Parametric analysis of domestic refrigerators using PCM heat exchanger

international journal of refrigeration 83 (2017) 1–13

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Parametric analysis of domestic refrigerators using PCM heat exchanger S. Bakhshipour, M.S. Valipour *, Y. Pahamli Faculty of Mechanical Engineering, Semnan University, P.O. 35131-19111, Semnan, Iran

A R T I C L E

I N F O

A B S T R A C T

Article history:

In the present study, numerical simulation of refrigeration cycle incorporated with a PCM

Received 16 March 2017

heat exchanger is carried out. To this end, the refrigeration cycle without PCM has been simu-

Received in revised form 18 July

lated and then, the performance coefficients of the refrigerator in either with and without

2017

PCM are evaluated. The PCM heat exchanger is located in the refrigeration cycle, at a loca-

Accepted 23 July 2017

tion after the condenser and before the expansion valve. The utilised PCM is N-Octadecane

Available online 28 July 2017

with fusion temperature of 27.5 °C. The simulation of heat exchanger is based on computational fluid dynamics (CFD) in which the flow inside the pipe is considered one-

Keywords:

dimensional in the axial extension and PCM surrounding it, is considered two dimensional.

Refrigerator

Numerical simulation is carried out using MATLAB software. Simulation results show that

Phase change material

utilizing PCM in refrigeration cycle of a refrigerator causes an improvement in the convec-

Condenser

tion procedure and results a 9.58% increase in performance coefficient of refrigerator.

Coefficient of performance

© 2017 Elsevier Ltd and IIR. All rights reserved.

Analyse paramétrique de réfrigérateurs domestiques utilisant un échangeur de chaleur à matériau à changement de phase Mots clés : Réfrigérateur ; Matériau à changement de phase ; Condenseur ; Coefficient de performance

1.

Introduction

Modern men, in many ways, are different from their early ancestors in utilization and the type of energy consumption. Since energy provides development of convenience, transportation and producing materials and food, it impacts on human life so that it is known as a measure to determine a country’s development. Growing demand for energy due to population increase and limited resources from one side and environmental concerns caused by industrial pollution on the other side, has led the human toward the clean and renewable energy

resources. Because of the intermittence of renewable energies, they need to be stored. Energy storage achievements are a balance between supply and demand and also decrease in fossil energy consumption. Thermal energy can be stored in three general ways: 1) sensible heat storage (SHS) which needs materials with high specific heat capacity 2) latent heat storage (LHS) by phase change of a material form one state to another (storing and releasing heat) and 3) chemical heat storage via absorbing heat during reaction and releasing heat in reverse reaction. Among these methods, latent heat storage using phase change materials (PCMs) are more functional in applications such as buildings

* Corresponding author. Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran. E-mail address: [email protected] (M.S. Valipour). https://doi.org/10.1016/j.ijrefrig.2017.07.014 0140-7007/© 2017 Elsevier Ltd and IIR. All rights reserved.

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international journal of refrigeration 83 (2017) 1–13

Nomenclatures A cp ce D,d F G h H K L  m N Nu P Pr q Q R Ra Re S t T U V w W

area [m2] specific heat at constant pressure [Jkg−1 K−1] mass flow factor diameter [m] liquid fraction gravity [m s−2] specific enthalpy [kJ kg−1] volumetric enthalpy [kJ m−3] thermal conductivity [W m−1K−1] tube length [m] mass flow 0rate [kg s−1] wetted perimeter [m] Nusselt number pressure [kPa] Prandtl number heat energy [kWh] heat [kW] radius [m] Rayleigh number Reynolds number stroke of piston [m] time [s] temperature [°C] total heat transfer coefficient [W m−2K−1] volume displacement of the compressor [m3] width [m] compressor power [W]

Greek symbols α thermal diffusivity [m2 s−1] β expansion coefficient [K−1] δ melt layer thickness [m] θ the difference of temperature: T-Tm [K] ηis isentropic efficiency volumetric efficiency ηv µ dynamic viscosity [Pa s−1] ρ density [m3 kg−1]

energy efficiency (Soares et al., 2013), vehicle components (Jankowski and McCluskey, 2014), solar energy (Sharma et al., 2015), electronic cooling (Pakrouh et al., 2015), air conditioning (Al-Abidi et al., 2012) heat exchangers (Pahamli et al., 2016) and house hold refrigeration (Joybari et al., 2015). Chemical stability, low vapour pressure at their operating temperature, large latent heat of fusion and heat absorption at constant temperature are favourite properties of phase change materials (PCMs). Household refrigerators are the most widely used home appliance which consumes a quarter of residential electricity. With the improvement in performance of household refrigerators electricity consumption decreases which lead to a reduction in greenhouse gas emissions. Many technical methods are developed to enhance the performance of household refrigerators such as the development of energy-efficient compressors, enhancement of thermal insulation, and enhancement of heat transfer from heat exchangers, i.e. condenser and evaporator

