UNCERTAINTY AND SENSITIVITY ANALYSIS OF FUEL ASSEMBLY HEAD

PARAMETERS IN THE FRAMEWORK OF KALININ-3 BENCHMARK TRANSIENT

I. Pasichnyk1, S. Nikonov

2, K. Velkov

1

1Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbH, Garching, Germany

{Ihor.Pasichnyk, Kiril.Velkov}@grs.de

2National Research Center „Kurchatov Institute“, Moscow, Russia

niks@vver.kiae.ru , niks.ki@mail.ru

The paper considers the application of uncertainty and sensitivity analysis in the framework of

the OECD/NEA Benchmark on Kalinin-3 NPP transient: “Switching off of one of the four

operating main circulation pumps at nominal reactor power”. An influence of the uncertain

hydraulic parameters in the fuel assembly head on the results is studied using the GRS

uncertainty and sensitivity software package SUSA. The thermo-hydraulic simulation model

uses a pseudo-3D parallel thermo-hydraulic channel methodology within the GRS system

code ATHLET. SUSA is applied to generate hydraulic uncertainties and to perform the post-

processing analysis. A statistically representative set of transient calculations is analyzed and

both integral and local output quantities are compared with the Benchmark measurements.

The present work is a step forward in establishing a “best-estimate calculations in

combination with performing uncertainty and sensitivity analysis” methodology.

АНАЛИЗ НЕОПРЕДЕЛЕННОСТИ И ЧУВСТВИТЕЛЬНОСТИ К ПАРАМЕТРАМ

ГОЛОВКИ ТЕПЛОВЫДЕЛЯЮЩЕЙ СБОРКИ ДЛЯ СТАНДАРТНОЙ ЗАДАЧИ

"КАЛИНИН 3"

И. Пасечник1, С.П. Никонов

2, К. Велков

1

1 Общество безопасности установок и реакторов (GRS mbH), Гархинг, Германия

2Национальный Исследовательский Центр “Курчатовский Институт”, Москва, Россия

В работе проводится исследование неопределенности и чувствительности результатов

стандартной задачи по изучению переходного процесса на третьем блоке Калининской

АЭС, обусловленного отключением одного из четырех главных циркуляционных

насосов (ГЦН) при работе на номинальной мощности. В частности, используя

программный пакет SUSA разработанный в GRS, рассматривается влияние к вариациям

теплогидравлических параметров головки тепловыделяющей сборки. Расчет

проводится по программе улучшенной оценки ATHLET, позволяющей описать

поперечное взаимодействие в системе параллельных каналов. SUSA используется в

качестве генерации набора случайных параметров и анализа результатов.

Анализируется статистически представительная выборка результатов переходного

процесса и проводится сравнение локальных и глобальных параметров с

экспериментом.

1. Introduction

The present paper continues an uncertainty and sensitivity (U&S) studies of the VVER-1000

reactor, started in [1]. It considers the OECD/NEA coolant transient Benchmark (K-3) on

measured data at Kalinin-3 Nuclear Power Plant (NPP) where a switch off of one main

coolant pump (MCP) at nominal reactor power (98.6% of nominal power, fuel assemblies

TVSA, first load, 130.6 effective days) is analyzed [2]. To model the reactor and in-vessel

structures the ATHLET [4] nodalisation scheme (Figure 1) which describes the spatial

distribution of objects based on a previous development in [3] is used. This scheme is already

successfully applied in the K-3 framework and has revealed a number of previously

unobserved phenomena in the calculations. As an example one can mention the observation of

the heterogeneity of the radial mass flow distribution of coolant in the upper part of the

reactor core.

The current analysis considers only the hydraulic uncertainty parameters in the fuel assembly

head, which might be important in the study of the temperature and flow distributions of the

coolant. After describing the simulation method the results of the US analysis are discussed in

Section [3].

