Recommendations on selecting the closing relations for calculating friction pressure drop in the loops of nuclear power stations equipped with VVER reactors

Closing relations describing friction pressure drop during the motion of two-phase flows that are widely applied in thermal-hydraulic codes and in calculations of the parameters characterizing the flow of water coolant in the loops of reactor installations used at nuclear power stations and in other thermal power systems are reviewed. A new formula developed by the authors of this paper is proposed. The above-mentioned relations are implemented in the HYDRA-IBRAE thermal-hydraulic computation code developed at the Nuclear Safety Institute of the Russian Academy of Sciences. A series of verification calculations is carried out for a wide range of pressures, flowrates, and heat fluxes typical for transient and emergency operating conditions of nuclear power stations equipped with VVER reactors. Advantages and shortcomings of different closing relations are revealed, and recommendations for using them in carrying out thermal-hydraulic calculations of coolant flow in the loops of VVER-based nuclear power stations are given.     

System of closing relations of a two-fluid model for the HYDRA-IBRAE/LM/V1 code for calculation of sodium boiling in channels of power equipment

The system of equations from a two-fluid model is widely used in modeling thermohydraulic processes during accidents in nuclear reactors. The model includes conservation equations governing the balance of mass, momentum, and energy in each phase of the coolant. The features of heat and mass transfer, as well as of mechanical interaction between phases or with the channel wall, are described by a system of closing relations. Properly verified foreign and Russian codes with a comprehensive system of closing relations are available to predict processes in water coolant. As to the sodium coolant, only a few open publications on this subject are known. A complete system of closing relations used in the HYDRA-IBRAE/LM/V1 thermohydraulic code for calculation of sodium boiling in channels of power equipment is presented. The selection of these relations is corroborated on the basis of results of analysis of available publications with an account taken of the processes occurring in liquid sodium. A comparison with approaches outlined in foreign publications is presented. Particular attention has been given to the calculation of the sodium two-phase flow boiling. The flow regime map and a procedure for the calculation of interfacial friction and heat transfer in a sodium flow with account taken of high conductivity of sodium are described in sufficient detail. Correlations are presented for calculation of heat transfer for a single-phase sodium flow, sodium flow boiling, and sodium flow boiling crisis. A method is proposed for prediction of flow boiling crisis initiation.     

Determining the onset of flow crisis in a multipurpose valve using a 3D thermohydraulic code

The characteristics the flow of water in the hydraulic path of the multipurpose valve with the parameters of coolant had at the moment when the accident began in Unit 4 at the Chernobyl nuclear power station are determined using a 3D thermohydraulic code.     

Verification of the computer code KORSAR taking into account the effect of nondensables on thermal-hydraulic processes

Calculations to verify the Russian computer code KORSAR were carried out for the B4.1 experimental operating conditions, in which nitrogen was supplied to the reactor coolant (primary) circuit of a reactor plant model, and which were simulated at the PKL III integral test facility. It is shown that dissolution of gases in coolant has an essential effect on the thermal-hydraulic processes during long-term passive removal of heat from the primary to secondary coolant circuit of the reactor plant model under the conditions of natural circulation.     

Experimental studies of local coolant hydrodynamics using a scaled model of cassette-type fuel assembly of a KLT-40S reactor

The results of experimental studies of local hydrodynamic and mass exchange characteristics of the coolant flow behind the spacer grid in the fuel assembly of a KLT-40S reactor are presented. The experiments were aimed at the investigation of representative domains of the fuel assembly with three tracer injection regions. The studies were performed at the aerodynamic test facility using the tracer gas diffusion method. According to the theory of hydrodynamic similarity, the obtained experimental results can be transferred to full-scale coolant flow conditions in standard fuel assemblies. The analysis of the tracer concentration propagation made it possible to determine in detail the flow pattern and find the main regularities and specific features of the coolant flow behind the plate spacer grid of KLT-40S fuel assembly. The hydraulic resistance coefficient of the spacer grid was experimentally determined. The coefficients of mass exchange between cells for representative cells of the displacer region in the KLT-40S fuel assembly were calculated for the first time; these results are presented in the form of the “mixing matrix.” The results of studies of local coolant flow hydrodynamics in the KLT-40S fuel assembly are used at AO Afrikantov OKBM for estimation of thermotechnical reliability of active cores for reactors of floating nuclear power stations. The experimental data on hydrodynamic and mass exchange characteristics are included in the database for verification of CDF codes and detailed cell-wise calculation of the active core for KLT-40S reactor installation. The results of these studies can be used at FSUE RFNC-VNIIEF for testing and verification of domestic three-dimensional hydrodynamic CFD codes (“Logos”) that are applied for substantiation of newly designed reactor installations. Practical recommendations on the application of the obtained results in thermohydraulic calculations of the active core for the KLT-40S reactor will be worked out. Proposals on further improvement of structural elements of active cores in the considered nuclear power installations will also be presented.     

