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ABSTRACT
An implicit numerical scheme is presented for solving the two-fluid model widely used in the analysis of a gas–liquid two-phase flow in light water nuclear reactors (LWRs). The pressure equation is established by combining the momentum and mass conservation equations. The implicit calculation of each governing equation is separated into phase- and space-link steps. In the phase-link step, the interfacial momentum and heat transfers are implicitly calculated. Then the solution accounting for the convection and diffusion terms is calculated simultaneously in space. The phase- and space-link steps are repeated for convergence. The numerical scheme is implemented in CUPID, which is a multidimensional two-phase flow analysis code for LWRs, and verified against a set of conceptual two-phase flow problems which include typical thermal hydraulic phenomena in LWRs. Calculations are performed using four numerical schemes, semi-implicit ICE and SMAC schemes, an implicit scheme, and an implicit scheme with increased time step size, and the results are discussed.
Nomenclature
| Cd | = | drag coefficient |
| e | = | internal energy |
| = | phase interface force | |
| = | gravity vector | |
| h | = | enthalpy |
| H | = | interface heat transfer coefficient |
| P | = | pressure |
| = | cell surface vector | |
| SRC | = | explicit source term |
| T | = | temperature |
| = | velocity vector of k-phase | |
| Vi | = | volume of i cell |
| Xn | = | noncondensable gas mass fraction |
| αk | = | volume fraction of k-phase, αl + αg = 0 |
| δ | = | increment |
| δt | = | time step size, tn+1−t1 |
| Γk | = | mass transfer rate of k-phase per volume |
| κk,eff | = | effective thermal conductivity of k-phase |
| μk,eff | = | effective viscosity of k-phase |
| ρ | = | density |
| Ψk, f | = | k-phase volume flow rate at cell surface f |
| Subscripts | = | |
| f | = | cell surface |
| g | = | gas |
| i | = | phase interface or cell number |
| ik | = | k-phase interface |
| j | = | neighboring cell number |
| k | = | k-phase (liquid or gas) |
| (k) | = | k-step value |
| l | = | liquid |
| v | = | vapor |
| Superscripts | = | |
| D | = | drag |
| n | = | old time step |
| n + 1 | = | new time step |
| ND | = | nondrag |
| VM | = | virtual mass |
| sat | = | saturated |
| * | = | intermediate value |
Nomenclature
| Cd | = | drag coefficient |
| e | = | internal energy |
| = | phase interface force | |
| = | gravity vector | |
| h | = | enthalpy |
| H | = | interface heat transfer coefficient |
| P | = | pressure |
| = | cell surface vector | |
| SRC | = | explicit source term |
| T | = | temperature |
| = | velocity vector of k-phase | |
| Vi | = | volume of i cell |
| Xn | = | noncondensable gas mass fraction |
| αk | = | volume fraction of k-phase, αl + αg = 0 |
| δ | = | increment |
| δt | = | time step size, tn+1−t1 |
| Γk | = | mass transfer rate of k-phase per volume |
| κk,eff | = | effective thermal conductivity of k-phase |
| μk,eff | = | effective viscosity of k-phase |
| ρ | = | density |
| Ψk, f | = | k-phase volume flow rate at cell surface f |
| Subscripts | = | |
| f | = | cell surface |
| g | = | gas |
| i | = | phase interface or cell number |
| ik | = | k-phase interface |
| j | = | neighboring cell number |
| k | = | k-phase (liquid or gas) |
| (k) | = | k-step value |
| l | = | liquid |
| v | = | vapor |
| Superscripts | = | |
| D | = | drag |
| n | = | old time step |
| n + 1 | = | new time step |
| ND | = | nondrag |
| VM | = | virtual mass |
| sat | = | saturated |
| * | = | intermediate value |
Acknowledgment
This work was supported by the National Research Foundation of Korea (NRF) and the Korea Radiation Safety Foundation (KORSAFe) grant funded by the Korean government (MSIP & NSSC) (Nuclear Research and Development Program: 2012M2A8A4025647, Nuclear Safety Research Center Program: 1305011).