ϑ ΔH Δx Δr Δt Subscripts is sol l g m sh tp sc f Air i o e ev con C Eff PCM COP Inl R w, e, n, s 1 2 3 4

kinematic viscosity [m2 s−1] latent heat of fusion [J kg−1] axial space step [m] radial space step [m] time step [s]

Isentropic Solid Liquid Gas Melt Superheat two-phase sub-cooled fluid in the tube (refrigerant) ambient air Inner Outer expansion valve Evaporator Condenser Compressor Efficient the phase change material the coefficient of performance Inlet Refrigerator west east, north and south faces of control volumes inlet to compressor or outlet of the evaporator the outlet of compressor or inlet to the condenser the outlet of condenser or inlet to the expansion valve the outlet of expansion valve or inlet to the evaporator

(Joybari et al., 2015). As reported by Hammond and Evans (2014), incorporation of Vacuum Insulation Panels (VIPs) is an effective way for thermal insulation in refrigerators where low temperature (freezer) cabinets have thinner insulators than desirable insulation VIPs. Azzouz et al. (2008, 2009) experimentally and numerically investigated the performance of a household refrigerator using PCM on the back side of the evaporator. They compared the results for two PCMs (water and eutectic mixture freezing point 3 °C) and three operating conditions (PCM thickness, ambient temperature, thermal load). They found that using PCM increases conduction heat transfer from evaporator to the PCM. Also they showed that the effect of using PCM and the efficiency depends on thermal load and they reached a steady operation of 5–9 hours. Oró et al. (2012a, 2012b) studied thermal performance of commercial freezers using phase change materials. The embedded PCM was Climsel with a melting temperature of -18 and packed it in a stainless steel panel with 10 mm thickness. They studied the effect of door

international journal of refrigeration 83 (2017) 1–13

openings and electrical power failure and compared the results with using no PCMs. They showed that during 3 hours of electrical power failure using PCM remains the freezer temperature 4–6 °C lower than that of without PCM. In an experimental and numerical study, Marques et al. (2014) investigated compressor performance and using PCMs in domestic refrigerators. Their model results indicated that using compressors with an 8m3 instead of 4m3 decreases energy consumption up to 19.5%. They also showed that a continues operation of 3–5h without any power supply was achieved by using 5 mm PCM slab into the refrigerator. They concluded that simultaneous use of thin PCM and a larger displacement compressor enhances refrigerator efficiency. According to Joybari et al. (2015), studies on using PCM in condenser are limited. Cheng et al. (2011) introduced new household refrigerator with a shape-stabilized phase change material (SSPCM) in condenser part and compared the results with ordinary refrigerators. In common refrigerators, heat transfer process from condenser is at ON time of compressor. While by adding SSPCM around the condenser pipes heat transfer continues even in OFF time of compressor. Thus, according to double time of OFF time to ON time, the COP increases up to 19%. They did this work for different ambient temperature and different evaporator temperature. They showed that lower condensation temperature, a higher evaporation temperature and a much larger sub cooling degree at the condenser outlet was achieved by heat transfer enhancement of condenser. Sonnenrein et al. (2015) experimentally studied power consumption and temperature distribution in household refrigerators by using different PCM elements in wire-andtube condensers. Their results showed that by integrating PCM leads to temperature decrease in the condenser which results in power consumption decrease too. The previous done works in utilizing PCM for enhancement in household refrigerators are not with a separate heat exchanger and the PCM is incorporated around the condenser tubes. Also the PCM heat exchanger used in refrigeration cycle was for different temperatures and working condition of the coolers in which the temperature conditions, PCM type and the melting temperature are different. In the current research heat transfer enhancement of domestic refrigerators investigated by integrating PCM between condenser and expansion valve. The entire refrigeration cycle with PCM heat exchanger is modeled continuously. The main feature of this work is that the study focuses on heat specifications and COP through parametric consideration. Thus the effects of type of refrigerant, PCM heat exchanger length, PCM heat exchanger tube diameter, PCM thickness and mass flow rate of refrigerant are studied and reported.

2.

Mathematical model

In this section, description of the entire system and assumptions made for mathematical modeling is carried out for each part separately. The system is consists of five parts including compressor, evaporator, expansion valve, PCM heat exchanger and condenser respectively. The studied PCM heat exchanger is located between the condenser and the expansion valve. The schematic view of the simulation system is depicted in Fig. 1.

