Proposal of a drag coefficient model for bubble chain rising in stagnant LBE pool based on volume of fluid method

In the event of a steam generator tube rupture (SGTR) accident in a liquid lead-bismuth eutectic (LBE)-cooled reactor (LFR), a small rupture in the tube wall may lead to the leakage of high-pressure, low-temperature liquid water into a low-pressure, high-temperature pool of liquid LBE. Consequently, the liquid water quickly vaporizes, and a chain of steam bubbles may be formed following the continuous leakage of liquid water. Existing drag models, primarily developed for isolated bubbles, show significant limitations when applied to bubble chains, in which interactions between bubbles are observed. This study investigates the effect of the spacing between adjacent bubbles on the terminal velocity in a chain in stagnant LBE and develops a novel drag coefficient model that incorporates this key parameter. Bubble dynamics obtained using neutron radiography, including terminal velocity in a chain and equivalent bubble diameter of a single bubble chain rising in stagnant LBE, were used to validate the volume-of-fluid (VOF) method. Subsequently, extensive numerical simulations covering a wider range of parameters were conducted to establish a comprehensive drag coefficient database. The numerical results demonstrated that the drag coefficient of the bubbles in the bubble chain decreases as the ratio of the bubble spacing to the equivalent bubble diameter decreases. A new drag model was proposed by introducing this ratio into the functional form of the correlation along with the bubble Reynolds number and Weber number. The proposed drag coefficient model shows excellent agreement with the numerical databases and significantly outperforms existing models.