NUREG/IA-0235

 International 

Agreement Report

Numerical Analysis of Mixing Factors in the 

RPV of VVER-440 Reactor Using the 

TRACE Code 

Prepared by:

P. Heralecky, M. Blaha 

TES Ltd

Prazska 597

674 01 Trebic, Czech Republic

A. Calvo, NRC Project Manager 

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

May 2010 

Prepared as part of

The Agreement on Research Participation and Technical Exchange 

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP) 

Published by

U.S. Nuclear Regulatory Commission
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NUREG/IA-0235

Numerical Analysis of Mixing Factors in the 

RPV of VVER-440 Reactor Using the 

TRACE Code 

Manuscript Completed: April 2010 

Date Published: May 2010 

Prepared by: Petr Heralecky, Martin Blaha 

TES Ltd 

Prazska 597 

674 01 Trebic, Czech Republic 

A. Calvo, NRC Project Manager 

Prepared for:

Division of Systems Analysis 

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001

iii 

ABSTRACT

Experimental investigations of coolant mixing under steady state conditions at the Dukovany 

(Czech Republic) VVER-440 NPP were performed. The main goal of these experiments was to 

evaluate the mixing factors under normal operations condition. An extensive TRACE input deck 

of VVER-440/213 reactor was developed in frame of R&D project 1H-PK/61 in the TES 

Company. The TRACE input deck of VVER-440/213 reactor includes the reactor pressure 

vessel, the core and all important RPV internals. This paper contains some post-test analyses 

of the NPP Dukovany experiments using TRACE code V4.160 in order to generate background 

data for the forthcoming standardization procedure. There was performed a RPV nodalisation 

study to analyze influence of division of RPV into theta-parts on the calculated mixing factor. 

The purpose of performed TRACE analyses is to assess the capability of the TRACE code and 

the developed input deck to solve coolant mixing problems in VVER-440 type of reactors. 
iv 
v 

CONTENTS 

Page

ABSTRACT ..................................................................................................................... iii

ACKNOWLEDGEMENT ................................................................................................. vii

ABBREVIATIONS ......................................................................................................... viii

1. Introduction ............................................................................................................. 1-1

2. Plant description ..................................................................................................... 2-1

2.1 The reactor pressure vessel ........................................................................................... 2-1

2.2 The core ......................................................................................................................... 2-2

2.3 The reactor coolant system ............................................................................................ 2-2

2.4 The main operational parameters .................................................................................. 2-3

3. The TRACE Code ................................................................................................... 3-1

3.1 Mixing phenomena modelling in the TRACE code ......................................................... 3-1

3.2 The TRACE code assessment ....................................................................................... 3-2

3.2.1 Code assessment with real plant data ............................................................... 3-2

3.2.2 VVER typical features related to code assessment ........................................... 3-3

4. Mixing Factors ......................................................................................................... 4-1

4.1 Measurements at NPP Dukovany .................................................................................. 4-2

4.2 Measurement uncertainty ............................................................................................... 4-4

5. Input model description ........................................................................................... 5-1

5.1 8-Theta TRACE model ................................................................................................... 5-1

5.2 16-Theta TRACE model ................................................................................................. 5-1

5.3 Validation of the TRACE models basic thermo-hydraulics ............................................. 5-2

6. Results .................................................................................................................... 6-1

6.1 Experiment at the 1-st unit of NPP Dukovany ................................................................ 6-1

6.1.1 8-ThetaTRACE model results............................................................................. 6-1

6.1.2 16-ThetaTRACE model results........................................................................... 6-4

6.1.3 Résumé of the TRACE VESSEL component nodalisation study ....................... 6-6

6.2 Experiment at the 4-th unit of NPP Dukovany ................................................................ 6-7

6.2.1 8-ThetaTRACE model results............................................................................. 6-8

6.2.2 16-ThetaTRACE model results........................................................................... 6-8

7. Run Statistics .......................................................................................................... 7-1

8. Conclusions ............................................................................................................ 8-1
vi 

9. References.............................................................................................................. 9-1

Appendices 

APPENDIX A: Measured mixing factors at the Dukovany NPP ........................................... A-1 

APPENDIX B: Nodalisation of the 8-Theta VESSEL component ........................................ B-1 

APPENDIX C: Nodalisation of the 16-Theta VESSEL component ...................................... C-1 

APPENDIX D: Comparison of measured and calculated mixing factors at the 1-st Unit of 

NPP Dukovany 1997 (8-Theta model) ......................................................... D-1 

APPENDIX E: Comparison of measured and calculated mixing factors at the 1-st Unit of 

NPP Dukovany 1997 (16-Theta model) ....................................................... E-1 

APPENDIX F: Comparison of measured and calculated mixing factors at the 4-th Unit of 

NPP Dukovany 1987 (8-Theta model) ......................................................... F-1 

APPENDIX G: Comparison of measured and calculated mixing factors at the 4-th Unit of 

NPP Dukovany 1987 (16-Theta model) ....................................................... G-1 

Figures

Page

1. Scheme of the VVER-440/213 Reactor ................................................................................. 2-1

2. Scheme of the Core of VVER-440/213 Reactor .................................................................... 2-2

3. Single Cell of VESSEL Component in a Cylindrical Geometry ............................................. 3-1

4. Measured Mixing factors of the 1-st Loop at the Dukovany NPP Unit 1 ............................... 4-2

5. Comparison of Mixing Factors Related to the Loop1 at Different VVER-440 Type Plants .... 4-3

6. Comparison of the VVER-440/213 Reactor Core Theta and Radial Discretisation ............... 5-1

7. Shape of Affected Area of Mixing Factors (8-Theta model) .................................................. 6-2

8. Weighted Relative Deviation of Measured and Calc. Mixing Factors (8-Theta Model) ......... 6-4

9. Shape of Affected Area of Mixing Factors (16-Theta model) ................................................ 6-4

10. Weighted Relative Deviation of Measured and Calc. Mixing Factors (16-Theta Model) ...... 6-5

11. Comparison of a Calculated Relative Deviation of Mixing Factors (8 vs. 16-Theta) ............ 6-7

Tables

Page

1. VVER-440/213 Main Operational Parameters during Normal Operation .............................. 2-3

2. TRACE Input Deck Initial Conditions Under Normal Operation Mode .................................. 5-2

3. TRACE Model Basic Thermo-Hydraulics Under Normal Operation Mode ............................ 5-2

4. Maximal Values of of Measured and Calculated Mixing Factors (8-Theta Model) ................ 6-3

5. Maximal Values of of Measured and Calculated Mixing Factors (16-Theta Model) .............. 6-5

6. The Differences of Maximal Values of Measured and Calculated Mixing Factors ................ 6-6

7. Maximal Values of of Measured and Calculated Mixing Factors (8-Theta Model) ................ 6-8

8. Maximal Values of of Measured and Calculated Mixing Factors (16-Theta Model) .............. 6-8

9. Run statistics (8-Theta Model) .............................................................................................. 7-1

10. Run statistics (16-Theta Model) ........................................................................................... 7-1
vii 

ACKNOWLEDGEMENT 

The project 1H-PK/61 was funded by Czech Ministry of Industry and Trade in frame of R&D 

activities. 
viii 

ABBREVIATIONS 

CFD Computational Fluid Dynamics 

CRA Control Rod Assembly 

ECCS Emergency Core Cooling System 

ECI Exterior Communication Interface 

FA Fuel Assembly 

ITF Integral Effect Test Facility 

LOCA Loss of Coolant Accident 

MCP Main Coolant Pump 

MSIV Main Steam Isolation Valve 

MSLB Main Steamline Break 

NC Natural Circulation 

NEA Nuclear Energy Agency 

NPP Nuclear Power Plant 

NRC Nuclear Regulatory Commission 

OECD Organization for Economic Co-operation and Development 

PKL Experimental Facility in Finland 

PWR Pressurized Water Reactor 

RCP Reactor Coolant Pump 

RCS Reactor Cooling System 

ROCOM Experimental Facility in Germany 

RPV Reactor Pressure Vessel 

RD Research and Development 

SETF Separate Effect Test Facility 

SG Steam Generator 

SPND Self Powered Neutron Detector 

TC Thermo Couple 

TH Thermal Hydraulic 

TR Thermo Resistor 

UP Upper Plenum 

VVER Russian Pressurized Water Type Reactor 
ix 
1-1 

1. INTRODUCTION

Coolant mixing inside the reactor pressure vessel is an important phenomenon for wide range of 

NPP including normal operation as well as accidental conditions. The mixing phenomena, 

associated flow patterns and temperature distribution during a normal plant operation are 

interesting especially from an economical operation point of view. Other processes are 

dependent on coolant mixing under accident conditions – for example boron dilution, structural 

integrity, asymmetrical reactor cooldown, etc. Solution of these problems was rather problematic 

using 1-D system codes such as RELAP5 up to now. Thus the computational fluid dynamics 

(CFD) codes have had to be frequently used despite of some limitations that especially come 

from huge input decks and a long calculation time. There is also CFD codes limitation in case of 

coolant phase changes (evaporation, condensation). 

The TRACE code is able to solve mixing problems avoiding above mentioned CFD limitations. 

TES Company intends to use the TRACE code for performing safety or licensing analyses in the 

Czech Republic for VVER type of reactors including e.g. analysis associated to coolant mixing 

phenomena. The extensive TRACE V4.160 input deck of VVER 440/213 reactor was developed 

in frame of R&D project 1H-PK/61 in TES Company in order to realise this intention. The Czech 

regulatory body SÚJB requires every code to undergo a standardisation procedure prior the 

application in safety or licensing analyses. The standardisation procedure consists of a 

representative set of comparative (validation) analyses that covers the extent of standardisation. 

Experimental investigation of coolant mixing under steady state conditions at the Dukovany 

(Czech Republic) VVER-440 NPP was performed in years 1987 and 1997. Mixing factors (i.e. 

the effect of each single primary loop on the core inlet condition) for normal operation were 

measured in frame of these experiments. Some comparative post test analyses of these 

experiments were performed at TES Company using the TRACE code V4.160 in order to 

generate background data for the forthcoming standardization procedure. 
1-2 
2-1 

2. PLANT DESCRIPTION 

Czech Dukovany NPP consists of four 6-loop units equipped with VVER440/213 reactors. 

VVER-440/213 is a light water-cooled and light water moderated pressurised thermal reactor of 

the Soviet design that was firstly commercially introduced in 1980s. Over 50 units with model 

213 reactors are presently in operation or in final stage of construction mainly in Czech 

Republic, Finland, Hungary, Russia, Slovakia and Ukraine (Ref 9). The model 213 unit is a 

second generation of VVER-440 design. The first design version of VVER-440s, known as 

model 230, has been in operation since the early 1970s 

2.1 The reactor pressure vessel

The reactor system is composed of the reactor pressure vessel (RPV) with the reactor internals 

(see the Figure 1). The reactor internals include the core barrel, the flow distribution structure, 

fuel assemblies and control assemblies. The total water volume inside the RPV is 94 m3

. The 

RPV has 6 inlet and 6 outlet nozzles of the inner diameter 0.496 m. The outlet nozzles are 

located at the higher elevation than the inlet nozzles. The inlet and outlet nozzles are at the 

same elevation. Three of the nozzles make an angle of 45 degrees, then after 90 degrees there 

are three other nozzles. The cold legs are connected to the top of the downcomer, and the hot 

legs to the upper plenum. The RPV head is bolted on to complete the vessel pressure boundary 

and to support and locate the control rod drives. 

