The effect of wall friction in single-phase natural circulation stability at the transition between laminar and turbulent flow

The present paper is focused on the prediction of stability of single-phase natural circulation in the range of Reynolds numbers characterizing the transition between laminar and turbulent flow. In particular, the predictions obtained by one-dimensional models making use of different assumptions for evaluating wall friction at this transition are discussed, also in front of experimental information from previous investigations. The starting point of the analysis is the discrepancy observed in the prediction of the linear stability behaviour of an unstable experimental loop obtained by thermal-hydraulic system codes adopting different friction laws. An in-depth investigation of the reasons for such discrepancy is made with the aid of computer programs developed for the one-dimensional linear and non-linear stability analysis of single-phase natural circulation loops. The programs allowed obtaining linear stability maps for the considered loop, which clearly show the effects of the assumptions made in dealing with friction at the transition between laminar and turbulent flow. The available information on the appropriate closure laws for friction in natural circulation, with particular emphasis on the transitional regime, is also discussed. Non-linear effects, coming into play when transient calculations are started far enough from the system fixed point, are shown to have a relevant role in the predicted stability behaviour. Finally, preliminary results obtained by the application of a computational fluid-dynamic code in the analysis of stability in the addressed loop are presented to point out an interesting field of future investigation