1. Introduction

2. Methodology

2.1. Calculation Design

With the initial design data for an R744 air conditioning system, the testing cycle has a cooling capacity of 1000W, an evaporation temperature of 10^oC, and a condensation temperature of 30.5^oC. Design parameters are calculated and expressed according to Figure 1 and Table 1.

In this study, the key components of a testing cycle were designed based on the computational theory of [16] with the following equations:

The cooling capacity was calculated as:

$$Q_0=G\left(h_5-h_4\right)$$

(1)

The condensing capacity for G kg was calculated as:

$$Q_k=G(h_2-h_{3\text{'}})$$

(2)

The work of adiabatic compression was determined by:

$$N=G(h_2-h_1)$$

(3)

The Coefficiency of Performance of the cycle was calculated as:

$$COP=\frac{Q_0}{N}$$

(4)

The overall heat transfer rate was calculated as:

$$A=\frac{Q_k}{U.{∆t}_{lm}}$$

(5)

Where $\mathrm{A}$ is the heat transfer area (m²)

$Q_k$ is condensing capacity (W)

$U$ is the overall heat transfer coefficient (W/m²_.K)

${∆t}_{lm}$ is Log mean temperature difference (^oC)

Based on the same overall heat transfer coefficient, this study offers two design configurations for the condenser consisting of Case 1 (5 layers of copper tube) and Case 2 (8 layers of copper tube) with dimensions and parameters shown in Figure 2 and Table 2. These condensers use mini-size tubes. For Case 2, there are two tube sets (banks) arranged in parallel; each set has four tube layers (or four passes). Each layer has 25 tubes with the outer and the inner diameters are 4 mm and 3 mm, respectively. The actual image is shown in Figure 3. The condensing mini tubes are flooded in the cooling water tank.

Figure 2. The design parameters of two condensers using mini tubes.

Figure 2. The design parameters of two condensers using mini tubes.

Figure 3. The actual photo of the condenser with 8 layers using mini tubes.

Figure 3. The actual photo of the condenser with 8 layers using mini tubes.

2.2. Numerical Simulation

This model was solved based on Conjugate Heat Transfer model, which formed of two models: (1) Heat transfer in Solid and Fluid and (2) Turbulent flow.

For Heat transfer in the Solids and Fluids model, the assuming equations are expressed by:

$$\mathsf{\rho }.C_{p}u.\nabla T+\nabla .q=Q+Q_{ted}$$

(6)

$$q=-k\nabla T$$

(7)

For the Turbulent flow model, the assuming equations are expressed by:

$$\mathsf{\rho }.\left(u.\nabla \right)u=\nabla .\left[-pI+K\right]+\mathrm{F}$$

(8)

$$\nabla .\left(\mathsf{\rho }u\right)=0$$

(9)

The transport equation for k reads by:

$$\begin{gathered} \mathsf{\rho }.\left(u.\nabla \right)k=\left[\left(\mu +\frac{{\mu }_T}{{\sigma }_k}\right)\right]\nabla k+P_k-\rho ϵ where: \\ K=\left(\mathsf{\mu }+{\mu }_T\right)\left(\nabla u+{\left(\nabla u\right)}^T\right)-\frac{2}{3}\left(\mathsf{\mu }+{\mu }_T\right).\left(\nabla u\right)I-\frac{2}{3}\rho k.I \end{gathered}$$

(10)

The transport equation for ε is as follows:

$$\mathsf{\rho }.\left(u.\nabla \right)ϵ=\left[\left(\mu +\frac{{\mu }_T}{{\sigma }_{ϵ}}\right)\right]+C_{ϵ1}\frac{ϵ}{k}{P}_k-C_{ϵ2}\rho \frac{{ϵ}^2}{k},$$

(11)

$$\mathrm{Where} \mathsf{ϵ}=\mathrm{e}\mathrm{p} \mathrm{and} {{\mu }_T=C}_{\mu }\rho \frac{k^2}{ϵ}$$

(12)

The momentum formulation is as follows:

$$P_k={\mu }_T\left[\nabla u:\left(\nabla u+{\left(\nabla u\right)}^T\right)-{\frac{2}{3}\left(\nabla .u\right)}^2\right]-\frac{2}{3}\rho k\nabla .u$$

(13)

Where ${\mu }_T$ is the turbulence viscosity (Pa.s)

$u$ is velocity of fluid (m/s)

$\rho$ is density of fluid (kg/m³)

$k$ is thermal conductivity (W/m.K)

The simulation focuses on a water-cooled condenser using COMSOL Multiphysics 6.1 software using a heat transfer model in the Conjugate Heat Transfer synthesis consisting of 2 models: the Turbulent Flow model, Low Renold k-$\mathit{\epsilon }$ combined with the Heat transfer in Solids and Fluids model.

To simplify the simulation model, there is an even division of rows of pipes between 2 sets, the R744 entering the condenser is evenly divided. Therefore, the simulation model uses a symmetrical method with a lower number of elements, saving time, improving convergence, and increasing accuracy.

Complete mesh consists of 692399 domain elements, 134042 boundary elements, and 24441 edge elements as shown in Figure 3. With the quality of the simulation mesh supporting a faster simulation process, the average Skewness acceptable index in the rows of pipes at the condenser ranges from 0.5 – 0.7 inside the tube bank and range from 0.75 – 0.8 at the manifolds as shown in Figure 4.