Figure 1: Scheme of the VVER-440/213 Reactor 

Key: 

1 – reactor pressure vessel 

2 – reactor pressure vessel head 

3 – bolt 

4 – core barrel 

5 – bottom of core barrel 

6 – lower core support plate 

7 – block of control assembly guide tubes 

8 – fuel assembly 

9 – control rod assembly 

Colour scheme: 

BLUE – downcomer and lower plenum 

ORANGE – core (fuel assemblies) 

GREEN – core (control rods) 

RED – upper plenum 

YELLOW – reactor upper head 
2-2 

2.2 The core

The core consists of 349 shrouded hexagonal assemblies arranged in a triangular lattice. The 

fuel is low enriched UO2. Criticality is controlled by the boric acid concentration and by the 

position of control rod banks. The active core height is 242 cm, the average core diameter is 

308 cm. There are two types of assemblies in the core of VVER-440 reactor. There are 312 fuel 

assemblies (FA) and 37 movable control rod assemblies. The bottom portion of the control rod 

assembly contains fuel and is in tandem with the upper portion containing boron steel control 

material. There is the rack and pinion drive mechanisms used to move the control rods. Control 

rods are sorted into 6 groups. In a VVER-440 reactor, 210 assemblies are equipped with outlet 

temperature measurements, 36 assemblies with self powered neutron detectors (SPND’s) – see 

the Figure 2. The flow rate through fuel assemblies is adjusted by means of throttling orifices, 

installed in the support plate of the core barrel. 

Figure 2: Scheme of the Core of VVER-440/213 Reactor 

2.3 The reactor coolant system

Reactor coolant system (RCS) consists of six main circulation loops. Each RCS loop 

includes a horizontal steam generator (SG), a main circulating pump (MCP) and isolation 

valves both in the hot and cold legs. The hydraulic diameter of hot/cold legs is 0.496 m and 

the total volume of primary coolant inside RCS (except the reactor and pressurizer) is 119 

m3

. Large volume of primary coolant, isolation valves and horizontal SG’s are considerable 

features of VVER-440 design compare to Western PWR’s. All the coolant loops have 

common flow paths through the reactor vessel, but are otherwise independent in operation. 

Operation with a loop out of service is possible, due to the use of primary coolant system 

isolation valves. However, it is not recommended because of asymmetrical distribution of 

flow in individual loops. In order to reduce primary coolant elevations the hot leg includes an 

U-shaped section. This feature provides loop seal effects during a LOCA accident. Also there 

is a cold loop seal between the SG outlet and a main circulating pump, which may contribute 

to the reactor level during LOCA conditions. The pressurizer, which maintains overall system 

pressure and compensates for changes in the volume of the primary coolant, is connected by 

two pipelines with the hot leg in one of the loops. The pressurizer is equipped with a relief 

Key: 

C – control rods (green colour) 

T – thermocouples (yellow colour) 

S – self powered neutron detectors 
2-3 

valve and two safety relief valves. During normal operation the pressurizer maintains RCS 

pressure within the prescribed limits using pressurizer sprays and heaters. 

2.4 The main operational parameters

Some of the main operational parameters of the VVER-440/213 model under normal 

operational conditions are provided in the table below: 

Table 1: VVER-440/213 Main Operational Parameters during Normal Operation 

Reactor thermal power 1375 MWt

Reactor coolant pressure 12.26 MPa 

Average coolant temperature at reactor inlet 267 ± 2 °C 

Average coolant temperature increase 31.0 °C 

Cold loop flow 6 x 6858.2 m3/h 

Flow through the reactor 41137 m3/h 

Core bypass 8.5 % 

Fuel assembly channel flow 312 x 113.36 m3/h 

Control rod assembly channel flow 37 x 150.83 m3/h 

Steam pressure in the steam generator 4.71 MPa 
3-1 

3. THE TRACE CODE 

The TRACE (TRAC/RELAP Advanced Computational Engine) code is a component-oriented 

reactor systems analysis code designed to analyse light water reactor transients up to the point 

of significant fuel damage. The TRACE code is a finite-volume two-fluid compressible flow code 

with one, two and three dimensional flow geometry. The TRACE code can model heat 

structures and control systems that interact with component models and the fluid solution. The 

TRACE code can be directly coupled with the 3 D reactor kinetics code PARCS or with the other 

TRACE jobs and other codes (CFD, CONTAIN ...) through its exterior communications interface 

(ECI). TRACE uses what is commonly known as a 6-equation model for two-phase flow (mass 

equation, equation of motion and energy equation for each phase). Additional equations can be 

solved for non condensable gas, dissolved boron, control systems and reactor power. There are 

five additional closure relationships for field equations: equations of state, wall drag, interfacial 

drag, wall heat transfer and interfacial heat transfer. These constitutive models are semi 

empirical equations. There are two numerical methods available in TRACE: semi-implicit 

method and the stability enhancing two-step (SETS) method. All TRACE calculations presented 

in frame of this report were performed using TRACE V4.160 code. 

3.1 Mixing phenomena modelling in the TRACE code

Modelling mixing phenomena requires 3-D computational environment. A 3-D Cartesian and/or 

cylindrical geometry flow calculation can be simulated within the reactor vessel or other reactor 

components where 3-D phenomena take place. All 3-D components can be modelled via 

VESSEL component. All basic equations for the 3-D VESSEL component are solved in the 

same form as the 1-D component. The vector form of the motion equation separates into three 

orthogonal coordinate velocity-component motion equations. The VESSEL nodalisation 

therefore becomes a collection of cells - see the Figure 3 (Ref 14), which are defined by their 

bottom and top faces (based on the level they occupy), their inner and outer faces (based on 

the ring they occupy) and by their two azimuth faces (based on the rotational location they 

occupy). All the field equations in the 3-D VESSEL component can have additional source terms 

to allow one or more 1-D component junctions to be connected to a mesh-cell interface 

anywhere in the 3-D VESSEL component. 

Figure 3: Single Cell of VESSEL Component in a Cylindrical Geometry 
3-2 

The 3-D implementation of the field equations in the TRACE code has two primary limitations 

(Ref 14). There is no model for turbulent diffusion and shear between fluid cells. This makes 

TRACE unsuitable for modelling circulation patterns in large open regions. The second 

limitation is related to the large computational volumes used in models of reactor vessels. Flow 

turns from the cold leg into the downcomer and normally from the downcomer to the lower 

plenum within a single volume. This yields an irrecoverable pressure loss within the calculation 

that is the same as can be obtained from a simple back of the envelop calculation for a sharp 

right angle turn. In fact the streamlines curve, and the pressure distribution is such that the 

actual pressure loss will be less than the right angle limit. The boron dilution problem is often 

analysed in frame of mixing phenomena. The set of field equations in the TRACE code can be 

further extended if a user chooses to follow the boron concentration in the system (Ref 13). An 

additional mass conservation equation can be activated to follow the concentration of boric acid, 

moving with the liquid. Total content of boric acid is assumed to be small enough that its mass 

is not used in the liquid momentum equation and it does not contribute to the thermodynamic or 

other physical properties of the liquid. Boron tracking capabilities are extended through the use 

of a model for solubility of boric acid, and a simple inventory of boric acid plated out in each cell 

in the system. Another solute could be modelled through a user option to replace the default 

solubility curve. 

3.2 The TRACE code assessment

Confidence in the computational tools (codes) and establishment of their validity for a given 

application depends on assessment. TRACE, like other two-fluid codes, is composed of 

numerous models and correlations. When applied to full scale nuclear power plant conditions, 

many of these models and correlations can be applied outside of their original database. By 

assessing the code against thermal-hydraulic tests, it is possible to show that the code and its 

constituent model packages can be extended to conditions beyond those for which many of the 

individual correlations were originally intended (Ref 15). The assessment process however, can 

also indicate potential deficiencies in the code. There are following four sources of data for code 

assessment (Ref 18): 

• “Fundamental” experiments 

• Separate effect test facilities (SETF) 

• Integral test facilities (ITF) 

• Real plant data 

3.2.1 Code assessment with real plant data 

The assessment of PWR safety codes is mainly performed on the basis of experimental data 

coming from scaled-down integral or separate test facilities. Besides the demonstration of the 

code capability in reproducing an experiment performed in a test facility, the code should be 

checked also in performing NPP calculation (Ref 18). Generally, there is a need to evaluate 

code performance in actual plant conditions as the final step of the independent code 

assessment. Using real plant data in process of code assessment brings a lot of advantages as 

well as disadvantages. The main benefit of application of the real plant data in frame of the code 

assessment is the real scale of the tests and true geometry. Test facilities are frequently scaled 

down models of the actual p′′wer plant. The scaling can increase the uncertainty of the results 
3-3 

of the test facility relative to the reactor performance. However the measurement error is 

certainly higher in the real reactor. The plant data mostly concern only conditions under fairly 

mild transients (operational transients and start-up and commissioning tests). Multidimensional 

effects, especially with respect to flow splitting and flow merging process (e.g. connection of the 

main coolant pipe to the pressure vessel) exist also in relatively small scale integral test facilities 

(Ref 18). Although there were performed extensive mixing tests at ROCOM (Ref 1) and PKL 

(Ref 4) facilities, using the real plant data seems to be substantiated in this case. Real plant 

data are also often used as reference base in case by OECD/NEA benchmark problems which 

deals with mixing phenomena or spatial problems, such as VVER1000 Coolant Benchmark 

V1000CT (Ref19) or PWR MSLB Benchmark (Ref 20). 

3.2.2 VVER typical features related to code assessment 

This paper deals with the mixing phenomena inside the reactor pressure vessel of VVER 

440/213 reactor. The TRACE code validation process is mainly based on the data from 

experimental facilities or real NPP’s of Western PWR type. VVER reactors are in many aspects 

similar to Western PWR’s (see the description of the VVER design in the Chapter 2). Therefore 

a lot of experimental data measured on PWR’s or PWR test facilities is valuable also for VVER 

research. On the other hand, the VVER design has several specific features. From the 

hardware point of view the main differences between VVER-440 and PWR relating to the mixing 

phenomena are the following (Ref 10): 

• Six loops of primary circuit equipped with loop seals in hot legs 

• Shrouded fuel assemblies with hexagonal fuel rod arrangement 

• Lower plenum volume larger and different internal structures 

• ECCS injection points 

• Two isolation valves in each main loop 

The first three bullets only are relevant to the analysed phenomena of the RPV coolant mixing. 

