In water-cooled nuclear power reactors, significant quantities of steam and hydrogen could be produced within the primary containment following the postulated design basis accidents (DBA) or beyond design basis accidents (BDBA). For accurate calculation of the temperature/pressure rise and hydrogen transport calculation in nuclear reactor containment due to such scenarios, wall condensation heat transfer coefficient (HTC) is used. In the present work, the adaptation of a commercial CFD code with the implementation of models for steam condensation on wall surfaces in presence of noncondensable gases is explained. Steam condensation has been modeled using the empirical average HTC, which was originally developed to be used for “lumped-parameter” (volume-averaged) modeling of steam condensation in the presence of noncondensable gases. The present paper suggests a generalized HTC based on curve fitting of most of the reported semiempirical condensation models, which are valid for specific wall conditions. The present methodology has been validated against limited reported experimental data from the COPAIN experimental facility. This is the first step towards the CFD-based generalized analysis procedure for condensation modeling applicable for containment wall surfaces that is being evolved further for specific wall surfaces within the multicompartment containment atmosphere.

Steam condensation in the presence of noncondensable gases is a relevant phenomenon in many industrial applications, including nuclear reactors. Condensation on the containment structures during an accident and associated computations are important for the containment design of all the existing reactors for LOCA DBA, DBA, and BDBA hydrogen distribution and recombination and passive emergency systems in the nuclear reactors of new generation. Rate of steam condensation at containment walls affects the transient pressure in the containment after loss of coolant accident. Apart from this during a severe accident in a water-cooled power reactor nuclear power plant (NPP), large amounts of hydrogen would presumably be generated due to core degradation and released into the containment. The integrity of the containment could be threatened due to hydrogen combustion. If composition of the hydrogen-steam-air mixture lies within a certain limits, the combustion will occur. The steam condensation phenomenon is important from hydrogen distribution point of view to locate the flammable region in the containment for adequate accident management procedures (Royl et al., 2000 [

Currently use of CFD techniques to model such scenario is popular, since CFD codes provide more detailed information in such scenario. These commercially available CFD codes generally do not have built-in steam condensations models. Consequently, it is necessary to implement steam condensation via user-defined subroutines. Two main approaches have been proposed by various authors to model wall condensation in CFD codes. In the first approach (two-phase flow approach) separate momentum equations are solved for vapour and liquid phases. A fine mesh is required, and liquid film and the diffusion of steam towards wall through boundary layer formed by noncondensable gases are modeled. This approach is quite close to first-principle condensation modeling but requires very large computational time and will probably take some time to be used for any practical applications (full containment modeling) in future. In the second approach a single-fluid model is used where steam is modeled as a separate species via species conservation equation. For modeling steam condensation, mass sink and corresponding energy sink are modeled in the very first cell near to condensing wall. In this second approach there are two ways to calculate these sink terms. The first one is based on diffusion theory which requires a very fine mesh near the wall and computes steam condensation rate that diffuses towards wall through species boundary layer. Houkema et al., in 2008, [

Wide ranges of HTCs have been reported which have come from condensation experimental setup largely different from actual containment accident situation during accident. Uses of the so-called conservative (safe values in context of peak pressure, temperature, or hydrogen concentration, etc.) individual HTC also have conflicting position in respect of containment pressure transient calculation and hydrogen distribution/management calculation. An HTC value which results in lower condensation of steam gives conservative results for containment pressure calculation, but gives nonconservative results for hydrogen management calculation due to artificial inerting atmosphere because of less condensation of steam. Authors try to overcome this weakness by trying to use many empirical correlations and theoretical calculations by making a generalized HTC from most of the generally reported approaches. The present combined approach allows relatively fast calculations and should be adequate for large industrial applications.

Steam condensation was modeled as a sink of mass and enthalpy by applying the correlation by Uchida et al., 1965 [

The present paper is about development and comparison of the wall condensation model based on semiempirical correlation (existing and proposed based on curve fit of various existing correlations) in CFD-ACE+ [

Review papers on condensation on the containment structures (Green and Almenas, 1996 [

Review of containment-specific steam condensation HTC.

S. no. | Name | Equation |
---|---|---|

1 | Uchida (Rosa et al., 2009 [ | ^{2}) |

2 | Tagami steady state (Rosa et al., 2009 [ | ^{2}) |

3 | Debhi (Rosa et al., 2009 [ | ^{2}), |

4 | Kataoka (Rosa et al., 2009 [ | ^{2}) |

5 | Murase (Rosa et al., 2009 [ | ^{2}) |

6 | Liu (Lee and Kim, 2008 [ | ^{2}), |

7 | Green (Green and Almenas, 1996 [ | ^{2}), |

8 | Kawakubo (Kawakubo et al., 2009 [ | ^{2}), |

9 | Nusselt UCB Multiplier (Park et al., 1999 [ | ^{2}) |

10 | Nusselt LEE Multiplier (Lee and Kim, 2008 [ | ^{2}) |

11 | Proposed fit from all the curves | ^{2}) |

The major limitations for individual HTC use in CFD codes which have been mentioned earlier come from the fact that, the use of global correlation as the local one, different length and energy addition/removal time scales, modeling of surface condensation phenomenon as volume phenomena, different reported range of experimental parameters like size, flow regimes of convection, type and quantity of combustible, type of walls, configuration of wall (mostly pipes), and so forth. Some of the HTCs are plotted in Figure

Various HTCs from the literature and proposed HTC based on curve fitting.

