=Paper=
{{Paper
|id=Vol-2763/CPT2020_paper_s2-2
|storemode=property
|title=The development of a model for predicting the stability boundaries of natural circulation process
|pdfUrl=https://ceur-ws.org/Vol-2763/CPT2020_paper_s2-2.pdf
|volume=Vol-2763
|authors=V.V. Andreev,E.E. Orekhova,N.P. Tarasova,Yu.S. Perevezentseva
}}
==The development of a model for predicting the stability boundaries of natural circulation process==
https://ceur-ws.org/Vol-2763/CPT2020_paper_s2-2.pdf
The development of a model for predicting the stability boundaries of
natural circulation process
V.V. Andreev, E.E. Orekhova, N.P. Tarasova, Yu.S. Perevezentseva
vyach.andreev@mail.ru | katrin_orehova@rambler.ru | tar06@list.ru | khohlova@pochta.ru
Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia
The concept of safety for facilities comprising nuclear power plants implies in large the use of passive systems. One of the main
passive systems in a nuclear power plant is a system for cooling the reactor core with its action based on gravitational forces. In this
regard, the importance of such a physical process as natural circulation is increasing with the development of nuclear power facilities.
However, this system has not only advantages but some drawbacks as well. These are the emergence of instability in the two-phase
coolant flow, pulsations of thermohydraulic parameters, possible circulation reversal and stagnation. This paper deals with the study of
a generalized model of the natural circulation stability. The said model is designed to simplify the design engineering of power
equipment. This model will also enable the operating personnel to predict the operating limits of the equipment and remain within the
coolant stability bounds. This paper presents a model for predicting the stability boundaries of natural circulation process.
Keywords: natural circulation, geyser instability, thermal pulsations, stability
equalizer, a hydraulic accumulator or some peculiarities of
1. Introduction performances of elements.
Nuclear energy is currently one of the most promising
3. Geyser instability
power sources. The importance of passive safety systems
is increasing with the development of the nuclear industry. The results of experimental studies have shown that
The main advantage of these systems is the independence one of the main types of instability at low pressures and
of their functioning of external energy sources and as a flow rates of the coolant is the flow instability caused by
consequence the simplification of their design. One of the the surge of the coolant boiling in the lifting section of
important reactor systems is a passive heat removal system the circulation loop. This type of instability is
required to cool the core. This system is based on the fluid characterized by periodic emission of a two-phase mixture
motion due to difference in specific gravities. The motion from the lifting section followed by filling the circulation
occurs without any forcing equipment (no pumps) and path with water.
represents the coolant circulation generated by the action The geysering-type instability was named so because
of natural forces. Moreover, equipment operated with the of its resemblance to natural geysers, which are
natural coolant circulation is characterized by reduced characterized by periodic emissions of a steam-water
installation noise, overall dimensions and the power mixture from the depths of the Earth.
consumption for self-supply. But notwithstanding these Such geyser instability was first studied in vertical
advantages the system has some drawbacks as well, pipes closed from below and filled with water [3,4]. When
namely, the occurrence of instability in the two-phase a pipe is heated with some heat flow in the lower part the
coolant flow during the reactor core cooling, pulsations of water boiling begins. In low-pressure systems it results in
thermohydraulic parameters and possible circulation the sudden increase of steam generation and the rapid
reversal and stagnation. discharge of the steam-water mixture into an expansion
vessel thereto the pipe is connected. Liquid which is not
2. Instability of two-phase flows warmed up to the saturation temperature is discharged
In natural-convection loops with the two-phase coolant from the vessel into the pipe. The system returns to the
condition the flow instabilities are noted, which are non-boiling state. The cycle is further repeated [5,6].
manifested themselves through a periodic change in the The cycle consists of the following several stages:
main thermohydraulic parameters of the flow under 1) energy accumulation;
constant external conditions. Such unstable flow regime 2) the coolant boiling at a temperature slightly above the
may result in deteriorating reliability of thermal power saturation temperature;
equipment. Periodic repeated fluctuations in the flow rate 3) the emission of a steam-water jet;
of the coolant in the loop may cause the premature loss of 4) the return to the initial state.
the equipment serviceability, the wall material destruction,
4. Methods and techniques for prediction of
low-frequency vibrations affecting the operation of the
the coolant flow regimes
plant as a whole. Furthermore, the loop instability imposes
restrictions on permissible limits of the thermal power; This paper is concerned with the study of the process
therefore, the determination of areas with stable operation of natural circulation and its stability using a few different
of natural circulation loops at low pressures is a very methods in order to create a single generalized system. The
urgent task [1,2]. following methods have been applied in the work:
Destabilizing mechanisms are often associated with experimental method, calculation method using
design features of a plant using a two-phase flow; the computational codes of hydrodynamics, method using
instability may be caused by the availability of a volume artificial neural networks. The results obtained using the
said methods are combined to create a generalized model.
