^{1}

^{*}

^{1}

Cooling in industrial production and refrigeration of perishable and
non-
perishable products is common practice throughout the world. Research studies have been conducted both experimentally and numerically to simulate Vapor Compression Refrigeration System (VCRS) and its performance respectively, however, experimental procedure often seems to be expensive and time-consuming to carry out due to the function of many variables. This study was therefore designed to numerically simulate the performance assessment of a nanoparticle enhanced VCRS. A numerical model of a vapor compression refrigeration system was developed using standard refrigeration equations on each of the major components of the refrigeration system such as compressor, evaporator, condenser and expansion valve. The model was then simulated on a MATLAB platform with a CoolProp installed packages via Python under two different simulation cases. In the first case, the mass fractions were varied for CuO,
TiO_{2} and Al_{2}O_{3} nanoparticles while their densities remained constant and a reversed condition was investigated for the second case. The results showed that both the refrigerating effect and the Coefficient Of Performance (COP) of the system increase as both the mass fraction and density of all the nanoparticles increases. It also shows that the compressor work decreases as both the mass fraction and density of all the nanoparticles were increased. On comparing the computational and numerical analysis results, the study established no significant difference in terms of COP and the use of nanoparticles were found to have improved the COP of the system.

More than a century ago, researchers have initiated the efforts to enhance inherently poor thermal conductivity of liquids by adding solid particles in base fluids. Earlier studies used millimeter or micrometer solid particles, which led to problems such as rapid settling of solid particles, clogging, surface abrasion & high-pressure drop, limiting their practical applications. Nanofluids have good potential to overcome these problems. In the last decade, the number of published articles mentioning nanoparticles has increased significantly in refrigeration field. Taiwo et al. [_{2}O_{3}) to improve the framework execution and decrease the power utilization. The outcomes demonstrate that by including the nanoparticles (Al_{2}O_{3}) to the other refrigerant blend (R290/R600a), the coefficient of execution is somewhat expanded while control utilization by blower is marginally diminished. The nano refrigerant (R290/R600a/Al_{2}O_{3}) can work ordinarily and proficiently in coolers. Contrasted and icebox with unadulterated (R290/R600a) as working liquids, 0.3 g/L convergences of (R290/R600a/Al_{2}O_{3}) can spare 29.33% vitality utilization. The authors concluded that the residential cooler execution will be improved by including the nanoparticles (Al_{2}O_{3}) to other refrigerant blend (R290/R600a). In 2020, Vipin Nair et al. [_{2}O_{3} nanoparticles were used for the preparation of the nano-oil. The COP of the system was found to be improved by as much as 6.5% due to nano-oil and the degree of sub-cooling in the condenser of the system was enhanced by Nano-oil.

Senthilkumar et al. in 2021 also investigated the performance of R600a vapour compression system using CuO/Al_{2}O_{3} hybrid nanolubricants [_{2}O_{3} hybrid nanolubricant refrigerator can be employed as better substitute for R134a refrigerator. In 2011, Subramani and Prakash [_{2}O_{3} Nano refrigerant and found that there is an enhancement in COP while nanoparticles were added to the system. They also determined the system’s COP theoretically for both R134a and R134a/Al_{2}O_{3}. They found that the COP of cycles that use R134a increases by 10.11% while the R134a/Al_{2}O_{3} mixture used in the actual refrigeration cycle and enhancement ratio was 9.74% when COP determined theoretically. Sajumon et al., in 2013 found through his study that Nanolubricants show higher viscosity and smaller friction co-efficient [

The vapor-compression refrigeration is a variety of refrigeration. Generally, the system of vapor-compression refrigeration as shown in

(1-2) compressing refrigerant in compressor isentropically;

(2-3) condensation at constant pressure;

(3-4) adiabatic expansion in the expansion valve;

(4-1) evaporation at constant pressure.

