Corresponding author: Aleksey A. Zaytsev (AlexeyZaycev@ssl.obninsk.ru)
Academic editor: Boris Balakin
The article gives a general description of the SIMCO calculation code designed to simulate thermohydraulic and physicochemical processes in containments of nuclear power facilities. The authors present a calculation technique based on a physicomathematical model in lumped parameters. As a numerical solution method, the modified semiimplicit SIMPLER procedure is used. The code was examined using analytical and qualitative tests. A comparison of the numerical and analytical solutions showed good agreement. The code was verified using the experimental data obtained at the NUPEC installation (Japan). Based on the results of testing and verification, it was concluded that, in general, physicomathematical code models adequately describe the processes of heat/mass transfer in the containment. Therefore, this SIMCO code version can be used to analyze the totality of thermophysical and physicochemical processes in nuclear power facilities with containments, including the transfer of hydrogen/steam/air mixtures.
Modernization of existing and development of new nuclear power plants meeting the increased requirements for reliability, safety and economical efficiency make it necessary to improve the calculation methods for reactors, heat exchange equipment as well as safety and accident localization systems. The containment is the fourth, final safety barrier to the spread of radioactive products to the environment. It is designed in accordance with regulatory documents, and heat/mass transfer processes in the containment during lossofcoolant accidents (LOCA) are complex spatial in nature: they are characterized by numerous thermal, physical and chemical phenomena that determine the safety system effectiveness and reliability. For this reason, research processes in the containment become an integral part of design works. For new generation NPPs, special attention is paid to hydrogen fire/explosion safety (
To simulate containment of NPPs, it is possible to use the SIMCO code originally developed as the KUPOLM code realtime version (
Simulating is performed using an arbitrary topology of control volumes inside the containment area.
The following basic values are calculated:
time changes of temperature and gas pressure in the containment;
nonstationary temperature distribution in the walls and equipment;
timedensity dependences of nitrogen, oxygen, steam, hydrogen, helium, carbon dioxide, carbon monoxide, an arbitrary inert component, and fine moisture in the containment;
steam condensation intensity and condensate temperature in each compartment;
temperature of water drained to the lower compartment trays;
gas mixture flowrate in penetrations between the compartments.
The calculation takes into account the effects of unsteady gas mixture heat/mass transfer, steam volume/surface condensation, gas mixture natural convection as well as the operation of the sprinkler system and passive catalytic hydrogen recombiners, pumps and ventilation systems.
Applicability constraints:
The use of the SIMCO code is limited to the region of atmospheric thermodynamic parameters in the containment in case of LOCAs at NPPs.
The code requires the following boundary conditions: flowrate and enthalpy (temperature) of the steamwater mixture entering under the containment from the leak;flowrates and temperatures of steamgas components entering the compartments;exhaust ventilation flowrate;flowrate and enthalpy of water supplied to the sprinklers.
Acceptable values of the gasmixture parameters: pressure from 0.07 to 1.5 MPa;temperature from 275 to 1200 K.
The mathematical model of heat/mass transfer in the containment (
The numerical solution to the obtained system of equations is carried out on the basis of the modified semiimplicit procedure SIMPLER (
The finitedifference system of algebraic equations, which generally has a sparse matrix of coefficients, is directly solved by the Gauss method or the lower relaxation method. The differential equation for the steamgas mixture flowrate in the bonds is solved by the RungeKutta method. The heat equation for the walls, approximated by an implicit difference scheme, is solved by the sweep method.
Let us consider the analytical solution of the linear problem of gas compression in an open vessel under external constant pressure. In order to linearize the problem, we neglect the gas temperature change due to the external influence, then the equation of motion can be written as
where
The gas density equation in an open vessel is as follows
where
Using the universal gas law, we replace the pressure in the vessel in equation (1) with the density and, after time differentiation, obtain
where
Assuming that the gas in the vessel is identical to the external gas and considering the initial conditions
we obtain the following solution to the equation
where λ = (4
The numerical simulation of this test was carried out using a twobox nodalization scheme with a linearized model for the equation of motion in the isothermal approximation. The external environment is simulated by the larger box, the volume of which is several orders of magnitude greater than the that of the open vessel. With equal initial gas densities in the boxes, the required pressure drop is created due to the weight of the gas column in the larger box.
The equation of gas density in an open vessel (2) is valid only for positive rate values (gas enters the open vessel from the environment), since the environmental gas density in the right hand side of this equation is constant. Therefore, the numerical solution is compared with the analytical solution in the initial period of time. The geometric characteristics of the nodalization scheme are given in Tab.
The input data for the “gasdynamic spring” test
Upper box volume, m^{3}  10^{6} 
Lower box volume, m^{3}  1.0 
Upper box height, m  10.0 
Bond flow cross section, m^{2}  0.1 
Characteristic bond length, m  1.0 
Hydraulic resistance coefficient, m/s  0.5 
Initial gas density, kg/m^{3}  1.0 
Temperature, K  333 
Gas molecular mass, kg/mol  0.028 
The dependence of the absolute solution error is shown in Fig.
