Unsteady Analysis of Heat Transfer Coefficient Distribution in a Static Ribbed Channel for An Established Flow

Turbulent-ribbed channels are extensively used in turbomachinery to enhance convective heat transfer in internally cooled components such as turbine blades. One of the key aspects of such a problem is the distribution of the heat transfer coefficient (HTC) in fully developed flows, and many studies have addressed this problem by the use of computational fluid dynamics (CFD). In the present document, large eddy simulation (LES) is performed for a configuration from a test-rig at the Von Karman Institute representing a square channel with periodic square ribs. The whole channel is computed in an attempt to better understand HTC maps in this specific configuration. Resulting mean and unsteady flow features are captured, and predictions are used to further explain the obtained HTC distribution. More specifically turbulent structures are seen to bring cold gas from the main flow to the wall. A statistical analysis of these events using the joint velocity-temperature probability density function (PDF), and quadrant method allows to define four types of events happening at every location of the channel and which can then be linked to the HTC distribution. First, the HTC is very high where the flow impacts the wall with cold temperature whereas it is lower where the hot gas is ejected to the main flow. In an attempt to link the HTC trace on the channel wall with structures in the flow field far-off the wall, the main modes are identified performing power spectral density (PSD) analysis of the velocity along the channel. Dynamic mode decomposition (DMD) of the flow field data is then used to present the spatio-temporal characteristics of two of the identified most dominant modes: a vortex-street mode linked to the first rib and a rib-to-rib mode appearing because of the quasi-periodicity of the configuration. However, DMD analysis of the HTC trace on the wall does not emphasize any dominant mode. This indicates a weak link between the main flow large scale features and the instantaneous and more local HTC distribution.