experimentally; one of those ways is

simulation of the system component analysis to

achieve rapid and accurate result. Simulation has

been widely used for performance prediction and

optimum design of refrigeration systems [1].

Simulation techniques have also been used by

researchers for design of vapor compression

refrigeration system under steady state conditions [2].

[3], gathered empirical information directly by testing

the vapor compression refrigeration system in a

controlled humidity and temperature chamber

T. S. Mogaji / Journal of Advanced & Applied Sciences (JAAS), 3 (6): 216-230, 2015

217 | P a g e

, and in other to achieve this, the system was properly

instrumented. In the system simulation they

employed the conservation laws to establish the

governing equations that describe the system

behavior, with each component modeled using a

lumped approach, based on physical principles and

employing empirical parameters such as friction

factor and heat transfer coefficient. They concluded

that the model showed good agreement with

experimental data. Also the results from the study of

[4] which is on validation of vapour compression

refrigeration system design model showed that the

model results were comparable to the actual system

data from both quantitative and qualitative points of

view under the same operational conditions. Typical

vapour compression refrigeration cycle uses capillary

tube, thermostatic expansion valve and other

throttling devices to reduce refrigerant pressure from

condenser to evaporator. Theoretically, the pressure

drop is considered as an isenthalpic process (constant

enthalpy). However, isenthalpic process causes a

decrease in the evaporator cooling capacity due to

energy loss in the throttling process. To recover this

energy subcooled liquid prior to expansion process

can be used by adding extra components such as

internal heat exchangers in single-stage cycles and in

two-stage cycles of the VCRS as pointed out in the

study [5] Moreso, [6], reported in their study that

liquid cooling below saturation in the conventional

vapour compression cycles reduces the throttling

losses and potentially increases COP of the system.

In the study of [7], development of sub-cool system

was carried out. The authors in their study presented

a concept of a sub-cool system in which the liquid

receiver is installed before the last pass to a parallel

flow micro channel condenser rather than at the exit

of the condenser. They observed COP improvement

benefitted from subcooling due to an increase in

enthalpy difference across evaporator. [8]

investigated the performance of a VCRS with R134a,

R152a and R12 employed as working fluid and

observed that the R134a refrigerant made the VCRS

to be highly efficient when compared to other

refrigerants, provided there is proper addition of

subcooling. The results from the study of [9] which

is on experimental analysis of vapor compression

refrigeration system with diffuser at condenser inlet

revealed approximately 4% and 16% increase in the

rate of heat rejection and COP respectively.

Additionally, nearly 14% reduction in compressor

work of the system was also observed by the authors.

[10], worked on the effect of condenser liquid

subcooling on system performance for refrigerants

CFC-12, HFC-134a and HFC-152a. Their result

revealed that the refrigeration cooling capacity of

refrigerants; R134a (12.5%), R12 (10.5%) and R152a

(10%), benefited from subcooling increase from 6°C

to 18°C, while condensing temperature was kept

artificially constant. [11] investigated the effects of

condensation and evaporation temperatures, motive,

suction and diffuser efficiencies as well as subcooling

on the performance of the vapour compression

refrigeration system. The result from his study

revealed that condensation temperature has the

highest effect on the performance improvement ratio

of the system such that, the performance

improvement ratio of the system is found to be

doubled as the condensation temperature increases

from 30 to 50°C.

The objectives of the present paper are to obtain

support data for the use of dedicated mechanical sub

cooling cycle in VCR system in improving

performance of the system using numerical

investigation approach. Simulation and comparative


218 | P a g e

analysis between the model results and experimental

results obtained by [12] over a wide range of

operating conditions was carried out. The effects of

condensation and evaporation temperatures on

refrigerating effect and coefficient of performance

(COP) of the system were also reported.

2. Vapour compression refrigeration system with

subcooling cycle description

Fig. 1a shows schematic diagram of a vapour

compression refrigeration system with subcooling

cycle and the corresponding P-h diagram of the

system is presented in Fig. 1b, where the basic

vapour compression refrigeration system and the

dedicated mechanical subcooled cycle system are

represented by processes 1-2-3-4-5 and processes 6-

7-8-9 respectively. The arabic numbers in Fig. 1a and

b from 1 to 9 show the different state of the vapour

compression refrigeration system with subcooling

cycle and the number sequence indicates the flow

direction of refrigerant in the system. The refrigerant

enters the compressor at state 1, as saturated vapor

and also with respect to the evaporation temperature.

