Bayesian inference of a multivariate model in a phase change situation around a cylinder in staggered arrangement

Abstract

The complexity of problem of fluid flow and heat transfer over an array of circular cylinders is common in industrial applications of fluid dynamics. The complex nature of the problem encountered in industry gives rise to certain significant dimensions in fluid dynamics theory. Some of them are fluid flow interaction, interferences in flow and vortex dynamics which are typically found in compact heat exchangers, cooling of electronic equipment, nuclear reactor fuel rods, cooling towers, chimney stacks, offshore structures, hot-wire anemometry, and flow control. The mentioned structures are subjected to air or water flows and therefore, experience flow induced forces which can lead to their failure over a long period of time. Basically, with respect to the free stream direction, the configuration of two cylinders can be classified as tandem, side-by-side, and staggered arrangements. The Reynolds Averaged Navier-Stokes (RANS) equations have been used to compute the flow and Eulerian model has been used to understand phase change situation in a staggered arrangement of cylinders. In the present study, nucleate boiling has been the cause of heat and mass transfer between the phases for different cylinder configurations in staggered arrangement. The study was carried out by keeping cylinders stationary as well as rotating to understand the difference and impact of these situations on VOF. The profound effects of arrangement of cylinders, the location of cylinder surface, surface temperature of the cylinder were investigated. To have a deeper and meaningful insight into the phase change phenomenon of water into water vapor, Bayesian inference of a multivariate model involving certain significant factors such as Nusselt number (Nu), Prandtl number (Pr), and Stanton number (St) along with volume fraction of vapor phase of water was carried out. The posterior probabilities computed from Bayesian inference for two statistically significant and experimentally verified datasets were obtained during the study. Through Principal Component Analysis (PCA) for the multivariate datasets used in the study, it was observed that some factors are positively and negatively correlated and individually contributing towards a meaningful finding from the study.