pyChannelJFNK

A coupled neutronics, thermal-hydraulics, and pin heat transfer solver for a single fuel channel in a sodium-cooled fast reactor (SFR), using the Jacobian-Free Newton-Krylov (JFNK) method.

Overview

pyChannelJFNK solves the steady-state coupled multiphysics problem for a representative fuel channel by simultaneously resolving:

• Multi-group neutron diffusion -- axial diffusion with temperature-dependent cross-sections and eigenvalue (k-eff) calculation
• Thermal-hydraulics -- mass and energy conservation for liquid sodium coolant with friction, acceleration, and gravity pressure drops
• Pin heat transfer -- 1D radial heat conduction through the fuel pellet, gap, and cladding with convection to the coolant

The three physics are tightly coupled through a JFNK solver that uses GMRES as the inner Krylov iteration, avoiding the need to explicitly form or store the Jacobian matrix.

Project Structure

pyChannelJFNK/
├── channel_solver.py          # Main entry point
├── JFNK.py                   # JFNK solver (Newton + GMRES)
├── initialize.py              # Input parsing and domain discretization
├── res_coupled.py             # Coupled residual assembly
├── res_nk_rel.py              # Neutron diffusion residuals
├── res_th_rel.py              # Thermal-hydraulics residuals
├── res_pin_rel.py             # Pin heat transfer residuals
├── XS_parametrization.py      # Cross-section library interface (HDF5)
├── thermo_Na.py               # Sodium thermophysical properties
├── matpro.py                  # Fuel and cladding material properties
├── correlations.py            # Heat transfer and friction correlations
├── input.yml                  # Case input parameters
├── dump.yml                   # Output dump configuration
├── XS_data.hdf5               # Multi-group cross-section library
└── LICENSE                    # GPLv3

Installation

Python 3.8+ is required. Install the dependencies with:

pip install -r requirements.txt

Usage

Configure the problem in input.yml, then run:

python channel_solver.py

Input Parameters (input.yml)

Section	Parameter	Description	Default
boundary_conditions	T_in	Inlet coolant temperature [K]	673
	v_in	Inlet velocity [m/s]	7.5
	p_out	Outlet pressure [Pa]	1.5
	qp_ave	Average linear power [W/m]	3.0e4
geometry	H	Channel height [m]	1.6
	Rfo	Fuel outer radius [m]	3.57e-3
	Rci	Cladding inner radius [m]	3.685e-3
	clad_thickness	Cladding thickness [m]	5.65e-4
	pin_pitch	Pin pitch (triangular lattice) [m]	9.8e-3
discretization	axial_nodes	Number of axial nodes	25
	radial_nodes_pin	Radial nodes in fuel pellet	5
numerics	tol_newton	Newton iteration tolerance	1.0e-8
	tol_krylov	GMRES (Krylov) tolerance	1.0e-7

Output

The solver prints the converged solution split into three vectors:

• sol_nk -- Neutron group fluxes and eigenvalue
• sol_th -- Coolant temperatures and velocities along the channel
• sol_pin -- Radial temperature distribution in the fuel pin at each axial level

Method

The JFNK approach works as follows:

1. Outer loop (Newton): Linearizes the coupled nonlinear residual system around the current iterate
2. Inner loop (GMRES): Solves the linear system using Krylov subspace iterations, where Jacobian-vector products are approximated via finite differences:

$$Jv \approx \frac{F(x + \epsilon v) - F(x)}{\epsilon}$$

This avoids forming the full Jacobian while retaining Newton-level convergence.

Material and Correlation Models

• Sodium properties -- density, specific heat, thermal conductivity, dynamic viscosity, and enthalpy from Sobolev correlations (SCK-CEN)
• Fuel conductivity -- ORNL MOX/UO2 model accounting for burnup and porosity
• Cladding conductivity -- AISI 316 stainless steel
• Friction factor -- Engel correlation for wire-wrapped bundles
• Gap conductance -- Pellet-cladding gap heat transfer model
• Cross-sections -- Temperature-parametrized multi-group data from HDF5 library

License

This project is licensed under the GNU General Public License v3.0.