Na-HPMR Multiphysics Model
Contact: Yinbin Miao (ymiao.at.anl.gov), Ahmed Abdelhameed (aabdelhameed.at.anl.gov)
Model link: HPMR Model
Inheritance from K-HPMR Model
This model is a sodium heat pipe variant of the K-HPMR model. For majority of the model description, please refer to the K-HPMR Multiphysics Model.
The motive for developing a sodium (Na) working fluid variant of the HPMR design is to better utilize the mechanistic heat pipe model (i.e., liquid-conductance vapor-flow (LCVF) model, also known as the "vapor-only" model) in Sockeye (Hansel et al., 2024) to enable advanced modeling features such as the start up transient. In the meantime, the majority of the HPMR design parameters are kept the same as the K-HPMR design. The Na-HPMR design is identical to the K-HPMR design except for the heat pipe working fluid. To better fit the operating temperature range of sodium, the design temperature is increased by 100 K.
Model Update for Na-HPMR
Aside from the increased design operating temperature, the main modifications made to generate the Na-HPMR variant are related to the switch of the heat pipe working fluid from potassium to sodium and the adoption of the Sockeye LCVF heat pipe model. Additionally, the cross-section is also updated to match the replacement of the potassium working fluid with sodium. On the other hand, the Griffin and BISON models are directly inherited from the K-HPMR model.
Cross-Section Generation Using Serpent Code
Similar to the K-HPMR model, the first step involves generating homogenized multi-group cross sections using Serpent-2**. The Serpent-2 model for the Na-HPMR is similar to that of the K-HPMR, except that sodium is employed as the working fluid in the heat pipes instead of potassium (K). An 11-group energy structure** is employed, with parameters defined over grids of:
Fuel temperature** (5 values)
Temperature of the moderator, reflector, monolith, and heat pipe** (5 values)
Hydrogen content** (7 values)
Control drum rotation** (1 value: control drums out)
The results obtained from Serpent-2 are consistent with expected reactor physics:
Increasing the hydrogen content within the tabulated range (from YH to YH) yields a higher value, due to enhanced moderation.
Increasing the fuel temperature consistently reduces , reflecting the negative reactivity feedback from Doppler broadening.
This multi-grid cross-section library enables analysis of thermal reactivity feedback effects as well as the impacts of hydrogen redistribution within the moderator. At present, simulations are being carried out for the control rod–out** configuration.
Finally, the generated cross sections are converted into an XML-file format** for compatibility with Griffin**.
Sockeye Model
For each heat pipe in the 1/6 HP-MR core, a Sockeye grandchild application is used to calculate its thermal performance.
Instead of the effective thermal conductance model used in the K-HPMR model, the LCVF heat pipe model is adopted in the Na-HPMR model. As the name implies, the advanced heat pipe model uses a mechanistic flow model to predict the heat transfer performance of the heat pipe kernel.
################################################################################
## NEAMS Micro-Reactor Application Driver ##
## Heat Pipe Microreactor with Na Working Fluid Steady State (Na-HPMR) SS ##
## Sockeye Grandchild Application input file ##
## Liquid-Conductance Vapor-Flow (LCVF) Heat Pipe Model (Vapor-Only) ##
################################################################################
t_start = -5e4
t_end = 0
length_evap = 1.8
length_adia = 0.3
length_cond = 0.9
n_elems_evap = 360
n_elems_adia = 60
n_elems_cond = 180
n_elems_wick = 8
n_elems_ann = 4
n_elems_clad = 4
D_clad_o = 2.10e-2
D_clad_i = 1.94e-2
D_wick_o = 1.80e-2
D_wick_i = 1.60e-2
porosity = 0.70
permeability = 2e-9
R_pore = 15e-6
fill_ratio = 1.1
T_ref_fill_ratio = 600
T_ref_rho_wick = 1000.0
T_ref_rho_clad = 1000.0
T_ext_cond = 900
htc_ext_cond = 1.0e6
[FluidProperties]
[fp_2phase]
