# Comparative Study on Boiling Heat Transfer Characteristics and Performance of Low-Temperature Heating System of R744 and Its Azeotropic Refrigerant

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}and a mass flux of 300 kg/m

^{2}·s, respectively, and that the heat transfer coefficients increase by 5% and 31%, respectively. Ozawa et al. [9] studied the flow pattern and boiling heat transfer of R744 in horizontal small-bore tubes. The result showed that the low surface tension and latent heat also have significant influences on two-phase flow patterns and heat transfer. Huai et al. [10] studied the flow boiling characteristics of R744 in multiport minichannels in an experiment. The result showed that the pressure drop along the test section is very small, and the two-phase R744 flow exhibits a higher heat transfer coefficient than that of the single-phase liquid or vapor flow. Jiang et al. [11] studied the characteristics of heat transfer for the R744 flow boiling at a low temperature in a minichannel. The result showed that the heat transfer coefficient increases with an increase in the mass flux rate but decreases with an increase in the tubes’ inner diameter and saturation temperature, and the boiling heat transfer of R744 has a greater effect on nucleate boiling and highly depends on the heat flux. Zhang et al. [12] studied the flow boiling heat transfer characteristics of R744 in a horizontal minitube in an experiment. The result showed that an increase in the heat flux has a significant effect on enhancing the nucleate boiling heat transfer, while it can also speed up the dry-out process and decrease the starting vapor quality of dry-out. Kim et al. [13] studied the evaporative heat transfer and pressure drop of R744 flowing upward in vertical smooth and microfin tubes with a diameter of 5 mm in an experiment. The result showed that the average evaporation heat transfer coefficients for the microfin tubes were approximately 111–207% higher than those for the smooth tube under the same test conditions, and the PF was increased from 106% to 123%.

^{2}, and the mass flux rate was 200–400 kg/(m

^{2}·s). The results showed that the heat transfer coefficient of the mixture was between R744 and R290 and decreased with an increase in the R290 mass ratio, which was directly proportional to the initial evaporation temperature, heat flux, and mass flux rate, and the critical dryness was also proportional to the mass flux rate of R290.

## 2. Numerical Approach

#### 2.1. Geometric Model

#### 2.2. Mathematical Model

#### 2.2.1. Basic Equation

#### 2.2.2. Turbulence Model

_{i}is the instantaneous velocity in the rectangular coordinate system; x

_{i}, x

_{j}are the different directions in the rectangular coordinates; ${\mu}_{eff}$ is the effective dynamic viscosity coefficient; ${G}_{k}$ is the turbulent kinetic energy due to the time averaged velocity gradient; and ${\alpha}_{k}$ = ${\alpha}_{\epsilon}$ = 1.39, ${C}_{2\epsilon}^{*}$ = 1.68, and ${C}_{2\epsilon}$ = 1.42.

#### 2.2.3. Interphase Transition Model

_{fg}is the vaporization latent heat.

#### 2.3. Boundary Condition

_{sat}), the saturation temperature (T

_{sat}), and the specific simulation conditions, which are shown in Table 1.

#### 2.4. Solution Strategy

#### 2.5. The Thermophysical Properties of Working Fluids

#### 2.6. Mesh Independent and Method Validation

^{2}·s, q = kW/m

^{2}, T

_{sat}= K) are applied to three kinds of grids. Through the simulation, the temperature values at different positions are obtained. Taking the temperature value obtained by the grid number (a) as the benchmark (max relative error of T = 0), the maximum temperature error is compared with the other two groups of grids. Table 5 shows the relative error of grids (b) and (c) relative to (a), which are 0.053% and 0.081%, respectively. This shows that when the number of grids is larger, there is no substantial impact on the results. Finally, grid (a) is selected for the following simulation, and the grid division is shown in Figure 2.