2. Model Description and Choice of Uncertain Parameters

As already mentioned U&S analysis of K3 is started in [1] and considers global hydraulic

parameters, such as coolant temperature in cold legs, inertia moment and rated torque of MCP

etc. The current work is devoted to the investigation of the influence of parameters onto the

mass flow and temperature distributions of coolant in the region of lower grid of shielding

tubes (ST) and in particular in the region of fuel assembly heads (Figure 2). The following

uncertainty parameters are chosen: 1) hydraulic resistance coefficients of the flow through

Figure 1: Common view of reactor and in-vessel structure (left – drawing, right – nodalisation

of the RPV and its cuts (only thermo-hydraulic objects are shown)

grids in the assembly head (Figure 3 - Figure 5); 2) hydraulic resistance in ST (Figure 4) and

3) hydraulic resistance coefficient in the control rods guide tube channels (Figure 5, right).

A fuel assembly head is axially divided into three parts by four perforated plates, with a

known number of holes (and known diameters) for the flow path of coolant. In the region

between first and third plate (from below) the flow path of coolant is possible both in vertical

and horizontal (between adjacent assemblies) directions. The upper part of assembly head is

located between third and fourth plates. This part is isolated from the sides, which excludes

the direct exchange of the coolant between neighboring assemblies.

STs are shown on Figure 4 (right). There are three openings from the assembly head to the

ST. One or two openings can be occupied by the wires of the self-powered neutron detectors

(SPND) or by thermocouple (Figure 6). The annular gap between control rod and the wall of

guide tube is added to the flow section. Assemblies which are placed on the periphery of the

core do not have shielding tubes, hence the coolant enters directly the region above lower

plate of STs (LPST) through free openings (maximal two of them can be nevertheless filled

with instrumentation cables) in the upper part of fuel assembly (Figure 4, right). STs

themselves, depending onto which assembly‘s instrumentation type they belong, are

characterized by the defined number of washers for the spacing of control rods and their

driving shaft in the region between lower and middle plates of block of STs.

Figure 2: Different groups of reactor’s objects in the region of lower plate of STs (LPST).

Figure 3: The region of the upper part of the fuel assembly and its components (right –

model). UH – the region of the upper part of heated section; UN – the region of the non-

heated part up to fuel rod end; AH1 – the region of the outer lower section of assembly head –

from lower assembly grid up to middle part of assembly’s head; AH2 – the region of the outer

upper part of assembly head – from middle assembly grid up to LPST; BT1 - the region of

the inner lower section of assembly head – from lower assembly grid up to middle part of

assembly’s head; BT2 - the region of the inner upper section of assembly head – from lower

assembly grid up to middle part of assembly’s head; HT – the region of the upper section of

assembly head – from upper grid of assembly head up to assembly head end; “GCH” the

region of the is the outlet from guide tubes and central channel in the vicinity of HT.

Figure 4: Fuel assembly head drawing (left) together with a schematic view of coolant mass

flow distribution in the region of lower plate of shielding tubes. Red color – mass flow of the

main coolant, blue – mass flow from guide tubes and baffle.

Figure 6: Core configuration together with detectors control groups positions. Red numbers

are assemblies used in analysis.

Figure 5: Fuel assembly head (left) and lower part of the guide channel (right). Red circle

– inlet region with varied hydraulic resistance coefficients

The above described scheme allows assigning for each assembly, according to the distribution

map of instrumentation and the position of the assembly itself, the set of hydraulic resistance

coefficients starting from the lower grid of assembly head up to the outlet of the ST. The basic

formula for calculating local hydraulic resistance coefficient in locations with sharp-edged

connection of two pipes (which is the case here) along the coolant flow path is given by [12]:

( )

( )

( )

( )

( ) ( )

( )

(1)

where – density; – diameter of opening in region “0”; – perimeter of the opening in

region “0”; - flow areas; - flow velocities; – friction coefficient; –

pressure drop (see Figure 7).

Figure 7: Sharp-edged connection of two pipes with different areas

In the region between first and third assembly head grids, where along the vertical component

of the flow velocity there is also a horizontal component, which can play a significant role

near LPST of the peripheral assemblies [6,8]. Applying the above formula can result in a

significant error. Estimating accuracy in the K-3 transient, based on the measurements of

thermocouples allows introducing a one-sided error of 25% from the value, calculated by the

Eq. (1). For the central fuel assemblies this variation covers the experimental curve, given by

the thermocouples measurements.

