Towards a Nusselt number – Friction factor analogy for heated turbulent fluids at supercritical pressure

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Abstract

Supercritical water reactor power plants are designed to use supercritical steam cycles with thermal efficiencies well over 40%. In such steam cycles, water at supercritical pressure (typically 25 MPa or higher) is heated by nuclear fuel. When a supercritical fluid is isobarically heated, its thermophysical properties change sharply. Due to the strong thermophysical properties’ variations, heat transfer to turbulent fluids is difficult to predict, as Nusselt number relations developed for fluids at sub-critical pressure fail to predict heat transfer at supercritical pressure accurately. Recently, researchers have focused on the effect of turbulence attenuation by buoyancy or acceleration on heat transfer. However, the effect of variable thermal conductivity and specific heat capacity on heat transfer has received less attention. To incorporate the effect of the variable thermal conductivity and specific heat capacity, we propose a new model. We start by writing the total heat flux as the sum of two contributions: conduction and the turbulent heat flux. Close analysis of DNS data shows that the largest contribution to the turbulent heat flux are fluid motions that convect hot fluid away from a heated surface, or those that convect cold fluid towards it. This suggests that heat transfer at the heated surface may depend on the thermophysical properties of both the hot part as well as the cold part of the turbulent fluid. Therefore, we regard the turbulent heat flux as a ‘hot jet’ moving away from a heated surface and a ‘cold jet’ towards the heated surface in a channel. The subsequent derivation results in a Nusselt relation that consists of a contribution by conduction, a hot jet contribution and a cold jet contribution. Using heuristic arguments, a new analogy between the friction factor and the Nusselt number is found, in which the thermal conductivity and specific heat capacity of the hot and cold parts of the fluid are accounted for in the form of a ‘hot’ and ‘cold’ Prandtl number. Compared to the Chilton-Colburn analogy, the new analogy attenuates and shifts the heat transfer coefficient maximum towards the start of a heated section. The new analogy yields enhanced results compared to the Chilton-Colburn analogy when comparing results from both analogies with results from experiments at low heat flux to mass flux ratios that are reported in literature.

Original languageEnglish
Title of host publicationProceedings of 17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH 2017
PublisherAssociation for Computing Machinery (ACM)
Volume2017-September
Publication statusPublished - 2017
Event17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH 2017 - Xi'an, Shaanxi, China
Duration: 3 Sep 20178 Sep 2017

Conference

Conference17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH 2017
CountryChina
CityXi'an, Shaanxi
Period3/09/178/09/17

Keywords

  • Heat transfer
  • Model
  • Supercritical pressure

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