Research Article 
Corresponding author: Ruslan M. Sledkov ( sledkov@grpress.podolsk.ru ) Academic editor: Yury Korovin
© 2022 Ruslan M. Sledkov, Valery Ye. Karnaukhov, Oleg Ye. Stepanov, Mark M. Bedretdinov, Igor A. Chusov.
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:
Sledkov RM, Karnaukhov VYe, Stepanov OYe, Bedretdinov MM, Chusov IA (2022) Results of validation and crossverification of the ROK/B design code on the problem of loss of cooling in the spent fuel pool ^{*}. Nuclear Energy and Technology 8(2): 107113. https://doi.org/10.3897/nucet.8.87809

The procedures of validation and crossverification of the newly developed computational code ROK/B are described. The main problem solved using the ROK/B code is the substantiation by calculation of the coolant density in the spent fuel pool (SFP) and the temperature regime of the fuel assemblies during a protracted shutdown of the cooling systems (break in the supply of cooling water). In addition to the above, it is possible to use the ROK/B code to carry out calculation of an accident with the discharge of the coolant from the SFP with simultaneous prolonged shutdown of the cooling systems.
The ROK/B code allows carrying out calculations for various types of designs of the fuel assemblies and VVER reactors, in particular, VVER1000, VVER1200 and VVER440 power units with single and twotiered fuel assembly arrangement, with clad pipes in racks (for compacted assemblies storage) and pipes without cladding, with cased assemblies and caseless ones.
During fuel reloading, a high level of the coolant is maintained, which makes it possible to do “wet” transportation of the assemblies from the reactor to the SFP. The mathematical model for heat and mass transfer calculation, including the boiling coolant model, implemented in the ROK/B code, includes: the motion equation, equations for calculating the enthalpy along the height of the fuel section of a fuel assembly with natural circulation of coolant within the channel containing the fuel assembly (lifting section) and in the interchannel space (lowering section), the equation of mass balance between the channels of the racks with assemblies and in the interassembly space and the amount of evaporated (and outflowed) water, the heat balance equation for a fuel rod in a steam environment. The system of equations is supplemented by closing relations for calculating the thermal physics properties of water and steam, fuel and cladding materials, as well as the coefficients of heat transfer from the wall to the steam, hydraulic resistance and density of the steamwater mixture in the channels, and the heat released in the reaction of steam with zirconium.
Validation of the computational code was carried out on the basis of the data of the ALADIN experiment performed by German specialists and the data of JSC OKB Gidropress. Crossverification of the ROK/B code was carried out in comparison with the results of calculation using the KORSAR/GP and SOKRAT/B1 codes. Based on the results of the validation, it has been concluded that the deviation of the ROK/B results from the experimental data is not more than 2 to 10% (10% for the option with a fuel rod power of 20 W). Based on the results of crossverification, it has been concluded that the discrepancy between the ROK/B results and the calculation results for the KORSAR/GP and SOKRAT/B1 codes is not more than 0.5% (for SOKRAT/V1) and less than 10% (for KORSAR/GP).
Spent fuel pond, ROK/B code, KORSAR/GP, SOKRAT/V1, loss of cooling, VVER, swelling, validation, fuel rod, fuel assembly
In connection with the fact that spent fuel assemblies (SFA) continue to evolve decay heat for as long as many years after they are withdrawn from the reactor, the spent fuel storage systems in the NPP designs include spent fuel pools (SFP) used to cool fuel for several years before it is shipped for disposal and recycling. The key purpose of SFPs is to reduce the FA activity and to remove decay heat. We shall note that the SFP design includes an SFA cooling system (
Beyonddesignbasis accidents can be expected to involve an admissibly prolonged failure of all active normaloperation channels and safety systems, which may lead to a severe accident scenario in the event when the spent fuel pool cannot be provided with makeup water in a timely manner using alternative designbasis technology (mobile machinery) (Phenomena Identification and Ranking Table). In Japan in 2011, for example, most of the critical safety components at the Fukushima Daiichi site were lost or severely damaged as the result of the beyonddesignbasis ocean wave impact (
The experimental studies used to verify Russian and foreign thermalhydraulic codes with the coolant parameters typical of the SFP emergencies include experiments undertaken at a reflooding test facility at OKB Gidropress in the 1960s and the 1990s (
The key issue addressed by the upgraded ROK/B code is to justify analytically the coolant density value in the SFP and the assembly temperature behavior during longterm failure of cooling systems (loss of cooling water). Besides, the ROK/B can be used for calculations for an accident with the SFP coolant escape involving a simultaneous longterm failure of the cooling systems.
The ROK/B validation in this study was based on the above experimental results. We shall note that the use of dedicated programs is a common practice within design organizations and is dictated by the need to:
Some examples of dedicated codes are STAR1, TIGRSK, TIGRSP and the ROK/B code presented by the authors (developed in 1990, in the process of upgrading since 1995).
This study aimed to:
We shall consider in brief the description of the ROK/B physical and mathematical models. The geometry of the region of interest is shown in Fig.
