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Investigation of the falling water flow with evaporation for the passive containment cooling system and its scaling-down criteria

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Abstract

Falling water evaporation cooling could efficiently suppress the containment operation pressure during the nuclear accident, by continually removing the core decay heat to the atmospheric environment. In order to identify the process of large-scale falling water evaporation cooling, the water flow characteristics of falling film, film rupture and falling rivulet were deduced, on the basis of previous correlation studies. The influences of the contact angle, water temperature and water flow rates on water converge along the flow direction were then numerically obtained and results were compared with the data for AP1000 and CAP1400 nuclear power plants. By comparisons, it is concluded that the water coverage fraction of falling water could be enhanced by either reducing the surface contact angle or increasing the water temperature. The falling water flow with evaporation for AP1000 containment was then calculated and the feature of its water coverage fraction was analyzed. Finally, based on the phenomena identification of falling water flow for AP1000 containment evaporation cooling, the scaling-down is performed and the dimensionless criteria were obtained.

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Abbreviations

a :

Width of the circular arc component, m

A arc :

Crossing -section area of the circular arc component, m2

b :

Width of the rivulet component, m

d:

Differential sign, −

D :

Containment diameter, m

E film,k :

Dynamic energy rate of the water film, J/s

E film,s :

Adhesion work rate of the water film, J/s

E rivulet,k :

Dynamic energy rate of the water rivulet, J/s

E rivulet,s1 :

Adhesion work rate at the rectangular crossing section, J/s

E rivulet,s2 :

Adhesion work rate at the circular arc crossing section, J/s

f :

Fractional coefficient, −

f θ :

Modification coefficient for the rivulet contact angle, −

f c :

Water coverage fraction for rivulet flow, %

g :

Acceleration of gravity, m/s2

h e,evap :

Equivalent heat transfer coefficient by evaporation, W/m2-K

h fg :

Latent heat of evaporation, J/kg

L a :

Length along the water flow direction, m

L b :

Width of the rivulet or film, m

L + :

Dimensionless length, −

m :

Mass flow rate, kg/s

P jet :

Thermal power from the broken pipe at the core primary system, W

q m :

Evaporation mass rate, kg/m2

Q :

Water flow rate, m3/h

Q rivulet :

Total evaporation heat rate of water rivulet flow, W

t :

Temperature, °C

u rivulet :

Water rivulet flow velocity, m/s

u film :

Water film flow velocity, m/s

U gas :

Mean air velocity, m/s

U film :

Mean water film velocity, m/s

U film,in :

Inlet water film velocity, m/s

U film,out :

Outlet water film velocity, m/s

U rect :

Mean velocity of the rectangular component, m/s

U arc :

Mean velocity of the circular arccomponent, m/s

x :

The coordinate in thickness direction, m, −

y :

The coordinate in the water flow direction, −

Y :

Distance, m

Y + :

Dimensionless distance, m

z:

The coordinate in the direction of the rivulet width, −

β :

Angle, rad

δ film :

Thickness of the water film, m

δ film,in :

Thickness of the inlet water film, m

δ film,min :

Maximum thickness of the water film, m

δ film,out :

Thickness of the outlet water film, m

δ rivulet :

Thickness of the water rivulet, m

δ rivulet,β :

Local thickness of the circular arc at the angle of β, m

δ rivulet,max :

Maximum thickness of the water rivulet flow, m

∆:

Difference, −

Γ :

Water film line rate, kg/m-s

Γ in :

Inlet water film line rate, kg/m-s

Γ out :

Outlet water film line rate, kg/m-s

Γ + :

Dimensionless water line rate, kg/m-s

η :

Water dynamic viscosity, m 2 /s

π:

Constant, π = 3.14, −

Π:

Dimensionless criteria number, −

θ :

Contact angle, rad

θ s :

Static contact angle, rad

θ R :

Receding contact angle, rad

ρ :

Density, kg/m3

σvl :

Vapor - liquid surface tension, m/s

τ :

Shearing force at the vapor-liquid interface, N/m

in:

Inlet, −

min:

Minimum value, −

max:

Maximum, −

out:

Outlet, −

w:

Water

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Authors and Affiliations

  1. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing, 100084, China

    Cheng Li & Junming Li

  2. Gas Turbine Research Center, Beijing, 100086, China

    Cheng Li

  3. INET, Tsinghua University, Beijing, 100084, China

    Le Li

Authors
  1. Cheng Li
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  2. Junming Li
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  3. Le Li
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Correspondence to Cheng Li.

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Li, C., Li, J. & Li, L. Investigation of the falling water flow with evaporation for the passive containment cooling system and its scaling-down criteria. Heat Mass Transfer 54, 473–482 (2018). https://doi.org/10.1007/s00231-017-2141-1

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  • DOI: https://doi.org/10.1007/s00231-017-2141-1

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