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY
4.0)
This model shall enable to predict the system behavior, to Institute of Nuclear Energy and Technical Physics, Nizhny
determine the limiting boundary conditions for the stable Novgorod State Technical University n.a. R.E. Alekseev.
operation of the system. The experiments were carried out at atmospheric
pressure. The system operating modes at atmospheric
5. Experimental research methods pressure simulate the emergency cooling process for a
Experimental studies were carried out at the nuclear plant.
Department of Nuclear Reactors and Power Plants, The scheme of the stand is shown in Fig. 1.
Fig. 1. The scheme of the test stand Designations: ТО1-1 - ТО1-5 – heat exchangers, Т1-2 - Т1-8 - thermocouples of the heating
section, Т1-9 - Т1-14 – thermocouples of the cooldown section, Т1-1 - Т1-3 – thermocouples at the inlet and outlet of the cooling
sections, Ф1-1 – Ф1-3 – ultrasonic steam sensors
The experiments were conducted as follows: ˗ cooling water temperature at the outlet of the
˗ measurement of the initial water temperatures in the refrigerator
circulation loop; ˗ differential pressure at the downcomer region
˗ measurement of the initial temperature in the cooling ˗ steam content at the outlet of the heated duct.
loop; Upon setting the pulsation mode the following
˗ measurement of the cooling water flow rate; parameters were recorded: the pulsation frequency and
˗ setting of the heater power; duration, the pressure drop, the coolant temperature at the
˗ activation of the data recording and archiving. outlet of the heated section and the pulsation
commencement temperature.
Parameters read out:
˗ heater power; 6. Experimental data processing results
˗ refrigerator power; Fig. 2 shows the curve of the natural circulation
˗ coolant temperature at the inlet and outlet of the stability obtained as a result of the experimental data
heating section; processing.
˗ duct wall temperature along the height of the lifting
region:
Fig. 2. Experimental Stability Curve
The curve has a left branch bent to the relative Similar results in regard to the natural circulation
temperature axis, a pronounced minimum and a right stability have been found in the literature and are shown in
branch. The operating mode characterized by the right Fig. 3 [7]
branch includes an interval of the unstable operation of the Based on the experimental data obtained and found in
system. Therefore, the left branch is of particular interest the literature a technique has been elaborated for creating
in the results obtained. a generalized model to predict the natural circulation
stability.
Fig. 3. Stability curves for natural circulation loops
The introduction of generalized coordinates enables us
7. Experimental computational system for to modify the model under study and reduce it to a simpler
studying the natural coolant circulation form:
The generalized model is a set of lines showing the
boundary conditions for the existence of a stable system
constructed on the Q-T axes. Such a combination of
boundary conditions is unique for a specific technical
system and enables to determine the limits for stable
operation of the equipment. The combination of boundary
conditions is a family of curves of a characteristic form:
the left branch of the family is bent at a certain angle to the
temperature axis (T), this angle depends on the geometry
of the contour. The salient point (kink) moves depending
on the conditions thereunder the coolant is located. The
suggested model is shown in Fig. 4
Fig. 4. Peculiarities of boundary conditions for natural circulation in the loop
therewith the system will still be stable and the coolant
8. Generalized model of stability boundaries boundary temperature at the inlet to the heated section
for systems with natural coolant circulation upon exceeding thereof the system will become unstable.
The generalized model is the summary of results This model enables to simplify the procedure of the design
obtained using experimental methods, computer and engineering of heat exchange equipment based on the
simulation and artificial neural networks. This model principle of natural circulation. The methodology for
enables to predict the limiting densities of heat flows constructing such a generalized model is shown in Fig. 5.