It is assumed that the SFP forced cooling system stops to operate at time t = 0 and cooldown is only through natural convection. The driving pressure drop is defined entirely by the temperature difference in the SFA lower and upper parts. The coolant boils up locally as it reaches the saturation temperature, this leading to the need to calculate the steamwater mixture parameters. We shall note another important circumstance imposed by the SFP design: the initial conditions for the second tier calculation with a twotier SFA arrangement are the coolant and steam flow rates obtained in the first tier calculations.
The mathematical model to calculate the heat and mass exchange, including the ROK/B coolant boiling model, includes
$\Delta {P}_{fr}+\Delta {P}_{ac}+{\int}_{0}^{{n}_{ch}}{\rho}_{mix}\left(z\right)gdz={H}_{ic}{\rho}^{\u2019}g$ (1)
$i\left(z\right)={i}_{in}+\frac{{Q}_{FA}}{{H}_{FA}{G}_{c}}{\int}_{0}^{z}q\left(z\right)dz$ (2)
$\frac{1}{2}\sum _{k=1}^{m}{\left[{\int}_{0}^{{H}_{ch}}{\rho}_{mix}(z{)}_{i1}dz{\int}_{0}^{{H}_{ch}}{\rho}_{mix}(z{)}_{i}dz\right]}_{k}{S}_{ch}{n}_{ch}+\left({H}_{ici}{H}_{ici1}\right){\rho}^{\u2019}{S}_{ic}=$
$=\left[\sum _{k1}^{m}\frac{{N}_{ch}\left(k\right)\xb7{n}_{ch}\left(k\right)}{r}+\sum _{k1}^{m}{G}_{stin}^{ch}\left(k\right)\xb7{n}_{ch}\left(k\right)\right]\Delta \tau +{G}_{cl}$; (3)
$\frac{{N}_{f}}{{H}_{f}}q\left(z\right)dz+\Delta {Q}_{szr}\left(z\right)={\alpha}_{z}\left(\frac{{F}_{f}}{{H}_{f}}\right)\left({t}_{f}\left(z\right){t}_{st}\left(z\right)\right)+\left(\frac{{\left(m{C}_{p}\right)}_{f}}{{H}_{f}}\right)\frac{d{t}_{f}\left(z\right)}{d\tau}$; (4)
${\alpha}_{z}\left({F}_{f}/{H}_{f}\right)\xb7\left({t}_{f}\left(z\right){t}_{st}\left(z\right)\right)dz={G}_{st}{\left({C}_{p}\right)}_{st}d{t}_{st}\left(z\right)$. (5)
The system of equations is complemented by closing relations to calculate the thermophysical properties of water and water steam, the fuel and cladding materials, the coefficients of heat transfer from the wall to steam, the steamwater mixture hydraulic resistances and the density in channels, and the steamzirconium reaction heat. Besides, they include formulas to calculate values ΔР_{fr} and ΔР_{ac} representing the local drag, friction and flow acceleration pressure loss for sections 1 and 2 respectively (
ΔP_{fr} = (ξ_{l} + ξ_{r} dz/D_{h})×(ρ'w_{c}^{2}/2)×Ψ {1 + x[(ρ'/ρ") – 1]},
ΔP _{ac} = ρ_{1}w_{1}^{2} – ρ_{2}w_{2}^{2}.
The density of the steamwater mixture in the channel is determined by the relation
ρ _{mix}(z) = ρ'(1 – φ (z)) + ρ"(z) φ (z).
More detailed information in the code’s mathematical model, including the rationale for selecting the ratio to calculate the coefficient of heat transfer from the fuel surface to a singlephase medium (water) and from the fuel surface to a twophase medium (steamwater mixture) is provided in (
Equations (1) through (5), Fig.
Value  Meaning  Dimension 

1  2  3 
H_{core}  Fuel rod heating height  m 
H_{ic}  Interchannel space water level height  m 
Н_{ch}  Channel swell level height  m 
ρ _{mix}  Steamwater mixture density  kg/m3 
Z  FA fuel part axial point coordinate  m 
G  Gravity acceleration  m/s2 
ΔP_{fr}  Friction pressure loss  Pa 
ΔP_{ac}  Flow acceleration pressure loss  Pa 
ρ'  Saturated water density  kg/m3 
i_{in}  SFA channel inlet enthalpy  kJ/kg 
Q_{FA}  SFA power  kV 
H_{FA}  SFA height  m 
q(z)  Power density value at axial point z  J/m 
m  Number of groups of channels with assemblies  
S_{ch}  Channel flow area  m2 
n_{ch}  Number of channels  
S_{ia}  Interassembly (interchannel) space flow area  m2 
N_{ch}  Channel power  W 
r  Specific heat of evaporation  J/kg 
G_{st in}^{ch}  Top rack channel inlet steam flow rate  kg/s 
Δτ  Time interval  s 
G_{cl}  SFP coolant leak rate  kg/s 
N_{f}  Fuel rod power  W 
H_{f}  Fuel rod heating height  m 
ΔQ_{szr}  Steamzirconium reaction heat  W 
a _{z}  Fueltosteam heattransfer coefficient  W/(m2×K) 
F_{f}  Fuel heatexchange surface  m2 
t_{f}  Fuel rod temperature  °C 
t_{st}  Steam temperature  °C 
C_{p}  Specific heat capacity of water  J/(kg×K) 
ΔP_{d}  Drag pressure loss  Pa 
ξ _{l}  Local drag coefficient  – 
ξ _{r}  Friction resistance coefficient  – 
D_{h}  Hydraulic diameter  m 
w_{c}  Coolant circulation rate  m/s 
Ψ  Twophase flow inhomogeneity correction factor  – 
x  Mass void fraction  – 
ρ"  Saturated steam density  kg/m3 
φ (z)  Channel void fraction  – 
G_{c}  Coolant natural circulation rate  kg/s 
The steam flow rate distribution obtained at the bottom rack outlet is used as the initial condition for calculating the heat exchange in the top rack. This steam flow rate is determined from the bottom rack SFA power.