With regard to the hydraulic resistance coefficients in guide tubes, namely inlet flow into the

guide tube through four holes, then merging of flows into one channel with a 90° turn, outlet

into the channel with larger area, inflow in the gap between guide channel wall and control

rod surface, outlet flow from the guide channel into upper part of fuel assembly head (see

Figure 5), it is proposed to use above mentioned Eq. (1) with the same one-sided error of

25%.

All hydraulic uncertain parameters with their ranges are listed in Table 1.

Table 1: Input uncertain resistance coefficients with their description

Parameter Description Ref.

value

Sigma Min Max

CAS_HB.FB Bottom spacer 7.74E+00 1.93E+00 1.93E+00 1.35E+01

CAS_HB.FM Middle spacer 1.83E+02 4.57E+01 4.57E+01 3.20E+02

CAS_HB.FU Upper spacer 3.24E+03 8.10E+02 8.10E+02 5.67E+03

CAS_AH.FB Around assembly head 7.12E+00 1.78E+00 1.78E+00 1.25E+01

UPB.STB Inlet flow in bottom part of

ST for assembly with control

rods and thermocouple 2.53E+04 6.32E+03 6.32E+03 4.42E+04

UPB.STT Outlet flow from bottom part

of ST for assembly with

control rods and

thermocouple

2.37E+02 5.93E+01 5.93E+01 4.15E+02

UPB.DB Inlet flow in bottom part of

ST for assembly with SPND 1.63E+03 4.07E+02 4.07E+02 2.85E+03

UPB.DT Outlet flow from bottom part

of ST for assembly with

SPND

8.63E+01 2.16E+01 2.16E+01 1.51E+02

UPB.TDB Inlet flow in bottom part of

ST for assembly with

thermocouple and SPND 3.80E+03 9.49E+02 9.49E+02 6.64E+03

UPB.TDT Outlet flow from bottom part

of ST for assembly with

thermocouple and SPND 2.08E+02 5.21E+01 5.21E+01 3.64E+02

UPB.TB Inlet flow in bottom part of

ST for assembly with

thermocouple 2.62E+03 6.55E+02 6.55E+02 4.59E+03

UPB.TT Outlet flow from bottom part

of ST for assembly with

thermocouple

1.26E+02 3.14E+01 3.14E+01 2.20E+02

UPM.ST Flow in middle part of ST

(with driving shaft) 1.61E+00 4.02E-01 4.02E-01 2.81E+00

GU_CH.1F Guide tube forward inlet flow 5.00E-01 1.25E-01 1.25E-01 8.75E-01

GU_CH.1B Guide tube backward inflow 1.00E+00 2.50E-01 2.50E-01 1.75E+00

GU_CH.2F Merging of flows into one

channel with 90° turn

(forward)

1.38E-01 3.45E-02 3.45E-02 2.41E-01

GU_CH.2B Merging of flows into one

channel with 90° turn

(backward)

1.86E-01 4.64E-02 4.64E-02 3.25E-01

GU_CH.3F Outlet flow into the tube with

larger area (forward) 1.44E-01 3.60E-02 3.60E-02 2.52E-01

GU_CH.3B Outlet flow into the tube with

larger area (backward) 9.61E-02 2.40E-02 2.40E-02 1.68E-01

GU_CH.4F Gap (forward) 1.55E-01 3.86E-02 3.86E-02 2.70E-01

GU_CH.4B Gap (backward) 1.39E-01 3.47E-02 3.47E-02 2.43E-01

GU_CH.5F Outlet flow from the guide

tube (forward) 1.00E+00 2.50E-01 2.50E-01 1.75E+00

GU_CH.5B Outlet flow from the guide

tube (backward) 5.00E-01 1.25E-01 1.25E-01 8.75E-01

3. Results and Discussions

SUSA package is applied for uncertainty and sensitivity studies via generating a set of 100

samples of varied parameters. Figure 8 shows the standard deviation of axial temperature

distribution in assemblies, which have different types of instrumentation. The inset clearly

shows that the variation of chosen hydraulic parameters leads to noticeable uncertainties only

in the upper part of the reactor core. This supports the hypothesis of the local influence of

uncertain parameters.

