Brian Axcell

Studies of mixed convection in vertical tubes

Abstract The early study of convective heat transfer considered the branches of forced and free convection independently with only passing reference to their possible interaction. In fact the two are extreme cases of the general condition of “mixed” or “combined” forced and free convection where both mechanisms operate simultaneously. The present contribution aims to provide an up-to-date review of those works concerned with mixed convection heat transfer in vertical tubes. The review is divided into two sections, the first dealing with laminar flow, and the second with turbulent flow; further subdivisions are made according to whether the work is theoretical or experimental. Comparisons between theory and experiment are made where possible, expressions defining the conditions for onset of buoyancy effects are presented and equations for determining heat transfer are given. The paper ends with some general comments and recommendations. The survey is restricted to fluids of moderate Prandtl number; mixed convection in liquid metals can display very different characteristics which will be discussed in a future paper.

Mixed-convection heat transfer to sodium in a vertical pipe

Experimental turbulent mixed-convection data are presented for sodium in a uniformly heated vertical pipe. The behavior is found to be opposite to that established for fluids of higher Prandtl number, including mercury, with heat transfer enhanced in upward flow and impaired in downward flow. Velocity and temperature profiles in the sodium have been measured using miniature magnet probes. Velocity profiles are similar to those observed under comparable conditions in other fluids; temperature profiles are somewhat different, with significant variation of temperature extending almost to the pipe centerline. Experimental measurements are compared with predictions obtained using a low-Reynolds-number κ-e turbulence model. Reasonable agreement is achieved for upward flow, but the model overpredicts heal transfer rates for downward flow, as in the case of conventional fluids.

Parameterization of buoyancy effects in generic PWR boron dilution scenarios

A computational investigation is undertaken into the role of buoyancy in a PWR boron dilution transient following a postulated Small Break Loss of Coolant Accident (SB-LOCA). In the scenario envisaged there is flow of de-borated and relatively high temperature water from a single cold leg into the downcomer; flow rates are typical of natural circulation conditions. The study focuses upon the development of boron concentration distributions in the downcomer and adopts a 3D-unsteady formulation of the mean flow equations in combination with the standard high-Reynolds-number k-e turbulence model. It is found that the Richardson number (Ri = Gr/Re2 ) is the most important group parameterizing the course of a concentration transient. At Ri values characterizing a ‘baseline’ scenario the results indicate that there is a stable, circumferentially-uniform, descent through the downcomer of a stratified region of low-borated fluid. Qualitatively the same behaviour is found at higher Richardson number, although at Ri values of approximately one-fifth the baseline level there is evidence of large-scale mixing and a consequent absence of concentration stratification.Copyright