Number of tubes per row  [−] 4 Approach temperature [K] 3

Length of one tube [m] 0。282 Air

Fin pitch [m] 0。00254 Temperature [°C] 32

Fin thickness [m] 0。00018 Mass flow rate [kg s−a] 0。096, 0。112 and 0。128

Height of frontal area (fin height) [m] 0。252 Volumetric flow rate [m3 h−h] 300, 350 and 400

flow rate: 56。4, 60。4 and 64。2 W m−2 K−1。 Clearly, it can be seen that the main thermal resistance is on the air-side, which had as expected the smaller heat transfer coefficients。 Also, that a higher air volumetric flow is beneficial for the air-side  heat

Fig。 3 – Local CO2 side heat transfer per unit of tube length for different air flow rates (position zero is the outlet piping)。

transfer and for the CO2 side heat transfer (the latter when taking into account the first row of tubes)。

Fig。 5 shows the behavior of the air side temperature as a function of the piping position and air volumetric flow  rate。 It is worth observing the considerable increase in the air outlet temperature on the second half of the second row (topmost part), meaning there is a high temperature region that can affect the heat transfer performance of the first row, and thus em- phasizing the importance of the split in the fin mentioned before (to create a break in the heat conduction)。 Relative to the air side pressure drop, the values 9。3, 11。5 and 14。4 Pa were re- spectively predicted when considering the air volumetric flow rates in ascending order。 Thus, a higher pressure drop for a higher volumetric flow, which must be considered when se- lecting the fan for such a gas   cooler。

Regarding the CO2 side, Fig。 6 shows a higher local pres- sure drop gradient when higher values of air volumetric flow rate are considered, which is associated with the higher local heat transfer and consequently higher gradient of CO2 tem- perature with length (also plotted in Fig。 6)。 In other words, one can say that for a higher air volumetric flow, the changes in thermodynamic properties of supercritical CO2 are much more intense since the fluid reaches the pseudo-critical and criti- cal regions sooner, which is characterized by considerable increases in density and viscosity, and thus, an increase in pres- sure drop。 Despite this, the overall CO2 pressure drop did not change with the air volumetric flow rate (0。03 bar), since the necessary piping length was shorter when the higher air volu- metric flow was simulated, and thus this self-compensated for the higher pressure drop gradient。

Finally, regarding the mass of CO2 in the gas cooler as a func- tion of the increased volumetric flow rate values, the following decreasing values were observed: 38。92, 36。24 and 34。22 g。 That is, a reduction of about 10% in CO2 mass is observed when in- creasing the volumetric flow rate from 350 to 450 m3 h−1, since a shorter length of heat exchanger is necessary to remove the 600 W of heat。

In summary, only 2 rows instead of 4 rows of the current cold drink vending machine are necessary for the gas cooler, which means a reduction of about 50% in aluminum and copper。 Also, when considering an air volumetric flow rate of 400 m3 h−1, the mass of CO2, the length of piping for 600 W of heat transfer, and the air and CO2 pressure drops will be 34。22 g,