Fig. 5. Scheme of the generalized model
9. Application of numerical methods for - to identify physical and mathematical models of
simulation of natural circulation process processes studied;
Experimentally obtained results are used to simulate 11. Description of a geometric model used for
systems using computational fluid dynamics. To apply the numerical experiments
computational fluid dynamics method, it is necessary to
The geometric model is a combination of several
construct a geometric model of the system under study, to
components:
construct a calculation - grid model based on the geometric
- the hot coolant circulation path corresponding to the
model, to create a mathematical model.
test stand;
10. Methodology for conducting experiments to - the coolant circulation path in the refrigerator
study the natural coolant circulation by corresponding to the test stand;
computational simulation methods - metal walls of the refrigerator.
All geometrical parameters of the computer model
To conduct numerical experiment, it is necessary: correspond to the natural test-stand under study. The
- to create the geometry of the loop under study; computer geometric model is shown in Fig. 6.
- to create a finite - element model;
Fig. 6. Computer geometric model of the stand
∂h r
12. Physical and mathematical model ρ = −div(q) + ω
∂τ
The physical parameters of the fluid are simulated as where �q⃗ shall be projections of the heat flow density onto
temperature-dependent using an integrated library. the coordinate axes; ω are internal heat sources.
The effect of gravity is taken into account.
The steam generation process is simulated in the 13. Application of artificial neural networks for
system. simulation of the natural circulation process
The loop walls are simulated without sliding.
The metal heating is set by the specific heat flow on Based on the results obtained using the above methods
the wall. artificial neural networks (ANNs) are simulated. An ANN
The thermal conductivity of metal is simulated. of the multilayer perceptron type is used in this work. [9]
The refrigerator parameters are simulated by setting When simulating ANN, the coolant characteristics of the
the coolant flow rate at the inlet to the heat exchanger; geometry and state are taken as input parameters. The
Description of Mathematical Model output parameters are the corrected value of the boundary
The mathematical fluid model is based on the solution heat flow and temperature thereat the instability occurs as
of the system of Navier-Stokes equations [8]: well as the value of tg(ɑ) characterizing the position of the
- the continuity equation: curve in space. The ANN simulation scheme is shown in
Fig. 7.
∂ρ ∂( ρui )
+ = 0,
∂t ∂xi
where ρ is the density, ui is the projection of the velocity
onto the axis under study, t is time; xi is the coordinate
thereon the flow is studied.
- the motion equation:
∂(ui ) ∂(ui ) 1 ∂p 1 ∂(σ ij )
+uj =− + + Ji ,
∂t ∂x j ρ ∂xi ρ ∂x j
Fig. 7. Scheme of ANN used for generalized model creation
where indices i =1,2,3 shall be the coordinate axis index; j f(Г) is characteristic of the circulation duct; f(У) is
is the summation index; Ji is the external force acting on characteristic of the coolant state conditions; tg(ɑ), Qпр, tпр are
the system (gravity force) output ANN data - system stability parameters
- the energy equation:
When developing a model using artificial neural Networks of the multilayer perceptron type with
networks the results of personal experiments have been different numbers of neurons in the intermediate layer and
used as well as the results found in reference data. several different activation functions have been studied
It may be noted that in the obtained dependences there during the simulation.
is a sharp ascending and descending section. To avoid The analysis of simulated networks is given in
ambiguity, two neural networks have been simulated: one Appendix B. Find below the results obtained with a neural
for each section. However, we lack of knowledge on on network having minimal errors.
the upper limit of each network use because of few
experimental data available.
Fig. 8. Results of simulation using ANN
circulation process corresponds to each point in the spatial
14. Simulation results coordinate system. It is noted that the said points are on
A set of points has been obtained in the course of the one curve in space and represent an integral system (fig.
simulation. A boundary stability curve of the natural 9).
Fig. 9. Type of a generalized curve
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About the authors
Acknowledgements Andreev Vyacheslav V., Head of the Department of Nuclear
reactors and power plants, Doctor of Technical Science,
This work was supported by the RFBR, grant № 19- Professor, Nizhny Novgorod State Technical University n.a. R.E.
07-00455. Alekseev. E-mail: vyach.andreev@mail.ru.
Orekhova Ekaterina E., Assistant of the Department of
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