Physical and mathematical simulation of aerodynamics and combustion in the furnace chambers of power installations

The possibilities of studying flows and heat transfer in various power installations using dedicated computer programs developed at the Institute of Thermal Physics, Siberian Branch of the Russian Academy of Sciences are shown. The results obtained from studies of processes in furnace chambers carried out on the experimental models of E-500 and P-67 boilers are presented.     

Correct numerical simulation of a two-phase coolant

Different models used in calculating flows of a two-phase coolant are analyzed. A system of differential equations describing the flow is presented; the hyperbolicity and stability of stationary solutions of the system is studied. The correctness of the Cauchy problem is considered. The models’ ability to describe the following flows is analyzed: stable bubble and gas-droplet flows; stable flow with a level such that the bubble and gas-droplet flows are observed under and above it, respectively; and propagation of a perturbation of the phase concentration for the bubble and gas-droplet media. The solution of the problem about the breakdown of an arbitrary discontinuity has been constructed. Characteristic times of the development of an instability at different parameters of the flow are presented. Conditions at which the instability does not make it possible to perform the calculation are determined. The Riemann invariants for the nonlinear problem under consideration have been constructed. Numerical calculations have been performed for different conditions. The influence of viscosity on the structure of the discontinuity front is studied. Advantages of divergent equations are demonstrated. It is proven that a model used in almost all known investigating thermohydraulic programs, both in Russia and abroad, has significant disadvantages; in particular, it can lead to unstable solutions, which makes it necessary to introduce smoothing mechanisms and a very small step for describing regimes with a level. This does not allow one to use efficient numerical schemes for calculating the flow of two-phase currents. A possible model free from the abovementioned disadvantages is proposed.     

MIF-SKD computation code for thermohydraulic design of a reactor core cooled by supercritical-pressure water

Presented here is the MIF-SKD computation code for channel-by-channel thermohydraulic calculations of fuel-rod assemblies cooled by supercritical-pressure water. The code allows one to calculate distributions of temperature and velocity of the coolant in channels of fuel-rod assemblies and temperatures of fuel-rod claddings and fuel-rod assembly casings with regular and irregular geometrical characteristics at various distributions of energy release along the length and the radius of fuel-rod assemblies.     

Experimental investigation of a new method for advanced fast reactor shutdown cooling

We consider a new method for fast reactor shutdown cooling using a decay heat removal system (DHRS) with a check valve. In this method, a coolant from the decay heat exchanger (DHX) immersed into the reactor upper plenum is supplied to the high-pressure plenum and, then, inside the fuel subassemblies (SAs). A check valve installed at the DHX outlet opens by the force of gravity after primary pumps (PP-1) are shut down. Experimental studies of the new and alternative methods of shutdown cooling were performed at the TISEY test facility at OKBM. The velocity fields in the upper plenum of the reactor model were obtained using the optical particle image velocimetry developed at the Institute of Applied Physics (Russian Academy of Sciences). The study considers the process of development of natural circulation in the reactor and the DHRS models and the corresponding evolution of the temperature and velocity fields. A considerable influence of the valve position in the displacer of the primary pump on the natural circulation of water in the reactor through the DHX was discovered (in some modes, circulation reversal through the DHX was obtained). Alternative DHRS designs without a shell at the DHX outlet with open and closed check valve are also studied. For an open check valve, in spite of the absence of a shell, part of the flow is supplied through the DHX pipeline and then inside the SA simulators. When simulating power modes of the reactor operation, temperature stratification of the liquid was observed, which increased in the cooling mode via the DHRS. These data qualitatively agree with the results of tests at BN-600 and BN-800 reactors.     