There are 50 operating of VVER type (Ref 9). It is a meaningful number compare to 216 

operating PWR reactors (Ref 9). Therefore corresponding attention should be given to code 

validation for VVER type of reactors. According to the (Ref 10) there is a phenomena of boron 

mixing and transport for VVER’s, which needs special consideration compare to typical PWR’s. 

The differences are not principal, but the mixing degree strongly depends on in-vessel 

geometry, which is different for VVER design compare to typical PWR design. This paper deals 

with modelling of coolant mixing during normal plant operation. This is the first step to code 

assessment for the whole mixing phenomena for the VVER type of reactors. 
3-4 
4-1 

4. MIXING FACTORS

Generally the mixing factor represents the effect of each single primary loop on the reactor core 

inlet condition. It is essential to know mixing factors distribution, because the mixing factors 

determine the temperature and boron concentration at the core inlet. Energy of the coolant at 

the each fuel assembly inlet is given by energy of the coolant coming from cold primary loops 

(Ref 16): 

∑=

⋅⋅=⋅

6

1

1 )( )( n

k k nnk THGATHg n (1) 

With gk ..... Mass flow through the k-th fuel assembly 

H(Tk) ..... Enthalpy of primary coolant at temperature Tk

Tk ..... Temperature at the k-th fuel assembly inlet 

Ank ..... Factor representing energy transmitted from n-th loop to k-th assembly 

Gn ..... Mass flow through the n-th primary loop 

T1n ..... Temperature at the n-th primary loop outlet 

There is practically no heat transfer to the coolant in the downcomer and lower plenum at nearly 

nominal temperatures in VVER-440 reactor. Thus coolant temperature at the core inlet does not 

depend on core power or core power distribution. If relative differences of the cold loop coolant 

temperature are small enough, it is acceptable to substitute coolant enthalpy by coolant 

temperature. The temperature at the inlet of the k-th fuel assembly (k = 1 – 312) is then given 

by: 

∑ ∑ = =

⋅=⋅⋅≅

6

1

1 1

6

1 n

n nnk

n k

n

k nk TBT

g

G AT (2) 

Where Bnk is the mixing factor of the n-th primary loop to the k-th fuel assembly. The mixing 

factor thus represents the weight of a particular loop to the coolant parameters at the inlet of a 

particular fuel assembly. Mixing factors related to all 6 primary loops then have to satisfy: 

∑=

=

6

1

1 nBnk (3) 
4-2 

4.1 Measurements at NPP Dukovany

There were performed some experimental investigations of coolant mixing in the VVER 440/213 

reactor under steady state conditions at the 1st unit of NPP Dukovany in 1997 (Ref 17) and at 

the 4th unit of NPP Dukovany in 1987 (Ref 22). Mixing factors under zero power operation were 

evaluated in frame of these experiments. There is no temperature instrumentation at the core 

inlet of VVER-440/213 reactor, therefore temperature at the outlet of particular fuel assemblies 

was measured and analysed by thermocouples (TC) of standard in-core instrumentation (see 

the VVER-440 core description in the Chapter 2.2). Thermo resistors (TR) were used to 

measure coolant temperature in the cold primary loops. Mixing factors were measured under 

zero power conditions in order to eliminate a spatial core power distribution and heat up through 

the core power. Thus the zero power reactor mode makes core inlet temperatures possible to 

substitute by core outlet temperatures. The main steam valves of steam generators were closed 

except of steam generator on the investigated primary loop. Thus significant deformation of the 

core inlet as well as the outlet temperature field was induced by the temperature change (a drop 

by several degrees of Celsius) of a particular cold primary loop. Relative temperature difference 

between investigated cold loop and the others was set up at about 2°C, so the above mentioned 

condition for substituting coolant enthalpy by temperature was satisfied. Influence of each of 6 

primary loops was separately investigated. Six matrices of mixing factors were calculated as a 

result, one for each primary loop. There is a layout of Dukovany experiment at the 1st unit of 

NPP Dukovany in 1997 on the next Figure 4, when the 1-st cold loop had been subcooled. The 

field of calculated mixing factors relevant to the 1-st loop is demonstrated. 

Loop 2

Loop 1

Loop 

Lo

3

op 4

Loop 5

Loop 6

subcooled

0.1

0.2

0.8

0.7

0.6

0.5

Loop 2

Loop 1

Loop 

Lo

3

op 4

Loop 5

Loop 6

subcooled

Loop 2

Loop 1

Loop 

Lo

3

op 4

Loop 5

Loop 6

subcooled

0.1

0.2

0.8

0.7

0.6

0.5

Figure 4: Measured Mixing factors of the 1-st Loop at the Dukovany NPP Unit 1 

The fields of calculated mixing factors relevant to the all of investigated loops at Dukovany NPP 

are for both experimental tests demonstrated in the Appendix A. The measured mixing factor 

field corresponds to the typical VVER-440 geometry. The effect of every loop approximately 
4-3 

covers the sector of 120 degrees adjacent to the investigated loop. The maximal values of 

measured mixing factors do not exceed 0.8 in any case. The fields of mixing factors for all the 

loops are not symmetrical. The symmetry was found only for central loops 2 and 5. This is first 

of all due to reactor inlet nozzles layout and also due to design of VVER-440 reactor internals. 

As you can see at the Figure A_1 in the Appendix A, the inlet nozzles of Loops 1 2 3 and Loops 

4 5 6 form an angle 45 degrees each other. Loops1 6 and Loops 3 4 form make an angle 120 

degrees, so there is larger clear area in the downcomer annulus related to the Loops 1,3,4,6. 

Thus coolant flowing from inlet nozzles of Loops 1 3 4 and 6 is deflected azimuthally towards 

the empty sectors. Generally we can say that there is a relatively poor mixing between the 

coolants of neighbouring loops. There were performed similar measurements of mixing factors 

at NPP Paks (Hungary), Rovno (Ukraine) and Loviisa (Finland) equipped with reactors VVER440. The main results of these measurements indicated good mutual accordance to Dukovany 

NPP experiments except the Loviisa experiment, where noticeable azimuthal swirling was 

found. There is demonstrated comparison of measured mixing factors relevant to Loop1 from 

tests which were performed at the 1-st Unit of Dukovany NPP (Ref 17), 4-th Unit of Dukovany 

NPP (Ref 22), Paks NPP (Ref 1) and Loviisa NPP (Ref 1) on the next Figure 5. The conformity 

of results from other loops is consistent. 

Figure 5: Comparison of Mixing Factors Related to the Loop1 at Different VVER-440 Type 

Plants 
4-4 

4.2 Measurement uncertainty

According to the equations in the Chapter 4, there are two following key parameters, which 

measurement uncertainty is crucial to assess the absolute error of the calculated mixing factor 

matrix: fuel assemblies outlet temperature measurement and cold loop temperature 

measurement. In a VVER-440 reactor, 210 fuel assemblies (FA) are equipped with outlet 

temperature measurements (thermocouples layout see the Figure 2). These temperatures are 

fundamental information in on-line core monitoring. Using them the radial distribution of the 

thermal neutron flux, the radial distribution of the heat power, mass flow of the fuel assemblies 

and by-pass mass flows are calculated. These temperatures play a significant role in the power 

limitation of the reactor too. Thermocouples TCHA 2076 at FA outlet are of Cr-Al type with the 

guaranteed measurement range 0-400°C and the declared overall measurement channel 

accuracy is 1.00% (Ref 21). There were performed detailed analysis of FA outlet temperature 

measurement channel accuracy in (Ref 22) and rather better accuracy was calculated to ±2.2 K, 

which is at about 0.85%. The real fuel outlet temperature measurement accuracy is better also 

due to TC calibration. There was performed calibration of in-core and loop thermocouples 

before the above described experiment at NPP Dukovany in order to minimise measurement 

uncertainty. The calibration is usually performed during especial isothermal modes at several 

temperature levels against accurate thermo resistors in primary loops. Such calibration is 

usually performed every year after refuelling and the average value of the mean root squared 

deviation of corrections for TC in reactor and TR in loops is at about 0.6°C (Ref 17). There are 

two thermo-couples and one thermo resistor in each cold and hot leg of VVER 1000. 

Thermoresistors (TR) TSP-8053 were used to measure coolant temperature in the cold primary 

loop during above described tests at Dukovany NPP. According to (Ref 22) the overall accuracy 

of loop temperature measurement (based on TR) is ±0.9°C, which is at about 0.35%. Then 

combined error of calculated mixing coefficients is at about 4.7% based on measurement 

channel accuracy from (Ref 22). A consistent error of the mixing coefficients was evaluated to 

about 3% in frame of similar tests which were performed at the Paks NPP (Ref 1). Above 

calculated value of combined error is valid for test which consists of 1 set of measurement in a 

definite time only. There were performed several sets of measurement for each test 

configuration under different coolant temperature. Thus over predicted matrix of linear equations 

had to be solved using least square method for each test configuration. This approach leads to 

reducing the resultant value of the calculated mixing factor accuracy. It was confirmed in 

(Ref 22), where the estimation of the least square method applied in such tests was performed. 

The values of the mean root squared deviation of differences between measured and finally 

calculated mixing factors varied from 0 to 0.15 with the most represented value 0.01-0.03 

(occurrence at 117 fuel assemblies from 210). Such low values prove a good accuracy of mixing 

factors which was measured in frame of experimental tests at Dukovany NPP.
5-1 

5. INPUT MODEL DESCRIPTION

Two extensive TRACE input decks of VVER-440/213 reactor was developed in TES Company 

in frame of R&D project 1H-PK/61. The aim of this project was to research of spatial thermohydraulic processes in VVER-440/213 reactors, especially in areas of upper plenum and reactor 

upper head. Both TRACE models deviate particularly from theta discrimination of reactor. Both 

models include all important reactor pressure vessel (RPV) internals. The 3-rd Unit of Dukovany 

NPP (Czech Republic) was chosen as reference plant. The basic hydraulics of these TRACE 

models was validated against plant data and reference data from Dukovany NPP plant 

database. 

5.1 8-Theta TRACE model

The original 8-Theta TRACE model of VVER 440/213 reactor consists of 2400 3-D cells. The 

VESSEL component consists of 32 axial layers, 8 azimuthal theta sectors and 6 radial rings 

(see the Nodalisation scheme on the Figure B_1 in the Appendix B). The reactor core consists 

of 12 axial levels, 4 radial rings and 8 theta sectors. A spatial core power distribution was 

implemented using measured plant data. Control rods (HRK) channels in the core and guiding 

tubes of control rods were separately modelled as 24 PIPE components consisting of 480 

volumes. 