type = SodiumIdealGasTwoPhaseFluidProperties
emit_on_nan = none
[]
[]
[Closures]
[closures]
type = HeatPipeVOClosures
[]
[]
[SolidProperties]
[sp_ss316]
type = ThermalSS316Properties
[]
[]
[Components]
[heat_pipe]
type = HeatPipeVO
position_evap_end = '0 0 0'
direction_evap_to_cond = '0 0 1' # to be compatible with the core mesh
gravity_vector = '9.8 0 0' # assume the core is horizontal
L_evap = ${length_evap}
L_adia = ${length_adia}
L_cond = ${length_cond}
D_clad_o = ${D_clad_o}
D_clad_i = ${D_clad_i}
D_wick_o = ${D_wick_o}
D_wick_i = ${D_wick_i}
porosity = ${porosity}
permeability = ${permeability}
R_pore = ${R_pore}
n_elems_evap = ${n_elems_evap}
n_elems_adia = ${n_elems_adia}
n_elems_cond = ${n_elems_cond}
n_elems_wick = ${n_elems_wick}
n_elems_ann = ${n_elems_ann}
n_elems_clad = ${n_elems_clad}
initial_T = ${T_ext_cond}
fill_ratio = ${fill_ratio}
T_ref_fill_ratio = ${T_ref_fill_ratio}
T_ref_rho_wick = ${T_ref_rho_wick}
T_ref_rho_clad = ${T_ref_rho_clad}
fp_2phase = fp_2phase
sp_wick = sp_ss316
sp_clad = sp_ss316
closures = closures
slope_reconstruction = NONE
stop_vapor_at_condenser_pool = true
startup_front_option = continuum_flow
D_collision = 0.362e-9
Kn_transition = 0.01
[]
[evaporator_boundary]
type = HSBoundaryExternalAppConvection
boundary = 'heat_pipe:hs:evap:outer'
hs = heat_pipe:hs
T_ext = virtual_Text
htc_ext = virtual_htc
[]
# This works but is simplified
# Improvement needed in the future
[condenser_boundary]
type = HSBoundaryAmbientConvection
boundary = 'heat_pipe:hs:cond:outer'
hs = heat_pipe:hs
T_ambient = ${T_ext_cond}
htc_ambient = ${htc_ext_cond}
[]
[]
[UserObjects]
[surf_T]
type = LayeredSideAverage
direction = z
num_layers = 180
variable = T_solid
boundary = 'heat_pipe:hs:evap:outer'
[]
[]
[AuxKernels]
[hp_var]
type = SpatialUserObjectAux
variable = hp_temp_aux
user_object = surf_T
[]
[virtual_Text]
type = ParsedAux
variable = virtual_Text
coupled_variables = 'T_solid master_flux virtual_htc'
expression = 'master_flux/virtual_htc + T_solid'
block = '3 4 5'
[]
[]
[AuxVariables]
[T_wall_var]
initial_condition = ${T_ext_cond}
[]
[operational_aux]
initial_condition = 1
[]
[master_flux]
initial_condition = 0
[]
[master_t_solid]
initial_condition = ${T_ext_cond}
[]
[hp_temp_aux]
initial_condition = ${T_ext_cond}
[]
[virtual_Text]
initial_condition = ${T_ext_cond}
[]
[virtual_htc]
initial_condition = 1.0
[]
[]
[Postprocessors]
[refill]
type = FunctionValuePostprocessor
function = '1'
execute_on = 'INITIAL TIMESTEP_END'
[]
[]
[Preconditioning]
[pc]
type = SMP
full = true
[]
[]
# Added dampers as some NAN behavior was observed
[Dampers]
[max_T]
type = MaxIncrement
increment_type = fractional
max_increment = 0.5
variable = T_solid
[]
[bd_rhoA]
type = BoundingValueElementDamper
variable = rhoA
min_value = 0.0
min_damping = 0.001
[]
[bd_rhoEA]
type = BoundingValueElementDamper
variable = rhoEA
min_value = 0.0
min_damping = 0.001
[]
[]
[Executioner]
type = Transient
scheme = bdf2
start_time = ${t_start}
end_time = ${t_end}
dtmin = 1e-4
dtmax = 5000
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.1
optimal_iterations = 15
iteration_window = 2
growth_factor = 2
cutback_factor = 0.8
[]
[Quadrature]
type = GAUSS
order = SECOND
[]
## PJFNK + superlu seems to make the problem converge faster
solve_type = PJFNK
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 101'
nl_abs_tol = 1e-8
nl_rel_tol = 1e-8
nl_max_its = 25
l_tol = 1e-3
l_max_its = 10
automatic_scaling = true
compute_scaling_once = false
[]
[Outputs]
exodus = false
[console]
type = Console
execute_postprocessors_on = 'NONE'
[]
[csv]
type = CSV
execute_on = 'INITIAL FINAL'
enable = false
[]
[]Steady-State Case Simulation
In the current Na-HPMR multiphysics model, only the steady-state case is simulated. Transient simulations are planned to be implemented in the near future.
References
- Joshua E Hansel, Carolina da Silva Bourdot Dutra, Lise Charlot, and Elia Merzari.
The liquid-conduction, vapor-flow heat pipe model in sockeye.
Nuclear Engineering and Design, 426:113359, 2024.[BibTeX]