On the possibility of cooling the high-power VVER reactor pressure vessel using an air-droplet spray in the event of a beyond design basis accident

On the possibility of cooling the high-power VVER reactor pressure vessel using an air-droplet spray in the event of a beyond design basis accident* Denis G. Zaryugin1, Sergey T. Leskin2, Stepan A. Mikhin2, Vladimir V. Sergeev3, Victor I. Slobodchuk2 1 State Atomic Energy Corporation Rosatom, 24 Bolshaya Ordynka St., 119017 Moscow, Russia 2 IATE MEPhI, 1 Studgorodok, 249039 Obninsk, Kaluga reg., Russia 3 IPPE JSC, 1 Bondarenko Sq., 249033 Obninsk, Kaluga reg., Russia Corresponding author: Victor I. Slobodchuk ([email protected]) Academic editor: Georgy Tikhomirov ♦ Received 4 February 2025 ♦ Accepted 25 March 2025 ♦ Published 14 November 2025 Citation: Zaryugin DG, Leskin ST, Mikhin SA, Sergeev VV, Slobodchuk VI (2025) On the possibility of cooling the high-power VVER reactor pressure vessel using an air-droplet spray in the event of a beyond design basis accident. Nuclear Energy and Technology 11(4): 251–257. https://doi.org/10.3897/nucet.11.176910 Abstract For reactors with high decay power (VVER-1000, VVER-1200, VVER-TOI, etc.), no reliable reactor vessel cooling is achieved via the concept of retaining the corium inside the reactor pressure vessel only by means of heat transfer to water in the process of its boiling within the reactor vessel vault since high heat fluxes (density above 106W/m2) cause boiling evolving into film boiling and to a heat transfer crisis. A comparative analysis of different cooling systems shows that the most reliable and effective way to prevent the heat transfer crisis is an intensification of heat transfer on the cooled surface by using an air-droplet spray device (ADSD), which can be used to retain the core melt inside the reactor pressure vessel. The paper provides an overview of studies on gas-droplet cooling of high-temperature surfaces, and presents preliminary calculations using correlations of the non-wetting cooling mode as being of greatest interest for the ADSD. Methods have been considered for simulating gas-droplet cooling in system codes. The qualitative agreement of the calculation results with experimental data is shown. The peculiarities of spray cooling of the large VVER reactor vessel are identified. A diagram of the possible locations of spray nozzles within the reactor vessel vault is demonstrated. Due to the lack of a single verified spray cooling model for high-temperature surfaces, experimental studies are considered to be the key approach in the scientific problem under consideration, that is cooling of the large VVER reactor vessel in the event of a beyond design basis accident. Keywords Gas-droplet cooling of high-temperature surfaces, heat transfer simulation, system codes, beyond-design-basis accident at high power NPPs Introduction The strategy for managing severe accidents for the most common large nuclear power plants in Russia and worldwide, both with operated and newly designed pressurized water reactors (VVER), involves ahighly topical issue addressing which requires as efficient arrangement of high power heat flux removal as possible. Copyright Zaryugin DG et al. 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. Nuclear Energy and Technology 11(4): 251–257 DOI 10.3897/nucet.11.176910 Research Article * Russian text published: Izvestiya vuzov. Yadernaya Energetika (ISSN 0204-3327), 2025, n. 1, pp. 81–95. Zaryugin DG et al.: Air-droplet spray in the event of a beyond design basis accident252 In the event of a beyond-design-basis accident at VVER-600 and VVER-600S reactors, the reactor vessel vault is flooded with water to confine corium within the reactor vessel, and the reactor vessel is cooled by bubble boiling in a large volume of water with natural circulation. For reactors with a higher decay power density (VVER1000, VVER-1200, VVER-TOI, and others), confining corium within the reactor vessel due only to the heat exchange of water as it boils in the large volume of the reactor vessel vault does not provide reliable vessel cooling, since boiling evolves into film boiling leading to a critical heat flux (CHF) (Sulatskii et al. 1998; Rezepov et al. 2003). A comparative analysis of different cooling systems shows that the most reliable and efficient way to prevent the CHF is to intensify the heat transfer on the cooled surface (for heat fluxes of over 106 W/m2) using an air-droplet spray device (ADSD), which can be used to confine corium within the reactor vessel. Descriptions can be found in literature of investigations concerning the practical use of spray cooling for high-power lasers, LEDs, microchips, etc. (Voitkov et al. 2017; Vertkov et al. 2018; Shteling