Evaporation of water at high mass-transfer rates by natural convection air flow with application to spent-fuel pools

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Abstract

A simple model of evaporation from warm pools of water with turbulent, natural convection flow in the vapor phase is presented. The model is applicable from the dilute, low mass-transfer rate regime (room temperature) through the high mass-transfer rate regime (up to 99 °C). The model is applied to spent-fuel pool (SFP) heat and mass transfer during emergency conditions (e.g., plant blackout), and, in particular, to Fukushima. Comparisons with previous models are made. A simple analytic formula is presented that is nearly explicit in solving for pool temperature. The formula separates the more temperature-dependent properties from less temperature-dependent ones via a non-dimensional ratio Q u = q u /q u,b , where q u is the arbitrary (but specified) evaporative (latent) heat flux (∼decay heat for SFP) and q u,b is the latent heat flux characteristic of incipient boiling. The latter has a simple, relatively temperature-independent expression, q u,b = (h fg Le 2/3 h * )/C p , where h * is the dilute-limit heat transfer coefficient. This formula predicts that for natural convection at 99 °C (h * ∼ 10 W/m 2 K) q u,b is approximately 18 kW/m 2 , slightly greater than, but of the same order of magnitude as, pool boiling heat flux at the onset of nucleate boiling. A new blowing factor correlation is presented for high-rate mass-transfer (B m > 1) of air–water vapor (Pr ∼ 0.7, Sc ∼ 0.6) turbulent natural convection flow over a heated horizontal surface for pool temperatures up to 99 °C (incipient boiling).

Original languageEnglish (US)
Pages (from-to)703-714
Number of pages12
JournalInternational Journal of Heat and Mass Transfer
Volume116
DOIs
StatePublished - Jan 1 2018

Fingerprint

spent fuels
Spent fuels
air flow
Natural convection
free convection
mass transfer
Evaporation
Mass transfer
evaporation
Water
boiling
heat flux
Air
Boiling liquids
water
latent heat
Heat flux
Latent heat
Temperature
temperature

Keywords

  • Mass transfer
  • Natural convection
  • Spent-fuel pool

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

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title = "Evaporation of water at high mass-transfer rates by natural convection air flow with application to spent-fuel pools",
abstract = "A simple model of evaporation from warm pools of water with turbulent, natural convection flow in the vapor phase is presented. The model is applicable from the dilute, low mass-transfer rate regime (room temperature) through the high mass-transfer rate regime (up to 99 °C). The model is applied to spent-fuel pool (SFP) heat and mass transfer during emergency conditions (e.g., plant blackout), and, in particular, to Fukushima. Comparisons with previous models are made. A simple analytic formula is presented that is nearly explicit in solving for pool temperature. The formula separates the more temperature-dependent properties from less temperature-dependent ones via a non-dimensional ratio Q u = q u /q u,b , where q u is the arbitrary (but specified) evaporative (latent) heat flux (∼decay heat for SFP) and q u,b is the latent heat flux characteristic of incipient boiling. The latter has a simple, relatively temperature-independent expression, q u,b = (h fg Le 2/3 h * )/C p , where h * is the dilute-limit heat transfer coefficient. This formula predicts that for natural convection at 99 °C (h * ∼ 10 W/m 2 K) q u,b is approximately 18 kW/m 2 , slightly greater than, but of the same order of magnitude as, pool boiling heat flux at the onset of nucleate boiling. A new blowing factor correlation is presented for high-rate mass-transfer (B m > 1) of air–water vapor (Pr ∼ 0.7, Sc ∼ 0.6) turbulent natural convection flow over a heated horizontal surface for pool temperatures up to 99 °C (incipient boiling).",
keywords = "Mass transfer, Natural convection, Spent-fuel pool",
author = "Brewster, {M Quinn}",
year = "2018",
month = "1",
day = "1",
doi = "10.1016/j.ijheatmasstransfer.2017.08.035",
language = "English (US)",
volume = "116",
pages = "703--714",
journal = "International Journal of Heat and Mass Transfer",
issn = "0017-9310",
publisher = "Elsevier Limited",

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TY - JOUR

T1 - Evaporation of water at high mass-transfer rates by natural convection air flow with application to spent-fuel pools

AU - Brewster, M Quinn

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A simple model of evaporation from warm pools of water with turbulent, natural convection flow in the vapor phase is presented. The model is applicable from the dilute, low mass-transfer rate regime (room temperature) through the high mass-transfer rate regime (up to 99 °C). The model is applied to spent-fuel pool (SFP) heat and mass transfer during emergency conditions (e.g., plant blackout), and, in particular, to Fukushima. Comparisons with previous models are made. A simple analytic formula is presented that is nearly explicit in solving for pool temperature. The formula separates the more temperature-dependent properties from less temperature-dependent ones via a non-dimensional ratio Q u = q u /q u,b , where q u is the arbitrary (but specified) evaporative (latent) heat flux (∼decay heat for SFP) and q u,b is the latent heat flux characteristic of incipient boiling. The latter has a simple, relatively temperature-independent expression, q u,b = (h fg Le 2/3 h * )/C p , where h * is the dilute-limit heat transfer coefficient. This formula predicts that for natural convection at 99 °C (h * ∼ 10 W/m 2 K) q u,b is approximately 18 kW/m 2 , slightly greater than, but of the same order of magnitude as, pool boiling heat flux at the onset of nucleate boiling. A new blowing factor correlation is presented for high-rate mass-transfer (B m > 1) of air–water vapor (Pr ∼ 0.7, Sc ∼ 0.6) turbulent natural convection flow over a heated horizontal surface for pool temperatures up to 99 °C (incipient boiling).

AB - A simple model of evaporation from warm pools of water with turbulent, natural convection flow in the vapor phase is presented. The model is applicable from the dilute, low mass-transfer rate regime (room temperature) through the high mass-transfer rate regime (up to 99 °C). The model is applied to spent-fuel pool (SFP) heat and mass transfer during emergency conditions (e.g., plant blackout), and, in particular, to Fukushima. Comparisons with previous models are made. A simple analytic formula is presented that is nearly explicit in solving for pool temperature. The formula separates the more temperature-dependent properties from less temperature-dependent ones via a non-dimensional ratio Q u = q u /q u,b , where q u is the arbitrary (but specified) evaporative (latent) heat flux (∼decay heat for SFP) and q u,b is the latent heat flux characteristic of incipient boiling. The latter has a simple, relatively temperature-independent expression, q u,b = (h fg Le 2/3 h * )/C p , where h * is the dilute-limit heat transfer coefficient. This formula predicts that for natural convection at 99 °C (h * ∼ 10 W/m 2 K) q u,b is approximately 18 kW/m 2 , slightly greater than, but of the same order of magnitude as, pool boiling heat flux at the onset of nucleate boiling. A new blowing factor correlation is presented for high-rate mass-transfer (B m > 1) of air–water vapor (Pr ∼ 0.7, Sc ∼ 0.6) turbulent natural convection flow over a heated horizontal surface for pool temperatures up to 99 °C (incipient boiling).

KW - Mass transfer

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