5.2 16-Theta TRACE model

The original 8-Theta TRACE input deck of VVER 440/213 reactor was modified in order to 

evaluate the influence of VESSEL component “Theta-mesh” density on the calculated mixing 

factors. The modified 16-Theta TRACE input deck consists of 4580 3-D cells. The modified 

VESSEL component consists of 32 axial layers, 16 azimuthal sectors and 6 radial rings (see the 

Nodalisation scheme on the Figure C_1 in the Appendix C). The reactor core consists of 12 

axial levels, 4 radial rings and 8 (eventually 16) theta sectors. The comparison of the core radial 

and theta discrimination of both TRACE models and comparison of relative location of THETA 

sectors to the reactor inlet nozzles is shown at the next Figure 6. The outer diameter of the core 

represents inner wall of the core barrel. 

Figure 6: Comparison of the VVER-440/213 Reactor Core Theta and Radial Discretisation 
5-2 

5.3 Validation of the TRACE models basic thermo-hydraulics

The basic hydraulics of these TRACE models was validated against plant data and reference 

data from Dukovany NPP plant database (Ref 11) and data from measurement performed at 

reference 3-rd Unit of NPP Dukovany (Ref 23). For both TRACE models, the standard initial 

conditions representing normal operation conditions were implemented: 

Table 2: TRACE Input Deck Initial Conditions Under Normal Operation Mode 

Parameter Unit TRACE model [24] Ref. data 8-Theta 16-Theta 

Pressure at reactor outlet nozzles MPa 12.5 12.26 (Ref 11) 

Temperature at reactor inlet nozzles °C 266.9 267 ± 2 (Ref 11) 

Flow rate in one loop m3/h 6858.2 (6 713÷7087) ±160 

(Ref 23) 

Core power MWt 1375 1375 (Ref 11) 

The comparison of basic reactor hydraulic parameters for both TRACE models to the plant 

reference data is presented in the next table. 

Table 3: TRACE Model Basic Thermo-Hydraulics Under Normal Operation Mode 

Parameter Unit TRACE model [24] Ref. data (Ref 11) 8-Theta 16-Theta 

Average coolant temp. increase °C 30.1 30.1 31.0 

Fuel assembly channel flow kg/s 24.1 24.1 24.40 

Control rod assembly channel flow kg/s 33.4 33.4 32.46 

Core bypass % 8.9 8.9 8.5 

Reactor inlet pressure drop MPa 0.0810 0.0811 0.0811 

Core pressure drop MPa 0.2009 0.2018 0.2015 

Reactor outlet pressure drop MPa 0.0265 0.0261 0.0266 
5-3 
6-1 

6. RESULTS 

Several comparative steady-state calculations of two NPP Dukovany experiments at the 1st unit 

of NPP Dukovany in 1997 and at the 4th unit of NPP Dukovany in 1987 were performed using 

the TRACE V4.160 input decks. The fields of calculated mixing factors relevant to the all of 

investigated loops at Dukovany NPP are presented in the Appendix A. An investigated loop was 

subcoolled by 5°C in a comparison with another loops and the temperature at the fuel 

assemblies inlet nozzles was subsequently measured. Then the mixing factor representing the 

weight of a particular single loop was analysed using calculated data. There is presented the 

method of calculation of mixing factor related to the investigated Loop1. Based on equations (1), 

(2) and (3) in the Chapter 4 and regarding particular test configuration described on the Figure 

4.1_1 the equation of mixing coefficients relating to k t-h fuel assembly and to the investigated 

Loop1 is given by: 

1 62

62

1

÷

÷

−

− =

Loop Loop

k Loop

k TT

TT

B (4) 

Where TLoop1 ..... temperature of investigated cold leg loop 1 

TLoop2÷6 ..... temperatures of non-investigated cold leg loops 2÷6 

Mixing factors related to other loops were calculated by the same way. Thus six matrices of 

mixing factors (each for one loop) were realised. The comparison of mixing factors calculated 

from TRACE post-test calculation to the Dukovany NPP experimentally measured data is 

presented bellow. 

6.1 Experiment at the 1-st unit of NPP Dukovany

The analysed experimental test of coolant mixing in the VVER 440/213 reactor under steady 

state conditions was performed at the 1st unit of NPP Dukovany in 1997 (Ref 17). Three factors 

were compared in order to evaluate influence of theta discretisation of TRACE VESSEL 

component on mixing phenomena inside the downcomer and lower plenum of VVER-440/213 

reactor 

• shape of affected area related to a given loop 

• maximal values of mixing factors related to a given loop 

• relative deviation of measured and calculated data to a given segment 

There are presented results related to loop 1, 2 and 3 only. The results of other three loops 4, 5 

and 6 are almost the same due to the plane of symmetry of the VVER 440/213 reactor which 

cuts the reactor vessel between loops 1-6 and 3-4. 

6.1.1 8-ThetaTRACE model results 

The 8-Theta VESSEL component consists of 8 azimuthal sectors THETA. Each of sectors is 

forming an angle 45 degrees – see Figure 6. This is a relatively rough discretisation compare to 
6-2 

measured fields of mixing factors, which covers the sector at about 120 degrees adjacent to the 

investigated loop. Despite the fact that there is less then three theta segments covering the 

sector related to one loop, the calculation of mixing factors using 8 Theta model was performed 

in order to investigate the lowest level of theta discretisation. The results of calculation using 

8-Theta model are documented on the Figure 7. 

0,1

Figure 7: Shape of Affected Area of Mixing Factors (8-Theta model) 

There are also Tables D_1-6 and Figure D_1 in the Appendix D which contains the summary of 

measured (maximal, minimal and averaged values) and TRACE calculated data. The red arrow 

indicates the location of a subcoolled loop, for which mixing factor was calculated. The TRACE 

calculated mixing factor fields correspond to the typical VVER-440 geometry (symmetry) 

analogous to the measured mixing factors. The effect of every loop covers the sector around 

180 degrees (measured sector covers 120 degrees) which is (the same way as measured 

sector) adjacent to the investigated loop – see the Figure 7. There is a significant symmetry of 

calculated sector related to the middle Loop 2 the same way as for measured data. 

The maximal values of TRACE calculated mixing factors related to the all investigated loops are 
6-3 

highlighted in the Tables D_1-6 in the Appendix D and concentrated in the next Table 4. 

Table 4: Maximal Values of of Measured and Calculated Mixing Factors (8-Theta Model) 

Loop No 1 2 3 4 5 6 

measured data 0.800 0.740 0.800 0.710 0.740 0.790 

8-Theta TRACE model 0.711 0.793 0.640 0.655 0.793 0.711 

DIFF [%] -11 7 -20 -8 7 -10 

The comparison of maximal values might be rather confusing due to the relative sharp peaks of 

measured maximal values, therefore experimentally measured values of mixing factors were 

averaged over segments related to TRACE Theta-Radial segments. The reason of weighting of 

the calculated deviation is to depress the significance of accuracy of the near zero values. The 

tables containing relative deviation of measured and calculated data weighted by average value 

of measured mixing factors related to investigated loop are presented in the Appendix D. 

Graphical presentation for loops 1, 2, 3 was done on Figure 8. As we can see from 

Tables D_1-6 there are relatively high values of weighted deviation depending on evaluated 

particular theta sector and radial ring. The maximal values of weighted deviations varies from -

26% to +42% for a given loop. Generally we can say that the highest values of weighted 

deviation occurred at theta sectors related to the investigated loop or at theta sector adjoining to 

the empty sector between loops 1-6 and 3-4. This result corresponds to the azimuthal deflection 

of the coolant streams in the downcomer described in the Chapter 4.1. 

Investigated Loop 1

Investigated Loop 2

Investigated Loop 3
6-4 

Figure 8: Weighted Relative Deviation of Measured and Calc. Mixing Factors (8-Theta Model) 

6.1.2 16-ThetaTRACE model results 

The 16-Theta VESSEL component consists of 16 azimuthal sectors THETA. Each of sector is 

forming an angle 22.5 degrees – see the Figure 6. Thus there are six theta segments covering 

the 120 degree sector related to one loop. The results of calculation using 16 Theta TRACE 

model are documented on the Figure 9 and in detail the results are presented in the tables and 

figures in the Appendix E. The red arrow indicates the location of a subcoolled loop, for which 

mixing factor was calculated. The effect of every loop covers the sector around 157.5 degrees 

(measured sector covers 120 degrees) which is adjacent to the investigated loop. The covered 

sector is due to the finer theta discretisation rather narrower compare to 8-Theta model results 

(180 degrees). The symmetry of calculated sector related to the middle Loop 2 occurred by the 

same way as for measured data and 8-Theta model data. There is a significant symmetry of 

calculated sector related to the middle Loop 2 the same way as for measured data. 

Figure 9: Shape of Affected Area of Mixing Factors (16-Theta model) 

The maximal values of TRACE calculated mixing factors related to the all investigated loops are 

highlighted in the Tables E-1-6 in the Appendix E and concentrated in the next Table 5. 
6-5 

Table 5: Maximal Values of of Measured and Calculated Mixing Factors (16-Theta Model) 

Loop No 1 2 3 4 5 6 

measured data 0.800 0.740 0.800 0.710 0.740 0.790 

16-Theta TRACE model 0.906 0.726 0.716 0.716 0.726 0.907 

DIFF [%] 13 -2 -11 1 -2 15 

The tables containing relative deviation of measured and calculated data weighted by average 

value of measured mixing factors related to investigated loop are also presented in the 

Appendix E. Graphical presentation for loops 1, 2, 3 was done on Figure 10. As we can see 

from Tables E-1-6 there are relatively high values of weighted deviation depending on evaluated 

particular theta sector and radial ring. The maximal values of weighted deviations varies from -

31% to +53% for a given loop. The localisation of the maximal values is more accurate in case 

of 16-Theta model (see highlighted values in the Tables E-1-6). 

Investigated Loop 3

Investigated Loop 1

Investigated Loop 2

Figure 10: Weighted Relative Deviation of Measured and Calc. Mixing Factors (16-Theta Model) 
6-6 

6.1.3 Résumé of the TRACE VESSEL component nodalisation study 

There were three key factors compared in order to evaluate influence of theta discretisation of 

TRACE VESSEL component on mixing phenomena inside the downcomer and lower plenum of 

VVER-440/213 reactor: 

• shape of affected area related to a given loop 

• maximal values of mixing factors related to a given loop 

• relative deviation of measured and calculated data to a given theta-radial segment 

Based on measured data, the effect of every loop approximately covers the sector of 120 

degrees adjacent to the investigated loop. Based on 8-Theta model data, the effect of every 

loop covers the sector around 180 degrees which is adjacent to the investigated loop. Based on 

16 Theta model data, the effect of every loop covers the sector around 157.5 degrees which is 

also adjacent to the investigated loop. The covered sector is due to the finer theta discretisation 

of the 16-Theta model rather narrower compare to 8-Theta model results. Thus 16-Theta model 

gives better results in this case, as it was anticipated. 

The maximum values of measured and calculated were then investigated. The relative 

differences of maximal values of measured and calculated mixing factors are compared in the 

next Table 6 for both 8 Theta TRACE model as well as for 16 Theta model. 

