Corresponding author: Rinat N. Shamsutdinov ( srn@sosny.ru ) Academic editor: Georgy Tikhomirov
© 2020 Rinat N. Shamsutdinov, Sergey V. Pavlov, Anton Yu. Leshchenko.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Shamsutdinov RN, Pavlov SV, Leshchenko AYu (2020) Development and verification of CFD model of carbothermal synthesis furnace for production of mixed nitride uraniumplutonium fuel. Nuclear Energy and Technology 6(1): 3742. https://doi.org/10.3897/nucet.6.51253

The retort batch furnace for the carbothermal synthesis of uranium and plutonium nitrides is a component of the mixed nitride uraniumplutonium (MNUP) fuel Fabrication/Refabrication Module (FRM), a part of the Pilot Demonstration Energy Complex (PDEC). A CFD model of the furnace was built in the SolidWorks Flow Simulation code to check the feasibility of its thermophysical operating modes (heating and cooling rates, temperature of the product loaded into the furnace). The experimental data obtained from the performance tests was used to verify the developed CFD model and to confirm its adequacy. The relative deviation of the calculated temperature of the loaded product from the experimental data in the process of isothermal annealing does not exceed 0.7%.
The temperatures of the loaded product predicted by the CFD model were used to justify engineering solutions for the uranium and plutonium nitrides carbothermal synthesis furnace. The CFD model can be used to define the furnace operation mode by selecting the gas flow rates inside and outside the retort, the heater temperature, and heating and cooling rates for the product loaded in the furnace.
CFD model, MNUP fuel, SolidWorks Flow Simulationv, furnace, carbothermal synthesis, mathematical model, grid model
For the past three decades, there has been an increasing tendency to use the Computational Fluid Dynamics (CFD) methods for computational justifications of engineering solutions in designing various industrial facilities (
Unlike other industries, the nuclear industry took the report by the joint technical meeting of the International Atomic Energy Agency (IAEA) and the Nuclear Energy Agency (NEA) held in Pisa, Italy, on 11 through 14 November 2002 as the starting point for a more extensive application of the CFD codes for computational studies and safety justifications of technologies (
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 CFD code, SolidWorks Flow Simulation (
The retort batch furnace for the carbothermal synthesis of uranium and plutonium nitrides, a 3D model of which is shown in Fig.
The furnace is designed to produce uranium and plutonium nitrides via carbonbased carbothermal reduction of uranium and plutonium dioxides in nitrogen and nitrogenhydrogen 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 H, the length L, and the width S, nitrogen with the temperature T_{ni} is fed into the retort space, and argon with the temperature T_{ar} is fed into the space behind the retort with the respective flow rates Q_{r} and Q_{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 Т_{h} followed by their isothermal annealing and cooling. A lining of the thickness H_{l}, on the outer surface of which there is a system of water cooling tubes with the overall flow rate Q_{w}, is used as the thermal insulation for the furnace hearth. Key assumptions: liquid and gases are considered to be singlephase 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 nonsteadystate and steadystate 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 CFD problem solving, the SolidWorks Flow Simulation code has a number of advantages the most prominent of which are
The developed CFD model of the furnace consists of a mathematical model and a grid model.
Reynoldsaveraged NavierStokes 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 (
$\frac{\partial \rho}{\partial t}+\frac{\partial \left(\rho {u}_{i}\right)}{\partial {x}_{i}}=0$
$\frac{\partial \left(\rho {u}_{i}\right)}{\partial t}+\frac{\partial \left(\rho {u}_{i}{u}_{j}\right)}{\partial {x}_{j}}+\frac{\partial P}{\partial {x}_{i}}=\frac{\partial \left({\tau}_{ij}+{\tau}_{ij}^{R}\right)}{\partial {x}_{j}}+{S}_{i}$
$\frac{\partial \rho H}{\partial t}+\frac{\partial \rho {u}_{i}H}{\partial {x}_{i}}=\frac{\partial \left({u}_{j}\left({\tau}_{ij}+{\tau}_{ij}^{R}\right)+{q}_{i}\right)}{\partial {x}_{i}}+\frac{\partial p}{\partial t}{\tau}_{ij}^{R}\frac{\partial {u}_{i}}{\partial {x}_{j}}+\rho \epsilon +{S}_{i}{u}_{i}+{Q}_{H}$
H = h + u^{2}/2,
where u is the fluid velocity; ρ is the fluid density; P is the fluid pressure; S_{i} is the external mass forces acting on the fluid unit mass; H is the total energy of the fluid unit mass; Q_{H} is the heat emitted by the source in the fluid unit volume; τ_{ij} is the tensor of elastic shear stresses; and q_{i} is the diffusion heat flux.
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 twoparameter turbulence model, k–ε (
Heat transfer in solidstate bodies is simulated using the equation
$\frac{\partial \rho cT}{\partial t}=\frac{\partial}{\partial {x}_{i}}\left({\lambda}_{i}\frac{\partial T}{\partial {x}_{i}}\right)+{Q}_{H}$
where c is the specific heat capacity; T is the temperature; λ is the thermal conductivity coefficient; and Q_{H} is the specific (volumetric) heat generation by the heat source.