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Fig. 1 – Schematic view of system compartments.

2.1.

Compressor modeling

By spending mechanical energy compressors suck gases into itself rapidly and compresses it. In this process, pressure and temperature of gas increases. Thus vapour refrigerant converts from saturated state to superheated vapour at high pressure. Following assumptions are considered for modeling the compressor (Wang et al., 2007): • Volumetric and Isentropic efficiencies are kept constant. • Heat dissipation in compressor shell and refrigerant charge are considered negligible. • The compression process is assumed to be adiabatic. Thus isentropic efficiency can be defined as bellows (Wang et al., 2007):

ηisen =

h2,is − h1 h2 − h1

(1)

mass flow rate of refrigerant is determined by (Wang et al., 2007):

 R = ρVRηv × m

RPM 60

(2)

where the volumetric efficiency of the compressor, ηv and compressor displacement is determined by (Wang et al., 2007):

ηv = 0.851 − 0.0241

V =π

p2 p1

D2 ×S 4

(3)

(4)

and compressor power is calculated according to the following equation (Wang et al., 2007):

c =m  R (h1 − h2 ) w

2.2.

(5)

Condenser

Refrigerant vapour with high pressure and temperature enters the condenser and then condenses. According to Fig. 2

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international journal of refrigeration 83 (2017) 1–13

in which Atp is two phase regions’ area and Utp is two phase regions’ heat transfer coefficient and calculated as follows (Bergman et al., 2011):

Sub cooled

Two Phase

1 ⎛ ⎞ ⎟ 1 ⎜ ⎛ Re ⎞ ln ⎜ ⎟ Utp = ⎜ ⎝ Ri ⎠ 1 ⎟ As,tp ⎜ 1 ⎟ + + ⎝ Aiui 2π kL A o uo ⎠

Super Heat

Fig. 2 – Different regions in the condenser.

2.2.3.

condenser is divided into three regions which are a superheated region, two-phase region and subcooled region. For modeling condenser heat transfer, equations must be extracted separately in one phase and two phase states (Wang et al., 2007). The following consumptions are used for modeling the condenser: • The flow is one-dimensional. • Heat transfer between refrigerant and pipes in the axial position is neglected. • Refrigerant pressure drop is neglected.

2.2.1.

The inlet refrigerant to the condenser is superheated state. The heat transfer in this area is calculated as below (Wang et al., 2007):

Ush

(7)

where ui is heat transfer coefficient in refrigerant tubes in which flow is superheat and in one phase. Also uo is heat transfer coefficient of air passing over pipes which is obtained from Chunnanond and Aphornratana (2004); Ding (2007); Wang et al. (2007).

2.2.2.

Heat transfer in two-phase region

Heat transfer in the two-phase region is equal to the heat gained by reaching refrigerant from superheat to saturated liquid at condenser pressure and is calculated from equation 8 (Wang et al., 2007):

 (h2,g − h2,l ) Q cond,tp = m

(8)

subsequent to calculating Q cond,tp , the length of superheated area can be calculated as (Wang et al., 2007):

Q cond,tp = Utp Atp (Tsat − Tair ) Atp = π di Ltp

 p (Tsat − Tair ) Q cond,sc = Usc Asc (Tsc − Tair ) = mC

(12)

Asc = π di Lsc

(13)

Lsc = L − (Lsh + Ltp )

(14)

Tsat + T3 2

(15)

Tsc =

Q cond = Q cond,sh + Q cond,tp + Q cond,sc

2.2.4. (6)

where Ash is superheat area, Tsh is average temperature in superheat area and Ush is total heat transfer coefficient and is calculated as (Bergman et al., 2011):

1 ⎛ ⎞ ⎟ 1 ⎜ ⎛ Re ⎞ ln ⎜ ⎟ = ⎜ ⎝ Ri ⎠ 1 ⎟ Ash ⎜ 1 ⎟ + + ⎝ Aiui 2π kL A o uo ⎠

Heat transfer in subcooled region

Heat transfer value and condenser outlet temperature, T3 , are calculated as below (Wang et al., 2007):

Thus heat transfer in condenser part is the sum of heat transfer in three regions (Wang et al., 2007):

Heat transfer in superheat region

 (h2 − h2,g ) = Ush Ash (Tsh − Tair ) Q cond,sh = m

(11)

(9) (10)

(16)

Expansion valve modelling

The expansion valve is a mechanical controller which controls the amount of fluid entering the evaporator. It can be modeled as a fixed orifice, capillary tube and thermostatic expansion valve. In this article expansion, valve is modeled as a fixed orifice. Thus following assumptions are considered for this model as (Wang et al., 2007): • Flow is one dimensional. • Gravity force and refrigerant charge are considered to be negligible. • Flow coefficient is constant. • The expansion process is considered constant enthalpy. mass flow rate in the orifice is (Wang et al., 2007):

 e = Cede2 ρin ( p2 − p1 ) m

(17)

where Ce is the mass flow factor which depends on geometry of orifice tube and di is inner tube diameter. As it is assumed, enthalpy is constant, thus (Wang et al., 2007):

h3 = h4

2.3.

