Assessment of Unsteadiness Modeling for Transient Natural Convection

Turbine flexible operations with faster startups/shutdowns are required to accommodate emerging renewable power generations. A major challenge in transient thermal design and analysis is the time scale disparity. For natural cooling, the physical process is typically in hours, but on the other hand, the time-step sizes typically usable tend to be very small (subseconds) due to the numerical stability requirement for natural convection as often observed. An issue of interest is: What time-step sizes can and should be used in terms of stability as well as accuracy? In this work, the impact of flow temporal gradient and its modeling is examined in relation to numerical stability and modeling accuracy for transient natural convection. A source term-based dual-timing formulation is adopted, which is shown to be numerically stable for very large time-steps. Furthermore, a loosely coupled procedure is developed to combine this enhanced flow solver with a solid conduction solver for solving unsteady conjugate heat transfer (CHT) problems for transient natural convection. This allows very large computational time-steps to be used without any stability issues, and thus enables to assess the impact of using different time-step sizes entirely in terms of a temporal accuracy requirement. Computational case studies demonstrate that the present method can be run stably with a markedly shortened computational time compared to the baseline solver. The method is also shown to be more accurate than the commonly adopted quasi-steady flow model when unsteady effects are non-negligible.