Heat exchange by radiation is simulated in accordance with the StefanBoltzman law:
Q_{H} = εσ_{0}(T_{w}^{4} – T_{s}^{4}),
where ε is the surface emissivity factor; σ_{0} is the StefanBoltzman constant; T_{w} is the radiationemitting surface temperature; and T_{s} is the environment temperature. The thermophysical properties of the furnace materials, gas and water (density, heat capacity, thermal conductivity coefficient, surface emissivity factor) were defined according to references (
In the case of coupled heat transfer, into account is taken of the heat flux between the solidstate body and the liquid (gas), the solidstate body wall temperature, the nearwall 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: T (x, y, z, 0) = 20 °C, and the gas and water pressure and velocity: P (x, y, z, 0) = 101325 Pa and V (x, y, z, 0) = 0 m/s, where x, y, z are their coordinates, were preset as the boundary conditions.
The Derichlet’s boundary conditions: T(x_{h}, y_{h}, z_{h}, t) = T_{i} = const, where x_{h}, y_{h}, z_{h} are the heater surface coordinates, and T_{i} is the value of the heater temperature et each time i, are defined for the heater surface (Fig.
∂V (x_{out}, y_{out}, z_{out}, t) / ∂n = 0,
∂T (x_{out}, y_{out}, z_{out}, t) / ∂n = 0,
∂P (x_{out}, y_{out,}z_{out}, t) / ∂n = 0,
where n is the vector of the normal to the boundary; and x_{out}, y_{out}, z_{вout} are the coordinates of the outlet tubes. The Derichlet’s boundary conditions for the pressure P (x_{b}, y_{b}, z_{b}, t) = 101325 Pa, the temperature T (x_{b}, y_{b}, z_{b}, t) = 20 °C, and the air velocity V (x_{b}, y_{b}, z_{b}, t) = 0 m/s, where x_{b}, y_{b}, z_{b} are the coordinates of the computational domain boundary, and t is the time, are defined for the computational domain boundary (see Fig.
V (x_{s}, y_{s}, z_{s}, t) = 0 m/s, ∂Φ / ∂n = 0,
where n is the vector of the normal to the symmetry boundary; and x_{s}, y_{s}, z_{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 parallelepipedshaped (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 secondorder accuracy (modified implicit Leonard QUICKapproximation (
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 solidstate body and fluid contact region is used to resolve relatively small geometrical features of the grid model. Regions with temperature gradients in solidstate bodies of the computational model (boats with the loaded product, the retort, nitrogen supply tubes, etc.) are solved in the same way.
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 CFD furnace model. The purpose of the experimental study is to estimate the temperature distribution on the loaded product in the boats during different temperature modes of the furnace operation (heating, annealing, and cooling). Five tungsten boats were placed inside the furnace retort, into which simulators of product (silica brick) with similar thermophysical properties were loaded instead of compacted uranium and plutonium dioxide powders. A mode close to the furnace commercial operation conditions was chosen for the experiment. Temperature values on the heaters and the loaded product, values of the nitrogen flow rates fed into the retort and into the space behind the retort, and the water flow rate in the furnace body water cooling circuit were recorded during the test. The loaded product temperatures were measured using three tungstenrhenium thermocouples with a temperature measurement accuracy of ± 5 °C in a range of 0 to 1000 °C and ± 0.005×t for the range of 1000 to 1950 °C (t is the measured temperature value). The working ends of the two thermocouples (hot junctions) were contained inside the boats at the extreme positions (boat 1 and boat 5), resting on the loaded product surface and at a distance of ~15 mm from the boat outer wall – area 1 and area 3 respectively (Fig.
The dependences of the loaded product temperature in the furnace boats at the thermocouple locations on time (Figs
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.
The obtained values of the relative deviation between the calculated and experimental data indicate that the accuracy of the calculations based on a CFD furnace model is sufficiently high.
1. A CFD model of a furnace for the carbothermal synthesis of uranium and plutonium nitrides has been developed in the SolidWorks Flow Simulation code, which makes it possible to simulate thermophysical modes of the furnace operation (heating, annealing and cooling of the loaded product) without regard for the physicochemical transformations taking place in the loaded fuel carbothermal synthesis process.
2. The developed CFD furnace model has been verified and its adequacy has been confirmed based on the experimental temperature test data for the uranium and plutonium nitrides carbothermal synthesis furnace. The relative deviation between the values of the calculated loaded product temperature in the boats at the extreme positions and in the central boat and the experimental data in the isothermal annealing process is 0.7% and 0.1% respectively. The estimated values of the loaded product temperature obtained using the developed CFD furnace model were used to justify the designs adopted for the uranium and plutonium nitrides carbothermal synthesis furnace. These results can be also used to simulate the kinetics of the MNUP fuel carbothermal synthesis reaction in the nitrogen (hydrogennitrogen mixture) flow in this furnace.
3. The developed CFD model of the uranium and plutonium nitrides carbothermal synthesis furnace can be used to choose the furnace operating mode by selecting among the values of the process gas flow rates fed into the furnace’s retort area and into the space behind the retort, the heater temperature, and the loaded product heating and cooling rates. The CFD model was used in the process of developing and justifying the serviceability of the commercial furnace design. The results obtained using the CFD model are a part of the detailed design documentation (DDD) and the technical reports for the considered furnace.