(18)

Evaporator modeling

The evaporator is a device which converts fluid from liquid to gas state by receiving heat. Following assumptions are considered for modeling evaporator: • Flow is one dimensional. • Axial heat transfer between refrigerant and tube is neglected.

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international journal of refrigeration 83 (2017) 1–13

Table 1 – Thermophysical Properties of n-octadecane (Qarnia, 2009).

PCM Refrigerant

x

Properties

N-octadecane

Tm [K] ρs [kg m-3] ρl [kg m-3] Cp [J kg-1K-1] k [W m-1K-1] h [kJ kg-1] β [K-1]

303.5 814 774 2165 0.358 244 0.00085

PCM Also thermophysical properties of used R-134a and R-600a are brought in Table 2.

a) 2.5.2.

Modeling the PCM heat exchanger

Following assumptions are considered for PCM:

PCM • PCM is homogeneous and isotropic (properties are independent of location and direction). • Thermophysical properties of PCM and refrigerant are independent of temperature. • The thermal resistance of inner tube is regardless. • Axial conduction is negligible in comparison with convection heat transfer. • Effects of natural convection in melting by effective thermal conductivity is calculated as (Qarnia, 2009):

Refrigerant b) Fig. 3 – Schematic view of the PCM heat exchanger a) axial (r,x) view and b) radial (r,θ) view.

• Pressure drop along the evaporator is regardless. • Superheating refrigerant in the evaporator is neglected and heat transfer includes two phases and is calculated as (Wang et al., 2007):

 (h1 − h4 ) Q ev = m

2.4.

(19)

Coefficient of performance

keff ⎛ δ ⎞ = C ⋅ Ran ⎜ ⎝ Re − Ri ⎟⎠ k1

m

(21)

where m and n are 0.8 and 0.25 respectively and C is dependent to HTF inlet temperature and calculated as (Qarnia, 2009):

⎧0.24 Tf ,inl ≤ 310.7 K ⎪ C = ⎨0.18 310.7 K ≤ Tf ,inl ≤ 320.7 K ⎪0.16 320.7 K ≤ T f ,iinl ⎩

(22)

By these assumptions governing equations for heat transfer in the PCM heat exchanger is as follows:

The COP is evaluated from equation (20) (Azzouz et al., 2008):

Q Q ev COP = ev =  W Q cond − Q ev

2.5.

Model simulation

2.5.1.

Geometry of PCM heat exchanger

• Refrigerant energy equation (Qarnia, 2009): (20)

The schematic view of the PCM heat exchanger has illustrated in Fig. 3 in which a heat storage unit is a 4.3m long. The inner and outer tube diameters are 5 and 20 mm respectively. PCM is filled in an annulus gap and R600-a as the main refrigerant flows through the inner tube. Heat transfer in PCM is both with conduction and convection mechanisms. The reason for choosing this geometry is for better heat transfer and also easy application. The PCM selected in this work is n-octadecane and its thermal properties are listed in Table 1.

(ρCp ) f π Ri2

∂T f dTf  p, f = −mC + u ( TPCM,r = Ri − Tf ) 2π Ri ∂t dx

(23)

• PCM energy equation (Qarnia, 2009)

Table 2 – Thermophysical Properties of R-134a and R-600a at ambient temperature (Sonntag et al., 1998). Properties

R-134a

R-600a

ρl [kg m ] Cp,g [J kg-1K-1] k [W m-1K-1] h [kJ kg-1]

1218 1.413 0.01353 410.79

554.4 1.772 0.0165 583.89

-3

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international journal of refrigeration 83 (2017) 1–13

∂HPCM 1 ∂ ⎛ ∂HPCM ⎞ ∂ ⎛ ∂HPCM ⎞ + = αr α r ∂r ⎝ ∂x ⎠ ∂t ∂r ⎠ ∂x ⎝ ∂f uair − ρPCM ΔhPCM − (TPCM − Tair ) ∂t N Where H (T ) = ∫