The ROK/B code makes it possible to calculate different types of the assembly and SFP designs, specifically, for the VVER1000, VVER1000 and VVER1000 units with single and twotier assembly arrangement, with shrouded tubes in racks (for compacted storage of assemblies), with bare and jacketed assemblies, and single and multicompartment SFP layouts (for VVER1000).
The computational pattern for the KORSAR/GP and SOKRAT/V1 codes (with no fuel part detailing) is as follows. The SFA group is simulated by a group of parallel channels. Axially, each channel is broken down into 12 sections. The ten inner sections along the channel height simulate the FA’s main (heated) part, the upper section simulates the FA’s unheated upper part, and the lower section simulates the unheated lower part.
The computational pattern for the ROK/B code is similar to that for the KORSAR/GP code with the only difference that the channels are grouped depending on the FA power, and each channel is broken down into 50 to 100 axial sections.
One of the most complicated issues in calculations of heat exchange for twophase flows is calculation of void fraction, φ. A comparative analysis in (
Δw = 0.13× exp(4.9×φ),
where Δw = w" – w' is the relative steam velocity, m/s; w" = w_{п} /φ is the true steam velocity, m/s; w' = w_{w} /(1 – φ) is the true water velocity, m/s; w_{st} = Q_{FA}/(ρ"×r×S_{ch}) is the steam velocity reduced to (crosssection S_{ch}), m/s; and w_{w} = G_{c}/(ρ_{w}×S_{ch}) is the reduced water velocity, m/s. At the present time, the OKB Gidropress correlation is used in the ROK/B code for the void fraction determination.
The ALADIN experiment (
The importance of measuring this parameter is obvious as the difference in levels is the initial parameter for the nuclear safety analysis. The experiment was undertaken for the following fuel power values: 20 W (the power for an assembly of 96×20 = 2.88 kW), 50 W (the assembly power is 7.20 kW), 70 W (the assembly power is 10.08 kW), and 100 W (the assembly power is 14.40 kW). These powers are comparable with the decay heat power for an FA after monthlong (or longer) cooling in the VVER SFP. In our opinion, it is exactly where the major experiment drawback lies as applied to the VVER SFPs (
Fig.
Fig.
The steamwater mixture weight is equal to
ρ _{mix}×F×H_{phys} = ρ'×F×H_{mass}
The collapsed level, H_{mass}, is the coolant level as it could be with the parameters on the saturation line, m; and F is the area, m^{2}. The collapsed level is occasionally referred to as the weight level. Since r_{mix} is an unknown value, no actual (swell) level can be determined. The instrumentmeasured pressure drop is converted to the collapsed level as follows:
H _{mass} = P/(ρ'×F).
Fig.
Experiment (Research Work Report 1985) was undertaken for a 126rod FA of 500 kW (fuel rod power of 4000 W) and at a pressure of 0.35 MPa. Experiment (
The cross verification results are presented in Fig.
Fig.
The time to the fuel uncovering onset obtained using the ROK/B code agrees well with the experimental data with the fuel rod power being over 50 W. The best experiment description is provided by the SOKRAT/V1 code. It should be however noted that no fuel power typical of an SFA after threeday cooling (~300 W) was considered in the experiment.
The ROK/B code was validated for the key parameters (coolant density, time to the onset of the fuel rod uncovering, swell and collapsed levels, fuel rod temperature). A conclusion has been made that the deviation of the ROK/B calculation results from the experimental data is not more than 0.5% for options with the fuel rod power of over 20 to 50 W, this corresponding to the VVER1000 FA residual power of 6200 to 15600 W (i.e. the power of an FA after more than one year of cooling).
The cross verification was undertaken by comparing the ROK/B calculation results with the available experimental data and the results of the calculations based on the KORSAR/GP and SOKRAT/V1 system codes. A conclusion has been made that the deviation of the ROK/B calculation results from the SOKRAT/V1 results is not more than 0.5%, and that from the KORSAR/GP results is not more than 10% to 15%.
The validation and cross verification results allow a conclusion that the ROK/B code can be used in thermalhydraulic calculations for the SFP fuel cooling in conditions with the loss of cooling and leak formation. Validation can be complete after experiments at test benches in the form of SFP models with several FAs. At the present time, such experiment is prepared by French experts (DENOPI test facility) (