Corresponding author: Rinat N. Shamsutdinov (srn@sosny.ru)

Academic editor: Georgy Tikhomirov

The retort batch furnace for the carbothermal synthesis of uranium and plutonium nitrides is a component of the mixed nitride uranium-plutonium (

The temperatures of the loaded product predicted by the

For the past three decades, there has been an increasing tendency to use the Computational Fluid Dynamics (

Unlike other industries, the nuclear industry took the report by the joint technical meeting of the International Atomic Energy Agency (

As part of the retort batch furnace design for the carbothermal synthesis of uranium and plutonium nitrides, requirements were defined for the thermophysical modes of the furnace operation, such as heating and cooling rates, the temperature of the product loaded into the furnace, flow rates of process gases overpressure, and others. To check the feasibility of the thermophysical modes set for the retort batch furnace operation, a need arose for building a computational thermophysical model. A

The retort batch furnace for the carbothermal synthesis of uranium and plutonium nitrides, a 3D model of which is shown in Fig.

3D model of the carbothermal synthesis furnace: 1, 6 – inlet (outlet) gate valves; 2 – furnace body water cooling circuit; 3 – furnace gas discharge pipe; 4 – electric heaters; 5 – furnace body; 7 – retort; 8 – boats with loaded product; 9 – lining.

The furnace is designed to produce uranium and plutonium nitrides via carbon-based carbothermal reduction of uranium and plutonium dioxides in nitrogen and nitrogen-hydrogen atmosphere at temperature of 1650 ± 50 °С. The retort batch furnace design and the carbothermal synthesis process are described in (

In a retort batch furnace of the height _{ni} is fed into the retort space, and argon with the temperature _{ar} is fed into the space behind the retort with the respective flow rates _{r} and _{b}. In the process of the heat transfer from the heaters installed inside the space behind the retort, the simulators of product loaded into the boats, which are placed inside the furnace retort, are heated to the given temperature _{h} followed by their isothermal annealing and cooling. A lining of the thickness _{l}, on the outer surface of which there is a system of water cooling tubes with the overall flow rate _{w}, is used as the thermal insulation for the furnace hearth. Key assumptions: liquid and gases are considered to be single-phase incompressible Newtonian continuums, and the inner and outer walls of the wetted parts are considered to be hydraulically smooth surfaces. We need to find the temperature distribution within the furnace during non-steady-state and steady-state modes of operation.

The SolidWorks Flow Simulation code was selected to solve the problem at hand. In a broad range of commercial software products for the

application of a rectangular structured computational grid (Sobachkin and Dumnov 2014);

capability to simulate complex geometries of the calculated assemblies;

user friendliness and a self-explanatory interface.

The developed

Reynolds-averaged Navier-Stokes equations are used in the SolidWorks Flow Simulation as the mathematical model’s base equations to describe the motion and heat exchange in liquid and gas in a 3D case. The mass, impulse and energy conservation laws for these fluids (

^{2}/2,

where _{i}_{H}_{ij}_{i}

These equations are supplemented with a gas or liquid state equation and with dependences of density, viscosity, heat capacity and thermal conductivity coefficient on temperature. A two-parameter turbulence model,

Heat transfer in solid-state bodies is simulated using the equation

where _{H}

Heat exchange by radiation is simulated in accordance with the Stefan-Boltzman law:

_{H}_{0}(_{w}^{4} – _{s}^{4}),

where ε is the surface emissivity factor; σ_{0} is the Stefan-Boltzman constant; _{w}_{s}

In the case of coupled heat transfer, into account is taken of the heat flux between the solid-state body and the liquid (gas), the solid-state body wall temperature, the near-wall layer characteristics, and the heat exchange by radiation (where required).

The initial and boundary conditions are defined to close the system of differential equations. The furnace material, gas and water temperature:

The Derichlet’s boundary conditions: T(_{h}, _{h}, _{h}, _{i}_{h}, _{h}, _{h} are the heater surface coordinates, and _{i}_{w}, _{w}, _{w}, _{w}, _{w}, _{w}, _{w}, _{w}, _{w} are the coordinates of the gas supply and water cooling surfaces, are defined for the surfaces of the nozzles for the gas supply into the retort space and into the space behind the retort, and for the surfaces of the water cooling tubes. The Newmann’s boundary condition are defined for the outlet of the tubes for the gas supply into the retort area and into the space behind the retort and for the outlet of the water cooling tubes

∂_{out}, _{out}, _{out},

∂_{out}, _{out}, _{out},

∂_{out}, _{out,}_{out},

where _{out}, _{out}, _{вout} are the coordinates of the outlet tubes. The Derichlet’s boundary conditions for the pressure _{b}, _{b}, _{b}, _{b}, _{b}, _{b}, _{b}, _{b}, _{b}, _{b}, _{b}, _{b} are the coordinates of the computational domain boundary, and

_{s}, _{s}, _{s},

where _{s}, _{s}, _{s} are the coordinates of the symmetry boundary.

Finite volume method is used to discretize the resultant system of differential equations in the SolidWorks Flow Simulation code. The test item is presented as a grid model the cells in which are parallelepiped-shaped (the values of independent variables are calculated at the cell centers, and the mass, impulse, and energy flows are calculated on the cell faces). Linearized equations describing the conservation law for the investigated scalar physical quantity are written for each cell. Spatial derivatives are approximated using implicit difference operators of the second-order accuracy (modified implicit Leonard QUICK-approximation (

To save the computational resources, a furnace half (see Fig.

The grid convergence was studied to estimate the dependence of the calculated temperature values for the furnace’s local regions on the size of the grid model. Fig.

Local fragmentation of the grid cells in the solid-state body and fluid contact region is used to resolve relatively small geometrical features of the grid model. Regions with temperature gradients in solid-state bodies of the computational model (boats with the loaded product, the retort, nitrogen supply tubes, etc.) are solved in the same way.

Computation region of the

Grid convergence investigation.

The results of temperature testing the retort batch furnace for the carbothermal synthesis of uranium and plutonium nitrides were used to check the adequacy of the developed

Boats 1 through 5 shown inside the furnace retort.

The dependences of the loaded product temperature in the furnace boats at the thermocouple locations on time (Figs

Temperature of the loaded product in the boats at the extreme positions inside the retort (areas 1 and 3).

Temperature of the loaded product in the central boat inside the retort (area 2).

It can be seen in Figs

The maximum relative deviation of the calculated average rate of the loaded product heating in the central boat and in the boats at the extreme positions from the experimental value for the time span of 0.15 to 0.33 rel. units is 7.6 and 3.6% respectively.

The maximum relative deviation of the calculated average rate of the loaded product cooling in the central boat and in the boats at the extreme positions from the experimental value after 0.45 rel. time units is 10 and 6% respectively.

Fig.

0.7% in the boats at the extreme positions;

and 0.1% in the central boat.

The obtained values of the relative deviation between the calculated and experimental data indicate that the accuracy of the calculations based on a

Loaded product surface temperature profile in the isothermal annealing process: –––– – calculation; ♦ – experiment (a screenshot).

1. A

2. The developed

3. The developed

^{rd}Intern. Conf. on Exascale Applications and Software. Edinburgh: 92–97.

* Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2019, n. 4, pp. 130–141.