Table 6: The Differences of Maximal Values of Measured and Calculated Mixing Factors 

DIFF [%]

Loop No 1 2 3 4 5 6 

8-Theta TRACE model -11 7 -20 -8 7 -10 

16-Theta TRACE model 13 -2 -11 1 -2 15 

The relative differences of maximal values of mixing factors differ loop by loop, when comparing 

the 8-Theta to the 16-Theta model data, though the absolute values are comparable each other. 

No dependency related to the theta discretisation has been discovered. 

The comparison of maximal values are rather confusing due to the relative sharp peaks of 

measured maximal values, therefore experimentally measured values of mixing factors were 

averaged over segments related to TRACE Theta-Radial segments. Then relative deviations of 

calculated mixing factors vs. measured ones were investigated. These relative deviations were 

weighted by average value of measured mixing factors related to investigated loop in order to 

depress the significance of accuracy of the near-zero values. The comparison of a relative 

deviation of mixing factors calculated by both TRACE models to experimentally measured 

values is presented on the next Figure 11 which gives us a good visualisation of nodalisation 

study result. Based on 8 Theta model data, the maximal values of weighted deviations varies 

from -26% to +42% for a given loop. Based on 16 Theta model data, the maximal values of 

weighted deviations varies from -31% to +53% for a given loop, which is wider range compare 

to the 8-Theta model data. On the other hand the localisation of the maximal values is more 

accurate in case of 16 Theta model (see highlighted values in the Tables E-1-6 in the 

Appendix E). Generally we can say that using 16-Theta model with finer theta discretisation did 

not contribute to significantly better results. This could be (e.g.) a consequence of the following 

factors. The first factor is the location of peak (maximum) of a measured mixing factor against 

given sector boundaries that are worse in case of the 16-Theta model. This should be taken into 
6-7 

account if a new TRACE input deck will be designed. The second factor is a smaller crosssectional area of the 16-Theta model sectors. Thus the weight of any extreme value on average 

value in a particular sector is bigger in comparison with the 8-Theta model. 

DEV

[%]

Figure 11: Comparison of a Calculated Relative Deviation of Mixing Factors (8 vs. 16-Theta) 

6.2 Experiment at the 4-th unit of NPP Dukovany

The analysed experimental test of coolant mixing in the VVER 440/213 reactor under steady 

state conditions was performed at the 4-th unit of NPP Dukovany in 1987 (Ref 22). The fields of 

calculated mixing factors relevant to the all of investigated loops at Dukovany NPP are 

presented in the Appendix A. The maximal values and relative deviations of measured and 

calculated data were analysed in order to verify previous results. 
6-8 

6.2.1 8-ThetaTRACE model results 

The results of comparative calculation of experimental test on 4-th Unit of NPP Dukovany 

confirmed results of previous calculations based on data from 1-st Unit test. The maximal values 

of TRACE calculated mixing factors related to the all investigated loops are presented in the 

next Table 7. 

Table 7: Maximal Values of of Measured and Calculated Mixing Factors (8-Theta Model) 

Loop No 1 2 3 4 5 6 

measured data 0.798 0.788 0.795 0.786 0.781 0.772 

8-Theta TRACE model 0.711 0.793 0.64 0.655 0.793 0.711 

DIFF [%] -11 1 -19 -17 2 -8 

Graphs of weighted deviations of calculated and measured mixing factors for all investigated 

loops are presented in the Appendix F. The maximal value of weighted deviations varies from 

-46% to +35% for a given loop. 

6.2.2 16-ThetaTRACE model results 

The results of comparative calculation of experimental test on 4-th Unit of NPP Dukovany 

confirmed results of previous calculations based on data from 1-st Unit test. The maximal values 

of TRACE calculated mixing factors related to the all investigated loops are presented in the 

next Table 8. 

Table 8: Maximal Values of of Measured and Calculated Mixing Factors (16-Theta Model) 

Loop No 1 2 3 4 5 6 

measured data 0.798 0.788 0.795 0.786 0.781 0.772 

16-Theta TRACE model 0.906 0.726 0.716 0.716 0.726 0.907 

DIFF [%] 14 -8 -10 -9 -7 17 

Graphs of weighted deviations of calculated and measured mixing factors for all investigated 

loops are presented in the Appendix G. The maximal value of weighted deviations varies from 

-48% to +51% for a given loop. 

 
7-1 

7. RUN STATISTICS 

The transients were calculated on personal computer with AMD Athlon X2 4200+ processor 

2.2 GHz under Microsoft Windows XP Professional, Service Pack 2. The run statistics is shown 

in Table 9 and Table 10. The calculations run substantially slower than real time. 

Table 9: Run statistics (8-Theta Model) 

Number of components 335 

Number of time steps 79 775 

Transient time 1000 s 

CPU time 29 747 s 

CPU time / Transient time 29.7 

Table 10: Run statistics (16-Theta Model) 

Number of components 476 

Number of time steps 120 887 

Transient time 1000 s 

CPU time 134 695 s 

CPU time / Transient time 134.7 
7-2 
8-1 

8. CONCLUSIONS

The new TRACE input decks of VVER-440/213 reactor were introduced in this paper. Mixing 

factors at the core inlet were defined and experiments under normal operation conditions at the 

1-st unit of NPP Dukovany in 1997 and at the 4-th Unit of NPP Dukovany in 1987 were 

described. The measured mixing factors at the inlet of VVER-440 reactor were presented as 

results of these tests. 

TRACE post-test calculations of VVER-440/213 mixing factors were presented in this paper. 

Calculated mixing factors were compared to measured ones at NPP Dukovany in order to 

investigate applicability of the TRACE code and the developed TRACE input decks to solve 

coolant mixing problems in VVER-440/213 type of reactors. Then the VESSEL component 

nodalisation study was performed to analyse the influence of theta discretisation on calculated 

mixing factors. It was showed that the calculated results indicate good agreement with the 

measured data first of all from qualitative point of view. The evaluation of calculated results from 

quantitative point of view was not so satisfactory. There are relatively high deviations between 

measured and calculated mixing factors even using fine 16-Theta discretisation of the VESSEL 

component. Though applicability of the TRACE code and the developed TRACE input decks 

were demonstrated to solve the coolant mixing phenomena in VVER 440/213 type of reactors. 

Moreover there was presented attainable accuracy of such calculations using the TRACE code. 

The performed TRACE nodalisation study indicated that THETA division of VESSEL component 

had low influence on calculated mixing factors accuracy. It was stated, that finer THETA division 

gives better results in case of shape (outer boundaries) of mixing factors fields but not in a case 

of average mixing factor values in a given sectors. An exception was found in sectors containing 

peak or extreme value of measured mixing factors. It was recommended to carefully prepare a 

design of TRACE input deck of a VESSEL component. 

Although a lot of work had been done in frame of this project, further investigation is necessary 

to asses the TRACE code application for mixing phenomena of VVER-440 (and other) reactors. 
8-2 
9-1 

9. REFERENCES

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Base. Nuclear Engineering and Design 235 (2005), 421-443 

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Type Reactors With the Code CFX-5.5.1. Technical Meeting on Use of Computational Fluid 

Dynamics (CFD) Codes for Safety Analysis of Reactor Systems, including Containment. 11-

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Nuclear Regulatory Commission, October 2008 
9-2 

15. Bajorek S. at al. TRACE V5.0 Assessment Manual – Main Report. Division of Risk 

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Regulatory Commission 

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A-1 

APPENDIX A 

MEASURED MIXING FACTORS AT THE DUKOVANY NPP 
A-2 

INTRODUCTION

In this appendix, the results of experimental investigations of coolant mixing in the VVER 

440/213 reactor under steady state conditions at the 1-st Unit of NPP Dukovany in 1997 and at 

the 4-th Unit of NPP in 1987 Dukovany are presented. The fields of measured mixing factors 

relevant to the all of investigated loops at Dukovany NPP are shown. 
A-3 

5

1

2

4 3

6

1

4 3

6

2 5

5

1

2

4 3

6

1

4 3

6

2 5

Figure A-1 Measured Mixing Factors at the 1-st Unit of Dukovany NPP 1997 (Ref 17) 
A-4 

Figure A-2 Measured Mixing Factors at the 4-thUnit of Dukovany NPP 1987 (Ref 22)
 B-1 

APPENDIX B 

NODALISATION OF THE 8-THETA VESSEL COMPONENT OF 

VVER-440/213 REACTOR 
 B-2 

Figure B-1 Nodalisation of the 8-Theta VESSEL Component of VVER-440/213 Reactor
C-1 

APPENDIX C 

NODALISATION OF THE 16-THETA VESSEL COMPONENT OF 

VVER-440/213 REACTOR 
C-2 

Figure C-1 Nodalisation of the 16-Theta VESSEL Component of VVER-440/213 Reactor 
D-1 

APPENDIX D 

COMPARISON OF MEASURED AND CALCULATED MIXING FACTORS 

1-ST UNIT OF NPP DUKOVANY 1997 (8-THETA MODEL) 
D-2 

INTRODUCTION 

In this appendix, there are demonstrated Tables D-1÷6 and Figure D-1 which contains the 

summary of measured (maximal, minimal and averaged values) and calculated data using 

8-Theta TRACE VESSEL input deck. The measured data came from experimental 

investigations of coolant mixing in the VVER-440/213 reactor under steady-state conditions at 

the 1-st unit of NPP Dukovany in 1997. The Tables D-1÷6 contain relative deviation of 

measured and calculated data weighted by average value of measured mixing factors related to 

investigated loop. The Figure D-1 contain 6 graphs (each for given investigated loop) of 

weighted relative deviation of measured an calculated mixing factors. The X-axis represents 

modelled Theta sectors. There are numbers of radial rings as independent parameter in these 

graphs. 
D-3 

Table D-1 Comparison of Measured an Calculated (8-Theta model) Mixing Factors for Loop1 

LOOP1 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.200 0.100 0.147 0.007 -6 0.150 0.050 0THETA2 (adj. to Loop2) 0.300 0.250 0.264 0.068 -15 0.400 0.100 0THETA3 (adj. to Loop1) 0.400 0.300 0.356 0.113 -26 0.600 0.400 0THETA4 (betw. Loop1-6) 0.400 0.200 0.319 0.107 -20 0.650 0.100 0THETA5 (adj. to Loop6) 0.000 0.000 0.226 0.021 -14 0.000 0.000 0THETA6 (adj. to Loop5) 0.200 0.150 0.138 0.014 -5 0.100 0.050 0THETA7 (adj. to Loop4) 0.100 0.100 0.079 0.007 -2 0.050 0.050 0THETA8 (betw. Loop3-4) 0.100 0.100 0.082 0.007 -2 0.050 0.050 0