The evaporation of the refrigerant occurs at a constant pressure during process (4-1) in the evaporator. The refrigerant at the inlet of the evaporator is vaporized by removing heat from the area desired to cool. Saturated vapor at point 1 goes into the compressor at low pressure and is exposed to a reversible

isentropic compression during the process from 1 to 2. During process (2-3), while the heat is rejected in the condenser at a constant pressure, the working fluid changes to a saturated liquid when exiting the condenser. Refrigerant at point 1 is saturated vapor at the evaporator temperature and at point 3 is saturated liquid at the condenser temperature. The working fluid at the exit of the expansion valve enters the evaporator, and the cycle is completed. Completely vaporized refrigerant enters the compressor, and its pressure and temperature increase during the compressing process. The working fluid at the condenser outlet is saturated liquid.

The system’s properties of interest are calculated using standard refrigeration Equations (1)-(10) as follows:

· Heat transfer rate of the evaporator or refrigerating effect (RE)

q e = h 1 − h 4 (1)

• Compressor work

w c o m p = h 2 − h 1 (2)

η i s e = h 2 s − h 1 h 2 a − h 1 (Isentropic efficiency) (3)

· Heat transfer rate of the condenser

q c = h 2 − h 3 (4)

· C .O .P = q e w c o m p (5)

The components can also be analyzed in terms of mass flow rates and specific heat as shown below;

1) Compressor

W ˙ c o m p = m ˙ 1 c p , n f ( T 2 − T 1 ) (6)

m ˙ 1 = m ˙ 2

where W ˙ c o m p = Power input into the compressor,

c p , n f = Specific heat of Nanofluid at constant pressure,

m ˙ 1 and m ˙ 2 are mass flow rates,

T_{1} and T_{2} are temperatures at the compressor inlet and exit respectively.

2) Condenser

Q ˙ C = m ˙ 2 c p , n f ( T 3 − T 2 ) (7)

m ˙ 2 = m ˙ 3

where Q ˙ C = rate of heat removal at the condenser,

c p , n f = Specific heat of Nanofluid at constant pressure,

m ˙ 2 and m ˙ 3 mass flow rates,

T_{2} and T_{3} are temperatures at the condenser inlet and exit respectively.

3) Capillary

T 4 = T 3 _{ }

m ˙ 4 = m ˙ 3 _{ }

where m ˙ 3 and m ˙ 4 mass flow rates.

T_{3} and T_{4} are temperatures at the capillary inlet and exit respectively.

4) Evaporator

Q ˙ e = m ˙ 4 c p , n f ( T 1 − T 4 ) (8)

m ˙ 4 = m ˙ 3

where Q ˙ e = rate of heat removal at the evaporator,

c p , n f = Specific heat of Nanofluid at constant pressure,

m ˙ 4 and m ˙ 3 = mass flow rates,

T_{4} = Inlet temperature of refrigerant,

T_{1} = outlet temperature of refrigerant.

C . O . P = Q ˙ e W ˙ c o m p (9)

While the Nano refrigerant’s thermo physical properties of interest are calculated as follows:

· Density

ρ N F = ω n ρ P + ( 1 − ω n ) ρ P R (10)

For the purpose of this work (theoretical modeling), we shall make use of three nanoparticles (CuO, TiO_{2} and Al_{2}O_{3}) with a density of 6500 kg/m^{3}, 4250 kg/m^{3} and 2200 kg/m^{3}, mass fraction of 0.06% and particle diameter of 45 nm. Also, pure R134a refrigerant will be used as the base fluid. Due to the limited number of studies regarding the experimental study of Nano refrigerants, Subramani and Prakash’s experimental database [_{PR3}) and saturation pressure (P_{PR3}) corresponding to T_{PR3} are specified at 45.6˚C and 11.8 bar, respectively. Then density is read from the Mollier chart of R134a. Density of Nano refrigerant (ρ_{NR}) is calculated by replacing nanoparticle mass fraction in Nano refrigerant (ω_{n}), ρ_{NP} and ρ_{PR} in the density equation with their respective values. Then saturation temperature and pressure and enthalpy of Nano refrigerant are read from chart R134a for point 3. Enthalpy at point 3 decreases to 116.49 kJ/kg from 116.73 kJ/kg.

