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ABSTRACT
In simulations of two-phase flow behavior in nuclear reactors, subchannel analysis codes are often used to evaluate the void fraction within a BWR fuel bundle in detail. When solving the momentum conservation equation averaged over a subchannel cross-section for upward two-phase flows, the distribution parameter is required to consider the void fraction and velocity distributions in the subchannel cross-section. In this paper, constitutive equations were developed for the distribution parameters for dispersed two-phase flows applicable to the inner, edge, and corner subchannels, which are typical subchannels in a fuel bundle. The distribution parameters could be calculated by giving the void fraction and the velocity distribution. Therefore, the distribution parameters were evaluated and modeled as a function of the geometrical parameters by assuming the void fraction and velocity distributions with bulk and subcooled boiling for each subchannel type. The developed constitutive equations were evaluated by comparing them with the distribution parameters estimated based on the NUPEC rod bundle void fraction test data. The developed distribution parameter model was implemented into the subchannel analysis code NASCA and compared with the measured cross-sectional average void fraction of the NUPEC rod bundle void fraction test data. In comparison with the original NASCA code, which assumed the distribution parameter to be unity, the improved NASCA with the distribution parameter model decreased the mean error of the measured cross-sectional average void fraction to less than half of the result of the original NASCA code, both in absolute and relative differences.
GRAPHICAL ABSTRACT
Nomenclature
| a | = | coefficient |
| Ac | = | flow area |
| Awp | = | bubble layer area |
| ai | = | interfacial area concentration |
| b | = | exponent |
| C0 | = | distribution parameter |
| CD | = | drag coefficient |
| D0 | = | rod diameter |
| j | = | mixture volumetric flux |
| jc,p | = | maximum mixture volumetric flux in a given radial direction of p-type subchannel |
| jc0,p | = | maximum mixture volumetric flux within a p-type subchannel |
| k | = | ratio of the gap between the rod and channel wall to the gap between rods |
| Mif | = | interfacial drag force acting on liquid phase |
| Mig | = | interfacial drag force acting on gas phase |
| md | = | mean absolute error |
| mj | = | exponent for volumetric flux distribution |
| mrel | = | mean relative deviation |
| mrel,ab | = | mean absolute relative deviation |
| mα | = | exponent for void fraction distribution |
| P0 | = | rod pitch |
| P1 | = | distance from rod center to the wall of the flow channel |
| R0 | = | rod radius |
| Rc | = | distance from the origin to the position where |
| Rp | = | radius of round tube |
| r | = | radial position from rod surface |
| sd | = | standard deviation |
| vr | = | relative velocity between gas and liquid phase |
| xwp | = | bubble layer thickness |
| Greek symbols | = | |
| α | = | void fraction |
| αc0,p | = | void fraction at the center of a p-type subchannel |
| αwp | = | void fraction at assumed square bubble layer |
| Λ | = | the ratio of the subchannel distribution parameter to round tube distribution parameter |
| ψ | = | shape factor |
| θ | = | azimuthal position |
| θ0 | = | threshold angle for edge subchannel |
| θ′ | = | angle where the maximum value of mixture volumetric flux occurs |
| ρ | = | density |
| Subscripts | = | |
| c | = | corner subchannel |
| cal | = | calculated value |
| e | = | edge subchannel |
| exp | = | measured value |
| f | = | liquid phase |
| g | = | gas phase |
| i | = | interior subchannel |
| p | = | subchannel type |
| rt | = | round tube |
| ∞ | = | asymptotic value |
Acknowledgments
One of the authors (T. Hibiki) appreciates the support provided by the City University of Hong Kong (Project Number: 7005924).
Disclosure statement
No potential conflict of interest was reported by the author(s).