NUMERICAL SIMULATION OF LOCAL NUSSELT NUMBER FOR TURBULENT FLOW IN A SQUARE DUCT WITH A 180° BEND

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Abstract
Numerical predictions of the local Nusselt number for the curved three-dimensional incompressible turbulent flow of air with heat transfer in a square-sectioned duct with a 180° bend are presented and compared with experiment. The results are obtained using a finite-volume discretization of the Reynolds and energy equations employed in a semielliptic algorithm that marches repeatedly through the computational domain until convergence is reached. Results for each of three wall treatments that model the flow and heat trasnsfer in the thermally important near-wall region are compared. The first treatment uses Prandtl's mixing length hypothesis with van Driest's damping function in a fine near-wall grid approach. The other treatments are “two-layer” approaches in which near-wall effects are integrated for a relatively coarse near-wall mesh. The two two-layer models are constructed to allow diffusion of turbulent kinetic energy in near-wall regions and are therefore more general than “local-equilibrium” treatments. The dimensionless width of the viscous sublayer (VSL) is assumed to be constant for the first two-layer treatment but allowed to vary for the second. Core flow is simulated using the standard k − ε turbulence model. The objective of this study is to determine the viability of the turbulence model and wall treatments developed using two-dimensional flow data for the present flow in predicting the local Nusselt number at Reynolds numbers based on hydraulic diameter of 5.6 × 104 and 9.2 × 104. Results for the two-layer approaches are broadly satisfactory, while the treatment assuming a constant dimensionless VSL width compares most favorably with the data. Broad agreement with experiment is achieved for local Nusselt number predictions even though significant disagreements occur between velocity field predictions in the core and the data. Discrepancies between predictions of the Nusselt number and experiment are at least partially attributed to the turbulence model, which fails to simulate near-wall anisotropy in the turbulence stresses.