https://orcid.org/0000-0001-6876-2405
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Abstract
In the study of safety enhancements on advanced sodium-cooled fast reactors (SFRs) by the Japan Atomic Energy Agency (JAEA), it has been essential to clarify the thermal hydraulics under various operating conditions at high and low flow rate conditions in a fuel assembly (FA) with wire-wrapped fuel pins to assess the structural integrity of the fuel pin that achieves a high-performance core with high burnup ratio and high power density. A finite element thermal-hydraulic analysis code named SPIRAL has been developed by JAEA to analyze the detailed thermal-hydraulic phenomena in the FA of a SFR.
In this study, numerical simulations of 37-pin bundle sodium experiments at different Reynolds (Re) number conditions, including a transitional condition between laminar and turbulent flows and turbulent flow conditions, were performed to validate the developed hybrid k-ε/kθ-εθ turbulence model equipped in SPIRAL to consider the low Re number effect near the wall in the flow and temperature fields. The temperature distributions predicted by SPIRAL were consistent with those measured in the sodium experiments at the Re number conditions. Through the validation study, the applicability of the hybrid turbulence model in SPIRAL to the thermal-hydraulic evaluation of sodium-cooled FAs in a wide range of Re numbers was confirmed.
Nomenclature
| Cε1, Cε2, Cε3 = | = | constants in transport equation for ε, Cε1 = Cε3 = 1.5, Cε2 = 1.9 |
| Cλ, Cm = | = | constants in turbulent thermal diffusivity equation, Cλ = 0.1, Cm = 0.5 |
| CP1, CP2, CD1, CD2 = | = | constants in transport equation for εθ, CP1 = 1.9, CP2 = 0.6, CD1 = 2.0, CD2 = 0.9 |
| Cμ = | = | constant in turbulent kinematic viscosity equation, Cμ = 0.09 |
| cp = | = | specific heat (J⋅kg−1⋅K−1) |
| Dh = | = | hydraulic equivalent diameter of the bundle (m) |
| fε1, fε2, fε3 = | = | functions in transport equation for ε, fε1 = fε3 = 1 |
| fP1, fP2, fD1, fD2 = | = | functions in transport equation for εθ, fP2 = 1, fD1 = fP1 |
| fλ = | = | function in turbulent thermal diffusivity equation |
| fμ = | = | function in turbulent kinematic viscosity equation |
| fμ,w, fλ,w = | = | function in boundary conditions for k and kθ |
| Gk = | = | buoyant production (J⋅kg−1⋅s−1) |
| Gr = | = | Grashof number |
| gi = | = | gravitational acceleration in i direction (m⋅s−2) |
| k = | = | turbulent kinetic energy (J⋅kg−1) |
| kθ = | = | temperature variance (K2) |
| M = | = | flow rate (kg⋅s−1) |
| m = | = | constant in boundary conditions for kθ, m = 1/2 |
| Pk = | = | production of turbulent kinetic energy (J⋅kg−1⋅s−1) |
| Pθ = | = | production of temperature variance (K2⋅s−1) |
| Pr = | = | Prandtl number |
| Prt = | = | turbulent Pr number |
| p = | = | pressure (Pa) |
| Q = | = | power (W) |
| q = | = | heat generation rate (W⋅m−3) |
| R = | = | ratio between the time scales of temperature and velocity fields |
| Re = | = | Reynolds number |
| Ret = | = | turbulent Re number |
| Ri = | = | Richardson number |
| Rij = | = | Reynolds stress (m2⋅s−2) |
| Rjθ = | = | turbulent heat flux (m⋅K⋅s−1) |
| r = | = | radial distance (m) |
| T = | = | temperature in the bundle (°C) |
| t = | = | time (s) |
| = | velocity components in i and j directions (m⋅s−1) | |
| uε = | = | Kolmogorov velocity scale (m⋅s−1) |
| uτ = | = | friction velocity (m⋅s−1) |
| u+ = | = | nondimensional velocity |
| w = | = | axial velocity (m⋅s−1) |
| = | coordinates in i and j directions (m) | |
| y = | = | distance from wall surface (m) |
| y+ = | = | nondimensional distance from wall surface |
| y* = | = | nondimensional distance from wall surface |
| z = | = | axial distance in the height direction (m) |
Greek
| α = | = | thermal diffusivity (m2⋅s−1) |
| = | turbulent thermal diffusivity (m2⋅s−1) | |
| β = | = | volumetric expansion coefficient (K−1) |
| δ = | = | boundary layer thickness (m) |
| δij = | = | Kronecker delta |
| Δt = | = | time difference (s) |
| ΔTe = | = | estimated temperature rise in the bundle (°C) |
| ε = | = | dissipation rate of turbulent kinetic energy (J⋅kg−1⋅s−1) |
| εθ = | = | dissipation rate of temperature variance (K2⋅s−1) |
| θ = | = | temperature (°C) |
| θw = | = | wall temperature (°C) |
| θτ = | = | friction temperature (°C) |
| θ+ = | = | nondimensional temperature |
| κ = | = | Von Kármán constant, κ = 0.41 |
| λ = | = | thermal conductivity (W⋅m−1⋅K−1) |
| μ = | = | dynamic viscosity (Pa⋅s) |
| ν = | = | kinematic viscosity (m2⋅s−1) |
| = | turbulent kinematic viscosity (m2⋅s−1) | |
| ρ = | = | density (kg⋅m−3) |
| σ(k), σ(ε), σ(kθ), σ(εθ) = | = | model constants for turbulent diffusion of k, ε, kθ, and εθ, σ(k) = σ(ε) = 1.4, σ(kθ) = σ(εθ) = 1.6 |
Subscripts
| in = | = | inlet |
| L = | = | laminar flow regime |
| m = | = | mean value on the cross section of the bundle |
| out = | = | outlet |
| T = | = | turbulent flow regime |
Superscript
| n = | = | time step |
Disclosure Statement
No potential conflict of interest was reported by the authors.