A note on the representation of rate-of-rise of the thermal stratification interface in reactor plenum

The quantification of the rate-of-rise of the thermal stratification interface, a 'thin' vertical zone where the temperature gradient is the steepest, is important in assessing the potential implications of thermally-induced stress problems in liquid-metal cooled reactors. Thermal stratification can likewise occur in confined volumes containing ordinary fluids (Pr ≥ 1), where there is an input of thermal convective energy. In the prominent case of liquid metal reactors, there have been many studies on quantifying the rate-of-rise of a defined stratification interface, in terms of one or more of the following dimensionless groups, mainly: Richardson (Ri), Reynolds (Re), Grashof (Gr), Rayleigh (Ra) and/or Froude (Fr) numbers. Stratification is also a transient process in the volume in question. In the present work the authors presents a derivation based on order-of-magnitude analysis (OMA), including an sensible energy balance, that produces a new representation more consistent than past studies. The representation is shown to work well for past results. Furthermore, the representation is shown to be consistent with OMA of the conservation equations for natural, mixed and forced convection problems. Some fine points and aspects of OMA and the results are described. (author)