Similar to the determination of enthalpy of Nano refrigerant at point 3, enthalpy of nanorefrigerant at point 1 can be found. Temperature (T_{PR1}) and saturation pressure (P_{PR1}) corresponding to T_{PR1} is specified at −7˚C and 2.25 bar, respectively. Then density is read from the chart of R134a. The density of Nano refrigerant (ρ_{NR}) is calculated by replacing nanoparticle mass fraction in Nano refrigerant (ω), ρ_{NP}, and ρ_{PR} in the density equation with their respective values. Then saturation temperature and pressure and the enthalpy of the Nano refrigerant are read from chart R134a for point 1. Enthalpy at point 1 (using Al_{2}O_{3}) increases to 249.32 kJ/kg from 245.87 kJ/kg. Further, enthalpy of Nano refrigerant at point 2 and 4 can be found using the specifications given at state 3 such as pressure and temperature. Temperature (T_{PR2}) at state 2 is specified at 81.5˚C while the pressure (P_{PR2}) is 11.8 bar, since condensation is at constant pressure. Then density is read from the chart of R134a. The density of Nano refrigerant (ρ_{NR}) is calculated by replacing nanoparticle mass fraction in Nano refrigerant (ω), ρ_{NP}, and ρ_{PR} in the density equation with their respective values. Then saturation temperature and pressure and the enthalpy of the Nano refrigerant are read from chart R134a for point 2. Enthalpy at point 1 decreases to 312.57 kJ/kg from 312.99 kJ/kg. At state 4, the enthalpy is equal to that of state 3 since process 3 - 4 is adiabatic. As for the isentropic work of the compressor, h_{2s} is read from the chart by making use of s_{1} and saturation pressure at point 3. The isentropic work is found to be 35.51 kJ/kg for pure refrigerant. At the outlet of the compressor, if isentropic efficiency is 1 and the refrigeration cycle is ideal, s_{1} and s_{2} must be equal. For this calculation, isentropic efficiency is 0.53. COP enhancement is 9.38%. _{2}O_{3}.

The Al_{2}O_{3} nanoparticle can be produced in a wide range of densities using recent techniques, thus, in this work, we take the density of Al_{2}O_{3} nanoparticle as 2200 kg/m^{3}. The results of our calculation approximate those of Subramani and Prakash [_{2}O_{3} density of 3690 kg/m^{3}. Some results from Subramani and Prakashexperimental study [

Thus, for the purpose of our main study which is the numerical simulation

Properties | PR (R134a) | NR1 (R134a/Al_{2}O_{3}) | NR2 (R134a/CUO) | NR3 (R134a/TiO_{2}) |
---|---|---|---|---|

P_{1} = P_{4} (bar) | 2.2 | 2.74 | 2.99 | 2.47 |

T_{1} (˚C) | −7.7 | −1.93 | 0.48 | −4.6 |

T_{2} (˚C) | 81.5 | 81.1 | 66.73 | 71.45 |

T_{3} (˚C) | 45.6 | 45.45 | 44.84 | 45.1 |

P_{3} = P_{2} (bar) | 11.8 | 11.76 | 11.58 | 11.67 |

h_{1} (kJ/kg) | 245.87 | 249.32 | 250.73 | 247.73 |

h_{2} (kJ/kg) | 312.99 | 312.57 | 297.03 | 302.178 |

h_{3} = h_{4} (kJ/kg) | 116.73 | 116.49 | 115.58 | 116.06 |

s_{1} (kJ/kg K) | 0.9362 | |||

q_{c} (kJ/kg) | 205.26 | 196.08 | 181.45 | 186.12 |

q_{e} (kJ/kg) | 129.14 | 132.83 | 135.15 | 131.67 |

w_{comp} (kJ/kg) | 67.12 | 63.25 | 46.3 | 54.45 |

C.O.P | 1.92 | 2.1 | 2.9 | 2.4 |

η_{ise} | 0.53 |

and performance assessment of a nanoparticle enhanced vapor compression refrigeration system, we propose a model of a vapor compression refrigeration system with three different nano refrigerants as the working fluid with state point properties as shown in the last three columns of _{2}O_{3} which serve as the baseline or reference are shown in

