Pressure drop and heat transfer rates in forced convection rotating square duct flows at high rotation rates

his paper presents and discusses numerical simulations of forced convection heat transfer in a rotating square duct at high rotation rates. The mean pressure gradient has been kept constant in the simulations that were conducted with a second order finite volume code with a dynamical localized subgrid scale model. The rotation number based on the bulk velocity was varied from 0.12 to 6.6 and consequently the Reynolds number ranged from 3900 to 1810 according to the fact that rotation tends to increase the pressure drop in the duct. A model for estimating the velocities and the corresponding friction coefficient has been developed by analytically solving simplified versions of the momentum budgets within the Ekman layers occurring near the opposite two walls of the duct perpendicular to the rotation axis. The model reproduces accurately the velocity profiles of the numerical simulation at high rotation rates and predicts that the boundary layer quantities scale as Ek^1/2. At Ro>1 the Ekman layers are responsible for most of the pressure drop of the flow while the maximum heat transfer rates are found on the wall where the stratification of the x-momentum is unstable with respect to the Coriolis force. Rotation enhances the differences between the contributions of the local friction coefficients and local Nusselt numbers of the four walls of the duct and considerably increases, in comparison with the non-rotating case, the pressure drop of the flow and the Nusselt number. The overall friction coefficient of the measurements and the simulations existing in the literature, as well as the present numerical predictions, are well correlated with the equation 1.09(Cf/Ek^1/2)^1.25=Ro in the range Ro>=1 for Re<=104.