Correcting for tube curvature effects on condensation in the presence of a noncondensable gas in turbulent free convection

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Condensation in the presence of noncondensable gasses (NCG) has many practical applications, and hence researchers continue to study its many facets. In the particular case when the vapor-NCG mixture is driven by free convection, the use of slender cylinders as condenser surfaces is very frequent, and one needs to estimate the effect of tube curvature in order to translate condensation rates from curved surfaces to flat ones, and vice-versa.In our previous investigation [1], we solved the coupled gas and condensate boundary layer equations to deduce the curvature correction factor for laminar free convection over a vertical tube. In this work, we aim at addressing the same issue for turbulent regimes which are much more prevalent. To this effect, we model the transport of the vapor-NCG mixture as an ideal gas, and solve the flow field within a CFD-based approach that employs the k-ε model of turbulence and fully resolves the gas boundary layer. Sink terms in the continuity, momentum, species and energy equations are used to account for the removal of vapor at the condenser wall. In contrast to most CFD approaches to date, condensate film resistance is taken into account to allow a general use of the model up to very high steam fractions.We first validate the model against experimental heat transfer databases for representative tube diameters of 12 mm and 38 mm. For these conditions, the Grashof number based on tube length varies between 4.2.109 and 3.5.1012, which denotes a fully turbulent regime. The model agreement with the data is very good, with discrepancies comparable to the experimental error. We also show that including film resistance is very important even at moderate steam mass fractions of the order of 0.5. The error for not modeling film resistance soars to 50% for steam fractions of order 0.9.We thereafter conduct an exhaustive set of 112 parametric CFD simulations that span tube diameters from 8 mm to 100 mm, steam mass fractions from 0.2 to 0.95, pressures from 1 bars to 5 bars, and wall temperature subcooling from 5 K to 80 K. The results of these simulations are subsequently presented in a compact correlation for the curvature correction factor. The proposed correlation reflects the simulation results within a ± 5% band.The outcomes of this investigation show qualitatively the expected trends. All other things held constant, the curvature correction factor decreases with tube diameter, steam fraction and Grashof number, and is insensitive to tube length. We show finally that the use of correlations developed for laminar regimes underestimate the effects of curvature in turbulent flows. Turbulence hence unequivocally promotes the heat transfer enhancements due to curvature.