## 3. Result and Discussion

#### 3.1. Pattern Distribution of Liquid Volume Fraction

#### 3.2. Effect of Mass Flux on Heat Transfer Coefficient of R744 and Azeotropic Refrigerant

^{2}·s, 75 kg/m

^{2}·s, and 100 kg/m

^{2}·s, the corresponding average heat transfer coefficients are 5137.58 W/m

^{2}K, 4678.85 W/m

^{2}K, and 4656.93 W/m

^{2}K, respectively, and when the mass flux is 50 kg/m

^{2}·s, the average heat transfer coefficients are 9.8% and 10.3% higher than when the mass fluxes are 75 kg/m

^{2}·s and 100 kg/m

^{2}·s, respectively. Similarly, the corresponding average heat transfer coefficients of the azeotropic refrigerants are 6527.55 W/m

^{2}K, 5881.89 W/m

^{2}K, and 5406.93 W/m

^{2}K; when the mass flux is 50 kg/m

^{2}·s, its average heat transfer coefficient is 10.9% and 20.7% higher than when the mass flux is 75 kg/m

^{2}·s and 100 kg/m

^{2}·s, respectively. The results show that the heat transfer performance of the azeotropic refrigerant is better than R744, and the increase in its heat transfer coefficient has certain advantages.

^{2}·s, 75 kg/m

^{2}·s, and 100 kg/m

^{2}·s, its heat transfer coefficient decreases by 25.8%, 7.1%, and 1.7%, respectively, with the increase in quality. The heat transfer coefficient of the azeotropic refrigerant decreases by 17.1%, 7.9%, and 2.5%, respectively.

#### 3.3. Effect of Heat Flux on Heat Transfer Coefficient of R744 and Azeotropic Refrigerant

^{2}, 20 kW/m

^{2}, and 30 kW/m

^{2}, the corresponding average heat transfer coefficients are 5137.58 W/m

^{2}K, 9648.19 W/m

^{2}K, and 12,688.94 W/m

^{2}K, respectively, and when the heat flux is 30 kW/m

^{2}, the average heat transfer coefficients are 146.9% and 31.5% higher than when the heat fluxes are 10 kW/m

^{2}and 20 kW/m

^{2}, respectively. Similarly, the corresponding average heat transfer coefficients of the azeotropic refrigerants are 6527.55 W/m

^{2}K, 12,176.86 W/m

^{2}K, and 16,017.91 W/m

^{2}K; when the heat flux is 30 kW/m

^{2}, its average heat transfer coefficient is 145.3% and 31.5% higher than when the heat fluxes are 10 kW/m

^{2}and 20 kW/m

^{2}, respectively. It can be seen that under the influence of different heat fluxes, the increases in their heat transfer coefficients are basically the same.

^{2}, 20 kW/m

^{2}, and 30 kW/m

^{2}, its heat transfer coefficient decreases by 25.8%, 40.8%, and 61.2%, respectively, with the increase in quality. The heat transfer coefficient of the azeotropic refrigerant decreases by 17.1%, 41.5%, and 61.7%, respectively.

#### 3.4. Effect of T_{sat} on Heat Transfer Coefficient of R744 and Azeotropic Refrigerant

_{sat}because the viscosity of the fluid decreases with the increase in the saturation temperature, and the decrease in the viscosity of the fluid increases the influence of the convective heat transfer, which is conducive to wetting the wall. At the same time, the nuclear boiling makes the liquid film on the inner wall of the tube thinner and easier to break, so the heat transfer coefficient increases when the viscosity is low. In addition, it is found that when R744 is 253 K, the heat transfer coefficient sharply decreases after the quality reaches a certain degree, which is also due to the high viscosity and the earlier drying, resulting in the deterioration of the heat transfer. However, because of the low viscosity of the azeotropic refrigerant increases, there is no sharp decrease in the heat transfer coefficient thanks to the lack of dry-out.

_{sat}of R744 are 253 K, 263 K, and 273 K, the corresponding average heat transfer coefficients are 5137.58 W/m

^{2}K, 6289.71 W/m

^{2}K, and 8004.55 W/m

^{2}K respectively, and when the T

_{sat}is 273 K, the average heat transfer coefficients are 55.8% and 27.3% higher than when the T

_{sat}values are 253 K and 263 K, respectively. Similarly, the corresponding average heat transfer coefficients of the azeotropic refrigerants are 6527.55 W/m

^{2}K, 7992.84 W/m

^{2}K, and 10,303.96 W/m

^{2}K; when the T

_{sat}is 273 K, its average heat transfer coefficient is 61.9% and 28.9% higher than when the T

_{sat}values are 253 K and 263 K, respectively. It can be seen that under the influence of different T

_{sat}values, the increase in the heat transfer coefficient of the azeotropic refrigerants has certain advantages.

