Comparative analysis of linear and non linear low-Reynolds-number eddy viscosity models to turbulent natural convection in horizontal cylindrical annuli

A computational study is presented of the natural convection flow within horizontal cylindrical annuli at a range of Rayleigh numbers from 8.02 x 10(5) to 1.18 x 10(9) and with a variation of outer and inner diameter ratio Between 2.6 and 4.58. The flow features large recirculation and the coexistence of turbulent and laminar, nearly stagnant regions, signifying the importance of effects arising from streamline curvature and wall viscosity on the evolution of boundary layers over inner and outer cylinder surfaces. This has,first, motivated the application of low-Reynolds-number models, which are able to take wall viscous effects into account. Two such models, a linear and a nonlinear variant, are examined in this study. The nonlinear model can, with the inclusion of cubic-order terms in the nonlinear stress-strain/vorticity relation, further sensitize the model to streamline curvature and is anticipated to give more faithful solutions than the linear model. At low-Rayleigh-number-flow, computational results indicate that both models return laminar and identical solutions, which are in good agreement with the experimental data. However, the nonlinear model is shown to return improved representation of the flow at high Rayleigh numbers, and the results obtained by both models are in reasonable agreement with the data.