SMR startup simulation (outdated)

Overview

In order to test and demonstrate the time dependent calculation capabilities of the Kraken framework in a reasonably realistic context, a time dependent simulation was conducted of the initial rise to power of a small modular reactor (SMR) core. The simulation used the Ants nodal neutronics code to resolve the evolution of neutronics and the xenon fission poison chain in the system and the SUBCHANFLOW thermal hydraulics code to solve the coolant flow and heat transfer in fuel rods.

The modelled SMR is the same 37 assembly Er-UO₂ fuelled core that has been previously used for the demonstration of the depletion capabilities of Kraken:

The transient starts from critical hot zero power (HZP) conditions (actually from 1 % power level) with all control rod banks at approximately 50 % insertion. The boron concentration in the coolant corresponds to the critical boron at all rods out (ARO) hot full power (HFP) conditions. The control rods are withdrawn from the core in a stepwise manner over 38 hours to allow for the accumulation of xenon in the core:

To reformulate the simulation setup:

• Evaluate (in a time-independent simulation) critical boron at hot full power all rods out conditions with convergence in
  • Neutronics
  • Thermal hydraulics
  • Fuel temperature
  • Xenon
• Using that critical boron, evaluate (in a time-independent simulation) critical control rod position at 1 % power level with convergence in
  • Neutronics
  • Thermal hydraulics
  • Fuel temperature
  • Xenon
• Save initial conditions from the 1 % power level time-independent calculation.
• Start a time dependent simulation from 1 % power level and slowly withdraw the control rods fully from the core.

If the time-independent and time-dependent calculation methodologies produce equivalent steady state solutions and have been correctly implemented, the simulation should (in the end) end up in the same state as the time-independent HFP ARO calculation.

Evaluating HFP ARO critical boron

The first part of the simulation is only needed here in order to obtain a more realistic and reasonable end state for the transient simulation by finding a realistic boron concentration for the coolant. The simulation is set up as a normal coupled steady state simulation between Ants and SUBCHANFLOW with Ants using its equilibrium xenon calculation mode and iterating the coolant boron concentration to reach a critical system. The system power is set to 50 MW, which corresponds to the nominal full power in the Er-UO₂ core.

The Cerberus input used for the calculation is included below and is a rather simple coupled calculation input. It may be interesting to note that since Ants is developed in the Kraken context, many of the basic input data can be sent to Ants via Cerberus (control rod positions, system power, xenon calculation mode, iteration mode etc.). The same Ants input is actually used for all of the simulations here with the relevant parts of the Ants model being modified via Cerberus instead of in the Ants input file. Conversely, as SUBCHANFLOW is developed by KIT and the Kraken-coupling is achieved via a VTT written SUBCHANFLOW wrapper the amount of possible input data accessible via Cerberus is more limited and the steady state simulations use a (very slightly) different input file for SUBCHANFLOW than the transient simulation.

Cerberus input for HPF ARO boron iteration

from os import environ
from pathlib import Path

import numpy as np

import cerberus as cb
from cerberus.solvers import CodeInput
from cerberus.solvers import Solver
from cerberus.interpolation import Interpolator
from numpy.core.fromnumeric import size

# Verbosity for terminal output of Cerberus

cb.LOG.set_verbosity(1)

# Create and start solvers

solver_defs = [["SCF", environ["SCFWRAP_EXE_PATH"], [], ["./Inputs/scf/input.txt"]],
               ["ANTS", environ["ANTS_EXE_PATH"], ["--cerberus","--port"], ["./Inputs/Ants8g.inp"]]]

solvers = {}

port_number = 2211

for name, solver_path, params, inputs in solver_defs:

    # Create input

    solver_input = CodeInput(name, inputs)

    # Create solver

    solver = Solver(name, solver_path, params)
    solver.input = solver_input
    solver.initialize(port_number)