T Tin

(24)

(ρCp )m dT and initial and boundary condi-

tions are (Qarnia, 2009):

Table 3 – Equations used for calculating thermal conductivity (Incropera and De Witt, 1996 and Kakac et al., 1986).

xe =

Re Re ≤ 2100

TPCM ( x, r, t = 0) = Tf ( x, t = 0) = Tair

(25)

Tf ( x = 0, t ) = Tf ,inl

(26)

Re > 2100

k

∂TPCM ∂T ( x = 0, r) = k PCM ( x = L, r) = 0 ∂x ∂x

(27)

k

∂TPCM ( x, r = Ri ) = uPCM, f (TPCM − Tf ) ∂x

(28)

∂TPCM ( x, r = Ro ) = uair (TPCM − Tair ) ∂r

(29)

k

Nu

xe ≤ 0.01

1.77 ⋅ xe−1 3 − 0.7

xe > 0.01

3.657 +

-

0.023 ⋅ Re0.8 ⋅ Pr 0.3

6.874

(1000 ⋅ xe )0.488

⋅ e(−57.2 xe )

According to Table 3 for calculating thermal conductivity in the tube for the laminar flow, Greatest equation (Incropera and De Witt, 1996) and for the turbulent flow, Dittus-Boetler equation (Kakac et al., 1986) are used: In the above table, Reynolds number is calculated as:

Re =

In equation 29, uair is air thermal conductivity and is calculated for a long cylinder in natural convection as below (Bergman et al., 2011):

xD ReD ⋅ Pr

 4m πμdi

(36)

Discretized energy equation for PCM from equation (23) is as below (Valipour et al., 2006):

Apθ p = Asθ s + ANθ N + AEθ E + AWθ W + B

(37)

where

NuD =

uD k

(30)

RaD ≤ 10

12

where RaD and Pr are dimensionless numbers Rayleigh and Prandtl, respectively and calculated by Bergman et al., (2011):

Ra =

gβ (Ts − Tair ) 3 D αν

(32)

Pr =

ν α

(33)

where D is characteristic length which is equal to the outer tube diameter.

b 1 θ f ,w + θ 0f , p Δx Δt ⎛a + b + 1 ⎞ ⎜⎝ ⎟ Δx Δt ⎠

αθ r = Ri +

(34)

where a and b are (Valipour et al., 2006):

a=

2u

(ρc) f Ri

,

b=

f m ρ f π Ri2

rs + rn , 2

Δx , Δrn

(35)

B = ρCp

AN = ksrs

Δx , Δrs

AW = kwr

rΔrΔx Δt

rΔrΔx 0 rΔrΔx θ p − ρΔh ( f p − f p0 ) Δt Δt

Δr Δxw (38)

(39)

Equation (37) is solved using TDMA method. Liquid fraction, f , in source term B shows fraction of control volume which is in liquid state. f is zero for solid state and is 1 for fully liquid and is guessed using enthalpy method by Voller (1990) as:

f pk + 1 = f pk +

ApTp rΔxΔr ρp Δh Δt

(40)

Guessed liquid fraction in equation (38) for each grid is (Voller, 1990)

⎧ f = 0 if ⎨ ⎩ f = 1 if

Discretizing equations

By supposing θ = T − Tm and discretizing equation (23), we have (Valipour et al., 2006):

θ f ,p =

AN = kn rn

(31)

r=

2.6.

Δr , Δxe

Ap = As + AN + AE + AW + ρCp

2

1 ⎧ ⎫ 0.378RaD6 ⎪ ⎪ NuD = ⎨0.06 + ⎬, 9 16 8 27 ⎡ ⎤ ⎩⎪ ⎣1 + ( 0.559 Pr ) ⎦ ⎭⎪

AE = ke r

f ≤0 f ≥1

(41)

Equations 34 and 35 are correlated with initial conditions of equations 28 and 29 and used to solve simultaneously and repeatedly at each time step. For each time step, convergence is in kth repeat and its criterion is (Voller, 1990):

⎡ θ kf , p − θ kf −, p1 ⎤ ≤ 10−4 Max ⎢ ⎥ k −1 ⎣ θ f ,p ⎦ p=1,Nx

(42)

q1 − q2 ≤ 5 × 10−3 q1

(43)

7

PCM Temperature C)

international journal of refrigeration 83 (2017) 1–13

Mesh (×104)

Fig. 4 – Mesh independency.