_{sat}of R744 is 253 K, 263 K, and 273 K, its heat transfer coefficient decreases by 25.8%, 19.5%, and 24.6%, respectively, with the increase in quality. The heat transfer coefficient of the azeotropic refrigerant decreases by 17.1%, 20.3%, and 25.3%, respectively.

#### 3.5. Comparison of Heat Transfer Performance of R744 and Its Azeotropic Refrigerant

_{sat}is 253–273 K, and the mass flux is 50–100 kg/m

^{2}·s. Similarly, when the mass flux is 50 kg/m

^{2}·s, the T

_{sat}is 253 K, and the heat flux is 10–30 kW; the boiling heat transfer coefficient of the azeotropic refrigerant is 26.61% higher than that of R744 on average. When the mass flux is 50 kg/m

^{2}·s, the heat flux is 10 kW and the T

_{sat}is 253–273 K; the boiling heat transfer coefficient of the azeotropic refrigerant is 27.73% higher than that of R744 on average.

#### 3.6. Comparison of Low-Temperature Heating System Performance of R744 and Its Azeotropic Refrigerant

## 4. Conclusions

- At the low mass flux, the heat transfer coefficients of R744 and its azeotropic refrigerant decrease with the increase in the mass flux.
- Within a given working condition, the heat transfer coefficients of R744 and its azeotropic refrigerant increase with the increase in the heat flux and the T
_{sat}. - Under the influence of different factors, the average boiling heat transfer coefficient of the azeotropic refrigerant is 24.37% (mass flux), 26.61% (heat flux), and 27.73% (T
_{sat}) higher than R744, respectively. - Under the given working conditions, compared with R744, the azeotropic refrigerant is not found to be dry.
- Compared with R744, the bubble change in the azeotropic refrigerant is more conducive to enhancing the heat transfer.
- It is found that the critical evaporation temperature makes the COP of the azeotropic refrigerant higher than that of R744.
- The critical evaporation temperature is determined by T
_{co}, and it increases with the increase in the T_{co}.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${c}_{p}$ | specific heat at constant pressure (kJ/kg·K) |

${C}_{2\epsilon}$ | turbulence model’s constants |

${C}_{2\epsilon}^{*}$ | turbulence model’s constants |

D | tube diameter (m) |

E | energy |

F | volume force |

g | acceleration due to gravity (m/s^{2}) |

G | mass flux (kg/(m^{2}·s)) |

G_{k} | turbulent kinetic energy due to time averaged velocity gradient |

h | heat transfer coefficient (W/m^{2}·K) |

h_{gf} | vaporization latent heat (kJ/kg) |

k | turbulence kinetic energy (m^{2}/s^{2}) |

m | mass of working fluid (kg) |

p | pressure (MPa) |

Q | quantity of heat (kW) |

q | heat flux (kW/m^{2}) |

Re | Reynolds number |

$r$ | interphase heat transfer coefficients |

s | source term |

T | thermodynamic temperature (k) |

v | velocity (m/s) |

x | cartesian coordinates (m) |

X | quality |

Greek symbols | |

$\alpha $ | volume fraction |

$\epsilon $ | rate of dissipation of k (m^{2}/s^{3}) |

$\lambda $ | thermal conductivity (W/(m·K)) |

$\mu $ | dynamic viscosity (Pa·s) |

$\rho $ | density (kg/m^{3}) |

$\sigma $ | tension (N/m) |

${\sigma}_{k}$ | turbulent Prandtl number for k |

${\sigma}_{\epsilon}$ | turbulent Prandtl number for ε |

$\kappa $ | interface curvature |

Subscripts | |

co | outlet temperature of condenser |

d | discharge temperature |

e | evaporation |

eff | effective |

l | liquid phase |

i,j | general spatial indices |

q | phase |

sat | saturation |

v | vapor phase |

Acronyms | |

R744 | carbon dioxide |

COP | coefficient of performance |

GWP | global warming potential |

ODP | ozone-depleting potential |

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**Figure 3.**Change in heat transfer coefficient with dryness (the experimental conditions include D = 6 mm, G = 240 kg/m

^{2}·s, T

_{sat}= 283 K, and q = 10–20 kW/m

^{2}[7]).