The simulation was performed with a package in REFPROP software called Coolprop. REFPROP is an acronym for Reference fluid Properties. This program,

Cycle fluid | T_{1} (˚C) | ρ_{P} (kg/m^{3}) | P_{1} (bar) | T_{2} (˚C) | T_{3} (˚C) | P_{3} (bar) | C.O.P (+) | % (−) | % |
---|---|---|---|---|---|---|---|---|---|

R134a (exp) | 19 | 2 | 82 | 45 | 12 | 1.6 | |||

R134a/Al_{2}O_{3} (exp) | 4 | 3690 | 2 | 80 | 38 | 12 | 1.78 | 10.11 | |

Current (R134a) | −7.7 | 2.2 | 81.5 | 45.6 | 11.8 | 1.92 | 20 | ||

Current (NR1) | −1.93 | 2200 | 2.74 | 81.1 | 45.45 | 11.76 | 2.1 | 9.4 | 18 |

Current (NR2) | 0.48 | 6500 | 2.99 | 66.73 | 44.84 | 11.58 | 2.9 | 51.1 | |

Current (NR3) | −4.6 | 4250 | 2.47 | 71.45 | 45.10 | 11.67 | 2.4 | 25 |

developed by the National Institute of Standards and Technology (NIST), calculates the thermodynamic and transport properties of industrially important fluids and their mixtures. The Cool prop is a package in REFPROP that has a dynamic library through which it runs its C++ encoded equations of states to get thermodynamic and thermo physical properties of states. It can be used on different programming platforms like MATLAB and FORTRAN. In this work, it was used on a MATLAB platform via python. In the first part of the simulation, the mass fraction of nanoparticles were varied from 0.06% to 0.6% on a mesh of ten equally spaced points. A constant nanoparticle size of about 45 nm was maintained for all the nanoparticles while a constant densities of 2200 kg/m^{3}, 6500 kg/m^{3} and 4250 kg/m^{3} were maintained for the AL_{2}O_{3}, CUO and TiO_{2} nanoparticles, respectively. The variations of the mass fraction with system properties and performance were carefully observed and plotted. In the second part, the densities of each nanoparticles were varied on a step of 5 kg/m^{3} with a constant mass fraction of 0.06%. Recent studies and techniques have shown that nanoparticles can be manufactured at different densities and the higher the density the higher the particle size diameter. Thus, the nanoparticle sizes were indirectly varied by density. In all the two simulation cases, the condenser pressure was maintained at 1.18 MPa and the evaporator pressure is 0.22 MPa and no appreciable pressure drops due to friction were assumed in the condenser and evaporator. After all the simulations, the results were plotted and validation was carried out using Subramani and Prakash’s experimental study as our basis of comparison in terms of COP [

In this work, we have studied the effects of mass fractions and densities of three different nanoparticles namely; Al_{2}O_{3}, CUO and TiO_{2} in a single R134a refrigerant on the properties and performance of a vapour compression refrigeration system. The model of the vapour compression refrigeration system was formulated by specifications using Subramani and Prakash’s experimental study [

MATLAB platform with a CoolProp thermodynamic library already installed via python. Constant densities were maintained for all three nanoparticles while mass fractions were varied at a step of 0.067% in the first phase of simulation while the mass fraction of 0.06% was maintained in the second part of the simulation and the densities were varied at a step of 5 kg/m^{3}. The results which reflect the various effects of mass fraction and density of nanoparticles on the properties of a vapor compression refrigeration system working with the nano refrigerants are presented in graphical form and extensively discussed in this section.

I considered testing for the accuracy and validity of the results by making a comparison between my results and that of the Subramani and Prakash’s experimental study as shown in the histogram presented in the next page.