LOOP1 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.000 0.000 0.000 0.008 0 0.000 0.000 0THETA2 (adj. to Loop2) 0.250 0.050 0.084 0.187 3 0.250 0.050 0THETA3 (adj. to Loop1) 0.750 0.300 0.556 0.690 22 0.800 0.300 0THETA4 (betw. Loop1-6) 0.750 0.050 0.525 0.385 -22 0.750 0.050 0THETA5 (adj. to Loop6) 0.000 0.000 0.070 0.121 1 0.000 0.000 0THETA6 (adj. to Loop5) 0.000 0.000 0.000 0.030 0 0.000 0.000 0THETA7 (adj. to Loop4) 0.000 0.000 0.000 0.007 0 0.000 0.000 0THETA8 (betw. Loop3-4) 0.000 0.000 0.000 0.006 0 0.000 0.000 0
D-4 

Table D-2 Comparison of Measured an Calculated (8-Theta model) Mixing Factors for Loop2 

LOOP2 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.250 0.250 0.165 0.156 0 0.350 0.100 0THETA2 (adj. to Loop2) 0.250 0.200 0.192 0.485 17 0.600 0.300 0THETA3 (adj. to Loop1) 0.250 0.050 0.060 0.517 8 0.500 0.050 0THETA4 (betw. Loop1-6) 0.000 0.000 0.000 0.256 0 0.150 0.050 0THETA5 (adj. to Loop6) 0.000 0.000 0.000 0.014 0 0.000 0.000 0THETA6 (adj. to Loop5) 0.000 0.000 0.000 0.015 0 0.000 0.000 0THETA7 (adj. to Loop4) 0.050 0.050 0.037 0.021 0 0.050 0.050 0THETA8 (betw. Loop3-4) 0.150 0.100 0.081 0.086 0 0.100 0.050 0

LOOP2 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.500 0.050 0.173 0.167 0 0.500 0.100 0THETA2 (adj. to Loop2) 0.700 0.450 0.625 0.753 24 0.740 0.500 0THETA3 (adj. to Loop1) 0.650 0.100 0.397 0.178 -26 0.650 0.100 0THETA4 (betw. Loop1-6) 0.150 0.050 0.013 0.117 0 0.100 0.050 0THETA5 (adj. to Loop6) 0.000 0.000 0.000 0.027 0 0.000 0.000 0THETA6 (adj. to Loop5) 0.000 0.000 0.000 0.011 0 0.000 0.000 0THETA7 (adj. to Loop4) 0.000 0.000 0.000 0.021 0 0.000 0.000 0THETA8 (betw. Loop3-4) 0.050 0.050 0.006 0.057 0 0.050 0.050 0
D-5 

Table D-3 Comparison of Measured an Calculated (8-Theta model) Mixing Factors for Loop3 

LOOP3 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.200 0.150 0.163 0.655 24 0.550 0.250 0THETA2 (adj. to Loop2) 0.150 0.100 0.091 0.269 5 0.400 0.100 0THETA3 (adj. to Loop1) 0.050 0.050 0.018 0.224 1 0.050 0.050 0THETA4 (betw. Loop1-6) 0.000 0.000 0.002 0.127 0 0.000 0.000 0THETA5 (adj. to Loop6) 0.000 0.000 0.003 0.087 0 0.000 0.000 0THETA6 (adj. to Loop5) 0.050 0.050 0.034 0.101 1 0.050 0.050 0THETA7 (adj. to Loop4) 0.100 0.100 0.089 0.185 3 0.250 0.050 0THETA8 (betw. Loop3-4) 0.200 0.150 0.152 0.450 13 0.500 0.250 0

LOOP3 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.750 0.450 0.623 0.640 3 0.800 0.500 0THETA2 (adj. to Loop2) 0.450 0.050 0.204 0.053 -9 0.500 0.050 0THETA3 (adj. to Loop1) 0.050 0.050 0.004 0.012 0 0.050 0.050 0THETA4 (betw. Loop1-6) 0.000 0.000 0.000 0.022 0 0.000 0.000 0THETA5 (adj. to Loop6) 0.000 0.000 0.000 0.009 0 0.000 0.000 0THETA6 (adj. to Loop5) 0.000 0.000 0.000 0.020 0 0.000 0.000 0THETA7 (adj. to Loop4) 0.150 0.050 0.052 0.184 2 0.150 0.050 0THETA8 (betw. Loop3-4) 0.700 0.200 0.395 0.457 7 0.700 0.200 0
D-6 

Table D-4 Comparison of Measured an Calculated (8-Theta model) Mixing Factors for Loop4 

LOOP4 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.150 0.050 0.104 0.185 3 0.350 0.050 0THETA2 (adj. to Loop2) 0.100 0.050 0.053 0.101 1 0.050 0.050 0THETA3 (adj. to Loop1) 0.100 0.050 0.042 0.087 1 0.000 0.000 0THETA4 (betw. Loop1-6) 0.050 0.050 0.053 0.127 1 0.050 0.050 0THETA5 (adj. to Loop6) 0.000 0.000 0.055 0.224 3 0.000 0.000 0THETA6 (adj. to Loop5) 0.150 0.100 0.088 0.269 5 0.250 0.050 0THETA7 (adj. to Loop4) 0.250 0.150 0.176 0.655 28 0.600 0.200 0THETA8 (betw. Loop3-4) 0.250 0.200 0.188 0.450 16 0.550 0.250 0

LOOP4 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.350 0.050 0.100 0.184 3 0.200 0.050 0THETA2 (adj. to Loop2) 0.000 0.000 0.000 0.020 0 0.000 0.000 0THETA3 (adj. to Loop1) 0.000 0.000 0.000 0.009 0 0.000 0.000 0THETA4 (betw. Loop1-6) 0.000 0.000 0.000 0.022 0 0.050 0.050 0THETA5 (adj. to Loop6) 0.000 0.000 0.000 0.012 0 0.000 0.000 0THETA6 (adj. to Loop5) 0.300 0.050 0.090 0.053 -1 0.300 0.050 0THETA7 (adj. to Loop4) 0.650 0.300 0.495 0.640 23 0.710 0.350 0THETA8 (betw. Loop3-4) 0.650 0.300 0.476 0.457 -3 0.650 0.200 0
D-7 

Table D-5 Comparison of Measured an Calculated (8-Theta model) Mixing Factors for Loop5 

LOOP5 

RING 1 

measured data TRACE 

DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.200 0.050 0.113 0.021 -3 0.150 0.050 0THETA2 (adj. to Loop2) 0.100 0.050 0.065 0.015 -1 0.050 0.050 0THETA3 (adj. to Loop1) 0.100 0.050 0.036 0.014 0 0.000 0.000 0THETA4 (betw. Loop1-6) 0.200 0.050 0.075 0.256 4 0.450 0.050 0THETA5 (adj. to Loop6) 0.000 0.000 0.179 0.517 19 0.000 0.000 0THETA6 (adj. to Loop5) 0.350 0.200 0.280 0.485 18 0.650 0.400 0THETA7 (adj. to Loop4) 0.350 0.250 0.285 0.156 -11 0.550 0.200 0THETA8 (betw. Loop3-4) 0.250 0.200 0.209 0.086 -8 0.250 0.050 0

LOOP5 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.000 0.000 0.000 0.021 0 0.000 0.000 0THETA2 (adj. to Loop2) 0.000 0.000 0.000 0.011 0 0.000 0.000 0THETA3 (adj. to Loop1) 0.000 0.000 0.000 0.027 0 0.000 0.000 0THETA4 (betw. Loop1-6) 0.450 0.050 0.000 0.117 0 0.500 0.050 0THETA5 (adj. to Loop6) 0.000 0.000 0.193 0.178 -1 0.000 0.000 0THETA6 (adj. to Loop5) 0.700 0.500 0.628 0.753 25 0.740 0.500 0THETA7 (adj. to Loop4) 0.600 0.150 0.328 0.167 -17 0.550 0.150 0THETA8 (betw. Loop3-4) 0.100 0.050 0.034 0.057 0 0.100 0.050 0
D-8 

Table D-6 Comparison of Measured an Calculated (8-Theta model) Mixing Factors for Loop6 

LOOP6 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.150 0.100 0.094 0.007 -2 0.100 0.050 0THETA2 (adj. to Loop2) 0.200 0.150 0.150 0.014 -6 0.150 0.050 0THETA3 (adj. to Loop1) 0.300 0.200 0.217 0.021 -13 0.300 0.050 0THETA4 (betw. Loop1-6) 0.450 0.250 0.307 0.107 -18 0.650 0.250 0THETA5 (adj. to Loop6) 0.000 0.000 0.316 0.113 -19 0.000 0.000 0THETA6 (adj. to Loop5) 0.300 0.150 0.209 0.068 -9 0.450 0.100 0THETA7 (adj. to Loop4) 0.150 0.050 0.057 0.007 -1 0.200 0.050 0THETA8 (betw. Loop3-4) 0.100 0.050 0.032 0.007 0 0.000 0.000 0

LOOP6 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 8-Theta model max. value min. value 

v

THETA1 (adj. to Loop3) 0.000 0.000 0.000 0.007 0 0.000 0.000 0THETA2 (adj. to Loop2) 0.000 0.000 0.000 0.030 0 0.000 0.000 0THETA3 (adj. to Loop1) 0.150 0.050 0.020 0.121 1 0.100 0.050 0THETA4 (betw. Loop1-6) 0.750 0.150 0.375 0.385 1 0.790 0.100 0THETA5 (adj. to Loop6) 0.000 0.000 0.630 0.690 11 0.000 0.000 0THETA6 (adj. to Loop5) 0.450 0.050 0.159 0.187 1 0.400 0.050 0THETA7 (adj. to Loop4) 0.050 0.050 0.000 0.008 0 0.050 0.050 0THETA8 (betw. Loop3-4) 0.000 0.000 0.000 0.006 0 0.000 0.000 0
D-9 

Figure D-1 Comparison of Weighted Relative Deviation of Measured and Calculated (8-The
E-1 

APPENDIX E 

COMPARISON OF MEASURED AND CALCULATED MIXING FACTORS 

1-ST UNIT OF NPP DUKOVANY 1997 (16-THETA MODEL) 
E-2 

INTRODUCTION 

In this appendix, there are demonstrated Tables E-1÷6 and Figure E-1 which contains the 

summary of measured (maximal, minimal and averaged values) and calculated data using 