    # Add to solver dict

    solvers[name] = solver

    port_number += 1

# Alias variables for solvers

scf = solvers["SCF"]
ants = solvers["ANTS"]

# Get SCF fields needed for coupled calculation

scf_cool_temperature = scf.get_transferrable("scf_of_cool_temperature_chan")
scf_cool_density = scf.get_transferrable("scf_of_cool_density_chan")
scf_fuel_temperature = scf.get_transferrable("scf_of_fuel_temperature_vol_ave")
scf_power = scf.get_transferrable("scf_if_fuel_power")

# Initialize SCF power field (50 MW divided uniformly over SCF cells)

scf_power.value_vec = 50e6/scf_power.n_values*np.ones(scf_power.n_values)

# Get Ants fields needed for coupled calculation

ants_cool_temperature = ants.get_transferrable("Ants_if_coolant_temperature")
ants_cool_density = ants.get_transferrable("Ants_if_coolant_density")
ants_fuel_temperature = ants.get_transferrable("Ants_if_fuel_temperature")
ants_power = ants.get_transferrable("Ants_of_supernode_power")
ants_boron = ants.get_transferrable("Ants_ov_boron")

# Create interpolators that handle data transfer between SCF and Ants

interp_ct = Interpolator.from_file(scf_cool_temperature,
                                   ants_cool_temperature,
                                   "./Inputs/scf_to_ants.txt")
interp_cd = Interpolator.from_file(scf_cool_density,
                                   ants_cool_density,
                                   "./Inputs/scf_to_ants.txt")
interp_ft = Interpolator.from_file(scf_fuel_temperature,
                                   ants_fuel_temperature,
                                   "./Inputs/scf_to_ants.txt")
interp_p = Interpolator.from_file(ants_power,
                                  scf_power,
                                  "./Inputs/ants_to_scf.txt")


################################################################################
################################################################################

# --- Coupled solution

max_iter = 50
for i in range(max_iter):
    # --- TH solution and communication

    scf_power.communicate()
    scf_power.write_simple(suffix_in=f"{i+1}")

    scf.solve()

    scf_cool_density.communicate()
    scf_cool_temperature.communicate()
    scf_fuel_temperature.communicate()

    # --- Transfers from SCF to Ants fields

    interp_ct.interpolate()
    interp_cd.interpolate()
    interp_ft.interpolate()

    # --- Neutronics solution and communication

    ants_cool_density.communicate()
    ants_cool_temperature.communicate()
    ants_fuel_temperature.communicate()

    ants.solve()

    ants_power.communicate()
    ants_boron.communicate()

    # --- Transfers from Ants to SCF

    interp_p.interpolate()

    print(f"Finished iteration {i+1}, boron is {ants_boron.value_vec[0]}")

# Choose field/value names to save

to_save = ["Ants_ov_keff", "Ants_ov_boron"]

# Output path. Create folder if necessary

output_path = Path(f"./output")
output_path.mkdir(exist_ok=True)
for name in to_save:
    tra = ants.get_transferrable(name)
    tra.communicate()
    tra.write_simple(suffix_in="final", folder_path=output_path)

As we can see from the Cerberus output, the coupled boron iteration convergences in a fast an orderly manner:

Part of Cerberus output for HPF ARO boron iteration

[...]
Finished iteration 1, boron is 241.11834260327765
Finished iteration 2, boron is 215.2718468141726
Finished iteration 3, boron is 185.87313896299054
Finished iteration 4, boron is 173.3774955249861
Finished iteration 5, boron is 168.31982440662546
Finished iteration 6, boron is 166.32566143451567
Finished iteration 7, boron is 165.53688601825667
Finished iteration 8, boron is 165.22148909016465
Finished iteration 9, boron is 165.09469219887114
Finished iteration 10, boron is 165.04377146272464
Finished iteration 11, boron is 165.02336734511618
Finished iteration 12, boron is 165.01519526345925
Finished iteration 13, boron is 165.01192023065747
Finished iteration 14, boron is 165.01060719962356
Finished iteration 15, boron is 165.01008083683476
Finished iteration 16, boron is 165.0098698863875
Finished iteration 17, boron is 165.00978535430409
Finished iteration 18, boron is 165.00975148002385
Finished iteration 19, boron is 165.00973790525023
Finished iteration 20, boron is 165.00973246547196
Finished iteration 21, boron is 165.00973028562368
Finished iteration 22, boron is 165.0097294122978
Finished iteration 23, boron is 165.00972906258608
Finished iteration 24, boron is 165.00972892269846
Finished iteration 25, boron is 165.00972886673708
Finished iteration 26, boron is 165.00972884457883
Finished iteration 27, boron is 165.0097288359729
Finished iteration 28, boron is 165.00972883267053
Finished iteration 29, boron is 165.0097288315528
Finished iteration 30, boron is 165.00972883133392
Finished iteration 31, boron is 165.0097288314835
Finished iteration 32, boron is 165.00972883169874
Finished iteration 33, boron is 165.00972883198824
Finished iteration 34, boron is 165.00972883232353
Finished iteration 35, boron is 165.0097288326507
Finished iteration 36, boron is 165.0097288330322
Finished iteration 37, boron is 165.0097288333984
Finished iteration 38, boron is 165.00972883373572
Finished iteration 39, boron is 165.00972883417126
Finished iteration 40, boron is 165.0097288345529
Finished iteration 41, boron is 165.00972883480839
Finished iteration 42, boron is 165.00972883514726
Finished iteration 43, boron is 165.00972883548843
Finished iteration 44, boron is 165.00972883586263
Finished iteration 45, boron is 165.0097288362657
Finished iteration 46, boron is 165.00972883654
Finished iteration 47, boron is 165.0097288368571
Finished iteration 48, boron is 165.00972883725518
Finished iteration 49, boron is 165.009728837629
Finished iteration 50, boron is 165.00972883798943

Evaluating critical control rod position at HZP fixed boron conditions

Cerberus input for HZP control rod iteration

Part of Cerberus output for HZP control rod iteration

[...]
Height is 150.0, keff is 1.0137994157229595 (based on 3 coupled iterations)
Height is 140.0, keff is 1.0097132150307848 (based on 3 coupled iterations)
Height is 130.0, keff is 1.004371680638068 (based on 3 coupled iterations)
Height is 120.0, keff is 0.9974297441040372 (based on 3 coupled iterations)
Height is 121.0, keff is 0.997992947986957 (based on 6 coupled iterations)
Height is 122.0, keff is 0.9986113787463294 (based on 6 coupled iterations)
Height is 123.0, keff is 0.999327881570897 (based on 6 coupled iterations)
Height is 124.0, keff is 1.000166398442108 (based on 6 coupled iterations)
Height is 123.9, keff is 1.0000762007919366 (based on 9 coupled iterations)
Height is 123.80000000000001, keff is 0.9999875162017355 (based on 9 coupled iterations)
Height is 123.81000000000002, keff is 0.9999963183709505 (based on 12 coupled iterations)
Height is 123.82000000000002, keff is 1.00000513516873 (based on 12 coupled iterations)
Height is 123.81900000000002, keff is 1.0000042528284148 (based on 15 coupled iterations)
Height is 123.81800000000001, keff is 1.000003370634821 (based on 15 coupled iterations)
Height is 123.81700000000001, keff is 1.0000024885879013 (based on 15 coupled iterations)
Height is 123.816, keff is 1.0000016066876227 (based on 15 coupled iterations)
Height is 123.815, keff is 1.0000007249339529 (based on 15 coupled iterations)
Height is 123.814, keff is 0.9999998433268541 (based on 15 coupled iterations)
Height is 123.8141, keff is 0.9999999314800674 (based on 18 coupled iterations)