Fig. 5 – Effect of using PCM in the refrigeration cycle.

where q1 and q2 are (Voller, 1990):

 f c f (θ f ,in − θ f ,out ) Δt q1 = m

reveals that the results of the present calculation are in a good agreement with those of Azzouz et al. (2008). (44)

3.2. M

q2 = 2π ∑ ∑ rj [( ρc )PCM (θ ij − θ ij 0 ) + ρPCM Δh ( fij − fij 0 )] Δx ⋅ Δr i =1 j =1

+ ( ρc ) f π r

2 o

2.7.

∑ (θ i =1

ij

− θ f ,i ) Δx 0

(45)

Mesh independency

The grid size and time step used for this simulation are 375 × 60 and 5s, respectively. The results of mesh independency are depicted in Fig. 4.

To validate the numerical model of refrigeration cycle with PCM in our simulation, a series of initial runs were performed and the obtained solutions are compared with the experimental results of Qarnia (2009). Fig. 8 shows the comparison of average refrigerant temperature profile versus time between these two investigations. The figure implies that the results of the present calculation are in a good agreement with those of Qarnia (2009).

4. 2.8.

System with PCM heat exchanger

N

Results and discussion

Simulating algorithm of the whole system

Inputs for simulating the refrigeration cycle are ambient temperature, refrigerator inner temperature and geometrical properties of refrigeration cycle (condenser and evaporator tube specifications, expansion valve dimensions, isentropic efficiency of the compressor, displacement volume and compressor speed). The desired outputs are compressor power, the refrigeration capacity, thermodynamic properties of the refrigerant at different parts of the cycle and COP. Also, inputs for PCM heat exchanger are mass flow rate and inlet temperature of fluid in the tube, the initial temperature, melting point of PCM and ambient temperature. The PCM and refrigerant temperature during the time and also melting ratio and the amount of heat transfer between PCM and the refrigerant are the outputs of this simulation. Effect of using PCM in the refrigeration cycle is depicted in Fig. 5. Also, an overview of relations and simulation algorithm are shown in Figs. 6 and 7 respectively.

3.

Validation

3.1.

Basic system without PCM heat exchanger

In order to validate the computational model of the basic refrigeration cycle in our code, some initial runs are performed and the results have been compared with the experimental data of Azzouz et al. (2008). Table 4 shows the COP results for both the present study and the cited reference. The comparison

The temperature variation trend of the refrigerant at three different axial positions is shown in Fig. 9. It should be noted that all the results and comparisons are for the first one hour of the process for all cases. As can be seen in the figure, at x* = 0.5, due to the high temperature difference between the refrigerant and the PCM, refrigerant temperature increases rapidly with the high slope in the curve. By time pass and a decrease in the PCM temperature, the thermal potential of refrigerant decreases which in turn leads to the lower temperature difference between two mediums. Thus at the final stages of the process, the temperature difference between the refrigerant and the PCM almost keeps constant and refrigerant temperature remains nearly constant. Also, it can be deduced from the figure that by moving along the axis, from x* = 0.5 to x* = 2, due to heat transfer between the refrigerant and the PCM at early stages of the PCM heat exchanger, the refrigerant temperature is less at the outlet in comparison to the inlet. Refrigerant temperature variation along the axis at different times is shown in Fig. 10. It can be observed that the

Table 4 – Comparison of COP results between present work and that of Azzouz et al. (2008). COP at ambient temperature T = 15 °C T = 20 °C T = 25 °C

Present work

Azzouz et al. (2008)

2.19 2.085 2.033

2.1 2 1.95

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international journal of refrigeration 83 (2017) 1–13

Fig. 6 – Overview of relations in refrigeration cycle utilising PCM.

temperature decrease at the outlet of the heat exchanger is more than the middle because of more heat transfer from the refrigerant to the PCM. Therefore refrigerant leaves the heat exchanger at a lower temperature than the inlet which is useful for the entire cycle. System COP using PCM in comparison without PCM is 2.1578 and 1.969, respectively, which shows 9.58 % increase by utilising PCM heat exchanger in the system. Thus generally, using PCM heat exchanger causes to reduce in condenser outlet temperature, therefore, increasing in COP.

4.1.

Effect of geometrical properties

4.1.1.

Effect of PCM heat exchanger tube length

Effect of PCM heat exchanger tube length on COP of the cycle is shown in Table 5. Base COP is 2.1578 for the 4.3 m long tube. Increasing the length of tube from 1.3 to 2.3, 3.3, 4.3 5.3 COP increases 1.06, 2.087, 3.076 and 4.017 percent, respectively. Thus for a one-meter increase in tube length, COP increases about 9.9%. Although in this increase, the effects of economic restrictions, pressure drop and the size must be considered.