It follows the irreversible compression process 1-2.

At state 2 the refrigerant is with extremely high

pressure and superheated. The compressed refrigerant

vapor runs from state 2 to state 3 where condensation

process occurred. The process 3-4 represents the

subcooling of the liquid refrigerant at the condenser

outlet before passing through the expansion valve,

hence arriving in state 3 as saturated liquid, the liquid

refrigerant undergo further subcooling process at

process 3-4. In this study, subcooling process is

carried out using a dedicated mechanical subcooling

cycle (6-7-8-9). With the dedicated subcooling

modification, liquid refrigerant leaving the condenser

is further cooled at constant pressure to an

intermediate temperature, T4, as shown in Fig. 1a.

The process 4-5 represents the expansion of the

subcooled liquid refrigerant by throttling from the

condenser pressure to the evaporator pressure.

Finally, the vaporized refrigerant is circulated

through the compressor (1-2) and then condensate in

the condenser (2-3). Shown in Fig. 2. is the system

refrigerant thermodynamic flow process. In this way,

less work is used to operate the compressor of the the

vapour compression refrigeration system with

dedicated mechanical subcooling cycle and,

consequently, enhance the performance of the

system.


219 | P a g e

Fig. 1a: schematic diagram of the vapor compression refrigeration system with subcooling

cycle

Fig. 1b: pressure-enthalpy diagram of the model


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Fig. 2: System refrigerant thermodynamic flow process

3. Mathematical model

In this section the system components level

mathematical models were developed based on the

mass and energy conservation principles described as

follows.

3.1 Refrigeration system cooling load model

In the present study, the system cooling load (CL

Q )

which comprises of both the product load (PT

Q )

and the infiltration load (l

Q ) is modelled as follows:

lPTCL QQQ

(1)

where PT

Q is the total product cooling load

estimated such that for n product stored in the

system, the total product cooling load is calculated

as:

n

PPT QQ1

(2)

The term P

Q in Eq. (2) is the total load required to

cool a product from storage temperature 1

t to final

temperature 3

t and is determined using Eq. (3):

BFFAFP QQQQ (3)

where the terms AF

Q , F

Q and BF

Q are defined

as sensible heat load above freezing, latent heat of

freezing, and sensible heat load below freezing

respectively for the selected products and they are

given as follow:

21 TTmcQ aAF (4)

fgF mhQ (5)

32 TTmcQ bBF (6)


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The detail of the terms ( fgba2

h,c,c,T,m,n ) for the selected products considered in the present study are

shown in Table 1.

Table 1: Properties of the selected products

Products Mass ,m

Kg

Highest freezing

temperature, 2

T

[oC]

Specific heat above

freezing, a

c

KgKKJ

Specific heat below

freezing, b

c

KgKKJ

Latent heat of

fusion,fg

h

KgKKJ

Apple 5 −1.5 3.64 1.88 506.26

Fresh meat 5 −1.67 3.18 2.13 418.40

Water 5 −0.3 3.94 2.01 310.24

Source: Heat load in refrigeration systems [13]

It is interesting to highlights that the average ambient

temperature of the environment 1

T and the final

temperature 3

T are assumed to be 30 oC and -10 oC

respectively.

The infiltration load (l

Q ) given in Eq. (1) is

calculated from:

3108.1 TTVQl

(7)

where 1.08 is a multiplying factor and V is the

average velocity of the door and is computed as:

r

a

r

rT

T

H

HvV (8)

where,

rv is the average velocity of the reference door

H is the height of the door

rH is the height of the reference door

aT is the temperature difference between the

refrigerated space and the environment

rT is temperature difference of the reference door.

Therefore, the total cooling load for the main system

is evaluated as follow:

PTlCL QQQ (9)

Thus, the mass flow rate of the systems working fluid

is calculated from :

'

51

9

hh

EqQm CL

(10)

In the present study, the concept of energy balance in

thermodynamics cycles, applying first Law of

thermodynamics for control volumes to obtain

performance result that can meet the operating

conditions imposed on each component shown in

Fig.1a was adopted and is mathematically expressed

according to Eq. (11)

VCii

iiVC

oo

ooVC Wgzv

hmdt

dEgz

vhmQ

22

22

(11)

Where the subscripts i and o in Eq. (11) stands for

inlet and outlet states, respectively.

