Wall heat transfer modelling for simulation of a transient thermal hydraulics

Nowadays it is common to simulate a transient fluid flow with heat transfer. One of the examples is an accident analysis in a large and complicated structure such as a nuclear power plant (NPP) containment. In numerical simulations of the transients, internal and boundary heat structures have an important role in a transient heat transfer of convection and thermal radiation because their heat capacities delay temperature change on the wall surfaces. If their thermal capacities are neglected in a numerical simulation, a thermal behaviour of the fluid may be very different from an expected one. As an example, if a constant heat flux boundary condition is used on a wall to simulate heat loss from the wall, it can be observed that the fluid temperature near the wall is quickly cooled down at the initial stage of a transient because of under-developed convective heat transfer. And finally the numerical simulation will be diverged with unphysical fluid temperature near the wall. OpenFOAM [1] has some boundary conditions for wall heat transfer such as wallHeatTransfer, turbulentHeatFlux- Temperature, thermalBaffle1D, and so on. But they are eligible for steady heat transfer cases because the thermal capacities of the walls or baffles are not considered, or they may be used conditionally. Unsteady heat structure models are implemented in OpenFOAM, which solve unsteady heat conduction equation for solid regions. One of them is a regional model of thermalBaffle to simulate unsteady conductive heat transfer for a thin internal structure. It has a functionality to generate a mesh for solid region by stacking cell layers in a direction normal to the wall surfaces. The other method is a multi-region method by considering solid and fluid regions separately. Even though they have some difficulties in applying to a complicated geometry, they can be successfully implemented to a simulation of a transient heat transfer. In a simulation of accident progression in a NPP containment, transient heat transfer by heat conduction in solid structures which are thermally linked to an atmosphere in the containment is very important because they may favourably reduce a build-up of a containment pressure by acting as a heat sink. For the transient simulations, conjugate heat transfer (CHT) method or regional thermalBaffle model are available. But more easy and efficient methods are required because of fast simulation of the long term behaviour. In this study, some methodologies are introduced for an analysis of a transient heat transfer. They are based on 1-dimensional unsteady heat conduction problem and implemented in OpenFOAM as wall boundary conditions. They are turbulentHeatFluxParabolicTemperature, externalSolidWallTemperature, and thermalBaffleUnsteady1D which solve an unsteady heat conduction equation instead of a heat balance equation used in the steady heat transfer boundary conditions. Those wall boundary conditions for heat transfer are useful for transient simulation in very complicated geometries such as NPP containment, where many compartment walls and floors must be modelled as thermal baffles to reduce a computational mesh size. The new boundary conditions were implemented in a gas species transport solver rhoReactingBuoyantFoam and tested