The first two bars of the histogram represent the COP for the pure refrigerant R134a while the other bars correspond to R134a/Al_{2}O_{3} nano refrigerant. It can be observed that the COP of the pure refrigerant R134a from our theoretical results compares favourably well with that of the [_{2}O_{3} is also in good agreement with a deviation of about 18%. This is also shown on

The effects of mass fraction of the nanoparticles on various system properties and performance are illustrated in Figures 4-6 shown in the next pages.

As shown in _{2}. As for the R134a/Al_{2}O_{3}, the compressor will not stop working for all the mass fraction values investigated.

Lastly, _{2} fell below positive values due to the negative values of the compressor work. The effects of density of the nanoparticles on the system’s refrigerating

R134a | R134a/Al_{2}O_{3} | Deviation | |
---|---|---|---|

Experimental COP | 1.6 | 1.78 | 20% |

Theoretical COP | 1.92 | 2.1 | 18% |

effect are illustrated in Figures 7-9 shown below.

As shown in the Figures 7-9 below, the refrigerating effect enhances significantly as the density of all the nanoparticles increase. This is due to the fact that nanoparticles have large radius at high densities and this gives them large surface areas for enhanced heat transfer qualities. Consequently, the refrigerating effect advances linearly with the densities.

The effects of density of the nanoparticles on the system’s compressor work are illustrated in Figures 10-12 shown below.

As shown in the Figures 10-12 above, the compressor work decreases linearly as the density of all the nanoparticles increase. This is because, the movement of highly density nanoparticles largely within the nano refrigerants largely contributes to the pressure of the nano refrigerants. Thus, lesser compressor work would be required to attain the desired condenser pressure.

The effects of density of the nanoparticles on the system’s coefficient of performance are illustrated in Figures 13-15 shown below.

Finally, as shown in Figures 13-15 below, the overall effect of the increase

Density (Al_{2}O_{3}) | COP |
---|---|

2200.0000 2205.0000 2210.0000 2215.0000 2220.0000 2225.0000 2230.0000 2235.0000 2240.0000 2245.0000 | 2.2064 2.2072 2.2079 2.2086 2.2093 2.2093 2.2108 2.2115 2.2122 2.2129 |

Density (CUO) | COP |
---|---|

6500.0000 6505.0000 6510.0000 6515.0000 6520.0000 6525.0000 6530.0000 6535.0000 6540.0000 6545.0000 | 2.9519 2.9529 2.9539 2.9550 2.9560 2.9571 2.9581 2.9592 2.9602 2.9613 |

Density (TiO_{2}) | COP |
---|---|

4250.0000 4255.0000 4260.0000 4265.0000 4270.0000 4275.0000 4280.0000 4285.0000 4290.0000 4295.0000 | 2.5276 2.5285 2.5293 2.5302 2.5311 2.5319 2.5328 2.5336 2.5345 2.5353 |

and decrease of refrigerating effect and compressor work respectively is that the COP increases as the densities of all the nanoparticles increase. All these are also illustrated in the given Tables 4-6 above.

In the present work, we have developed a numerical model for the simulation of nanoparticle enhanced vapor compression refrigeration system and we have carried out the performance assessment of the system. The results of the investigation established the followings:

v Both the refrigerating effect and the COP of the system increase as the mass fraction of all the nanoparticles increases.

v The compressor work decreases as the mass fraction of all the nanoparticles increased.

v The refrigerating effect and the COP of the system increase as the density of all the nanoparticles are increased.

v The compressor work decreases as the density of all the nanoparticles increased.

v Generally from these results, it can be concluded that more works still need to be done to investigate the effects of other properties of nanoparticles on a vapour compression refrigeration system as this aspect is of utmost importance in engineering field.

The authors declare no conflicts of interest regarding the publication of this paper.

Odunfa, M.K. and Oseni, O.D. (2021) Numerical Simulation and Performance Assessment of a Nanoparticle Enhanced Vapour Compression Refrigeration System. Journal of Power and Energy Engineering, 9, 33-49. https://doi.org/10.4236/jpee.2021.911002