16-Theta TRACE VESSEL input deck. The measured data came from experimental 

investigations of coolant mixing in the VVER-440/213 reactor under steady-state conditions at 

the 1-st unit of NPP Dukovany in 1997. The Tables D-1÷6 contain relative deviation of 

measured and calculated data weighted by average value of measured mixing factors related to 

investigated loop. The Figure E-1 contains 6 graphs (each for given investigated loop) of 

weighted relative deviation of measured a calculated mixing factors. The X-axis represents 

modelled Theta sectors. There are numbers of radial rings as independent parameter in these 

graphs. 
E-3 

Table E-1 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop1 

LOOP1 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.150 0.150 0.145 0.020 -5 0.100 0.050 THETA4 (betw. Loop3-2) 0.250 0.200 0.196 0.029 -10 0.200 0.050 THETA3 (adj. to Loop2) 0.300 0.300 0.264 0.056 -16 0.350 0.100 THETA4 (betw. Loop2-1) 0.350 0.350 0.324 0.107 -21 0.400 0.250 THETA5 (adj. to Loop1) 0.400 0.300 0.361 0.181 -19 0.550 0.450 THETA4 (betw. Loop1-6) 0.400 0.350 0.361 0.230 -14 0.650 0.450 THETA7 (betw. Loop1-6) 0.350 0.350 0.315 0.166 -14 0.550 0.350 THETA8 (betw. Loop1-6) 0.300 0.250 0.276 0.008 -22 0.350 0.150 THETA9 (adj. to Loop6) 0.250 0.250 0.223 0.008 -14 0.200 0.100 THETA10 (betw. Loop6-5) 0.200 0.200 0.184 0.007 -10 0.150 0.100 THETA11 (adj. to Loop5) 0.200 0.150 0.138 0.007 -5 0.100 0.050 THETA12 (betw. Loop5-4) 0.100 0.100 0.095 0.007 -2 0.050 0.050 THETA13 (adj. to Loop4) 0.000 0.000 0.077 0.007 -2 0.050 0.050 THETA14 (betw. Loop4-3) 0.000 0.000 0.074 0.007 -2 0.050 0.050 THETA15 (betw. Loop4-3) 0.100 0.100 0.080 0.010 -2 0.050 0.050 THETA16 (betw. Loop4-3) 0.200 0.100 0.105 0.015 -3 0.000 0.000 
E-4 

Table E-1 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop1 (continued) 

LOOP1 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.000 0.000 0.000 0.011 0 0.000 0.000 THETA4 (betw. Loop3-2) 0.000 0.000 0.000 0.024 0 0.000 0.000 THETA3 (adj. to Loop2) 0.150 0.050 0.069 0.110 1 0.150 0.050 THETA4 (betw. Loop2-1) 0.450 0.200 0.273 0.343 6 0.500 0.150 THETA5 (adj. to Loop1) 0.700 0.450 0.585 0.872 50 0.750 0.500 THETA4 (betw. Loop1-6) 0.750 0.650 0.713 0.824 24 0.800 0.750 THETA7 (betw. Loop1-6) 0.700 0.400 0.533 0.397 -22 0.700 0.350 THETA8 (betw. Loop1-6) 0.400 0.150 0.253 0.069 -14 0.400 0.150 THETA9 (adj. to Loop6) 0.150 0.050 0.043 0.022 0 0.100 0.050 THETA10 (betw. Loop6-5) 0.050 0.050 0.002 0.008 0 0.000 0.000 THETA11 (adj. to Loop5) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA12 (betw. Loop5-4) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA13 (adj. to Loop4) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA14 (betw. Loop4-3) 0.000 0.000 0.000 0.006 0 0.000 0.000 THETA15 (betw. Loop4-3) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA16 (betw. Loop4-3) 0.000 0.000 0.000 0.007 0 0.000 0.000 
E-5 

Table E-2 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop 2 

LOOP2 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.250 0.250 0.163 0.399 12 0.250 0.100 THETA4 (betw. Loop3-2) 0.200 0.200 0.197 0.486 17 0.650 0.300 THETA3 (adj. to Loop2) 0.250 0.250 0.197 0.608 25 0.700 0.650 THETA4 (betw. Loop2-1) 0.250 0.100 0.152 0.623 22 0.700 0.500 THETA5 (adj. to Loop1) 0.100 0.050 0.055 0.575 9 0.500 0.250 THETA4 (betw. Loop1-6) 0.000 0.000 0.000 0.549 0 0.250 0.050 THETA7 (betw. Loop1-6) 0.000 0.000 0.000 0.389 0 0.050 0.050 THETA8 (betw. Loop1-6) 0.000 0.000 0.000 0.008 0 0.000 0.000 THETA9 (adj. to Loop6) 0.000 0.000 0.000 0.008 0 0.000 0.000 THETA10 (betw. Loop6-5) 0.000 0.000 0.000 0.008 0 0.000 0.000 THETA11 (adj. to Loop5) 0.000 0.000 0.000 0.008 0 0.000 0.000 THETA12 (betw. Loop5-4) 0.050 0.050 0.006 0.008 0 0.000 0.000 THETA13 (adj. to Loop4) 0.000 0.000 0.043 0.009 0 0.000 0.000 THETA14 (betw. Loop4-3) 0.100 0.050 0.050 0.010 -1 0.000 0.000 THETA15 (betw. Loop4-3) 0.100 0.100 0.083 0.062 -1 0.000 0.000 THETA16 (betw. Loop4-3) 0.150 0.150 0.123 0.343 8 0.050 0.050 
E-6 

Table E-2 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop 2 (continued) 

LOOP2 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.250 0.100 0.142 0.276 6 0.300 0.150 THETA4 (betw. Loop3-2) 0.650 0.300 0.446 0.494 6 0.650 0.300 THETA3 (adj. to Loop2) 0.700 0.650 0.659 0.719 12 0.740 0.600 THETA4 (betw. Loop2-1) 0.700 0.500 0.609 0.616 1 0.700 0.500 THETA5 (adj. to Loop1) 0.500 0.250 0.339 0.133 -21 0.500 0.200 THETA4 (betw. Loop1-6) 0.250 0.050 0.094 0.095 0 0.200 0.050 THETA7 (betw. Loop1-6) 0.050 0.050 0.005 0.115 0 0.000 0.000 THETA8 (betw. Loop1-6) 0.000 0.000 0.000 0.017 0 0.000 0.000 THETA9 (adj. to Loop6) 0.000 0.000 0.000 0.009 0 0.000 0.000 THETA10 (betw. Loop6-5) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA11 (adj. to Loop5) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA12 (betw. Loop5-4) 0.000 0.000 0.000 0.008 0 0.000 0.000 THETA13 (adj. to Loop4) 0.000 0.000 0.000 0.010 0 0.000 0.000 THETA14 (betw. Loop4-3) 0.000 0.000 0.000 0.014 0 0.000 0.000 THETA15 (betw. Loop4-3) 0.000 0.000 0.000 0.043 0 0.050 0.050 THETA16 (betw. Loop4-3) 0.050 0.050 0.036 0.139 1 0.100 0.050 
E-7 

Table E-3 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop3 

LOOP3 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.200 0.200 0.168 0.557 19 0.550 0.250 THETA4 (betw. Loop3-2) 0.000 0.000 0.137 0.479 14 0.450 0.200 THETA3 (adj. to Loop2) 0.150 0.100 0.094 0.352 7 0.300 0.100 THETA4 (betw. Loop2-1) 0.100 0.100 0.049 0.289 3 0.100 0.050 THETA5 (adj. to Loop1) 0.050 0.050 0.010 0.258 1 0.000 0.000 THETA4 (betw. Loop1-6) 0.000 0.000 0.003 0.245 0 0.000 0.000 THETA7 (betw. Loop1-6) 0.000 0.000 0.002 0.218 0 0.000 0.000 THETA8 (betw. Loop1-6) 0.000 0.000 0.002 0.033 0 0.000 0.000 THETA9 (adj. to Loop6) 0.000 0.000 0.003 0.023 0 0.000 0.000 THETA10 (betw. Loop6-5) 0.000 0.000 0.007 0.025 0 0.000 0.000 THETA11 (adj. to Loop5) 0.050 0.050 0.039 0.029 0 0.050 0.050 THETA12 (betw. Loop5-4) 0.100 0.100 0.056 0.039 0 0.050 0.050 THETA13 (adj. to Loop4) 0.100 0.100 0.093 0.053 -1 0.150 0.050 THETA14 (betw. Loop4-3) 0.150 0.150 0.116 0.070 -2 0.300 0.150 THETA15 (betw. Loop4-3) 0.200 0.200 0.155 0.090 -3 0.450 0.250 THETA16 (betw. Loop4-3) 0.150 0.150 0.170 0.570 20 0.500 0.250 
E-8 

Table E-3 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop3 (continued) 

LOOP3 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.750 0.550 0.664 0.659 -1 0.800 0.650 THETA4 (betw. Loop3-2) 0.650 0.300 0.437 0.475 5 0.650 0.350 THETA3 (adj. to Loop2) 0.350 0.100 0.192 0.194 0 0.350 0.100 THETA4 (betw. Loop2-1) 0.150 0.050 0.045 0.067 0 0.100 0.050 THETA5 (adj. to Loop1) 0.000 0.000 0.000 0.021 0 0.000 0.000 THETA4 (betw. Loop1-6) 0.000 0.000 0.000 0.021 0 0.000 0.000 THETA7 (betw. Loop1-6) 0.000 0.000 0.000 0.034 0 0.000 0.000 THETA8 (betw. Loop1-6) 0.000 0.000 0.000 0.009 0 0.000 0.000 THETA9 (adj. to Loop6) 0.000 0.000 0.000 0.008 0 0.000 0.000 THETA10 (betw. Loop6-5) 0.000 0.000 0.000 0.009 0 0.000 0.000 THETA11 (adj. to Loop5) 0.000 0.000 0.000 0.015 0 0.000 0.000 THETA12 (betw. Loop5-4) 0.000 0.000 0.000 0.034 0 0.000 0.000 THETA13 (adj. to Loop4) 0.100 0.050 0.037 0.073 0 0.100 0.050 THETA14 (betw. Loop4-3) 0.300 0.150 0.178 0.159 -1 0.250 0.100 THETA15 (betw. Loop4-3) 0.550 0.300 0.396 0.405 1 0.600 0.300 THETA16 (betw. Loop4-3) 0.750 0.550 0.612 0.708 17 0.750 0.600 
E-9 

Table E-4 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop4 

LOOP4 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.150 0.100 0.099 0.053 -1 0.250 0.050 THETA4 (betw. Loop3-2) 0.050 0.050 0.064 0.039 -1 0.100 0.050 THETA3 (adj. to Loop2) 0.050 0.050 0.054 0.029 0 0.000 0.000 THETA4 (betw. Loop2-1) 0.100 0.050 0.042 0.025 0 0.000 0.000 THETA5 (adj. to Loop1) 0.000 0.000 0.041 0.023 0 0.000 0.000 THETA4 (betw. Loop1-6) 0.100 0.050 0.049 0.033 0 0.000 0.000 THETA7 (betw. Loop1-6) 0.050 0.050 0.054 0.218 3 0.050 0.050 THETA8 (betw. Loop1-6) 0.000 0.000 0.054 0.245 3 0.050 0.050 THETA9 (adj. to Loop6) 0.000 0.000 0.055 0.258 4 0.050 0.050 THETA10 (betw. Loop6-5) 0.000 0.000 0.060 0.289 4 0.050 0.050 THETA11 (adj. to Loop5) 0.100 0.100 0.089 0.352 8 0.150 0.100 THETA12 (betw. Loop5-4) 0.150 0.150 0.132 0.479 15 0.300 0.150 THETA13 (adj. to Loop4) 0.200 0.200 0.177 0.557 22 0.550 0.250 THETA14 (betw. Loop4-3) 0.250 0.200 0.203 0.570 24 0.600 0.300 THETA15 (betw. Loop4-3) 0.000 0.000 0.192 0.090 -6 0.500 0.300 THETA16 (betw. Loop4-3) 0.000 0.000 0.156 0.070 -4 0.400 0.200 
E-10 

