The distribution of R134a vapor (compared with nitrogen) at various inlet mass flow rate is shown in Figure 6.3. It is noteworthy that the distribution is not uniform even if the fluid is single-phase. The bottom tube has the highest flow rate. It is lower for the top tubes, due to the pressure drop in the header, as discussed in the following analysis.
Figure 6.3: Maldistribution of nitrogen and R134a vapor
Figure 6.4 presents the pressure drop in the header corresponding to loca-tions of tubes. The differential pressure transducer in ∆P2 does not produce reasonable values for nitrogen and R134a vapor. Thus, ∆P2 is estimated by averaging ∆P1 and ∆P3. The pressure drop of R134a vapor is lower than that of nitrogen because the density of R134a vapor is higher, so the velocity of R134a vapor is lower than that of nitrogen at same mass flow rate. As R134a vapor or nitrogen branches out along the flow, the mass flow rate or velocity in the header decreases. Therefore, the pressure drop in the header also reduces. For R134a vapor, ∆P5 may be higher than ∆P4. This may be due to the fact that there is no flow in the last part of the header, and there is a stagnation region at the top. Based on the results in Fig. 6.4, the stagnation pressure seems to affect R134a vapor more significantly than nitrogen, specifically at high inlet mass flow rate.
In each flow path from MCHX inlet to outlet, the pressure drop is equal.
Take R134a vapor flow at min = 4.19 g s−1 as an example. Tube #1 is
closest to the inlet and the pressure drop in the header is just ∆P1, which is 66.12 Pa. Along the upward flow, R134a vapor experiences longer distance in the header and the pressure drop in the header is higher. The top tube is farthest from the inlet. It experiences the longest distance in the header and thus the highest pressure drop in the header, i.e. the sum of ∆P1 to ∆P5, which is 93.82 Pa. Therefore, the mass flow rate in Tube #1 is the highest corresponding to the highest pressure drop in the tube, whereas the pressure drop in Tube #5 is the lowest, so the mass flow rate in this tube is lowest.
This causes single-phase vapor maldistribution in Figure 6.3.
Figure 6.4: Local pressure drop in the header (nitrogen and R134a vapor) Ren and Hrnjak [95] investigated the pressure drop of compressed air in a horizontal header. The overall pressure drop in the header includes the acceleration ∆Pacc, gravitation ∆Pgra, and friction ∆Pf ri pressure drops and minor pressure drop due to protruded microchannel tubes ∆Ppro, as shown in Eq. 5.3. ∆Pacc, ∆Pgra, ∆Pf ri, and ∆Ppro are calculated as in Eq. 6.1, Eq. 6.2, Eq. 6.3, and Eq. 6.4, respectively. The density ρ in Eq. 6.1 to Eq. 6.4is constant and estimated based on Pheader. For ∆Pf ri, the equations for Darcy friction factor are from White [97]. The notations for Sef f and Stube are shown in Figure 6.5. The hydraulic diameter Dh is calculated at the section of Sef f and St. The Reynolds number is calculated based on Dh. For ∆Ppro, based on their results of compressed air in a horizontal header, Ren and Hrnjak [95] proposed the empirical correlations, as in Eq. 6.5, to
calculate the minor pressure loss coefficient ζ.
Figure 6.5: Parameters notation for Eq. 6.3
In this study, Eq. 6.1, Eq. 6.2, and Eq. 6.3 are used to calculate ∆Pacc,
∆Pgra, and ∆Pf ri, respectively. ∆Ppro is obtained by subtracting Eq. 6.1, Eq. 6.2 andEq. 6.3from the measured overall pressure drop ∆P . Figure 6.6 presents each component of pressure drop. ∆Pacc and ∆Ppro are the main components of overall ∆P . Due to the short distance, ∆Pf ri is very small.
∆Pgra is also small because the vapor density is much lower (than liquid). ζ is calculated based on measured ∆P inEq. 6.4and compared with the values from Eq. 6.5in Figure 6.7. It is found that only at Location #1, the values are very close, within ±20% of Eq. 6.5. In other locations, the deviation fromEq. 6.5is from 30% to 200%. As flow moves downstream, the deviation becomes larger.
Figure 6.6: Total, acceleration, gravitation, friction, and minor pressure drop due to tube protrusion (R134a vapor)
However, in the first few tubes, the values of ∆Ppro are high and the effects are significant, as shown in Figure 6.4. Although ζ from Eq. 6.5 deviates from the measured values in the last few tubes, it does not affect too much on the pressure drop calculation. The predicted ∆Ppro based on Eq. 6.5 is compared with the measured ∆Ppro in Figure 6.8. It is usually within ±15 Pa, especially for R134a vapor. This is the same accuracy range as reported in Ren and Hrnjak [95]. The most deviated data are at i = 2 for nitrogen and R134a vapor. This may be due to the fact that the experimental results of ∆P2 are estimated by averaging ∆P1 and ∆P3, which may not be accurate enough. However, by comparing Figure 6.8 with Figure 6.9, it can be conceived that Eq. 6.5 from [95] improves ∆Ppro prediction rather than
(a) Location #1 (b) Location #2
(c) Location #3 (d) Location #4
Figure 6.7: Minor pressure loss coefficient due to tube protrusion with nitrogen and R134a vapor
Figure 6.8: The predicted tube protrusion pressure drop using Eq. 6.5 agrees reasonably with the measured (nitrogen and R134a vapor)
Figure 6.9: The predicted tube protrusion pressure drop based on Yin et al. [11] deviates from the measured (nitrogen and R134a vapor)