**Figure 4.**Volume fraction distribution of R744 liquid phase at different mass fluxes: (

**a**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.28; (

**b**) T

_{sat}= 253 K, G = 75 kg/m

^{2}·s, q = 10 kW, X = 0.19; (

**c**) T

_{sat}= 253 K, G = 100 kg/m

^{2}·s, q = 10 kW, X = 0.14.

**Figure 5.**Volume fraction distribution of R744 liquid phase at different heat fluxes: (

**a**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.28; (

**b**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 20 kW, X = 0.56; (

**c**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 30 kW, X = 0.84.

**Figure 6.**Volume fraction distribution of R744 liquid phase at different T

_{sat}values: (

**a**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.28; (

**b**) T

_{sat}= 263 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.31; (

**c**) T

_{sat}= 273 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.35.

**Figure 7.**Volume fraction distribution of az-refrigerant liquid phase at different mass fluxes: (

**a**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.26; (

**b**) T

_{sat}= 253 K, G = 75 kg/m

^{2}·s, q = 10 kW, X = 0.18; (

**c**) T

_{sat}= 253 K, G = 100 kg/m

^{2}·s, q = 10 kW, X = 0.13.

**Figure 8.**Volume fraction distribution of az-refrigerant liquid phase at different heat fluxes: (

**a**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.26; (

**b**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 20 kW, X = 0.52; (

**c**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 30 kW, X = 0.78.

**Figure 9.**Volume fraction distribution of az-refrigerant liquid phase at different T

_{sat}values: (

**a**) T

_{sat}= 253 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.26; (

**b**) T

_{sat}= 263 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.29; (

**c**) T

_{sat}= 273 K, G = 50 kg/m

^{2}·s, q = 10 kW, X = 0.32.

**Figure 16.**Comparison of heat transfer coefficients between azeotropic refrigerant and R744 at different mass fluxes: (

**a**) G = 100 kg/m

^{2}·s; (

**b**) G = 75 kg/m

^{2}·s; (

**c**) G = 50 kg/m

^{2}·s.

**Figure 17.**Comparison of heat transfer coefficients between azeotropic refrigerant and R744 at different heat fluxes: (

**a**) q = 10 kW; (

**b**) q = 20 kW; (

**c**) q = 30 kW.

**Figure 18.**Comparison of heat transfer coefficients between azeotropic refrigerant and R744 at different T

_{sat}values: (

**a**) T

_{sat}= 253 K; (

**b**) T

_{sat}= 263 K; (

**c**) T

_{sat}= 273 K.

**Figure 22.**Comparison of COP values of azeotropic refrigerant and R744 varies with evaporation temperature at different outlet temperatures of condenser: (

**a**) T

_{co}= 273 K; (

**b**) T

_{co}= 278 K; (

**c**) T

_{co}= 283 K.

**Figure 23.**Comparison of discharge temperature of azeotropic refrigerant and R744 varies with evaporation temperature at different outlet temperatures of condenser: (

**a**) T

_{co}= 273 K; (

**b**) T

_{co}= 278 K; (

**c**) T

_{co}= 283 K.

**Figure 24.**Comparison of COP of azeotropic refrigerant and R744 varies with evaporation temperature at different outlet temperatures of condenser: (

**a**) T

_{co}= 273 K; (

**b**) T

_{co}= 278 K; (

**c**) T

_{co}= 283 K.

**Figure 25.**Comparison of discharge temperature of azeotropic refrigerant and R744 varies with evaporation temperature at different outlet temperatures of condenser.