Table E-4 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop4 (continued) 

LOOP4 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.250 0.050 0.085 0.073 0 0.100 0.050 THETA4 (betw. Loop3-2) 0.050 0.050 0.004 0.034 0 0.000 0.000 THETA3 (adj. to Loop2) 0.000 0.000 0.000 0.015 0 0.000 0.000 THETA4 (betw. Loop2-1) 0.000 0.000 0.000 0.009 0 0.000 0.000 THETA5 (adj. to Loop1) 0.000 0.000 0.000 0.008 0 0.000 0.000 THETA4 (betw. Loop1-6) 0.000 0.000 0.000 0.009 0 0.000 0.000 THETA7 (betw. Loop1-6) 0.000 0.000 0.000 0.034 0 0.000 0.000 THETA8 (betw. Loop1-6) 0.000 0.000 0.000 0.021 0 0.000 0.000 THETA9 (adj. to Loop6) 0.000 0.000 0.000 0.021 0 0.000 0.000 THETA10 (betw. Loop6-5) 0.000 0.000 0.000 0.067 0 0.050 0.050 THETA11 (adj. to Loop5) 0.200 0.050 0.074 0.194 3 0.200 0.050 THETA12 (betw. Loop5-4) 0.450 0.200 0.278 0.475 18 0.500 0.250 THETA13 (adj. to Loop4) 0.600 0.400 0.504 0.659 26 0.650 0.500 THETA14 (betw. Loop4-3) 0.650 0.600 0.626 0.708 17 0.710 0.600 THETA15 (betw. Loop4-3) 0.650 0.400 0.477 0.405 -11 0.650 0.350 THETA16 (betw. Loop4-3) 0.400 0.150 0.273 0.159 -10 0.350 0.100 
E-11 

Table E-5 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop5 

LOOP5 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.150 0.150 0.114 0.009 -4 0.100 0.050 THETA4 (betw. Loop3-2) 0.150 0.050 0.075 0.008 -2 0.050 0.050 THETA3 (adj. to Loop2) 0.000 0.000 0.064 0.008 -1 0.050 0.050 THETA4 (betw. Loop2-1) 0.050 0.050 0.054 0.008 -1 0.000 0.000 THETA5 (adj. to Loop1) 0.100 0.050 0.031 0.008 0 0.000 0.000 THETA4 (betw. Loop1-6) 0.150 0.150 0.039 0.008 0 0.000 0.000 THETA7 (betw. Loop1-6) 0.050 0.050 0.074 0.389 7 0.050 0.050 THETA8 (betw. Loop1-6) 0.150 0.150 0.125 0.549 17 0.150 0.050 THETA9 (adj. to Loop6) 0.200 0.200 0.175 0.575 22 0.350 0.200 THETA10 (betw. Loop6-5) 0.250 0.250 0.239 0.623 29 0.450 0.300 THETA11 (adj. to Loop5) 0.350 0.200 0.284 0.608 29 0.650 0.400 THETA12 (betw. Loop5-4) 0.000 0.000 0.299 0.486 18 0.600 0.450 THETA13 (adj. to Loop4) 0.350 0.300 0.287 0.399 10 0.500 0.250 THETA14 (betw. Loop4-3) 0.300 0.250 0.252 0.342 7 0.300 0.150 THETA15 (betw. Loop4-3) 0.250 0.200 0.212 0.062 -10 0.250 0.100 THETA16 (betw. Loop4-3) 0.200 0.150 0.159 0.010 -7 0.150 0.050 
E-12 

Table E-5 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop5 (continued) 

LOOP5 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.000 0.000 0.000 0.010 0 0.000 0.000 THETA4 (betw. Loop3-2) 0.000 0.000 0.000 0.008 0 0.000 0.000 THETA3 (adj. to Loop2) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA4 (betw. Loop2-1) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA5 (adj. to Loop1) 0.000 0.000 0.000 0.009 0 0.000 0.000 THETA4 (betw. Loop1-6) 0.000 0.000 0.000 0.017 0 0.000 0.000 THETA7 (betw. Loop1-6) 0.000 0.000 0.000 0.115 0 0.000 0.000 THETA8 (betw. Loop1-6) 0.100 0.050 0.021 0.095 0 0.100 0.050 THETA9 (adj. to Loop6) 0.350 0.100 0.182 0.133 -3 0.300 0.100 THETA10 (betw. Loop6-5) 0.600 0.300 0.452 0.616 23 0.650 0.300 THETA11 (adj. to Loop5) 0.700 0.650 0.673 0.719 10 0.740 0.650 THETA12 (betw. Loop5-4) 0.700 0.500 0.574 0.494 -15 0.700 0.450 THETA13 (adj. to Loop4) 0.500 0.250 0.324 0.276 -5 0.450 0.200 THETA14 (betw. Loop4-3) 0.200 0.100 0.114 0.139 1 0.200 0.100 THETA15 (betw. Loop4-3) 0.050 0.050 0.027 0.043 0 0.050 0.050 THETA16 (betw. Loop4-3) 0.000 0.000 0.000 0.014 0 0.000 0.000 
E-13 

Table E-6 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop6 

LOOP6 

RING 1 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.000 0.000 0.099 0.007 -3 0.100 0.050 THETA4 (betw. Loop3-2) 0.150 0.150 0.118 0.007 -4 0.100 0.050 THETA3 (adj. to Loop2) 0.200 0.200 0.150 0.007 -6 0.150 0.050 THETA4 (betw. Loop2-1) 0.000 0.000 0.178 0.007 -9 0.150 0.050 THETA5 (adj. to Loop1) 0.250 0.200 0.215 0.008 -13 0.250 0.050 THETA4 (betw. Loop1-6) 0.350 0.200 0.262 0.009 -20 0.350 0.100 THETA7 (betw. Loop1-6) 0.400 0.350 0.310 0.107 -19 0.500 0.350 THETA8 (betw. Loop1-6) 0.450 0.300 0.334 0.251 -8 0.650 0.500 THETA9 (adj. to Loop6) 0.350 0.350 0.320 0.205 -11 0.650 0.450 THETA10 (betw. Loop6-5) 0.000 0.000 0.278 0.117 -13 0.500 0.350 THETA11 (adj. to Loop5) 0.300 0.200 0.210 0.063 -9 0.350 0.150 THETA12 (betw. Loop5-4) 0.200 0.100 0.129 0.034 -4 0.250 0.100 THETA13 (adj. to Loop4) 0.100 0.050 0.052 0.024 0 0.100 0.050 THETA14 (betw. Loop4-3) 0.100 0.050 0.016 0.018 0 0.050 0.050 THETA15 (betw. Loop4-3) 0.050 0.050 0.030 0.010 0 0.000 0.000 THETA16 (betw. Loop4-3) 0.100 0.100 0.065 0.007 -1 0.050 0.050 
E-14 

Table E-6 Comparison of Measured an Calculated (16-Theta model) Mixing Factors for Loop6 (continued) 

LOOP6 

RING 3 

measured data TRACE DEVw 

(%) 

measured data 

max. value min. value avg value 16-Theta model max. value min. value 

THETA1 (adj. to Loop3) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA4 (betw. Loop3-2) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA3 (adj. to Loop2) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA4 (betw. Loop2-1) 0.000 0.000 0.000 0.008 0 0.000 0.000 THETA5 (adj. to Loop1) 0.050 0.050 0.006 0.023 0 0.000 0.000 THETA4 (betw. Loop1-6) 0.250 0.050 0.113 0.072 -1 0.200 0.050 THETA7 (betw. Loop1-6) 0.550 0.250 0.377 0.396 2 0.600 0.200 THETA8 (betw. Loop1-6) 0.700 0.600 0.631 0.823 36 0.750 0.550 THETA9 (adj. to Loop6) 0.750 0.550 0.670 0.872 40 0.790 0.550 THETA10 (betw. Loop6-5) 0.650 0.300 0.421 0.342 -10 0.600 0.200 THETA11 (adj. to Loop5) 0.250 0.050 0.139 0.109 -1 0.250 0.050 THETA12 (betw. Loop5-4) 0.100 0.050 0.014 0.023 0 0.050 0.050 THETA13 (adj. to Loop4) 0.000 0.000 0.000 0.011 0 0.000 0.000 THETA14 (betw. Loop4-3) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA15 (betw. Loop4-3) 0.000 0.000 0.000 0.007 0 0.000 0.000 THETA16 (betw. Loop4-3) 0.000 0.000 0.000 0.006 0 0.000 0.000 
E-15 

Figure E-1 Comparison of Weighted Relative Deviation of Measured and Calculated (16-The
F-1 

APPENDIX F 

COMPARISON OF MEASURED AND CALCULATED MIXING FACTORS 

4-TH UNIT OF NPP DUKOVANY 1987 (8-THETA MODEL) 
F-2 

INTRODUCTION 

In this appendix, there is demonstrated Figure F-1 which contains the summary of measured 

and calculated data using 8-Theta TRACE VESSEL input deck. The measured data came from 

experimental investigations of coolant mixing in the VVER-440/213 reactor under steady-state 

conditions at the 4-th unit of NPP Dukovany in 1987. The Figure F-1 contains 6 graphs (each for 

given investigated loop) of weighted relative deviation of measured a calculated mixing factors. 

The X-axis represents modelled Theta sectors. There are numbers of radial rings as 

independent parameter in these graphs. 
F-3 

Figure F-1 Comparison of Weighted Relative Deviation of Measured and Calculated (8-The
G-1 

APPENDIX G 

COMPARISON OF MEASURED AND CALCULATED MIXING FACTORS 

4-TH UNIT OF NPP DUKOVANY 1987 (16-THETA MODEL) 
G-2 

INTRODUCTION 

In this appendix, there is demonstrated Figure G-1 which contains the summary of measured 

and calculated data using 16-Theta TRACE VESSEL input deck. The measured data came from 

experimental investigations of coolant mixing in the VVER-440/213 reactor under steady-state 

conditions at the 4-th unit of NPP Dukovany in 1987. The Figure G-1 contains 6 graphs (each 

for given investigated loop) of weighted relative deviation of measured a calculated mixing 

factors. The X-axis represents modelled Theta sectors. There are numbers of radial rings as 

independent parameter in these graphs. 
G-3 

Figure G-1 Comparison of Weighted Relative Deviation of Measured and Calculated (16-The
G-4