Difference between the analytical and numerical solutions
The numerical solution after the time point τ > 0.03 s is oscillatory. Damping of oscillations occurs as a result of the mechanical power dissipation due to hydraulic resistance. In real objects described by the square resistance law (as well as an increase in temperature due to the work of external compression forces), oscillations damp out much faster.
Let us consider the circulation loop (its nodalization scheme is shown in Fig.
Nodalization scheme of the closed “natural circulation” loop
The loop is thermally insulated, there are no heat and mass sources, the gas is homogeneous.
With the height invariable dencity gas inside the box, the pressure throughout its height varies linearly. If the pressure drop across the top bond is zero, then the gas density in both branches at the top elevation is the same and equal to r_{0}. The pressure in the left branch at the “0 m” elevation is equal to Р_{0} + 40r_{0}
Figures
Parameters of the closed “natural circulation” loop
Box  1  2  3  4  5 
Box floor elevation, m  0.0  0.0  10.0  20.0  30.0 
Box ceiling elevation, m  40.0  10.0  20.0  30.0  40.0 
Box initial gas density, kg/m^{3}  1.14  1.14  1.14  1.14  1.14 
Bonds  
Bond cross section, m^{2}  0.1  
Bond hydraulic resistance coefficient  0.5 
Occurrence of a stationary “parasitic” natural circulation in the loop (the model ignores the gas compressibility inside the box)
Absence of a stationary circulation in the loop (SIMCO code model)
The gas “parasitic” circulation rate in the loop without sources approximates to 0.7 m/s. The SIMCO code model, which takes into account the steamgas mixture compressibility in the calculated box volume, after the transient stage associated with the initial conditions, shows the absence of a “parasitic” circulation in the system of connected boxes. The transient period duration is determined by the hydraulic characteristics, box geometry and gas mixture composition. Thus, the incorrectness of the physicalmathematical natural gas convection model can lead to significant errors in calculations of circulation loops in the containment, which is especially important when stratified flows are calculated in the hydrogen safety analysis.
The code was verified using the experimental data obtained at the NUPEC installation (Japan). The NUPEC integrated installation is a model of a PWR containment (linear scale 1: 4) with a volume of 1300 m^{3} (height = 17.4 m; internal diameter = 10.8 m). The inner space of the containment is divided into 25 compartments simulating the interior of the prototype containment.
Table
Rooms characteristics




4.54  5.95  2.097  3.316 
6.76  14.95  3.200  2.213 
13.06  28.91  3.200  2.213 
14.84  32.84  3.200  2.213 
14.84  32.84  3.200  2.213 
13.06  28.91  3.200  2.213 
4.88  10.80  3.200  2.213 
5.72  12.66  3.200  2.213 
1.46  3.74  3.200  2.563 
5.72  12.66  3.200  2.213 
4.88  10.80  3.200  2.213 
28.10  53.05  5.425  1.888 
28.10  53.05  5.425  1.888 
4.88  9.22  5.425  1.888 
5.72  10.80  5.425  1.888 
1.46  2.14  5.775  1.463 
5.72  10.80  5.425  1.888 
4.88  9.22  5.425  1.888 
12.70  24.14  5.425  1.900 
1.465  2.01  7.325  1.371 
1.47  2.016  7.325  1.371 
1.46  5.44  7.250.  3.725. 
1.47  2.016  7.325  1.371 
1.465  2.01  7.325  1.371 
91.8  931.3  7.325  12.1175. 
Total  1312.272 
A series of integral experiments were conducted on this experimental installation. In contrast to the experiments on the HDR installation (
The necessary initial conditions in the compartments of the containment model (1.4 bar, 70 °C) were provided by preliminary heating due to steam supply for 3.5 hours. During the experiment, the steamhelium mixture was fed with a linear change in the flow of the components. The steam flow decreased from 0.08 to 0.03 kg/s during the injection period of 30 minutes. The helium flow during the same period increased from zero to a maximum (0.03 kg/s) and again decreased to zero. The supplied sprinkler water flow was kept constant for 30 minutes being equal to 19.4 kg/s.
According to (
pressure in the experimental installation;
two points on the steamgas mixture temperature;
two points on the light component (helium) local concentrations.
Although the initial conditions in the containment model established as a result of preheating contain a number of uncertainties, it is possible to verify the code using available experimental data.
A compartment with a steam/helium leak was simulated by two calculated volumes.
Figures
Pressure dynamics in the M71 experiment
Helium concentration dynamics in the compartment with steamhelium mixture leak in the M71 experiment
Helium concentration dynamics in the dome space in the M71 experiment
The maximum discrepancies between the calculated and experimental data for the gas mixture pressure and temperature are observed at the sprinkler system shutdown stage. Similar results for this period of the experiment were obtained when calculations were made by other containment codes (
The SIMCO code version 1.0 was developed at the Experimental ScientificResearch and Methodology Center “Simulation Systems” (SSL). Based on the results of testing and verification calculations, it may be concluded that physicomathematical code models quite adequately describe the processes of heat/mass transfer in the containment. The described SIMCO code version can be used to analyze the totality of thermophysical and physicochemical processes in nuclear power facilities with containments.
✩ Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 02043327), 2018, n. 2, pp. 114126.