Numerical Investigation of a Developed Turbulent Flow and Heat Transfer in a Rectangular Channel with Single-Sided Internal Ribs

Abstract

The problem of a fully developed turbulent flow and developed heat transfer was solved numerically at a Reynolds number ranging from 5 × 10⁴ to 2 × 10⁵ for a spatially periodic model of a one-sided ribbed channel as a prototype of the flow path of an internal convective cooling system for a gas turbine blade. The flow and heat transfer were investigated at the Prandtl number of 0.7. The channel has a rectangular cross-section with an aspect ratio of 1.5. Square ribs with a 10% rib-to-channel height ratio are installed on one of the wide channel walls at an angle of 45° to the longitudinal axis of the channel. To quantify the effect of ribs on the flow and heat transfer, the integral parameters, such as hydraulic resistance factor and Nusselt number determined from the grid-converged solutions, are compared with the integral parameters for a fully developed flow and heat transfer in a smooth channel predicted by the same numerical method. The results of numerical simulation for the ribbed channel are also compared with published experimental data obtained under partly similar conditions. The predicted hydraulic resistance factor agrees well with the experiment. The predicted heat transfer agrees with the experiment within 11%, but the trends in heat transfer with increasing Reynolds number obtained using numerical and physical simulation are different. This difference may be caused by the fact that fully developed heat transfer could not be attained in the short experimental channel. Analytical power-law dependences on the Reynolds number are obtained for the hydraulic resistance factor and the Nusselt number pertaining to all channel walls and only to the ribbed wall. It is pointed out that the hydraulic resistance factor depends weakly on the Reynolds number, which is typical for local resistances, and the dependences for Nusselt numbers corrected for the specifics of the problem are close to the dependences for near-wall layers and flows in smooth channels.