Thermally Developing Flow in an Annulus with a Boiling Boundary

Abstract

Heat transfer from a liquid flowing in an annulus to a boiling fluid flowing in a tube was analyzed using four general formulations and several variations of them. The degree of complexity varied significantly among these analysis methods due primarily to the assumption of thermally fully developed flow applied in some methods and not in others. Measurements from a sodium-heated boiling water experiment provided the boundary conditions for the annulus heat-transfer problem. Finite-difference techniques were employed in some of the analyses, and an appropriate inverse heat-transfer technique was included in one of them. Comparisons of heat-transfer parameters calculated from the analysis methods are presented and the accuracies assessed. Three of these methods compared favorably with the most complete and complex of the analyses considered. Nomenclature= initial sodium temperature distribution at z=0, °C h = heat transfer coefficient, W/m 2 K k = thermal conductivity, W/m K k e = effective turbulent thermal conductivity, W/m K M = mass flowrate, kg/s q = heat flux at tube inner surface, W/m 2 r = radial coordinate measured from centerline of water tube, m T = temperature, °C TSAT = saturation temperature, °C TWALL = temperature at Z), (wall i.d. temperature), °C V = axial velocity, m/s z = axial coordinate in direction of sodium flow, m p = density, kg/m 3

Heat Transfer to Dispersed Swirl Flow of High-Pressure Water With Low Wall Superheat

“…The most complete model (the developing method) was used in this study as described [21,22]. (The results [21] indicate that simpler models also will give good accuracy in the post-CHF region.) The developing method involves a two-dimensional (radial and axial) analysis of the turbulent flowing sodium in the test section annulus.…”

“…Several models for this calculation were treated in detail in [21]. The most complete model (the developing method) was used in this study as described [21,22]. (The results [21] indicate that simpler models also will give good accuracy in the post-CHF region.)…”

“…Several models for this calculation were treated in detail in [21]. The most complete model (the developing method) was used in this study as described [21,22].…”