The classical Nusselt theory gives the HTC as the conductivity of the liquid film divided by the film thickness, so the classical HTC will be a fixed value. Subsequently Nusselt theory gets modified with the use of two multipliers (UCB multipliers): first one takes care of enhancement of the HTC due to liquid film shearing and the associated effects, and the second multiplier takes care of the degradation of the HTC due to presence of non condensable gases. Authors have also suggested and used the multiplier developed by Lee and Kim, 2008 [

Another issue is about the conservatism of the HTC in nuclear regulatory organization suggesting HTC and practical HTC due to large variations in reported values. We use a correlation with small HTC value (being conservative) for containment pressure and temperature calculation which will result in higher containment peak pressure values. But the same conservatism aspect may not be valid for hydrogen distribution in the reactor containment atmosphere as higher pressure differences in multiple-compartment configurations will result in increased intercompartmental mixing and reduction in hydrogen concentration. The lower HTC may also result in relatively uniform temperature field which will decrease the amount of hydrogen stratification due to buoyancy and also results in lower hydrogen concentration values. A lower HTC gives non-conservative results for hydrogen management calculation due to artificial inerting atmosphere due to low condensation of steam. Another issue of bias for use in the lower HTC values was with regard to the earlier correlations developed for low velocity of steam and calm and undisturbed atmosphere. The actual accident scenario may have more turbulent flow dynamics. In real accident situation the accident conditions will be very complex and uncertain. The most logical approach could be to fit a curve from all the possible HTC correlations for the most dominating parameter of interest, that is, amount of non condensable gases. A finite film of preidentified thickness is always assumed to be sticking to the wall.

The general-purpose CFD code CFD-ACE+ solves the local instantaneous transport equations for mass, momentum, energy, species, and turbulence parameters. The general transport equation for variable

In the present work steam condensation was modeled as a sink for mass and enthalpy by applying the empirical correlation based on experiments on forced convection and implemented in a subroutine. The condensate film on structures was considered to have a fixed thickness. Basically, the steam condensation rate was obtained from the expression

The COPAIN experimental facility (CEA, Grenoble) Cheng et al., 2001 [^{2}, and maximum inwards velocity of 3 m/s, with different fraction of air, steam, and, helium. Inside the channel forced or natural convection was observed depending on prevailing conditions. The database selected to validate the wall condensation model is shown in Table

Parameters of the COPAIN tests.

Test no. | Convective heat transfer | Air velocity at inlet (m/s) | Pressure (bar) | Air temperature at inlet (K) | Wall temperature (K) | Mass fraction of noncondensible gases |
---|---|---|---|---|---|---|

P0441 | Forced | 3 | 1.02 | 353.23 | 307.4 | 0.767 |

P0443 | Free | 1 | 1.02 | 352.33 | 300.06 | 0.772 |

P0444 | Natural | 0.5 | 1.02 | 351.53 | 299.7 | 0.773 |

P0344 | Natural | 0.3 | 1.21 | 344.03 | 322 | 0.864 |

Figure

Steam mass fraction on the condensing wall for test P0444.

Variation of condensation flux with height, test P0441.

Variation of condensation flux with height, test P0443.

Variation of condensation flux with height, test P0444.

Variation of condensation flux with height, test P0344.

A model for steam condensation was implemented and tested based on various correlations developed for volume-averaged approach in the computational fluid dynamics code CFD-ACE+. The CFD code CFD-ACE+ was used to simulate condensation experiments that were performed in the COPAIN facility. There was a reasonable agreement between simulated and experimental results for proposed approach derived from fitting of various experimental data. However further validations are needed against other experimental data. This approach does not solve the phenomenon from the first principle, but this approach can be considered as effective for industrial problem where solution for large computational domain is required. The present work suggests that the approach could be used for integrated hydrogen distribution/management calculation with steam condensation in nuclear reactor containment required for safety analysis. Another useful application of the present approach could be to obtain a first-order simplified generalized analysis result for a containment wall surface, and subsequently different wall surfaces can be studied in detail where specific correlations can be used within the CFD framework.

General transport variable

Diffusion coefficient for variable

Source term for variable

Steam condensation rate (kg/s)

Density of steam (kg/m^{3})

Density of noncondensible gases (kg/m^{3})

Area of condensation surface (m^{2})

Temperature (K)

Average temperature of condensation surface (K)

Latent heat of steam (J/kg)

Enthalpy sink due to condensation (W)

Specific heat of steam at constant pressure (J/kgK)

Specific heat of air at constant pressure (J/kgK)

Reference temperature (K)

Pressure (Pa)

Constants.