CHAPTER 5. FLOW VISUALIZATION AND HTC CORRELATION UNDER FIELD FREE
5.5 Evaluate boiling convective heat transfer correlation with experimental data
experimental data
Seven different flow boiling heat transfer coefficient prediction correlations for vertical flow boiling were discussed earlier and are summarized in Table 5-2 and subsequently evaluated against the experimental results in this section. The prediction deviations between the experimental and predicted values from each correlation are listed in Table 5-2, where the MRD is the mean relative deviation (a negative MRD indicates that the correlation under predict the HTC), the MAD is the mean absolute deviation and the (RMS) root mean square of deviation and are defined as follows:
(96)
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(98)
Table 5-2. Comparison between experimental data and correlation predictions.
Correlations MRD MAD RMS
1 Wattelet et al [65] 21% 21% 21%
2 Shah [71] -19% 21% 26%
3 Gungor & Winterton [75] 33% 33% 34% 4 Kandlikar correlation [66] 35% 46% 51% 5 Gungor & Winterton [73] 108% 108% 110%
6 Chen [67] 251% 251% 277%
7 Jung & Radermacher [77] 260% 260% 456%
Table 5-2 shows that the Shah [71] and Wattelet et al. [65] correlations have given the best agreement with the measured data. The negative MRD indicates that the second correlations under predict the HTC, while the last four correlations over predict HTC, and quite significantly.
The Chen correlation [67] has been found to over predict the HTC with a high MAD of 251 %, see Table 5-2. Furthermore, this correlation seems very sensitive to mass flux, as clear in Figure 5-18, which does not agree with the experimental measurements of this investigation.
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Figure 5-18. Measured HTC vs Chen correlation [67]
The Shah correlation [71] predicts the convective boiling HTC using four different general correlations that depend on the Boiling number, Bo, and a dimensionless convection number, Co,, such that the larger value of hnb or hcb is then taken for htp. This procedure of separating the regions causes a discontinuity in predicted HTC, and this has been noted from many researchers [66]. This has been avoided here by using only the first equation in Table 2-4 for all test regions, which eliminated the discontinuity and slightly under predicts the HTC. The MAD and RMS are found to be 21% and 26 % respectively which is considered as acceptable agreement with measured data. The MRD is -19% which illustrates that this correlation consistently under-predicts the experimental data. However, Figure 5-19 does show that this correlation is sensitive to mass flux.
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Figure 5-19. Measured HTC vs Shah correlation [71]
The Gungor and Winterton [73] correlation significantly over predict the measured HTC, with MAD, MRD and RMS of ~108 %, as seen in Figure 5-20. This correlation incorporates Cooper correlation to predict the nucleate HTC. Cooper correlation is very sensitive to surface roughness. Here the default roughness of 0.1 μm which is close to the 0.2 μm roughness measured on the outside of the tube, though the inside could be rougher or smoother but could not be measured. A significant reduction in the roughness would have to be imposed to improve the agreement with the measurements. Furthermore, although not largely sensitive to flow rate, the correlation predicts an increase in heat transfer coefficient with decreasing flow rate which is counter intuitive.
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Figure 5-20. Measured HTC vs Gungor & Winterton [73]
The Wattelet et al. correlation [65] correlations also uses Cooper correlation to predict the nucleate HTC. Figure 5-21 shows the result using the default surface roughness of 0.1 μm and good agreement with the measurements is found, with MAD, MRD and RMS of 21% which is reasonable for a two phase flow correlation. It is noted that the correlation is not sensitive to flow rate for the range tested which agrees with the measured trend.
Figure 5-21. Measured HTC vs Wattelet et al. correlation [65]
0 2 4 6 8 10 0 2 4 6 8 10 Meas ured Hea t Tr ans fer Coe fficien t (kW/ m 2K)
Predicted Heat Transfer Coefficient (kW/m2K) M=50 kg/m2 s
M=100 kg/m2 s M=150 kg/m2 s
+ 35%
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Jung & Radermacher Correlation[77] over predict the HTC at lower quality, at higher quality it suffer from discontinuity as shown in Figure 5-22. The suppression factor depends on the Martinelli parameter (Xtt), which is a function of vapour quality, when the quality changes from 0.08 to 0.1 the Xtt changes from 1.01 to 0.84, and the suppression factor calculation method changes from Equation (51) to Equation (52) which occur an increases of 6.1 times, this causes a jump of predicted HTC as shown in Figure 5-22. This correlation is insensitive to flow rate for the most of tested range which agrees with the measured trend.
Figure 5-22. Measured HTC vs Jung & Radermacher [77]
The updated Gungor & Winterton [75] correlation shows quite good agreement with the measured data as shown in Figure 5-23. Here the MAD and RMS are 33, which can be considered acceptable agreement for an empirical boiling correlation. The MRD is quite high, at 34%, as the data as there is an almost over predictions as shown in Table 5-2. Although there is some sensitivity to flow rate, it is not severe.