It is well known that in vapour compression

refrigeration system, changes in kinetic, 22v and

potential energies, gz are negligible. Thus Eq. (11)

becomes:

iiooVCVC hmhmWQ (12)


222 | P a g e

Referring to the P-h diagram shown in Fig. 1b and

application of Eq. (12) to each component of the

system, the mathematical equations used to obtain the

energy balance in each component are presented in

the next subsections.

3.2. Heat exchangers model: evaporator,

condenser and subcooler

The heat rejected by the main VCR and sub-cooling

VCR system condenser are calculated as follows:

32 hhmQCmain (13)

98 hhmQCsub (14)

The refrigeration capacity of the main and sub-

cooling VCR systems are accounted as follows:

'51 hhmQEmain (15)

67 hhmQEsub (16)

3.3. Compressor model

The work done by the main and the sub-cooling VCR

systems compressor is calculated as follows:

12 hhWCmain (17)

78 hhWCsub (18)

where, the subscript 2 and 8 refers to the enthalpy at

the exit of the main and the sub-cooling VCR system

compressor. Thus, the compressor power required by

the main and the sub-cooling VCR system is

estimated using Eqns. 19 and 20 given below

respectively as:

cmainCmain WmP (19)

csubCsub WmP

(20)

3.4. Capillary tube model

For the expansion process, the overall energy balance

in the capillary tube for both main and sub-cooling

systems is accounted for using Eqns. 21 and 22

respectively:

69 hmhm (21)

54 hmhm (22)

The Mathematical models described above was

implemented in MATLAB software to predict the

response of principles components for both main and

sub-cooling systems i.e compressor, condenser,

expansion valve (capillary tube) and evaporator. The

simulation model of the vapour compression

refrigeration system with subcooling cycle shown in

Fig.1a was devised assuming the following

conditions (i) the refrigeration system operates at

steady state regime, (ii) irreversibilities within the

evaporator, condenser and compressor are ignored,

(iii) no frictional pressure drops, (iv) refrigerant

flows at constant pressure through the two heat

exchangers (evaporator and condenser) , heat loss to

the surrounding are ignored and compression process

is isentropic. The solution algorithm is illustrated in

the information flow diagram depicted in Fig. (3).


223 | P a g e

Compute product, Infiltration, Cooling load

Select Refrigerant

R134a

Input Condenser Temperature and

Evaporator Temperature (Te, Tc)

Input Product Properties and Air

infiltration parameter

Print Product, Infiltration &

Cooling load.

Is Te & Tc available in the Cool pack

Software saturation table[13]?

Set Values of enthalpy, entropy, Specific volume & Pressure

from the Cool pack Software Saturation table [13].

Compute Refrigeration effect, COPmain

Print Refrigeration effect,

COPmain

Input Subcooling System

Temperature (Tes, Tcs)

and Subcooling degree

Is Tes & Tcs available in the Cool pack

Software saturation table[13]?

Set Values of enthalpy, entropy, Specific

volume & Pressure from the Cool pack

Software Saturation table [13].

Compute Refrigeration effect, COPsub

Print Refrigeration

effect, COPsub

STOP

No

Yes

Yes

No

START

Fig. 3: Flow chart of the simulation program


224 | P a g e

The software input data are, product properties,

evaporation temperature and condensation

temperature. It is interesting to point out that the

effect of quantity of products refrigerated on the

performance of vapour compression refrigeration

system can be evaluated with the developed model

taking into consideration Eqns. 1-8 thus, the

performance prediction and optimum design of

refrigeration systems can be achieved with this

model. The simulation of both refrigeration systems

are characterized by refrigerating effect in terms of

cooling capacity, compress power and coefficient of

performance (COP) of the systems.

