Flow and Heat Transfer in an Internally Ribbed Duct With Rotation: An Assessment of Large Eddy Simulations and Unsteady Reynolds-Averaged Navier-Stokes Simulations

Large eddy simulations (LES) and unsteady Reynolds averaged Navier-Stokes (URANS) simulations have been performed for flow and heat transfer in a rotating ribbed duct. The ribs are oriented normal to the flow and arranged in a staggered configuration on the leading and trailing surfaces. The LES results are based on a higher-order accurate finite difference scheme with a dynamic Smagorinsky model for the subgrid stresses. The URANS procedure utilizes a two equation $k-ε$ model for the turbulent stresses. Both Coriolis and centrifugal buoyancy effects are included in the simulations. The URANS computations have been carried out for a wide range of Reynolds number $(Re=12,500-100,000)$⁠, rotation number $(Ro=0-0.5)$ and density ratio $(Δρ∕ρ=0-0.5)$⁠, while LES results are reported for a single Reynolds number of 12,500 without and with rotation $(Ro=0.12,Δρ∕ρ=0.13)$⁠. Comparison is made between the LES and URANS results, and the effects of various parameters on the flow field and surface heat transfer are explored. The LES results clearly reflect the importance of coherent structures in the flow, and the unsteady dynamics associated with these structures. The heat transfer results from both LES and URANS are found to be in reasonable agreement with measurements. LES is found to give higher heat transfer predictions (5–10% higher) than URANS. The Nusselt number ratio $(Nu∕Nu0)$ is found to decrease with increasing Reynolds number on all walls, while they increase with the density ratio along the leading and trailing walls. The Nusselt number ratio on the trailing and sidewalls also increases with rotation. However, the leading wall Nusselt number ratio shows an initial decrease with rotation (till $Ro=0.12$⁠) due to the stabilizing effect of rotation on the leading wall. However, beyond $Ro=0.12$⁠, the Nusselt number ratio increases with rotation due to the importance of centrifugal-buoyancy at high rotation.