A supercritical R-744 heat transfer simulation implementing various Nusselt number correlations
Venter, Philip van Zyl
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During the past decade research has shown that global warming may have disastrous effects on our planet. In order to limit the damage that the human race seems to be causing, it was acknowledged that substances with a high global warming potential (GWP) should be phased out. In due time, R-134a with a GWP = 1300, may probably be phased out to make way for nature friendly refrigerants with a lower GWP. One of these contenders is carbon dioxide, R-744, with a GWP = 1. Literature revealed that various Nusselt number (Nu) correlations have been developed to predict the convection heat transfer coefficients of supercritical R-744 in cooling. No proof could be found that any of the reported correlations accurately predict Nusselt numbers (Nus) and the subsequent convection heat transfer coefficients of supercritical R-744 in cooling. Although there exist a number of Nu correlations that may be used for R-744, eight different correlations were chosen to be compared in a theoretical simulation program forming the first part of this study. A water-to-transcritical R-744 tube-in-tube heat exchanger was simulated. Although the results emphasise the importance of finding a more suitable Nu correlation for cooling supercritical R-744, no explicit conclusions could be made regarding the accuracy of any of the correlations used in this study. For the second part of this study experimental data found in literature were used to evaluate the accuracy of the different correlations. Convection heat transfer coefficients, temperatures, pressures and tube diameter were employed for the calculation of experimental Nusselt numbers (Nuexp). The theoretical Nu and Nuexp were then plotted against the length of the heat exchanger for different pressures. It was observed that both Nuexp and Nu increase progressively to a maximal value and then decline as the tube length increases. From these results it were possible to group correlations according to the general patterns of their Nu variation over the tube length. Graphs of Nuexp against Nus, calculated according to the Gnielinski correlation, generally followed a linear regression, with R2 > 0.9, when the temperature is equal or above the pseudocritical temperature. From this data a new correlation, Correlation I, based on average gradients and intersects, was formulated. Then a modification on the Haaland friction factor was used with the Gnielinski correlation to yield a second correlation, namely Correlation II. A third and more advanced correlation, Correlation III, was then formulated by employing graphs where gradients and y-intercepts were plotted against pressure. From this data a new parameter, namely the turning point pressure ratio of cooling supercritical R-744, was defined. It was concluded that the employed Nu correlations under predict Nu values (a minimum of 0.3% and a maximum of 81.6%). However, two of the correlations constantly over predicted Nus at greater tube lengths, i.e. below pseudocritical temperatures. It was also concluded that Correlation III proved to be more accurate than both Correlations I and II, as well as the existing correlations found in the literature and employed in this study. Correlation III Nus for cooling supercritical R-744 may only be valid for a diameter in the order of the experimental diameter of 7.73 mm, temperatures that are equal or above the pseudocritical temperature and at pressures ranging from 7.5 to 8.8 MPa.
- Engineering