et al. 2022). However, there is no currently single comprehensive calculation theory for heat transfer in an air-droplet mode. An analysis of phenomena involved in the liquid boiling in the wall film formed in the course of gas-droplet cooling shows that theoretical modeling of this process is highly challenging. One of the earliest attempts to systematize and generalize the peculiarities of heat exchange mechanisms in the event of jet and spray cooling is described in Isachenko and Kushnyrev 1984. Due to the physical processes in the course of spray cooling with phase transitions being highly difficult to describe, the key research methods in this field are experimental methods, despite the development of computational hydrodynamics and its wide-scale introduction in engineering in the form of modern CFD codes. Experimental investigations on gas-droplet cooling A review of papers (Isachenko and Kushnyrev 1984; Bratuta 1986; Koldin and Platonov 2013; Voitkov et al. 2017; Vertkov et al. 2018; Karpov 2021; Shteling et al. 2022) on gas-droplet cooling of high-temperature surfaces shows the following. For gas-droplet cooling, experimental results have been traditionally processed in the form of a “boiling curve” with the presence of a peak and a further transition to a film boiling mode. In contrast to the boiling curve for liquid in a large volume, the cases of gas-droplet cooling under consideration involve an upward displacement of both the temperature and heat flux peaks. Besides, there is a smoother transition to the film boiling mode (from the maximum to the minimum flux). The maximum density of the heat flux removed increases as water subcooling grows in the injector (nozzle), i.e., the supply of subcooled water to the surface increases both the limiting (critical) and the minimum heat fluxes. The delivery of subcooled water directly to the hot surface is achieved due to droplets, which explains the increase in the efficiency of this cooling method. The maximum and the minimum densities of the heat flux removed increase as there is a growth in the density of spraying (liquid flow rate per 1 m2 of the surface) for spray cooling. When gas-droplet cooling is used, the water consumption is smaller compared to other cooling methods, such as jet cooling, which is of practical importance. Some experimental studies note that spray cooling leads to the same heat transfer values as with jet cooling, but with a much lower mass flow rate of liquid (Koldin and Platonov 2013; Karpov 2021). Gas-droplet cooling increases the ratio of interfacial surface to liquid volume. The water-to-air evaporation factor and the convective component of heat transfer increase accordingly. A liquid drop in the air represents an internal heat sink as it evaporates. The state of the droplet, vapor and gas boundary layer defines therefore the heat removal intensity, and it is possible to achieve the maximum heat removal intensity using gas-droplet spraying. Effect of spraying density on the maximum and minimum heat fluxes during spray cooling Apart from flow rate, a new parameter is introduced, that is, spraying density of cooled surface. Spraying density is the volumetric or mass flow rate of liquid per cooled surface area unit. Fig. 1 presents experimental data on spray cooling (Bratuta 1986) for the following parameters: • water (droplet) and air temperature of 17 to 22 °С (subcooling of dispersed water jet to saturation of 80 °С); • flow rate of droplet onto cooled surface (11 to 13 m/s); • spraying density range of 5 to 80 mm3/(mm2·s) or 5 to 80 kg/(m2·s). Figure 1. Spray cooling boiling curves for spraying densities of 8, 22.7, 45, 54.5 and 75.7 kg/(m2·s); q – heat flux density, ts – surface temperature. Nuclear Energy and Technology 11(4): 251–257 253 The results of the studies are presented in the form of boiling curves. The key result is that the heat flux density exceeds 2·106 W/m2 in the cooled surface temperature range of 200 to 400 °C and the spraying density range of 22 to 75 kg/ (m2·s). The maximum heat flux density (up to 7·106 W/m2) is reached at a surface temperature of 180 to 220 °C. The maximum heat flux has a strong direct dependence on the spraying density in the mentioned range. There is a monotonous (low-gradient) heat flux decrease in the surface temperature range of 200 to 400 °C. In other words, the transition to film boiling for spray cooling is heavily temperature “extended”. The mass fraction of generated vapor is only 3.7 to 7.3%. Generalization of experimental data on heat transfer during gas-droplet cooling of hightemperature surfaces In Isachenko and Kushnyrev 1984 the authors summarized the results of investigating experimentally the intensities of cooling high-temperature surfaces using dispersed water jets. The results are presented as criterial ratios for the surface average heat transfer coefficient: Nu = α·R/λ = F(Re, We, Kr, Pr) (1) where α is the surface average heat transfer coefficient, W/ (m2·K); λ is the thermal conductivity of liquid, W/(m·K); Re = j·x/µ is the Reynolds number for spraying density and linear dimension of the cooling surface; We = j2·R/ (σ·p) is the Weber number for droplet radius and spraying density; Kr = r/[cp (Tw–T0)] is the boiling number; Pr is the Prandtl number for liquid; j is the surface spraying density, kg/(m2·s); x is the linear dimension of the cooling surface, m; µ is the dynamic viscosity of liquid, Pa·s; R is the liquid droplet radius, m; σ is the liquid surface tension factor, N/m; ρ is the liquid density, kg/m3; r is the phase transition heat, kJ/kg; cp is the isobaric heat capacity of liquid, kJ/(kg·K); Tw is the cooled surface temperature, °С; and T0 is the liquid temperature in the injector, °C. The determining parameters in this generalization are the refore droplet size, spraying density, and surface and injector liquid temperature (measurable parameters). This approach allows analyzing the dependence of the key factors as listed on the heat transfer intensity. One can find specific ratios and their applicability limits in Isachenko and Kushnyrev 1984. In Isachenko and Kushnyrev 1984 authors identify three modes of cooling with dispersed liquid: a film mode, a wetting mode and a non-wetting mode. Film mode suggests that a continuous liquid film flows on the cooled surface. Bubble boiling is visually observed in the film. A vapor bubble collapse process is possible due to the film bombardment by subcooled liquid. Wetting mode takes place at a surface temperature of over 200 °C. There is no continuous liquid film. Droplets reach the surface with formation of visible spots of 3 to 4 mm in size. It can be assumed that the entire droplet mass is assumed to be “insufficiently used” for evaporation on the surface and repels some of the droplets from the surface. Non-wetting mode takes place at a surface temperature of over 400 °C. No impacting droplets can be visually seen on the surface. Droplets evaporate in the flow, without reaching the surface, due to radiation from the surface, convection with vapor and air, and thermal conductivity. It is exactly the mode that is of greatest interest. Fig. 2 presents preliminary calculations using correlations Isachenko and Kushnyrev 1984 for non-wetting mode. The following parameters have been used for the calculations, which fit the correlation applicability range for the given mode: • atmospheric pressure (1 bar); • injector water temperature (50 °C); • cooling surface radius – 0.1 m; • spraying density – 3.5 kg/(m2·s); • water droplet radius range –(1–5)·10-5 m (10 to 50 microns). Accordingly, Re = 1250, We = 2·10-6 – 1.1·10-5. The correlation applicability boundaries for the mode are We = 0.8·10-8 – 7.32·10-6. The calculation results for this mode have shown the following: • the threshold density of heat flux removed in a non-wetting mode is higher the smaller is the dispersion degree of the cooling liquid; specifically, the heat transfer coefficient is inversely proportional to the droplet radius raised to a power of 0.88, i.e., a strong and nearly inverse relationship is observed; • the heat flux density in this mode depends nonlinearly on the spraying density and is proportional to the spraying density raised to a power of 0.22. We shall consider the available computational models for cooling high-temperature surfaces using a number of known codes. Figure 2. Heat flux density as a function of the cooled surface temperature for non-wetting mode for different droplet sizes R (Isachenko and Kushnyrev 1984). Zaryugin DG et al.: Air-droplet spray in the event of a beyond design basis accident254 Results of heat transfer simulation in a dispersed gas-droplet flow in the KORSAR system code System codes, such as RELAP, TRACE (USA) and KORSAR (Russia), are unidimensional two-phase circuit thermal hydrodynamics codes used for NPP cooling systems. Accordingly, a unidimensional two-phase statement requires a highly developed system of closing ratios for heat transfer and hydraulic resistance for a large array of two-phase flow and heat transfer modes (mode maps). At the same time, there are three types of ratios identified in terms of heat transfer and resistance: wall – liquid, wall –vapor– gas, liquid – gas (interfacial interaction). Most of the ratios are empirical and describe modes representative of exactly nuclear power plant cooling systems. These are modes with a longitudinal flow in the channels. Annular-dispersed and dispersed modes in network codes are those closest to the problem in question. Dispersion mode in a unidimensional statement (with a longitudinal flow along the hot wall) can be considered as a gas-droplet injection cooling step after the flow changes from transverse to longitudinal, i.e., at a certain distance from the jet center. The transition from an annual dispersed mode to a dispersed mode in network codes means the transition to a post-CHF boiling mode. The CHF calculation is based on skeletal tables of CHFs in pipes (Kirillov et al. 1990). The tables present (in this first-kind CHF case with a small vapor content) the critical flux dependence on the flow pressure, mass velocity (longitudinal) and relative enthalpy (enthalpy vapor content). As a result, any gas-droplet water-air flow at an atmospheric pressure (i.e. with a low mass velocity and a negative enthalpy steam content) will be calculated in the system code (e.g., KORSAR) with a critical heat flux limit of about 0.9·106 W/m2. The latter value corresponds to the critical heat flux during water boiling in a large volume at an atmospheric pressure. We shall also note the following points. It is not possible to control the droplet size in a dispersed heat exchange mode in a system code. This value is calculated based ona range of correlations that describethe natural dispersion of liquid in channels in a dispersed mode. Accordingly, it is not possible to introduce a mechanical “disperser” (injector) of liquid, used in the course of spray cooling, to control the liquid dropletsize into the calculation. At the same time, the following heat transfer mechanisms are taken into account in the KORSAR code fora dispersed vapor-water or gas-droplet mode (Yudov 2021; Yudov et al. 2022): • convective heat transfer of vapor (and gas) with the wall (two standard correlations for forced convection of gas in pipes and two correlations for natural convection) (mechanism 1); • heat flux to liquid droplets evaporating in the wall layer (q1) (mechanism 2); • heat flux to droplets as they contact (bombard) the wall (q2) (mechanism 3); • radiation heat transfer of droplets with the wall (standard ratios) (mechanism 4). The correlation for mechanism 2 (evaporation in the wall layer) has the form: φ λ α (2) where φ is the volumetric vapor-gas content; λg is the thermal conductivity of vapor (gas), W/(m·K); Ts is the water saturation temperature, K; αg is the convective wall – vapor (gas) heat transfer coefficient, W/(m2·K); and d is the droplet diameter, m. Since this ratio does not differentiate between the composition of the vapor-gas (vapor-air medium), “evaporation” means boiling of water droplets in a vapor or air flow without contacts with the wall. It is important to note that the heat flux densityin the process of droplet boiling in a flow is inversely proportional to the square of the droplet diameter, i.e., the flow droplet dispersion degree affects the heat flux density. This conclusion is in linewith the experimental results of Isachenko and Kushnyrev 1984. The correlation for mechanism 3 has the form: q2 = (ρw)d·r·ε (3) where (ρw)d is the wall droplet spraying intensity (Yudov et al. 2022), kg/(m2·s); and ε = exp(1–(Tw/Ts)2) is the efficiency of the droplet thermal perception by the surface. This is a systemically attractive approach in terms of developing computational spray cooling models. In general, the mentioned system codes do not allow simulating heat removal in a dispersed mode with a heat flux density that exceeds the CHF skeleton table data for boiling in pipes. Preliminary analysis of a gas-droplet flow – hot wall heat transfer model in the ANSYS FLUENT code Currently, a number of theoretical models have been developed to simulate gas-droplet cooling processes (Bell 1987; Yudov 2021). In Yudov 2021, specifically, it is used a differential equation of the liquid droplet heat and mass transfer dynamics in a hot vapor-gas medium flow. The equation describes the variation process of the droplet temperature T, and mass m, for the time t via convective heating of the hotter surrounding gas, thermal radiation from the wall, and the droplet evaporation and boiling in the flow. Three modes are considered: • convective heating of the droplet taking into account the radiation under the condition that T≤Tg (the droplet temperature is lower than the gas temperature Tg); Nuclear Energy and Technology 11(4): 251–257 255 • droplet evaporation mode under the condition that Tg≤T≤Ts (the droplet temperature is higher than the gas temperature, but lower than the saturation temperature); • droplet boiling mode in the gas flow under the condition that T≥Ts (the droplet temperature has reached or exceeds the saturation temperature). For the droplet evaporation