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.
Similar content being viewed by others
Change history
05 February 2022
A Correction to this paper has been published: https://doi.org/10.1007/s42757-022-0132-z
References
Bearman, P. W., Wadcock, A. J. 1973. The interaction between a pair of circular cylinders normal to a stream. J Fluid Mech, 61: 499–511.
Deng, J., Ren, A., Chen, W. 2005. Numerical simulation of flow induced vibration on two circular cylinders in tandem arrangement. J Hydrodyn Ser B, 17: 660–666.
Ding, H., Shu, C., Yeo, K. S., Xu, D. 2007. Numerical simulation of flows around two circular cylinders by mesh-free least square-based finite difference methods. Int J Numer Meth Fluids, 53: 305–332.
Farrant, T., Tan, M., Price, W. G. 2001. A cell boundary element method applied to laminar vortex shedding from circular cylinders. Comput Fluids, 30: 211–236.
He, J. W., Glowinski, R., Metcalfe, R., Nordlander, A., Periaux, J. 2000. Active control and drag optimization for flow past a circular cylinder. J Comput Phys, 163: 83–117.
Henderson, R. D. 1995. Details of the drag curve near the onset of vortex shedding. Phys Fluids, 7: 2102–2104.
Kitagawa, T., Ohta, H. 2008. Numerical investigation on flow around circular cylinders in tandem arrangement at a subcritical Reynolds number. J Fluid Struct, 24: 680–699.
Li, J., Chambarel, A., Donneaud, M., Martin, R. 1991. Numerical study of laminar flow past one and two circular cylinders. Comput Fluids, 19: 155–170.
Linnick, M. N., Fasel, H. F. 2005. A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. J Comput Phys, 204: 157–192.
Liu, K., Ma, D., Sun, D., Yin, X. 2007. Wake patterns of flow past a pair of circular cylinders in side-by-side arrangements at low Reynolds numbers. J Hydrodyn, 19: 690–697.
Liu, M., Lu, L., Teng, B., Zhao, M., Tang, G. 2014. Re-examination of laminar flow over twin circular cylinders in tandem arrangement. Fluid Dyn Res, 46: 025501.
Ljungkrona, L., Norberg, C., Sunden, B. 1991. Free-stream turbulence and tube spacing effects on surface pressure fluctuations for two tubes in an in-line arrangement. J Fluid Struct, 5: 701–727.
Mahir, N., Altac, Z. 2008. Numerical investigation of convective heat transfer in unsteady flow past two cylinders in tandem arrangements. Int J Heat Fluid Fl, 29: 1309–1318.
Meneghini, J. R., Saltara, F., Siqueira, C. L. R., Ferrari Jr., J. A. 2001. Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. J Fluid Struct 15: 327–350.
Mittal, S., Kumar, V., Raghuvanshi, A. 1997. Unsteady incompressible flows past two cylinders in tandem and staggered arrangements. Int J Numer Meth Fluids, 25: 1315–1344.
Moriya, M., Alam, M., Takai, K., Sakamoto, H. 2002. Fluctuating fluid forces of two circular cylinders in tandem arrangement at close spacing. T Jpn Soc Mech Eng Ser B, 68: 1400–1406.
Pullepudi, R., Maharana, S. K. 2019. Numerical investigation on effect of orientation and rotation on liquid-vapor phase change around a cylinder in staggered arrangement. Int J Appl Eng Res, 14: 220–227.
Rajani, B. N., Kandasamy, A., Majumdar, S. 2009. Numerical simulation of laminar flow past a circular cylinder. Appl Math Model, 33: 1228–1247.
Rocca, J. 2019. Bayesian inference problem, MCMC and variational inference, towards data science. Available at https://towardsdatascience.com/bayesian-inference-problem-mcmc-andvariational-inference-25a8aa9bce29.
Ryu, S., Lee, S.-B., Lee, B.-H., Park, J.-C. 2009. Estimation of hydrodynamic coefficients for flow around cylinders in side-by-side arrangement with variation in separation gap. Ocean Eng, 36: 672–680.
Singha, S., Sinhamahapatra, K. P. 2010. High-resolution numerical simulation of low Reynolds number incompressible flow about two cylinders in tandem. J Fluid Eng, 132: 011101.
Wang, Z. L., Fan, J., Cen, K. 2009. Immersed boundary method for the simulation of 2D viscous flow based on vorticity-velocity formulations. J Comput Phys, 228: 1504–1520.
Zdravkovich, M. M. 1997a. Flow around Circular Cylinders. Vol. 1. Fundamentals. Oxford University Press.
Zdravkovich, M. M. 1997b. Review of flow interference between two circular cylinders in various arrangements. J Fluids Eng, 37: 993–1010.
Zdravkovich, M. M. 2003. Flow around Circular Cylinders. Vol. 1. Fundamentals. Oxford University Press.
Zhang, H., Melbourne, W. H. 1992. Interference between two circular cylinders in tandem in turbulent flow. J Wind Eng Ind Aerod, 41: 589–600.
Zhang, X., Ni, S., He, G. W. 2008. A pressure-correction method and its applications on an unstructured Chimera grid. Comput Fluids, 37: 993–1010.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pullepudi, R., Maharana, S.K. Bayesian inference of a multivariate model in a phase change situation around a cylinder in staggered arrangement. Exp. Comput. Multiph. Flow 3, 113–123 (2021). https://doi.org/10.1007/s42757-020-0060-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42757-020-0060-8