Abstract
The isothermal mixing of a heavy and a light liquid of different physical properties is numerically investigated by means of Large Eddy Simulations. The validation is based on experimental data held in a system reproducing various components of a pressurized water nuclear reactor, during a scenario of cold water injection at a low Atwood number of 0.05. The flow has two distinct stages: first a buoyancy-driven phase is characterized by a fluid front development in the cold leg and gives rise to Kelvin–Helmholtz whorls under the action of density changes. Then, the heavy liquid discharges into the downcomer filled with light liquid, which causes a turbulent mixing. These phenomena are analyzed through a single-phase approach where the density of the working fluid is either variable or modeled by the Boussinesq approximation. The influence of grid refinement is deeply examined, which shows that the mesh convergence is well achieved for the main flow quantities, unlike the low-magnitude spanwise components. Overall, the numerical solutions are found to reproduce the experimental measurements with a fair accuracy for both physical models used. These latter exhibit similar trends, due to the small density difference under consideration. The predictions in the downcomer appear to be more challenging owing to a strongest turbulence than in the cold leg, some flow features being not properly captured. However, the experimental data in the downcomer are found to be incomplete and somewhat dubious for a strict validation of the numerical simulations. Lastly, the flow distribution in the dowcomer is investigated, providing further insight on the mixing process.
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Notes
These equations are written here following the notational convention where the indices i and j are implicitly summed over when repeated.
To lighten the notations, the symbols for Favre average and filtered quantities are omitted from this point on.
Abbreviations
- \(\mathrm {A}\) :
-
Atwood number
- \(({\mathscr {C}})\), \(({\mathscr {L}})\) :
-
Circular and straight lines
- (\({\mathbf {e}}_r\) ; \({\mathbf {e}}_\theta\) ; \({\mathbf {e}}_{z^\prime }\)):
-
Cylindrical coordinate system
- f :
-
Time frequency
- \(\mathrm {Fr}\) :
-
Froude number
- \({\varvec{g}} = (g_i)_{1 \le i \le 3}\) :
-
Gravity field
- \({\mathscr {I}}\) :
-
Time-averaging interval
- \({\mathscr {M}}\) :
-
Mesh
- \({\mathcal {K}}\) :
-
Turbulent kinetic energy
- N :
-
Number of experimental points
- \({\mathscr {N}}\) :
-
Error norm
- p, \(p^*\) :
-
Pressure, modified pressure
- \({\mathcal {Q}}^\text {\tiny sgs}_i\) :
-
Subgrid-scale mass flux vector
- \(\mathrm {Ri}\) :
-
Richardson number
- \(\mathrm {Sc}\), \(\mathrm {Sc}_t\) :
-
Schmidt, turbulent Schmidt numbers
- t :
-
Time
- \({\mathcal {T}}^\text {\tiny sgs}_{ij}\) :
-
Subgrid-scale stress tensor
- \(u_1\), u, U :
-
Horizontal velocity components
- \(u_2\), v, V :
-
Vertical velocity components
- \(u_3\), w, W :
-
Spanwise velocity components
- (\(U_r\) ; \(U_\theta\) ; \(U_{z^\prime }\)):
-
Cylindrical velocity components
- (x, y, z) or (\(x_1\), \(x_2\), \(x_3\)):
-
Space coordinates
- \(\varDelta x^+\), \(\varDelta y^+\), \(\varDelta z^+\) :
-
Mesh size in wall units
- \(y^+\) :
-
Dimensionless wall distance
- \(\alpha _0\) :
-
Coefficient of mass
- \(\delta _{ij}\) :
-
Kronecker delta
- \(\theta\) :
-
Azimuthal angle
- \(\mu\) :
-
Dynamic viscosity
- \(\rho\) :
-
Density
- \(\sigma _{ij}\) :
-
Rate-of-strain tensor
- \(\phi\) :
-
Mass fraction
- 0:
-
Reference quantity
- cl:
-
Relative to cold leg
- dc:
-
Relative to downcomer
- H:
-
Relative to the heavy liquid
- L:
-
Relative to the light liquid
- mean:
-
Time-averaged
- sd:
-
Standard deviation
- sgs:
-
Subgrid-scale
- \({\widetilde{\cdot }}\) :
-
Favre filter
- \({\overline{\cdot }}\) :
-
Spatial filter
- BA:
-
Boussinesq approximation
- CLM:
-
Cold leg mixing
- FVE:
-
Finite volume element
- LES:
-
Large eddy simulation
- PTS:
-
Pressurized thermal shock
- PWR:
-
Pressurized water reactor
- RMSE:
-
Root-mean-square error
- SGS:
-
SubGrid-scale
- VD:
-
Variable-density
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This work was granted access to the HPC resources of TGCC under the allocation 2019-A0072A10460 attributed by GENCI (Grand Équipement National de Calcul Intensif).
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Angeli, PE. Wall-Resolved Large Eddy Simulations of the Transient Turbulent Fluid Mixing in a Closed System Replicating a Pressurized Thermal Shock. Flow Turbulence Combust 108, 43–75 (2022). https://doi.org/10.1007/s10494-021-00272-z
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DOI: https://doi.org/10.1007/s10494-021-00272-z