For heat transfer variables, the GMRES (Generalized Minimal Residual Method) iterative solver was used. This method produces an approximate solution to the linear system after a finite number of steps. These methods are useful for large systems of equations where it is reasonable to trade-off precision for a shorter run time. Iterative methods use the coefficient matrix only indirectly, through a matrix-vector product or an abstract linear operator. Iterative methods can be used with any matrix, but they are typically applied to large sparse matrices for which direct solves are slow. Besides, for turbulence variables, the PARDISO (Parallel Sparse Direct Solver) was used to improve sequential and parallel sparse numerical factorization performance, they exploit pipelining parallelism with a combination of left-looking and right-looking supernode techniques. PARDISO is multithreaded on platforms that support multithreading for saving solving time.

Figure 3. Meshing for the test sample.

Figure 3. Meshing for the test sample.

Figure 4. Skewness index for simulation model.

Figure 4. Skewness index for simulation model.

3. Results and discussion

4. Conclusion

Nomenclature

References

1. Xinyu Zhang, Yunting Ge, Jining Sun, Liang Li, Savvas A. Tassou, "CFD Modelling of Finned-tube CO₂ Gas Cooler for Refrigeration Systems", Energy Procedia, vol. 161, 2019, pp. 275-282. [CrossRef]
2. Sánchez, Daniel, Jesús Catalán-Gil, Ramón Cabello, Daniel Calleja-Anta, Rodrigo Llopis, and Laura Nebot-Andrés, "Experimental Analysis and Optimization of an R744 Transcritical Cycle Working with a Mechanical Subcooling System", Energies 13, no. 12: 3204, 2020. [CrossRef]
3. Yang, Junlan, Linxiu Wang, Yifei Han, Xin Zhang, and Yufan Du, "Simulation and Experimental Study of CO2 Transcritical Heat Pump System with Thermoelectric Subcooling" Designs 6, no. 6: 115, 2022. [CrossRef]
4. Yinhai Zhu, Yulei Huang, Conghui Li, Fuzhen Zhang, Pei-Xue Jiang, "Experimental investigation on the performance of transcritical CO2 ejector–expansion heat pump water heater system", Energy Conversion and Management, vol. 167, pp. 147-155, 2018. [CrossRef]
5. Jian-qiang Deng, Pei-xue Jiang, Tao Lu, Wei Lu, "Particular characteristics of transcritical CO2 refrigeration cycle with an ejector", Applied Thermal Engineering, vol. 27, pp. 381-388, 2007. [CrossRef]
6. F.Z. Zhang, P.X. Jiang, Y.S. Lin, Y.W. Zhang, "Efficiencies of subcritical and transcritical CO₂ inverse cycles with and without an internal heat exchanger", Applied Thermal Engineering, vol. 31, pp. 432-438, 2011. [CrossRef]
7. X.P. Zhang, F. Wang, X.W. Fan, X.L. Wei, F.K. Wang, “Determination of the optimum heat rejection pressure in transcritical cycles working with R744/R290 mixture”, Applied Thermal Engineering, vol. 54, pp. 176-184, 2013. [CrossRef]
8. Paride Gullo, Armin Hafner, Krzysztof Banasiak, "Transcritical R744 refrigeration systems for supermarket applications: Current status and future perspectives", International Journal of Refrigeration, vol. 93, pp. 269-310, 2018. [CrossRef]
9. Mihir M. Hazarika, Maddali Ramgopal, Souvik Bhattacharyya, "Studies on a transcritical R744 based summer air-conditioning unit: Impact of refrigerant charge on system performance", International Journal of Refrigeration, vol. 89, pp. 22-39, 2018. [CrossRef]
10. Carlos Sanz-Kock, Rodrigo Llopis, Daniel Sánchez, Ramón Cabello, Enrique Torrella, "Experimental evaluation of a R134a/CO2 cascade refrigeration plant", Applied Thermal Engineering, vol. 73, pp. 41-50, 2014. [CrossRef]
11. Yeqiang Zhang, Yongning He, Yanling Wang, Xuehong Wu, Mingzheng Jia, Yi Gong, "Experimental investigation of the performance of an R1270/CO2 cascade refrigerant system", International Journal of Refrigeration, vol. 114, pp. 175-180, 2020. [CrossRef]
12. Rodrigo Llopis, Carlos Sanz-Kock, Ramón Cabello, Daniel Sánchez, Enrique Torrella, "Experimental evaluation of an internal heat exchanger in a CO2 subcritical refrigeration cycle with gas-cooler", Applied Thermal Engineering, vol. 80, pp. 31-41, 2015. [CrossRef]
13. Giovanni Di Nicola, Fabio Polonara, Roman Stryjek, Alessia Arteconi, "Performance of cascade cycles working with blends of CO2 + natural refrigerants", International Journal of Refrigeration, vol. 34, pp. 1436-1445, 2011. [CrossRef]
14. J. Alberto Dopazo, José Fernández-Seara, "Experimental evaluation of a cascade refrigeration system prototype with CO2 and NH3 for freezing process applications", International Journal of Refrigeration, vol. 34, pp. 257-267, 2011. [CrossRef]
15. Tzong-Shing Lee, Cheng-Hao Liu, Tung-Wei Chen, "Thermodynamic analysis of optimal condensing temperature of cascade-condenser in CO2/NH3 cascade refrigeration systems", International Journal of Refrigeration, vol. 29, pp. 1100-1108, 2006. [CrossRef]
16. Bejan et al., Heat Transfer Handbook, John Wiley & Sons, 2003.