A shape function approach for predicting deteriorated heat transfer to supercritical pressure fluids on account of a thermal entry length phenomenon

Abstract

The paper addresses the problem of predicting deteriorated heat transfer to supercritical pressure fluids, trying a novel approach whose main features are obtained by consideration of the experimental trends of a meaningful series of experimental data. This approach takes into consideration the modifications that the axial velocity profile undergoes at the entrance of a bare tube, when a supercritical pressure fluid is heated at the wall and decreases its density owing to thermal expansion, giving rise to buoyancy effects. Combining the observation of measured wall temperature trends with their successful predictions by CFD RANS models, the effects giving rise to flow laminarization are firstly interpreted as a very peculiar form of the entry length problem applicable to supercritical pressure fluids. Then, their quantitative prediction is addressed by the use of an iterative procedure based on shape functions tailored on the observed trends of the Nusselt number and of the consequent wall temperature trends. In this frame, the results of a recently developed fluid-to-fluid similarity theory for heat transfer at supercritical pressures provide indication about the relevant dimensionless numbers to be involved in determining the shape functions. Being based at the moment on a series of water experimental data collected at 25 MPa for vertical upward flow, the methodology may suggest a way for predicting heat transfer deterioration in the proposed supercritical water nuclear reactor conditions, providing an additional means to tackle this critical problem by a different approach that may result useful as a practical means to bound expected wall temperature trends.