Time histories of two assemblies #29 and #75 are chosen for further analysis. The assembly

#29 is located in the central part of the core, whereas assembly #75 belongs to the peripheral

assemblies. Figure 9 and Figure 10 show the statistics of coolant temperature evolution in

both assemblies compared with the measured values. The blue curve shows the median of the

sampled set and the blue ribbon – the 95% quantile. In the case of assembly #75 there is a

deviation between calculated and measured values. It means that varying only the hydraulic

resistance coefficients in the fuel assembly head one does not cover the thermocouple

measurements curve for the peripheral assemblies. For these assemblies a significant role

plays the coolant flow distribution in the region of lower plate of STs and the region in the

upper part of the baffle. In the paper [6] is shown, that the change of the hydraulic resistance

coefficient in the gap between upper part of the baffle and lower plate of STs results in the

changes of the vertical component of the coolant mass flow above fuel rods between 105%

and 130% of the averaged reactor core value. Hence these changes influence the whole region

of fuel assembly head. This is particularly noticeable in the peripheral assemblies.

Unfortunately it is difficult to find a theoretical justification for hydraulic resistance

coefficient in the gap between baffle and lower plate of STs. Therefore in the current paper

this coefficient is not varied and is taken as constant equal to with the

hydraulic area equal to 2 .

Figure 8: Standard deviation of axial temperature distribution in assemblies 29, 31, 54, 68, 75

in stationary state. Inset shows the distribution in the objects UH-UN-UP-BT1-BT2, which

correspond to unheated upper part of assembly.

Figure 9: Coolant temperature evolution in the HT region of assembly head #29. The

assembly is located in the central part of the core (5th radial layer) with installed

thermocouple and SPND; output channel goes through the tube of a small diameter in the

region of STs block.

Figure 10: Coolant temperature evolution in the HT region of assembly head #75. The

assembly is located in the last row of the core (corner, 8th radial layer) with installed

thermocouple.

The results of the sensitivity analysis are represented by Spearman’s rank correlation

coefficient (RCC) [13]. These coefficients describe the influence of each uncertain input

parameter on the uncertainty of the corresponding output variable.

For the sample size of N = 100 those RCC-values, which are lower than 0.2, are not

statistically significant and are not considered in the analysis.

At first the sensitivity of the coolant temperature in the head of assembly #29 is considered

(Figure 11). Shortly after the beginning of the transient the RCC of the “CAS_AH.FB”

coefficient starts to increase. But after 40 sec it goes down and becomes statistically

unimportant. On the contrary RCC coefficients of “GU_CH.3F” and “GU_CH2F” play major

role in the transient. It means the temperature evolution in assembly #29 is most sensitive to

the changes of hydraulic properties of the guide tubes.

The behavior of the RCC in case of peripheral assembly #75 reveals a new effect (see Figure

12). Along with higher RCCs for “GU_CH”, there is a strong influence of the “CAS_HB.FU”

hydraulic resistance coefficient. Moreover its influence is negative, i.e. an increase of

“CAS_HB.FU” leads to decrease of the coolant temperature in the vicinity of the

thermocouple. It sounds plausible, since the increase of the resistance coefficient of assembly

head upper spacer favors the entrance of cold water from the guide channels, which decreases

the coolant temperature in the HT region.

Figure 11: Spearman coefficient for assembly #29.

Figure 12: Spearman coefficient for assembly #75.

4. Summary and Conclusions

A detailed ATHLET model describing the local mixing phenomena in the assembly head of

the VVER-1000 reactor is implemented. Measurements are used to validate the ATHLET

model. Using SUSA methodology a U&S studies are performed for the case of the

OECD/NEA Benchmark on Kalinin-3 NPP transient: “Switching off of one of the four

operating main circulation pumps at nominal reactor power”. The paper describes the

uncertainty and sensitivity studies of some hydraulic parameters in the framework of the

OECD/NEA Kalinin-3 benchmark. Parameters that can be potentially important for the

coolant flow distribution in the upper part of assembly head are considered. It is shown, that

the behavior of the sensitivity coefficients has different character for assemblies on the

periphery and in the central part of the reactor core.

Further studies will concentrate on the influence of the hydraulic resistance coefficient of the

gap between upper part of the baffle and upper part of fuel assembly which is expected to

influence strongly the mixing processes in the fuel assembly heads in the vicinity of the lower

plate of the shielding tubes. As a consequence it will allow better modeling and interpretation

of thermocouple readings.

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