mode, specifically, heat and mass transfer dynamics equation has the form: α σ ε (4) where σr is the Stefan-Boltzmann constant, W/(m2·K4); αd is the interfacial heat transfer coefficient, W/(m2·K); εg is the reduced emissivity factor; dm/dt is the drop evaporation rate, kg/s; F is the droplet surface area, m2; and r is the vaporization heat, J/kg. To close equation (4) in terms of the convective component αd, a known correlation is used for the heat transfer of a ball (drops with the diameter d) in a gas flow: α λ (5) where Red is determined from the difference in the gas and droplet velocities, as well as from the droplet diameter and the liquid viscosity. To close equation (4) in terms of evaporation rate, a method is used based on the analogy of heat and mass transfer processes (the Lewis number equal to unity). The evaporation rate is determined by the product of the evaporation coefficient by the difference in the vapor concentration on the droplet surface and in the gas flow. The vapor concentration on the droplet surface is equal to the concentration of saturation at the droplet temperature. The vapor concentration in the flow is a calculated value and depends on the gas temperature. The evaporation coefficient is equal to the heat transfer coefficient, according to equation (5), divided by the gas heat capacity. For the droplet boiling mode in the gas flow, the following differential equation is used for the droplet diameter dynamics: λ ρ (6) where λg is the thermal conductivity of gas, W/(m·K); and cpg is the isobaric heat capacity of gas, J/(kg·K). The droplet boiling out (evaporation) rate follows from the above equation. The characteristic evaporation time is determined as follows: τ (7) where λ ρ is the combination of parameters in the right-hand side of equation (6). The calculation by equation (7) with a droplet diameter of 50 μm, a gas (air) temperature of 400 °C, a droplet temperature of 100 °C, an atmospheric pressure, and a phase slip value of 3 m/s shows that the droplet evaporation time τ = 0.038 s, i.e., the evaporation frequency for droplets of the given size is 26 Hz. The presented equations are a component for developing spray cooling models. Since the droplet mass is proportional to the cubed droplet radius, and the interfacial surface is proportional to the squared droplet radius, then it follows from equation (4) that the droplet warmup rate is inversely proportional depending on the droplet radius. Accordingly, the intensity of heat transfer will be also inversely proportional to the droplet radius which roughly fits the generalization of experimental data for the non-wetting mode of cooling with a dispersed flow (Isachenko and Kushnyrev 1984). The presented model of gas-droplet cooling with dispersed liquid is of systemic interest but it was not used for the calculations. Therefore: • the model of cooling with dispersed liquid considered briefly in the ANSYS Fluent code (ANSYS Fluent Theory Guide 2013 is of major interest in terms of estimating maximum heat fluxes; • the model content replicates the experimentally observed qualitative manifestations of interfacial processes in the course of droplet cooling, such as evaporation of droplets in the gas flow and droplet boiling with no contacts with the wall; • the content of the computational theoretical model confirms the experimental conclusion that the intensity of heat transfer is larger with a smaller liquid droplet diameter; • the model is applicable both to longitudinal cooling with dispersed liquid and to transverse cooling, which is important in design. Possibility of using air-droplet spray cooling (ADSC) in NPP safety systems To find out if it is possible to use ADSC to cool the reactor vessel, one needs to bear in mind the peculiarities of the item under consideration to be cooled. First, a vertical or inclined surface is cooled. Second, the cooling surface has a large area, which requires many spray nozzles to be installed for spraying the surface cooled. Third, the cooled surface axial temperature is variable in a broad range. Fourth, passive operation of the cooling system is maintained. Considering that most of the experimental studies are normally undertaken for individual nozzles and a small cooling area, the recommendations and generalizations obtained cannot be directly used to justify operation of the large reactor vessel cooling system. Zaryugin DG et al.: Air-droplet spray in the event of a beyond design basis accident256 Since the heat transfer surface has a large area, and much of it is vertical, a large number of nozzles are required to be used in the system to be installed at different elevations and at different distances from each other at the same level. An optional