Prediction of friction pressure drop for low pressure two-phase flows on the basis of approximate analytical models

Wide use of natural circulation loops operating at low redused pressures generates the real need to develop reliable methods for predicting flow regimes and friction pressure drop for two-phase flows in this region of parameters. Although water–air flows at close-to-atmospheric pressures are the most widely studied subject in the field of two-phase hydrodynamics, the problem of reliably calculating friction pressure drop can hardly be regarded to have been fully solved. The specific volumes of liquid differ very much from those of steam (gas) under such conditions, due to which even a small change in flow quality may cause the flow pattern to alter very significantly. Frequently made attempts to use some or another universal approach to calculating friction pressure drop in a wide range of steam quality values do not seem to be justified and yield predicted values that are poorly consistent with experimentally measured data. The article analyzes the existing methods used to calculate friction pressure drop for two-phase flows at low pressures by comparing their results with the experimentally obtained data. The advisability of elaborating calculation procedures for determining the friction pressure drop and void fraction for two-phase flows taking their pattern (flow regime) into account is demonstrated. It is shown that, for flows characterized by low reduced pressures, satisfactory results are obtained from using a homogeneous model for quasi-homogeneous flows, whereas satisfactory results are obtained from using an annular flow model for flows characterized by high values of void fraction. Recommendations for making a shift from one model to another in carrying out engineering calculations are formulated and tested. By using the modified annular flow model, it is possible to obtain reliable predictions for not only the pressure gradient but also for the liquid film thickness; the consideration of droplet entrainment and deposition phenomena allows reasonable corrections to be introduced into calculations. To the best of the authors' knowledge, it is for the first time that the entrainment of droplets from the film surface is taken into consideration in the dispersed–annular flow model.     

Experimental studies of heat exchange for sodium boiling in the fuel assembly model: Safety substantiation of a promising fast reactor

Numerical simulation of the ULOF-type accident development in a fast reactor with sodium coolant performed using the COREMELT code indicates that sodium boiling in the active core takes place. The boiling is accompanied by oscillations of the technological parameters of the reactor installation; these oscillations can go on during several tens of seconds. In this case, it is possible that a stable regime of removal of heat from residual energy release is implemented. The model of the two-phase coolant flow applied in the code has an important effect on the numerical results; that is why this model needs experimental verification. For eliminating the development of an accident resulting in destruction of the active core elements, a structural solution is proposed; the essence of it is the application of the sodium void above the reactor active core. The experimental installation was developed and the heat exchange at sodium boiling in the model fuel assembly of the fast reactor in the regimes of natural and forced circulation in the presence of the sodium void and the top end shield was studied. It was demonstrated that, in the presence of the sodium void, it is possible to provide long-term cooling of the fuel assembly for a thermal flux density on the fuel element simulator surface of up to 140 and 170 kW/m² in the natural and forced circulation modes, respectively. The obtained data are used for more precise determination of the numerical model of sodium boiling in the fuel assembly and verification of the COREMELT code.     

采用颗粒团离散单元方法研究颗粒浓度的非均匀分布

气固两相流中尤其是稠密气固两相流中颗粒浓度在空间的分布总是非均匀，局部颗粒聚集。该文直接以颗粒团为研究对象，采用颗粒团离散单元方法(DEM)，建立非球形颗粒团的运动碰撞的模型与算法，基于真实碰撞，跟踪每个颗粒团的运动，模拟3种均匀或非均匀流场内的颗粒团运动经历。计算结果展现了颗粒浓度非均匀局部聚集的过程，揭示不同工况下流场中颗粒团的大小，颗粒分布及局部颗粒聚集的规律，结果表明在均匀流场中，颗粒均匀密集，非均匀流场中，颗粒浓度的非均匀性加剧。所得计算结果合理，与前人的模拟结果及实验结果相符。同时计算表明，采用颗粒团DEM模型能真实地揭示稠密气固两相流的特性，并使计算量有效减少。     

排烟脱硫循环流化床内脱硫过程的数值模拟

该文采用欧拉坐标和拉格朗日坐标相结合数值模拟了排烟脱硫循环流化床内的脱硫过程。将循环流化床内的生石灰粉和飞灰物料形成的颗粒团作为离散项，建立了床内两相运动及脱硫化学反应的模型与算法，得到了详细合理的计算结果。结果表明，采用该文的模型和算法模拟工程意义上的循环流化床内的稠密气固两相反应流是可行的。     

System studies for analyzing the efficiency of renewable energy sources

Methods and mathematical models are presented that have been developed at the Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences for studying the efficiency of renewable energy sources and estimating the field in which they can compete with the traditional energy technologies and prospects for their further applications. Results obtained from studies of renewable energy sources at global and local levels are analyzed. An approach applied to modeling methods for economically stimulating the use of renewable energy sources is described.     

