A generalized correlation for steam condensation rates in the presence of air under turbulent free convection A. Dehbi ⇑ Laboratory for Thermal-Hydraulics, Paul Scherrer Institut, Villigen 5232, Switzerland article info Article history: Received 28 September 2014 Received in revised form 11 February 2015 Accepted 12 February 2015 Keywords: Film condensation Noncondensable gases Correlation Nuclear plant safety abstract In the past several decades, experimentalists have proposed a large number of correlations to estimate steam condensation rates in the presence of noncondensable gases in free convection regimes. These cor- relations are largely empirical, and usually of limited scope, which often leads to their use outside their range of validity, thus incurring the risk of significant errors. In this investigation, we disregard the cor- relations altogether, and instead go back to their underlying original data, consolidate them in a single set, and propose a generalized correlation that is compatible with the heat and mass transfer analogy. This best-estimate correlation for steam–air mixtures, based on six different investigations and 350 data points, covers two orders of magnitude in the heat transfer coefficient, and is valid for pressures up to 20 bars and steam mass fraction from 0.1 to 0.95. The consolidated raw data are self-consistent and col- lapse around a curve with a standard deviation of 16%, thus well within typical experimental error bands. This demonstrates that there is no physical justification for the large deviations (factor 2 or more) observed sometimes when one compares the heat transfer coefficients predicted by different empirical correlations. Finally, the generalized correlation also shows that in the special case when the noncon- densable gas density is held constant as the steam content is varied, the heat transfer coefficient can be expressed solely in terms of the steam to noncondensable gas density ratios. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Vapor film condensation is a topic of considerable importance in a variety of nuclear Light Water Reactor (LWR) safety applica- tions. In many instances, vapor condensation takes place in the presence of some amounts of noncondensable (NC) gases, typically air or nitrogen, and sometimes hydrogen if the transient scenario progresses into a severe accident. As an example, vapor condenses in the presence of air along cold containment walls and structures following a LWR Loss of Coolant Accident (LOCA). In-tube steam generator reflux condensation in the presence of NC gases can also occur in accidents caused by loss of residual heat removal in mid- loop operation of pressurized water reactors (PWRs). Moreover, nitrogen injected from accumulators in some accident sequences may find its way to the steam generator tubes and greatly reduce core water make-up. In addition, in recently designed advanced LWR’s, passive containment cooling systems (PCCS) are in fact designed to operate with high NC gas content [1]. The main concern has always been that small amounts of NC gases result in large decreases of steam condensation rates. The early experiments by Al Diwani and Rose [2] highlighted the fact that condensation rates can be degraded by as much as 50% with a NC gas content of no more than one percent by mass in laminar free convection regimes. Many analyses, e.g. Sparrow and Minkowycz [3,4] and Rose [5], have provided theoretical explanations of this great reduction in heat transfer by even tiny amounts of NC gas. Solving boundary layer equations for the steam-NC mixtures, the authors showed that a diffusion boundary layer is formed, whereby the NC gas accumulates near the gas-condensate film interface, considerably lowering the steam partial pressure, and hence condensation rate. The deterioration in heat transfer is more pronounced for free con- vection flows than it is for forced flows. A large body of experiments on the condensation degradation by NC gases has been produced over the years to cover a variety of conditions of interest to nuclear safety. The earliest such work is due to Uchida [6] who proposed a simple correlation for the heat transfer coefficient (HTC) in free convection regimes typical of LWR containment flows. The Uchida correlation is used until today in safety simulation codes, and is generally regarded as conservative for design basis accidents (DBA). Following this early work, a num- ber of correlations have been developed to estimate the condensa- tion HTC in the presence of NC gases at pressures of less than http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.02.034 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Tel.: +41 56 310 27 11. E-mail address: abdel.dehbi@psi.ch International Journal of Heat and Mass Transfer 86 (2015) 1–15 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt