New models of droplet deposition and entrainment for prediction of liquid film flow in vertical annuli

Critical heat flux (CHF), colloquially termed ‘dryout’ in nuclear physics, describes the thermal limit of a phenomenon where a phase change occurs during heating, which suddenly decreases the efficiency of heat transfer, thereby causing localized overheating of the heating surface. During thermal hydraulic design and analysis of nuclear reactors, the avoidance of occurrence of this phenomenon is one of the most important concerns. Consequently, prediction of CHF has long been at the heart of much research for nuclear reactors and other relevant equipment. Ideally, the usual approach to evaluate CHF is purely empirical and the use of specific empirical correlations. In essence, these methods provide perhaps the simplest and most cost-effective way to identify CHF in many conditions. However, their applicability is limited to the test conditions and is generally less effective in complex cases, and in particular cases where the heat flux is axially nonuniform. Previously researchers reported several alternative approaches that reveal droplet deposition and entrainment significantly affect dryout occurrences in annular two-phase flow. Currently, most of the correlations for droplet deposition and entrainment are derived from flows in tubes. However, for more complex flows in annuli, no verified droplet deposition and entrainment correlations has been proposed, which makes the accurate modeling of the dynamics of liquid films on both rod and tube more difficult.

Generally, the deposition and entrainment processes are highly complex and all details are not well understood, even in tubular system. For the annular flow in annuli, there is no experimental information on droplet deposition and entrainment and few models of the same have been proposed. To address this, Professor Haibin Zhang at the Xi’an Jiaotong University in China, in collaboration with Professor Geoffrey Frederick Hewitt from the Imperial College in the UK investigated the applicability of several tube-based droplet deposition and entrainment correlations to the annular geometry (effectively a ‘‘one-rod” bundle). Their work is currently published in the research journal, Applied Thermal Engineering.

In their approach, two sets of modified correlations for annular geometry proposed previously by other researchers were analyzed and deviations of the prediction from the measured data obtained. By considering the characteristics of annular flow in an annulus, the researchers implemented modifications on the deposition and entrainment rates from the tube and the rod based on the tube-based Hewitt-Govan correlations. Overall, the performance of the newly proposed correlations for annular flow in annuli was tested by using the experimental measurements of dryout in annuli with uniform and nonuniform axial heat flux distribution.

The authors reported that the modified correlations could predict the film flow rates in annulus very well. The two researchers also showed that with the proposed assumptions on the initial conditions at the onset of annular flow, the dryout occurrence were all well predicted in varied situations.

In summary, the study described the development of a set of elegant models of entrainment and deposition in annuli. Remarkably, good agreement between adiabatic annulus measurements and new methods was achieved. More so, it was reported that the new correlations were more suitable for dryout prediction of flows in annuli.  In a statement to Advances in Engineering, Professor Haibin Zhang explained that their results indicate that the present simple and easy to-implement models for deposition and entrainment rates in annuli, despite lack of rigorous theoretical basis, leads to an essential improvement in the predictive capability of phenomenological model of annular flow, and thus can help us to the analysis and prediction of dryout occurrence in annuli.