Nuclear Engineering and Design 236 (2006) 1800–1809 A generalized flow correlation for two-phase natural circulation loops M.R. Gartia, P.K. Vijayan ∗ , D.S. Pilkhwal Reactor Engineering Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India Received 10 October 2005; received in revised form 2 February 2006; accepted 2 February 2006 Abstract A generalized correlation has been proposed to estimate the steady-state flow in two-phase natural circulation loops. The steady-state governing equations for homogeneous equilibrium model, viz. continuity, momentum and energy equations have been solved to obtain the dimensionless flow rate as a function of a modified Grashof number and a geometric number. To establish the validity of this correlation, two-phase natural circulation flow rate data from five different loops have been tested with the proposed correlation and found to be in good agreement. © 2006 Elsevier B.V. All rights reserved. 1. Introduction Two-phase natural circulation is capable of generating larger buoyancy forces and hence larger flows. Two-phase natural circulation finds application in nuclear steam generators, ther- mosyphon boilers, boilers in fossil fuelled power plants, reactor core cooling, etc. The heat transport capabilities of natural cir- culation loops depend on the flow rate it can generate. For two-phase natural circulation loops, explicit correlations for steady-state flow are not available. This makes it difficult to compare the performance of different two-phase natural circu- lation loops. Therefore, we present an analytical correlation for steady-state flow, which is then non-dimensionalized to obtain a generalized correlation. This generalized correlation has been tested against data generated in five test facilities differing in diameter. Pioneering work in the field of scaling laws for nuclear reactor systems have been carried out by Nahavandi et al. (1979), Zuber (1980), Heisler (1982), Ishii and Kataoka (1984), Kocamustafaogullari and Ishii (1987), Schwartzbeck and Kocamustafaogullari (1989), Yadigaroglu and Zeller (1994), Reyes Jr. (1994) and Vijayan et al. (1999). The scaling law proposed by Zuber (1980) is also known as the power-to- volume scaling philosophy. The integral test facility being set-up to simulate the advanced heavy water reactor (AHWR) has been designed based on this philosophy. However, the power- ∗ Corresponding author. Tel.: +91 22 2559 5157; fax: +91 22 2550 5151. E-mail address: vijayanp@apsara.barc.ernet.in (P.K. Vijayan). to-volume scaling philosophy has certain inherent distortions (especially in downsized components), which can suppress cer- tain natural circulation specific phenomena like the instability (Nayak et al., 1998). Scaling laws provided by Ishii and Kataoka (1984) had been widely used for two-phase natural circula- tion loops. The PUMA facility simulating the simplified boiling water reactor (SBWR) has been designed based on this phi- losophy. Kocamustafaogullari and Ishii (1987) have given a scaling law for two-phase flow transients using reduced pres- sure Freon (R-11 or R-113) systems. A flow pattern transition- dependent scaling law has been given by Schwartzbeck and Kocamustafaogullari (1989). Yadigaroglu and Zeller (1994) had given a fluid-to-fluid scaling law for gravity and flashing driven natural circulation loop. Reyes Jr. (1994) has applied catastrophe functions to describe the scaling for two-phase natural circula- tion loops. One of the problems associated with these scaling laws is that the numbers of similarity groups are too many and they do not provide steady state or stability solutions in terms of the proposed similarity groups. Therefore, testing of these scal- ing laws with the available experimental data is rather difficult without the use of system codes. This arises due to the fact that more than one scaling parameter is a function of the flow rate, which for a natural circulation loop is not known a priori. To overcome this problem, Vijayan et al. (2000) proposed a scaling procedure by which the steady-state flow rate can be obtained as a function of just one similarity group for uni- form diameter loops with adiabatic pipes operating without any sub-cooling. But the proposed correlation had not been tested rigorously. In the present paper, a generalized scaling philoso- phy has been proposed for two-phase natural circulation loops. 0029-5493/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2006.02.004