Evaluation of the conduction shape factor with a CFD code for a liquid–metal heat transfer in heated triangular rod bundles

A heat transfer due to conduction through a coolant itself is not negligible in a liquid–metal cooled reactor (LMR). This portion of a heat transfer is frequently described with a conduction shape factor during the thermal-hydraulic design of an LMR. The conduction shape factor, which is highly dependent on a pitch-to-diameter (P/D) ratio, is defined as the ratio of the local conduction heat flux at a gap between two subchannels to the reference heat flux calculated by the averaged subchannel temperatures. The shape factors in heated triangular rod arrays for three different pitch-to-diameter ratios are generated through CFX calculations in the present study. The flow paths of 1.0–2.0 m in length are meshed into 180,000–360,000 volumes depending on the flow velocities. The SSG Reynolds stress model is used as a turbulent model in the calculations. The evaluated data fell between the heated-rod data and the plane-source data obtained by theoretical investigations. The conduction shape factors were found to be independent of the heating pattern of the rod arrays. Based on the evaluated data, a correlation for a liquid sodium coolant is suggested, which will improve the accuracy of the subchannel analysis codes for the thermal-hydraulic design of an LMR. When it is compared with the existing correlations, the suggested correlation is expected to enhance the reliability of the conduction shape factor because the data is evaluated by a more realistic numerical experiment.