The cooling capacity is calculated as:

51 hhmQsub (23)

The compressor power is obtained as follows:

21 hhmPsub (24)

Thus, based on the simulation procedure carried out

for both main and sub-cooling systems, the

performance of the systems is evaluated as follows:

sub

subsub

P

QCOP (25)

The COP improvement 𝐶𝑂𝑃𝑖𝑚𝑝 expressed in % is

calculated as follows;

COPmain

COPmainCOPsubCOPimp

(26)

where, the 𝐶𝑂𝑃𝑚𝑎𝑖𝑛 is the COP at the same

evaporator and condenser temperatures of the main

VCR system.

3.5 Simulation model validation

The simulation results were compared against the

experimental data obtained in the study of [12] for a

wide range of condensation (35 to 55°C) and

evaporation (-5 to15°C) temperatures in Fig. 4. In

this figure, it can be noted the simulation results have

a good agreement with the published data from

literature. Table 1 presents the results of the statistical

analysis of comparisons between the simulation data

and the experimental data. The variation between the

model and the experimental data is due to heat loss,

which at present it is almost impossible to prevent

since there is no perfect insulation of heat.

Comparisons are based on the following parameters:

(i) the percentage of the experimental data predicted

by the model results within an error band of ±10%,

(ii); and the absolute mean error defined as follows:


225 | P a g e

points data

ofnumber

points data ofnumber exp

exp

erimentalimp

erimentalimpestimatedimp

COP

COPCOP (27)

Table 1: Statistical analysis of comparisons between the simulation data and experimental data obtained in the study of [12].

Methodology [%] ζ [%]

Evaporation

Temperature [oC]

Condensation

Temperature [oC]

Evaporation

Temperature [oC]

Condensation

Temperature [oC]

Model

validation/Prediction

result

80 % 80% 25.4 29.3

Fig. 4: Comparison between present study model and previous experimental data from [12]

It is interesting to point out that the comparisons

results presented in Table 1 and Fig. 4 shows that the

model predicts the system performance to a

reasonable accuracy.

4. Result and discussion

In this section, analysis of performance of vapour

compression refrigeration system (VCRS) with and

without subcooling cycle based on the use of

numerical model developed for the systems are

comparatively reported. Simulation data was

generated over a wide range of evaporator and

condenser temperatures of (−5 to 15oC) and (35 to

55oC) respectively.

4.1 Comparative analysis

An overview of the performance evaluation of the

VCRS with and without subcooling cycle based on

the effects of evaporation and condensation

temperatures using the simulation model developed

are shown in Figures 5-7. It should be noted that

when one of them varied, the other parameters

remain constant at a practical value. Figure 5

illustrate the effects of the evaporation temperature

on COPs of both the VCRS with and without

subcooling cycle. According to this figure, as

expected the COPs of the systems increase with

increasing the evaporation temperature. The VCRS

with subcooling cycle is more sensitive to increase in

evaporation temperature as higher COP is observed at

any operational condition considered in this study.

30.0 35.0 40.0 45.0 50.0 55.0 60.0

2.0

4.2

6.4

8.6

10.8

13.0

Condensation temperature (oC)

CO

Pim

pro

vem

ent(

oC

)

Mogaji and Yunisa [12]

Present study model

-10.0 -5.0 0.0 5.0 10.0 15.0 20.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

12.0

Evaporation temperature (oC)

CO

Pim

pro

vem

ent(

oC

)

Mogaji and Yunisa [12]

Present study model


226 | P a g e

Such behavior is related to the fact that less work is

used to operate the compressor of the VCRS with

subcooling cycle compared to its counterpart without

subcooling cycle. This trend is similar to those

observed in the studies of [11] and [14]. Moreover, as

can be noticed in Figure 4, the COP improvement

ratio of the modified system is observed to increase

from 3.3 to 11.4%,as the evaporation temperature

increases from -5 to15℃ , these simulated values

validate those obtained experimentally in our

previous study predicting 80% of the data within an

error band of ±10 and the absolute mean error of

25.2% which proves the high energy efficiency of the

VCRS with subcooling cycle.

