etries, and those proposed by Wang et al。 (2002) for wavy fin and tube configurations。

Finally, the implemented simulation code considers a dis- cretization  along  the  piping  length  with  steps  of constant

increment in length。 The inlet air temperature is updated   for

The parameters D, ΔL, µb, µw, ρb, ρf and ρpc are respectively the tube diameter, the length of the tube section, the dynamic viscosities evaluated at the bulk and wall temperatures, and the densities evaluated at the bulk, film and pseudo-critical temperatures。 The film temperature is the average between the bulk and wall temperatures。 Furthermore, fiso,b is the isother- mal single-phase friction factor, which is determined as follows at the bulk temperature (ε is the tube absolute   roughness)。

each row of tubes and each control volume。 A staggered tube layout was assumed based on industrial practice and the ε-NTU method was used for the thermal design。 Fig。 1 shows a flow- chart highlighting the main inputs, the loops of iteration and the convergence parameters implemented in the simulation code。 Compared to the previous simulation codes described in the literature survey above, the present code distinguishes itself in that it includes the effects of: (i) lubricating oil, (ii) in-tube piping diameter, (iii) type of fins, and also (iv) the more recent and accurate correlations for heat transfer and pressure drop。

3。 Impact of tube-side and air-side parameters on the design of a typical CO2   gas

The wall temperature is determined considering an energy

balance between the fluid (bulk) and the wall, and thus an it- erative process is necessary to converge the final value at each control volume of the discretized domain along the tube。 Finally, the pseudo-critical temperature is obtained via the adjusted equation proposed by Oh and Son (2010), which was based on the data from NIST Refrigerants Database REFPROP 7。0, where pgc  is the gas cooler  pressure:

tpseudo-critical  122。6 6。124 pgc  0。1657 p2

A parametric study evaluating the impact of key parameters on the thermal hydraulic performance of gas coolers is pre- sented in this section。 Basically, the air volumetric flow rate, the tube diameter, the type of fin and the oil concentration were investigated considering ranges normally applicable in the light commercial refrigeration field, more specifically for the bev- erage industry, such as cold drink vending machines。 As a

baseline case, the simulations considered an actual current  CO2

gas cooler widely used in a cold drink vending machine (copper tubes, aluminum fins, 48 tubes, 4 rows, 28。2 cm length per tube,

For the in-tube friction pressure drop, the new friction factor

correlation proposed by Fang et al。 (2012) was selected here, which was based on 390 experimental data from several sources available in the literature。 When compared with the best ex- isting prediction models (8 existing correlations available for supercritical friction factor), those authors obtained an in- crease of accuracy by more than 10%。 Two important aspects were included in their updated method: (i) the acceleration pres- sure drop, which must be considered when analyzing the experimental data, and (ii) the tube roughness。 They also high- lighted the differences regarding conventional single-phase flow, since at supercritical pressures the fluid’s thermophysical prop- erties change considerably with local fluid and wall temperatures, which means that conventional single-phase fric- tion factor correlations are unsuitable。 Thus, the total pressure drop (Δptotal), which is the sum of the friction and acceleration terms, is determined as  below: