Predictions of turbulent heat transfer of super-critical carbon dioxide flow in a square duct with an elliptic-blending second moment closure

The present contribution describes the application of elliptic-blending second moment closure to the prediction of gas cooling process of turbulent super-critical carbon dioxide flow in a square cross-sectioned duct. The gas cooling process under super-critical state experiences a drastic change in thermodynamic and transport properties. Thus it induces the extraordinary variations of heat transfer coefficients of the duct walls much different from those of single or two phase flows. Redistributive terms in the Reynolds stress and turbulent heat flux equations are modeled by an elliptic-blending second moment closure in order to represent strongly inhomogeneous effects produced by the presence of walls. The main feature of Durbin's elliptic relaxation model which avoids the need for quasi-homogeneous algebraic models and damping functions for near wall modeling of redistributive terms is maintained by the elliptic-blending second moment closure but it involves only one scalar elliptic equation. Computations were performed for the developing turbulent flow during the cooling process of super-critical carbon dioxide flow in a square duct. The results will be used usefully to establish a new heat transfer coefficient correlation widely applicable to the gas cooler design involving turbulent super-critical carbon dioxide flow.