Table 5 – Effect of heat exchanger length on COP. Length (m) 1.3 2.3 3.3 4.3 5.3

COP

Increase Ratio (%)

2.0934 2.1156 2.1371 2.1578 2.1775

1.06 2.087 3.076 4.017

Table 7 – Effect of PCM heat exchanger tube diameter on COP. di (mm) 5 10 15

Table 6 – Slope of curve for refrigerant temperature in axial position for different PCM heat exchanger length. slope of curve

1.3

2.3

3.3

4.3

5.3

t = 2 min t = 12 min t = 30 min

1.41 0.88 0.96

1.27 0.83 0.91

1.22 0.83 0.75

1.44 0.81 0.84

1.15 0.77 0.82

COP

Increase Ratio (%)

2.1578 2.2039 2.2418

2.136 3.89

Table 8 – Effect of PCM thickness on COP. PCM thickness (mm) 10 15 20 25

COP

Increase Ratio (%)

2.126 2.1578 2.156 2.154

1.49 1.41 1.31

international journal of refrigeration 83 (2017) 1–13

9

Fig. 7 – Simulation algorithm in refrigeration cycle utilising PCM heat exchanger. Fig. 11 shows temperature variation of refrigerant via time for different tube lengths according to x* = 0.5, 0.75 and 1. It can be seen from the figure that for L = 1.3m, variations in temperature of the refrigerant in the middle point of the heat exchanger is 36.2 to 36.3 °C, for L = 2.3 from 35.65 to 35.8, L = 3.3 from 34.95 to 35.3, L = 4.3 from 34.15 to 34.8 and for L = 5.3 from 33.4 to 34.6 for a period of one hour. It can be deduced that increasing the tube length causes a decrease in temperature of refrigerant. Also the refrigerant temperature decrease at the outlet (x* = 1) is more than the middle of the tube because of more heat transfer between the PCM and refrigerant. Because the refrigerant temperature is constant for half an hour and is equal to 37 °C, PCM decreases the temperature of refrigerant as a while and till complete melting of PCM, remains the refrigerant at a constant temperature. Also for one meter increase in length, temperature decreases 1 °C.

For better comparison, the refrigerant temperature results for different PCM heat exchanger length at different times are brought with curve slope in Table 6 (according to Fig. 10). The slope of the curve shows temperature variation by location at a specific moment. The values of curve slope in Table 6 reveals that at the earliest moments of the process, refrigerant temperature variation by location is high and it decreases by time lapse. It can be deduced from the Table 6 that by increasing the heat exchanger length, heat transfer surface increases which leads to more heat transfer between the refrigerant and PCM, thus decreasing the refrigerant temperature.

4.1.2.

Tube diameter

Effect of tube diameter of the PCM heat exchanger on COP of the refrigerator for three different diameters is shown in Table 7.

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40

Refrigerant Temperature (°C)

Refrigerant average temperature C)

39

37 36 35 34 33 32 31 30

Fig. 8 – Comparison of refrigerant average temperature profile between the present numerical study and that of Qarnia (2009).

As can be seen, by changing the diameter of the tube, COP increases from 2.1578 to 2.2418 which is 3.89%. Fig. 12 shows a variation of refrigerant temperature for different tube diameters at different locations along the PCM heat exchanger. According to Fig. 10, at x* = 0.5, refrigerant temperature variation for di = 5 mm is 34.15 to 34.8, for di = 10 mm is 31.2 to 33.75 and for di = 15 mm is 32.15 to 33 for one hour. Also this variation for the outlet of the PCM heat exchanger for di = 5 mm is 32.62 to 33.88, for 10 mm is 27.9 to 31.25 and for 15 mm is 27.2 to 29.8. It can be deduced that increasing tube diameter have a considerable effect on decreasing refrigerant temperature due to increase in heat transfer area.

PCM thickness

Effect of PCM thickness on COP of cycle is depicted in Table 8. As can be seen from the table, the most COP increase of refrigerator is for 15 mm and is equal to 1.49%. It can be realised from the table that increasing PCM thickness has a little effect on the performance of the cycle.

Refrigerant Temperature (°C)

36

34 33

30

*

x =0.5 * x =0.75 x*=1

4.2.

Effect of refrigerant properties

4.2.1.

10

20

30

Time (min)

*

0.75

1

Effect of refrigerant type

For comparing using different refrigerant types, results for two different refrigerants, R600-a and R134-a are obtained. System COP for R-134-a and R600-a are 2.06 and 2.1578, respectively. It can be deduced that there is 4.78 percent increase in using R600-a instead of R134-a. This is because Joule-Thomson coefficient is more for R600-a than R134-a (Joule-Thomson coefficient is 0.106 for R600-a and 0.057 for R134-a).

