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Abstract
This paper aims to revise the critical flow criterion and flashing inception of the analytical critical flow model and to further explore the effect of upstream conditions on critical mass fluxes. The flashing inception of the model is considered to be affected by the Reynolds number and the Jakob number. Model predictions show strong similarities with test results compared with other models, with average errors of less than 10.1% for simulated slits and 15.8% for natural cracks. Upstream parameters of the liquid, such as the stagnation pressure, subcooling, and aspect ratio, directly influence the rate of depressurization, the thermodynamic nonequilibrium constant, and the friction pressure drop, respectively, which determine the critical mass flux. This research provides the theoretical basis for accurate assessment of critical crack, providing safeguards for monitoring nuclear reactor leaks.
Nomenclature
| D = | = | hydraulic diameter (m) |
| G = | = | mass flux (kg∙m−2 ∙ s−1) |
| Gc = | = | critical mass flux (kg ∙ m−2 ∙ s−1) |
| Ja = | = | Jakob number |
| ln = | = | nucleation inception point (m) |
| lt = | = | minimum cross-section point (m) |
| L = | = | channel length (m) |
| N = | = | thermodynamic constant |
| p = | = | pressure (Pa) |
| pc = | = | critical pressure of liquid (Pa) |
| pi = | = | upstream pressure of liquid (Pa) |
| pn = | = | nucleation pressure (Pa) |
| ps = | = | saturation pressure (Pa) |
| Re = | = | Reynolds number |
| S = | = | slip ratio |
| SA = | = | multiplier of Amos and Schrock |
| SL = | = | multiplier of Lee and Schrock |
| SM = | = | multiplier |
| T = | = | temperature (K) |
| Tc = | = | critical temperature (K) |
| Ti = | = | upstream temperature (K) |
| Tr = | = | reduced temperature (K) |
| Tsub = | = | subcooling (K) |
| u = | = | velocity (m ∙ s−1) |
| x = | = | mass quality |
| xe = | = | equilibrium mass quality |
| z = | = | axis distance from entrance (m) |
Greek
| ρ = | = | density (kg ∙ m−3) |
| Σ = | = | depressurization rate (Pa ∙ s−1) |
| υ = | = | specific volume (m3 ∙ kg−1) |
Subscript
| g = | = | vapor |
| i = | = | entrance |
| l = | = | liquid |
| n = | = | flashing inception point |
| sat = | = | saturation |
| sub = | = | subcooled |
Acknowledgments
The authors appreciate the support from the State Key Laboratory of Nuclear Power Safety Monitoring Technology and Equipment (no. K-A2018.430) and the National Natural Science Foundation (grant no. 11675128) of China.