Case | D (mm) | G (kg/m^{2}·s) | Q (kW/m^{2}) | P_{sat} (MPa) | T_{sat} (K) |
---|---|---|---|---|---|

R744 | 1 | 50/75/100 | 10/20/30 | 2.3/3.03/3.92 | 253/263/273 |

azeotropic refrigerant | 1 | 50/75/100 | 10/20/30 | 1.96/2.64/3.47 | 253/263/273 |

Parameter | R744 | R744 | R744 |
---|---|---|---|

T_{sat} (K) | 253 | 263 | 273 |

${\rho}_{1}$ (kg/m^{3}) | 1032.4 | 983.7 | 928.33 |

${\rho}_{v}$ (kg/m^{3}) | 51.45 | 70.85 | 97.18 |

C_{PL} (kJ/(kg·K)) | 2.1636 | 2.3046 | 2.5377 |

C_{PV} (kJ/(kg·K)) | 1.2867 | 1.5050 | 1.8578 |

${\lambda}_{1}$ (mW/(m·K)) | 134.82 | 122.72 | 110.61 |

${\lambda}_{v}$ (mW/(m·K)) | 15.069 | 16.928 | 19.621 |

${\mu}_{1}$ (μPa·s) | 1.4 × 10^{−4} | 1.2 × 10^{−4} | 1.0 × 10^{−4} |

${\mu}_{v}$ (μPa·s) | 1.31 × 10^{−5} | 1.38 × 10^{−5} | 1.4 × 10^{−5} |

h_{gf} (kJ/kg) | 282.78 | 259 | 231.35 |

$\sigma $ (N/m) | 8.62 | 6.53 | 4.57 |

P_{sat} (MPa) | 1.96 | 2.64 | 3.47 |

Parameter | Az-Refrigerant | Az-Refrigerantv | Az-Refrigerant |
---|---|---|---|

T_{sat} (K) | 253 | 263 | 273 |

Liquid density (kg/m^{3}) | 748.9 | 704.14 | 649.59 |

Vapor density (kg/m^{3}) | 58.99 | 81.49 | 114.01 |

L of specific heat capacity (kJ/(kg·K)) | 2.5278 | 2.8231 | 3.4261 |

V of specific heat capacity (kJ/(kg·K)) | 1.7603 | 2.1978 | 3.1137 |

T-conductivity of l (mW/(m·K)) | 109.53 | 98.56 | 87.47 |

T-conductivity of v (mW/(m·K)) | 17.54 | 20.53 | 25.54 |

Liquid viscosity (μPa·s) | 0.9 × 10^{−4} | 0.78 × 10^{−4} | 0.65 × 10^{−4} |

Vapor viscosity (μPa·s) | 1.2 × 10^{−5} | 1.3 × 10^{−5} | 1.4 × 10^{−5} |

Latent heat of vaporization (kJ/kg) | 301.12 | 276.34 | 247.42 |

Tension (N/m) | 5.24 | 3.56 | 2.03 |

P_{sat} (MPa) | 2.3 | 3.03 | 3.92 |

Number of Grid | 156,104 | 182,104 | 226,228 |
---|---|---|---|

Grid | |||

(a) | (b) | (c) | |

Grid quality | 1 | 1 | 1 |

Number of Grids | Grid Quality | Max Relative Error of T |
---|---|---|

156,104 | 1 | 0% |

182,104 | 1 | 0.053% |

226,228 | 1 | 0.081% |

Parameter | Critical Pressure (MPa) | Critical Temperature (K) |
---|---|---|

R744 | 7.37 | 304.13 |

azeotropic refrigerant | 4.87 | 305.32 |

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## Share and Cite

**MDPI and ACS Style**

Sun, D.; Zhang, X.; Liu, Z.; Zhang, H. Comparative Study on Boiling Heat Transfer Characteristics and Performance of Low-Temperature Heating System of R744 and Its Azeotropic Refrigerant. *Energies* **2023**, *16*, 1313.
https://doi.org/10.3390/en16031313

**AMA Style**

Sun D, Zhang X, Liu Z, Zhang H. Comparative Study on Boiling Heat Transfer Characteristics and Performance of Low-Temperature Heating System of R744 and Its Azeotropic Refrigerant. *Energies*. 2023; 16(3):1313.
https://doi.org/10.3390/en16031313

**Chicago/Turabian Style**

Sun, Dahan, Xin Zhang, Zhongyan Liu, and Hao Zhang. 2023. "Comparative Study on Boiling Heat Transfer Characteristics and Performance of Low-Temperature Heating System of R744 and Its Azeotropic Refrigerant" *Energies* 16, no. 3: 1313.
https://doi.org/10.3390/en16031313