arrangement of nozzles is presented in Fig. 3 (Loktionov 2019). The most efficient cooling of the heat transfer surface requires determining the optimal distance between the nozzles at the same installation level, the distance between the individual rows of nozzles taking into account the axial power density (and heat flux) distribution, as well as, potentially, the optimal nozzle installation angles with respect to the cooled surface. Besides, it is necessary to determine the best possible flow rate of the cooling medium for the nozzles, and the best possible size of the dispersed flow droplets, taking into account the distance from the nozzle to the cooled surface. To ensure passive operation of the system, a principle can be used which suggests that the cooling liquid circulates due to the residual heat power removed from the reactor vessel, and converted to electrical energy using a machine-free method, and to mechanical energy of the pump drive for pumping cooling liquid and that of the compressor for supply of air (Soloviev et al. 2024). Thermal energy is converted to electrical energy to power the pump and the compressor using thermoelectric generators (TEG). Preliminary estimates showed that TEG composed of thermoelectric batteries (TEB) were capable, in the given thermal-physics conditions, to generate 40 kW of electricity or more, which is quite enough to power the circulation pump and the air compressor. A pilot plant is required to bed eveloped to justify the possibility for and the boundaries of using the gas-droplet model of dispersed cooling to ensure stable heat removal of heat fluxes with a density of over 1.5 MW/m2 from the vessel of a reactor with a high thermal power, optimized for conditions of severe beyond-design-basis accidents at NPPs. This installation is expected to enable experimental simulation to justify the best possible arrangement of nozzles, the direction and rate of the dispersion flow atomization, and the size of the surface spraying flow area to ensure as efficient heat removal from the reactor vessel as possible. Based on the experimental data obtained for the interaction of the jet droplet cooling flow with the heat transfer surface, it is necessary to develop a simplified computational model and a code based on this model and undertake calculations to justify the selection of the model and designs for the gas-droplet cooling of the VVER vessel under the action of high-intensity thermal loads in conditions of severe accidents. Conclusions The paper, based on selected experimental studies on cooling high-temperature surfaces with a continuous or a dispersed water jet, shows that it is possible to achieve a heat flux density of over 1 MW/m2, which corresponds to a critical heat fluxin the process of water boiling at an atmospheric pressure in a large volume. An analysis of the possibility for gas-droplet cooling of high-temperature surfaces has shown the following: • the most important components of the model are the description of the droplet boiling processes in the vapor-gas flow (without contacts with the heating surface) and determination of the droplet flow onto the wall – simulation of these processes is highly uncertain and complex, and so it is the description of these processes that is expected to form the largest part of the computational model development for spray cooling of high-temperature surfaces; • the use of system codes for numerical simulation of spray cooling is possible but limited, since they use a skeletal table of critical heat fluxes obtained for pipes in the event of a longitudinal flow of subcooled or boiling liquid. Grounds are needed to formally adjust the table towards increased critical fluxes (this being technically feasible). There is no currently single verified model of spray cooling for high-temperature surfaces. In the given context, experimental research is central to the scientific problem under consideration – that is cooling of the large VVER reactor vessel in a beyond-design-basis accident. Figure 3. Reactor vessel nozzle cooling diagram: a. Cross-section; b. Vertical profile: 1 – reactor vessel; 2 – water and air supply line; 3 – thermoelectric generator in the form of a jacketed flat TEB “belt” circumscribing the VVER vessel barrel; 4 – nozzles; 5 – air supply line; 6 – compressor with control valve; 7 – air duct connection lead; 8 – air duct connection lead; 9 – pump with control valve; 10 – water supply line. a b Nuclear Energy and Technology 11(4): 251–257 257 References ANSYS Fluent Theory Guide (2013) ANSYS Inc., 814–814. Bell KJ (1987) Handbook of heat exchangers. In 2 volumes. Translation from English. Edited by O.G. Martynenko. 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