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Figure 5-23. Measured HTC vs Gungor & Winterton [75]
Kandlikar correlation [66] gives a good agreement with the measured data MAD 46 %, but it also suffer from discontinuity as shown in Figure 5-24.
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To investigate the effect of mass flux on the prediction correlations, the intercept and slop for the prediction data for each mass flux has been calculated, and then the averaged was determined along with the STD from the mean. This gives a sense of the sensitivity of the correlation to flow rate and is plotted in Figure 5-25 shows, where the line is the average data and the mean STD is the error bars. For the example case here the Shah correlation [71] and Wattelet et al. [65] correlations were considered. Figure 5-25 shows a large sensitivity of the Shah correlation to mass flux, while Wattelet et al. correlation does show a minor sensitivity, which is more consistent with the experimental. This also confirmed by considering the mean STD, which was 46 % for Shah correlation and only 11% for Wattelet et al. correlation, which indicates to the insensitivity of Wattelet et al correlation to mass flux change.
Figure 5-25. Measured data vs Wattelet et al. [65] and Shah [71] errors
5.6
Pool boiling Cooper correlation
The result above suggests strongly that, for the range of parameters tested, convective effects are not dominant and the boiling dynamics dominate the heat transfer. Thus, one may expect that a pool boiling-type correlation would give reasonable predictions of the heat transfer and of course not be sensitive to the flow rate. To this end, the
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Cooper pool boiling correlation, which is the one used in the Wattelet et al. correlation, was also compared with measured data and this is shown in Figure 5-26. The figure shows that there is quite good agreement with this straight forward correlation, and is in fact the best performing correlation of all those considered above. In fact, there is growing evidence, including flow boiling in channels [119] and jet impingement boiling [120] [121], including a wide range of fluids, that tend to show not only the same insensitivity to flow rate, but that the Cooper correlation does an excellent job at predicting the experimental data.
Figure 5-26. Measured HTC vs Cooper correlation
So when boiling starts the heat transfer is dominated by the bubble dynamics and the mechanisms of heat transfer are basically the same as pool boiling. Thus the Cooper correlation can be used for flow boiling when not enough data is available. As it’s easy to use and seems to be very accurate across a broad range of flow boiling configurations, including a wide range of fluids.
0 2 4 6 8 10 0 2 4 6 8 10 M eas ur ed Hea t Tr ans fer Coe fficien t (kW /m 2K)
Predicted Heat Transfer Coefficient (kW/m2K)
M=50 kg/m2 s M=100 kg/m2 s M=150 kg/m2 s
+ 35%
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5.7
Conclusions
An experimental investigation of upward vertical flow boiling for HFE 7000 has been performed in a circular and annular heat exchanger. To the best of knowledge this is one of the first studies that obtained local heat transfer data together with full visual access to determine the associated flow regime at the measurement location. Results shows that the heat transfer coefficient is a very strong function of imposed heat flux, which is evidence to suggest that the dominant heat transfer mechanisms are associated with the local bubble activity opposed to convective influences. In particular the boiling dictates the flow regime and an interesting result is that the boiling heat transfer coefficient asymptotically matches a linear line for nucleate boiling at lower heat fluxes and a higher slope linear line at higher heat fluxes for the more rigorous slug and churn flow regimes. The inflection region was observed to occur at the transition from bubbly flow to slug flow.
Tests were performed to study the influence of mass flux between 50-150 kg/(m2 s) as well as semi-confinement. The measurements showed no significant influence of these parameters.
The experimental boiling heat transfer data for HFE 7000 were then compared against seven predictions correlations for vertical upflow convective boiling. Each correlation has a unique behaviour in predicting the experimental results as each accounted for the influence of convection and boiling on the overall heat transfer in different ways. The results demonstrate good agreements between experimental data and the prediction of the Wattelet et al. correlation [65] with MRD, MAD, and RMS of 21%. The Shah [71] and Gungor & Winterton [75] correlations show acceptable agreements, while the Kandlikar [66] correlation predicted result that are outside of what can be considered acceptable. The Gungor & Winterton [73], Chen correlation [67] and Jung & Radermacher [77] correlations display a largest deviation and must be used with caution. The end result was that correlations that showed the least sensitivity to flow rate and used the Cooper pool boiling correlation were the most accurate.
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Finally, the Cooper pool boiling correlation was tested against the experimental measurements and, consistent with some earlier and more recent published studies, the correlation did a very good job at predicting the vertical upflow convective boiling data for the range of parameters tested. This result tends to support the conclusion that the nucleate boiling activity at the heated surface is the dominant mechanism of heat transfer for the cases studied.
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