### 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 language | English (US) |
---|---|

Pages (from-to) | 703-714 |

Number of pages | 12 |

Journal | International Journal of Heat and Mass Transfer |

Volume | 116 |

DOIs | |

State | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Mass transfer
- Natural convection
- Spent-fuel pool

### ASJC Scopus subject areas

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

### Cite this

**Evaporation of water at high mass-transfer rates by natural convection air flow with application to spent-fuel pools.** / Brewster, M Quinn.

Research output: Contribution to journal › Article

}

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

KW - Natural convection

KW - Spent-fuel pool

UR - http://www.scopus.com/inward/record.url?scp=85029698858&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029698858&partnerID=8YFLogxK

U2 - 10.1016/j.ijheatmasstransfer.2017.08.035

DO - 10.1016/j.ijheatmasstransfer.2017.08.035

M3 - Article

AN - SCOPUS:85029698858

VL - 116

SP - 703

EP - 714

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

ER -