The upgraded Cheng and Todreas correlation for pressure drop in hexagonal wire-wrapped rod bundles

Abstract

The Cheng and Todreas (detailed) correlation (CTD) for wire-wrapped rod bundle friction factor published in 1986 has been identified in Chen et al. (2014) as the most used correlation for design and safety analyses for the Generation IV Sodium Fast Reactor(SFR). Since its publication in 1986, sixteen additional wire wrapped fuel bundle experiments have been performed worldwide providing data to supplement regions of minimal data in the bundle test data base. Based on this valuable new data, the CTD correlation has been refined in the following three aspects and renamed the Upgraded CTD (UCTD) Correlation.1.The laminar to transition boundary Reynolds value has been significantly reduced. As well, a new laminar boundary equation is adopted which gives much lower value for the laminar boundary (RebL) as a function of P/D.2.The transition region equation for bundle friction factor modified by Chen et al. (2013) to make the friction factor trajectory smoother moving through the turbulent boundary now has the exponent λ reassessed to the value of 7.3.The UCTD is now applicable to 7-pin bundle geometry. This has been achieved by adjusting the bundle average friction factor predicted by CTD for most bundle geometries such that the bundle fiction factor increases as the pin number increases. The cause of the previous inverse behavior was identified as the formulation of the wire drag and wire swirl empirical constants. A new process for finding these empirical constants is proposed and the constants set is calibrated by an 80 bundle data set. For Rehme’s set of twenty 7 pin bundle experiments, the mean error prediction is now 9% which is about the measurement uncertainty and improved from 26% with CTD.The new correlation incorporating the above three improvements to the original CTD correlation is designated as the Upgraded CTD (UCTD) correlation. For the available 118 wire-wrapped bundles with pin number greater than 7 bundles, UCTD predicts the data in the transition and turbulent regimes with a mean error of 0.95% and a 90% confidence interval of ±14.8%, while both the CTD and the Rehme correlations (REH) have 1.5% higher values of this index. For the 27 available bundles with laminar data,(none of which are as small as 7 pin bundles) the performance of UCTD is slightly better than CTD with mean and RMS values of −2.0%, and 9.5% versus −3.0%, and 9.6%. (The REH correlation is not applicable to the laminar regime).A web-based numerical code of the UCTD correlation which incorporates these advances has been provided on the web for convenient design and research use.