Studies of heat transfer in power installations and apparatuses carried out at the United Institute of High Temperatures,Russian Academy of Sciences (on the 50th Anniversary of the Institute)

Works carried out at the United Institute of High Temperatures, Russian Academy of Sciences in the field of heat transfer in power installations are briefly reviewed. The main lines of scientific research works currently conducted at the Institute are described.     

Modeling the transport of nitrogen in an NPP-2006 reactor circuit

Efficient radiation protection of the public and personnel requires detecting an accident-initiating event quickly. Specifically, if a heat-exchange tube in a steam generator is ruptured, the ¹⁶N radioactive nitrogen isotope, which contributes to a sharp increase in the steam activity before the turbine, may serve as the signaling component. This isotope is produced in the core coolant and is transported along the circulation circuit. The aim of the present study was to model the transport of ¹⁶N in the primary and the secondary circuits of a VVER-1000 reactor facility (RF) under nominal operation conditions. KORSAR/GP and RELAP5/Mod.3.2 codes were used to perform the calculations. Computational models incorporating the major components of the primary and the secondary circuits of an NPP-2006 RF were constructed. These computational models were subjected to cross-verification, and the calculation results were compared to the experimental data on the distribution of the void fraction over the steam generator height. The models were proven to be valid. It was found that the time of nitrogen transport from the core to the heat-exchange tube leak was no longer than 1 s under RF operation at a power level of 100% N_nom with all primary circuit pumps activated. The time of nitrogen transport from the leak to the γ-radiation detection unit under the same operating conditions was no longer than 9 s, and the nitrogen concentration in steam was no less than 1.4% (by mass) of its concentration at the reactor outlet. These values were obtained using conservative approaches to estimating the leak flow and the transport time, but the radioactive decay of nitrogen was not taken into account. Further research concerned with the calculation of thermohydraulic processes should be focused on modeling the transport of nitrogen under RF operation with some primary circuit pumps deactivated.     

Verification of the Mathematical Model and Numerical Investigation into the Thermal–Hydraulic Parameters of Fuel Assemblies Containing Microspherical Fuel Elements

The article presents the results from numerical investigations into the hydrodynamics and temperature field in the KLT-40S reactor’s fuel assembly (FA) in the case of using microspherical fuel elements as nuclear fuel. The simulated FA has the same overall dimensions as the existing FA containing fuel rods, due to which it can be accommodated in the reactor core without the need of modifying the reactor design. The specific feature of an FA with micro fuel elements (MF FA) is the need to set up radial flow of coolant through the bed of micro fuel elements, which is achieved by using distribution and collection headers. The numerical simulation was carried out using the ANSYS Fluent computer code. The mathematical model implemented in the code has been refined and verified against the experimental data obtained by the authors on a model experimental setup whose design is similar to that of the considered FA containing micro fuel elements. Radial flow of coolant through the pebble bed is arranged in the model installation. The numerical and experimental data on pressure loss and temperature distribution in the bed estimated at different values of coolant mass velocity mass are compared with each other. The design of an FA containing micro fuel elements for the KLT-40S reactor is proposed. It has been found that almost purely radial flow of coolant can be set up with the perforation parameters (cross-section coefficients) higher than those mentioned in the literature. The serviceability of such a fuel assembly is demonstrated. The distributions of temperature, excess pressure, and coolant velocity and current lines are obtained. The perforation parameters of jackets confining the bed of micro fuel elements are presented.     

Metal hydride technologies of hydrogen energy storage for independent power supply systems constructed on the basis of renewable sources of energy

Studies of the technology of hydrogen energy storage for renewable sources of energy carried out at the Joint Institute for High Temperatures, Russian Academy of Sciences, are reviewed.