https://orcid.org/0000-0003-0492-3462
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Abstract
Subchannel code analysis is one of the key thermal-hydraulic approaches for nuclear reactor design and safety analysis. At present, subchannel codes are employed to compute local thermal-hydraulic conditions on the rod bundle fuel assemblies of nuclear reactor cores and to predict the performance of nuclear cores during normal and hypothetical accident conditions. Currently, the subchannel code is still the main tool for thermal-hydraulic analysis in the process of nuclear fuel licensing.
For inter-subchannel transfer, the widely accepted key mechanisms are (1) single- and two-phase cross flow, (2) single- and two-phase turbulent mixing, and (3) two-phase void drift. Turbulent mixing has been recognized as a vortex train moving along the gap between rods. As one of the key phenomena, the turbulent mixing model has been embedded in the subchannel code for decades. Originally, the turbulent mixing model was developed based on various adiabatic and diabatic subchannel turbulent mixing tests. Numerous correlations or coefficients have been developed for different codes. For commercial applications, the large-scale rod bundle tests of thermal mixing and critical heat flux (CHF) are the main approaches to obtain a specific model for a particular fuel/spacer design. The turbulent mixing coefficient and other parameters are determined in this process for the specific mixing vane grid design. In this process, various approaches to obtain the turbulent mixing coefficient have been proposed.
Conventionally, in the subchannel codes the combined bare rod mixing and spacer grid–enhanced turbulent mixing effects on coolant have been represented by the turbulent mixing coefficient. The lack of a grid-dependent directional cross-flow model has always led to the prediction bias of local condition, especially for the hot channel where CHF generally occurs. However, in recent years, modified grid models with directional diversion cross flow have been developed to improve the prediction of spacer grid performance.
In recent years, owing to the very fast improvement and rapid growth of computational resources, computational fluid dynamics (CFD) has gained popularity and advancement in the model development of subchannel codes. To substitute the costly and time consuming tests, instead of a simple turbulent mixing coefficient in the lumped parameter approach, various CFD approaches for turbulent mixing model development in subchannel codes have been proposed. CFD takes great advantage of lower cost, high resolution, and versatility. Though verification and validation are still required, CFD will be a very important tool for developing turbulent mixing models for subchannel codes.
In this critical review, the development and application of turbulent mixing models in various subchannel codes for liquid metal-cooled reactor analysis are reviewed and summarized. The codes, models, tests, simulations, and future modifications are reviewed in detail.
Acronyms
| ATHAS = | = | Advanced Thermal-Hydraulics Analysis Subchannel code |
| BWR = | = | boiling water reactor |
| CEA = | = | Commissariat à l’Energie Atomique et aux Energies Alternatives |
| CFD = | = | computational fluid dynamics |
| CHF = | = | critical heat flux |
| COBRA = | = | Coolant-Boiling in Rod Arrays |
| CU-HTRF = | = | Columbia University Heat Transfer Research Facility |
| DNS = | = | direct numerical simulation |
| DRM = | = | distributed resistance model |
| FW = | = | flow weighted |
| LDV = | = | laser Doppler velocimetry |
| LES = | = | large eddy simulation |
| LWR = | = | liquid metal-cooled reactor |
| MATRA = | = | Multichannel Analyzer for steady states and Transients in Rod Arrays |
| MRI = | = | match of refractive index |
| MVG = | = | mixing vane grid |
| PIV = | = | particle image velocimetry |
| PLIF = | = | planar laser-induced fluorescence |
| PSBT = | = | Pressurized water-cooled reactor Subchannel and Bundle Test |
| PWR = | = | pressurized water-cooled reactor |
| RANS = | = | Reynolds-Averaged Navier-Stokes Model |
| RSM = | = | Reynolds stress model |
| SCWR = | = | supercritical water-cooled reactor |
| TMC = | = | turbulent mixing coefficient |
Nomenclature
Dimensional parameters
| A = | = | flow area (m2) |
| CP = | = | heat capacity (J·kg−1·°C−1) |
| CRW = | = | rod-to-wall clearance (m) |
| De = | = | hydraulic equivalence diameter of subchannel (m) |
| D, Drod = | = | diameter of rod (m) |
| F = | = | interchange flux of energy, momentum |
| G = | = | mass flux (kg·m−2·s−1) |
| = | bundle average mass flux (kg·m−2·s−1) | |
| h, H = | = | fluid enthalpy (kJ·kg−1) |
| H′ = | = | fluctuation fluid enthalpy (kJ·kg−1) |
| k = | = | turbulent kinetic energy (J·kg−1) |
| Lh = | = | heating length (m) |
| l = | = | centroid distance between subchannels i and j (m) |
| lt = | = | mixing length (m) |
| = | mass flow (kg·s−1) | |
| P = | = | rod pitch (m) |
| = | heat flux (W·m−2) | |
| s = | = | gap length between the adjacent channels (m) |
| T = | = | temperature (K) |
| u = | = | axial velocity of subchannel (m·s−1) |
| Δu = | = | axial velocity difference of neighboring subchannel (m·s−1) |
| v = | = | radial/lateral velocity of subchannel (m·s−1) |
| = | Reynolds stress (m2·s−2) | |
| w = | = | diversion cross flow per length per second (kg·m−1·s−1) |
| = | turbulent fluctuating mass flow per length (kg·m−1·s−1) | |
| Δx = | = | node axial length (m) |
| Δy = | = | central distance of adjacent subchannels (m) |
| z = | = | axial length downstream of MVG (m) |
Dimensionless parameters
| K, Kg = | = | dimensionless factors in equation |
| N = | = | number of subchannels |
| Pr = | = | Prandtl number |
| Re = | = | Reynolds number |
| St = | = | Stanton number |
Greek
| β = | = | turbulent mixing coefficient in COBRA series codes (dimensionless) |
| ε = | = | eddy diffusivity (m2·s1) |
| εTDR = | = | turbulent dissipation rate (dimensionless) |
| λ = | = | thermal conductivity coefficient (dimensionless) |
| μ = | = | dynamic viscosity (Pa·s−1) |
| ν = | = | kinematic viscosity (m2·s−1) |
| ρ = | = | density (kg·m−3) |
| τ = | = | shear stress (Pa) |
| Θ = | = | turbulent mixing coefficient spacer grid multiplier (dimensionless) |
Subscripts
| Central Sub = | = | central subchannels |
| cond = | = | conduction |
| E = | = | energy |
| exp = | = | experimental |
| g = | = | gas phase |
| h = | = | heating |
| i = | = | channel i |
| j = | = | channel j |
| M = | = | momentum |
| m = | = | mass or measured |
| ij = | = | channel i to j |
| l = | = | liquid phase |
| p = | = | predicted |
| SP = | = | single phase |
| sub = | = | subchannels |
| t, turb = | = | turbulent |