Fig 6 shows that the COPs for both VCRS with and

without subcooling cycle decrease as the

condensation temperature increases. It can also be

notice that the COP of the modified system at lower

condensation temperature of 35oC is more sensitive

higher than the COP of the VCRS without subcooling

cycle. Additionally, as condensation temperature

decreases from 55 to 35°C, the improvement ratio in

COP increases from 3.1% to 12.2% these simulated

values as displayed in Figure 4 predicted 80% of the

experimental data obtained in our previous study

within an error band of ±10% and the absolute mean

error of 25.2% .These trends are similar to those

observed in the study of [11] and [15]. This rate of

improvement can be attributed to the fact that during

a process through the VCRS with dedicated

subcooling cycle, temperature of refrigerant

increases. Due to this difference between temperature

of refrigerant flows through condenser tubes and that

of outside air flowing over condenser tubes increases

resulting into increase in the rate of heat transfer from

the condenser. Illustrated in Fig. 7 is the comparison

between COP of the VCRS with and without

subcooling cycle for a wide range of subcooling

degrees. Obviously as can be notice from this figure,

as subcooling degree increases both COPs are

increased but with different rates. This behavior is

due to reduction in exergy loss of the system under

these operating conditions. (i.e decreasing

condensation temperature). Thus, dedicated

subcooling modification is responsible for the

betterment of the system performance.

From Figs.5 and 6, it was observed that by using

dedicated subcooling cycle, up to 11.4 and 12.2 %

performance improvement ratio of VCR system are

achieved at evaporation temperature of 15 oC and

condensation temperature of 35 oC respectively.

Applying first law of thermodynamics to VCRS with

subcooling cycle, it was observed that increase in

subcooling degree increasing refrigerating effect, due

to the reduction of the condenser exit temperature.

Hence, net compressor work was reduced which

result in betterment performance of the VCR system.


227 | P a g e

Fig. 5: Variation of coefficient of performance with evaporation temperature

Fig. 6: Variation of coefficient of performance with condensation temperature

-10 -5 0 5 10 15 20

4

5

6

7

8

9

10

Evaporation temperature (oC)

Co

effi

cien

t o

f p

erfo

rman

ce

COPmain

COPsub

30 35 40 45 50 55 60

2

3

4

5

6

Condensation temperature (oC)

Co

effi

cien

t o

f p

erfo

rman

ce

COPmain

COPsub


228 | P a g e

Fig.7: Variation of performance improvement with sub-cooling temperature

5. Conclusion

In this study, a simulation model is developed for

VCRS with sub-cooling cycle where a main system is

mechanically sub-cooled with another complete cycle

system using R-134a as the working fluid. Numerical

analysis on the performance of the system

considering the effect of evaporation temperature,

condensation temperature and subcooling degree

using the simulation model has been identified. The

performance evaluation of the system was

characterized by refrigerating effect in terms of

cooling capacity, compressor power and coefficient

of performance (COP). Subsequently, the obtained

simulation data were comparatively analyzed with

experimental result from the study according to [12].

The model results compared with the experimental

results revealed good agreement with the later. From

the present study, the following main conclusions can

be drawn:

i. The COP of VCR system with dedicated

mechanical sub-cooling cycle is higher

compares with the main VCR system

counterpart.

ii. By using dedicated mechanical subcooling

cycle, up to 11.4 and 12.2 % performance

improvement ratio of vapour compression

system are observed at evaporation

temperature of 15 oC and condenser

temperature of 35 oC respectively

iii. As the subcooling degree temperature

increases the COP of the VCR system

increases. Similarly, Refrigerating effect of

the system increases.

iv. Evaporation temperature has the highest

effect on the system performance

improvement ratio. As the evaporation

temperature increases from -5 to 15 oC, the

performance improvement ratio of the

system increases geometrically.

v. According to experimental and simulation

data the preceding comparative analysis on

performance evaluation of both basic VCR

system with and without subcooling cycle. It

2 4 6 8 10 12 14 16

0

3

6

9

12

15

Subcooling temperature (oC)

CO

Pim

pro

vem

ent(

oC

)

COPsub

COPmain


229 | P a g e

can be concluded that the use of dedicated

mechanical sub cooling cycle in VCR

system is most efficient and suitable for any

cooling system application (air conditioning

refrigeration and freezing).

Acknowledgement

The authors would like to acknowledge the

assistance of the Refrigeration and Air

Conditioning Unit of the Department of

Mechanical Engineering, Federal University of

Technology Akure in supplying the equipment

used in the present study. The technical support

given to this investigation by Mr K. R. Yunisa

and Mr. K. A. Adewole are also appreciated and

deeplyrecognized.

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