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

Turbulent channels are extensively used in turbomachinery to enhance convective heat transfer in internally-cooled components like turbine blades. One of the major techniques to increase the flow turbulence is to roughen the channel with periodic ribs and previous studies have conducted to retrieve the distribution of the Heat Transfer Coefficient (HTC) in such configuration in fully developed flows.

The mean steady flow has been shown to contain two Counter Rotating Vortices (CRV) generated as a result of the flow interaction between the ribs and the channel walls. These vortices are also shown to laterally partition the main flow. The present study aims at understanding further the HTC distribution on the channel flow by looking at the flow unsteady effects on HTC. This is done by performing a numerical analysis of a test rig installed at the Von Karman Institute which represents a square channel with periodic ribs. These ribs are square and perpendicular to the flow direction, with pitch to height ratio of 10 and a 10% rib blockage. For the simulation, Large Eddy Simulation is adopted using a constant heat-flux on the inter-rib walls to closely replicate the experimental conditions considering the entire complexity of the configuration. Resulting mean and unsteady flow features already mentioned in the previous studies are captured here and these new predictions are used to further explain the obtain HTC.

To deepen the understanding of the HTC distribution, a specific attention is devoted to the prediction of unsteady flow behavior. At each instant, turbulent structures are indeed seen to bring cold gases from the main flow to the wall. The impact of these cold gases on the bottom channel wall causes the heated gases present near the wall to be swept away. A statistical analysis of these events using the quadrants method allows to define 4 types of events which can happen at every location in the channel. Using this analysis, a direct link is established between the events occurring at a particular point and the value of HTC at the same location: primarily 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. With this established understanding of the heat transfer trace on the channel wall, the next step is to comment on the link between the structures in the flow field and the HTC trace on the channel wall.  This is done by first identifying the unsteady flow structures located far off the wall. In that case, Fast Fourier Transform is used to extract the frequential information related to the dominant modes in the far flow field. 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. The first mode, at Strouhal number 0.15, corresponds to the flow detachment behind the ribs. This mode extends up to the third rib where it is observed to disappear quickly due to increasing flow turbulence along the channel. A second mode with a lower frequency and intensity emerges after the third rib with a spatial periodicity equating the interval between the ribs. This mode is seen to appear because of the quasi-periodicity of the geometry along the flow direction. Contrarily to flow DMD analysis, a DMD of the HTC over the channel shows no particular mode dominance for that wall quantity. This indicates of a weak link between the main flow large scale features and the instantaneous and more local HTC distribution. Although the mean flow is organized around the CRV pair, these only increase the probability that a turbulent structure carrying cold gases impinges the bottom wall at specific locations increasing the HTC nearby.