5. 0

0.5

Axial Position (x )

40

Effect of refrigerant mass flow rate

Effect of refrigerant mass flow rate on refrigerant temperature is depicted in Fig. 14. As can be seen form the figure, for a mass flow rate of 0.04 kg s−1 refrigerant temperature varies from 32.6 to 33.9 °C and it is 34.15 to 34.88 °C for 0.06 kg s−1 and 34.95 to 35.35 °C for 0.08 kg s−1 in a one hour process. It can be deduced that increasing mass flow rate increases outlet temperature of refrigerant because of more heat transfer rate from refrigerant to the PCM.

35

31

0.25

The liquid fraction of PCM for different PCM thicknesses at 12 min is shown in Fig. 13. As can be seen, during the process, for 10 mm thickness of PCM, PCM penetration length along the tube is more in comparison with 15, 20 and 25 mm. This is because the more the PCM thickness, the more PCM is in the system and the time needed for complete melting is higher. Thus because of this almost less time, PCM cannot decrease the refrigerant temperature effectively and COP is less for 10 mm thickness of PCM through the Table 8. Although by increasing the PCM thickness, there is an optimised thickness which by exceeding from that, COP does not improve much. Thus optimum thickness can be 15 mm. By increasing from this amount there is a need to more time to fully melt the PCM and this affects the performance of the cycle.

4.2.2.

32

0

Fig. 10 – Refrigerant temperature variation along the axis at different times.

Time (min)

4.1.3.

t= 2min t= 12min t= 30min

38

50

Conclusion

60

Fig. 9 – Refrigerant temperature at different axial positions.

In this paper mathematical modeling of household refrigerators using phase change materials (PCMs) is studied. The general

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international journal of refrigeration 83 (2017) 1–13

36

Refrigerant Temperature (°C)

Refrigerant Temperature (°C)

37

36

35 L= 1.3m L= 2.3m L= 3.3m L= 4.3 L= 5.3m

34

33

0

10

20

30

Time (min)

40

50

35 34 33

31 30

60

di= 5mm di= 10mm di= 15mm

32

0

10

20

(a)

Refrigerant Temperature (°C)

Refrigerant Temperature (°C)

60

35 34 L= 1.3m L= 2.3m L= 3.3m L=4.3m L= 5.3m

33 32

0

10

20

30

Time (min)

40

50

50

60

50

60

34 33 32 31 30 29

60

di= 5mm di= 10mm di= 15mm

0

10

20

30

40

Time (min)

(b)

(b)

36

35

35

Refrigerant Temperature (°C)

Refrigerant Temperature (°C)

50

35

36

34 33 32 L= 1.3m L= 2.3m L= 3.3m L= 4.3m L= 5.3m

31 30 29

40

(a)

37

31

30

Time (min)

0

10

20

30

Time (min)

40

50

60

(c)

34 33 32 31 30 di= 5mm di= 10mm di= 15mm

29 28 27

0

10

20

30

40

Time (min) (c)

Fig. 11 – The refrigerant temperature for different tube lengths a) x* = 0.5 b) x* = 0.75 c) x* = 1.

model consists of compressor, evaporator, expansion valve and condenser and PCMs are located as a heat exchanger between condenser and expansion valve. R600-a is used as refrigerator flows in inner tube and PCM with a transition temperature of 21 °C is located in the shell side. Therefore the effect of parameters including a geometrical property (tube length and tube diameter), PCM thickness and refrigerant property (mass flow rate and type) on refrigerant temperature and coefficient of performance (COP) of the cycle are investigated. The simulation

Fig. 12 – Refrigerant temperature for different tube diameters at different axial locations a) x* = 0.5 b) x* = 0.75 c) x* = 1.

results of the system show that using PCM decreases the outlet refrigerant temperature of the condenser which leads to increase in COP to 9.58%. Also parametric study reveals that geometrical and refrigerant properties of the system have positive effect on performance of the system and COP. However there must be an optimum PCM thickness for better performance of the system.

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international journal of refrigeration 83 (2017) 1–13

(b)

(a)

(d)

(c)

Fig. 13 – Phase front displacement for different PCM thicknesses at 12 min a) 10 mm b) 15 mm c) 20 mm d) 25 mm.

Refrigerant Temperature (°C)

36

35

34

m.=0.04 kg/s m.=0.06 kg/s m.=0.08 kg/s

33

32

0

10

20

30

40

50

60

Time (min) Fig. 14 – The refrigerant temperature for a different mass flow rate of refrigerant at x* = 0.5.

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