Therefore, based on these recent studies reported above, one can say that modeling efforts to significantly improve the design of fin and tube gas coolers for light refrigeration and air con- ditioning systems are just starting, but more detailed studies are needed。 Thus, with this intention, the present study in- vestigates the effects of air volumetric flow, in-tube piping diameter, type of fins, oil concentration, gas cooler width, trans- versal pitch of tubes and fin pitch on the thermal hydraulic performance of the gas coolers。 Until now, only the latter three geometric parameters were considered to be the most rel- evant but this will be greatly expanded to show the important influence of other parameters in the present study。 The se- lected models for pressure drop and heat transfer, air and CO2 sides, are described below。

The heat transfer prediction method for in-tube supercritical CO2 cooling chosen here is a modified version of the Fang model (Fang, 1999) which was recently proposed by Fang and Xu (2011)。 It was based on 3 different published sources containing 297 experimental data points (Dang and Hihara, 2004; Huai et al。, 2005; Krasnoshchekov et al。, 1969) and compared against 13 existing heat transfer correlations, showing a mean absolute relative deviation of only 8。9%, which was 14。6% lower than the next best literature correlation。 Their method is de- scribed below for predicting the Nusselt number (Nu), where Pr , Reb, f, q and G are respectively the average Prandtl number, the Reynolds number considering the fluid proper- ties evaluated at the bulk temperature, the friction factor, the heat flux from tube wall to fluid and the mass flux。 The average Prandtl number is determined with the dynamic viscosity (µb) and thermal conductivity (kb) calculated at the fluid bulk tem- perature。 The specific heat at constant pressure ( cp ) is obtained from the values of tb, tw, hb and hw, which are the bulk and wall temperatures and the specific enthalpies at these two tem- peratures。 The Nusselt number for turbulent flows is predicted as follows:

capable  of  optimizing  the  performance  of  finned  tube gas

coolers (counter cross flow) through the proper selection of op-  ⎛⎞ Pr

erating conditions and design parameters。 The main     parameters   evaluated, i。e。 their effects on the thermal hydraulic     perfor-    

mance of the gas cooler, were: (i) operating pressure, (ii) CO2 mass flow rate, (iii) air velocity and temperature, (iv) number of tubes per row and (v) number of CO2 flow circuits。 Summa-

rizing their work, the highest gas cooler thermal performances

were observed when high air velocities were considered, which was due to the lower approach temperature and higher heat transfer rate。 However, after an upper limit of air velocity, which seems to be 2 m s−1, no significant changes in the approach tem- perature were obtained。 A simplified analysis was also   done

The friction factor is determined as   below:

considering an entire cooling system, i。e。 compressor with isen- tropic compression, heat exchangers and expansion device  with

where fnoniso and fac are the non-isothermal single-phase fric- tion factor and acceleration friction factor, respectively, and are calculated as:

0。49f  pc 1。31

For the air-side flow, the leading correlations for heat trans- fer and pressure drop found in the literature, which were developed from a large multi-lab database, were selected: the correlations for heat transfer and pressure drop proposed by Wang et al。 (2000) were used for plain fin and tube geom-