Unsteady flow and heat transfer in periodic complex geometries for the transitional flow regime

Diesel engines are facing significant challenges with upcoming changes in emissions standards. In general, meeting the increased emission standards will require a larger fraction of the engine heat rejection to occur in the vehicle cooling system. For certain applications, the surface geometry must also be such that it resists particulate fouling, precluding common interrupted surfaces such as louvered fins. Although acceptable continuous surface geometries such as bumped fin geometries are in use, the impacts of changing the parameters of this geometry are unknown. This study investigates the transport characteristics of bumped fins in the transitional flow regime using unsteady multi-dimensional solutions of the incompressible Navier-Stokes equations. In the first of three parts, a two-dimensional model is used to examine the impact of channel aspect ratio for fixed absolute bump height and corrugation angle. Oscillatory behavior is observed and critical Reynolds numbers determined for the onset of supercritical flow behavior. In the second part, two-dimensional simulations are performed which consider the variation in corrugation angle for a fixed aspect ratio and relative bump height. Corrugation angles ranging from 25 to 90° are examined and compared with the wavy channel limit and the singly grooved channel. The results reveal that even at a fixed aspect ratio, the shape of the bump cavity influences the stability of the flow and its transport behavior. In the third and final part, a detailed three-dimensional numerical investigation of a channel element with a width aspect ratio of 3.7 is presented. The critical Reynolds number and primary oscillation frequency is shown to be largely unchanged from the two-dimensional predictions. However, detailed characteristics of the oscillatory behavior are influenced by longitudinal vortices captured in the three-dimensional model. The predicted transport characteristics both increase but do so in such a way that the surface efficiency is nearly unchanged from that predicted by the two-dimensional model.