NUREG/IA-0460 

International 

 Agreement Report

Model 3D Cores for PWR Using Vessel 

Components in TRACEv5.0P3

 

 

Prepared by: 

C. Mesado, R. Miró, T. Barrachina, G. Verdú

Institute for Industrial, Radiophysical and Environmental Safety (ISIRYM) 

Universitat Politècnica de València 

Camí de Vera, s/n 

46021 Valencia, SPAIN

K. Tien, NRC Project Manager 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: September 2015

Date Published: January 2016

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-0460 

International 

 Agreement Report

Model 3D Cores for PWR Using Vessel 

Components in TRACEv5.0P3

 

 

Prepared by: 

C. Mesado, R. Miró, T. Barrachina, G. Verdú

Institute for Industrial, Radiophysical and Environmental Safety (ISIRYM) 

Universitat Politècnica de València 

Camí de Vera, s/n 

46021 Valencia, SPAIN

K. Tien, NRC Project Manager 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: September 2015

Date Published: January 2016

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

iii

ABSTRACT

New models for Pressurized Water Reactor (PWR) with fully 3D cores were developed using 

TRACE thermal-hydraulic code. To develop these new models, TRACE code was chosen 

because it is been developed and will be probably licensed by the Nuclear Regulatory 

Commission (NRC). Thus, it is easy to take advantage of current and future features of TRACE. 

Three 3D different models were developed, they make use of the 3D vessel component in 

TRACE, either cartesian or cylindrical type. These models are especially suitable to simulate 

cross-flow, instabilities and in general asymmetric phenomena. All three models have been 

successfully tested.
iv
v

FOREWORD

This report represents one of the assessment or application calculations submitted to fulfill the 

bilateral agreement for cooperation in thermal-hydraulic activities between the Consejo de 

Seguridad Nuclear (CSN) and the U.S. Nuclear Regulatory Commission (NRC) in the form of a 

Spanish contribution to the NRC’s Code Assessment and Management Program (CAMP), the 

main purpose of which is to validate the TRAC/RELAP Advanced Computational Engine 

(TRACE) code.

CSN and the Asociación Española de la Industria Eléctrica (UNESA, Electric Industry 

Association of Spain), together with some relevant universities, have established a coordinated 

framework (CAMP-Spain) with two main objectives: to fulfill the formal CAMP requirements and 

to improve the quality of the technical support groups that provide services to the Spanish 

utilities, CSN, research centers, and engineering companies.

The AP-28 Project Coordination Committee has reviewed this report: the contribution of a

Spanish University to the above-mentioned CAMP-Spain program, for submission to CSN.

ISIRYM - UPV

June 2015
vi
vii

CONTENTS

Page

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

FOREWORD................................................................................................................... v

FIGURES ........................................................................................................................ix

TABLES..........................................................................................................................xi

EXECUTIVE SUMMARY ..............................................................................................xiii

ABBREVIATIONS..........................................................................................................xv

NOMENCLATURE.......................................................................................................xvii

1. INTRODUCTION.....................................................................................................1-1

2. MODEL DESCRIPTION..........................................................................................2-1

2.1 Shape model .................................................................................................2-1

2.2 Split model.....................................................................................................2-9

2.3 Cylindrical model .........................................................................................2-12

3. BYPASS FLOW ADJUSTMENT.............................................................................3-1

4. MODEL-TO-MODEL COMPARISON .....................................................................4-1

5. CONCLUSIONS......................................................................................................5-1

6. REFERENCES........................................................................................................6-1
viii
ix

FIGURES

Page

Figure 1 Cartesian Vessel Radial Cut, White Cells have Zero Flow Area Fraction, Gray 

Cells Represent Fuel Assembly Cells and Blue Cells Represent Bypass Cells. .... 2-1

Figure 2 Shape Model Sketch, Simplified 5x5 Vessel. ........................................................ 2-2

Figure 3 Cell Representing the Bypass Dimensions in a Cartesian Vessel. ........................ 2-5

Figure 4 Split Model Sketch, Simplified 5x5 Vessel............................................................. 2-9

Figure 5 Cartesian Vessel Distribution in the Split Model (Size and Shape)...................... 2-10

Figure 6 Left: Cylindrical Vessel (Radial Cut) with Three Theta Sectors. Right: Cartesian 

Vessel with the Fuel Assembly-Theta Sector Association. .................................. 2-13

Figure 7 Cylindrical Model Sketch, Simplified 5x5 Vessel. ................................................ 2-13

Figure 8 Error if Single Junctions are used as Sideways Connections.............................. 2-18

Figure 9 Bypass Friction Factor Adjustment Iteration Process. ........................................... 3-1

Figure 10 Friction Factor Input Value for Different Simulation States. ................................... 3-3

Figure 11 Cylindrical Model with Three Theta Sectors, Bypass Flow in z-Direction............... 3-3

Figure 12 Traditional Collapsed Model Sketch...................................................................... 4-1

Figure 13 Moderator Density 3D Distribution. ....................................................................... 4-2

Figure 14 Mass Flow 3D Distribution. ................................................................................... 4-2

Figure 15 Moderator Temperature 3D Distribution................................................................ 4-3

Figure 16 Fuel Center Temperature 3D Distribution.............................................................. 4-3

Figure 17 Fuel Surface Temperature 3D Distribution. ........................................................... 4-4

Figure 18 Bypass Mass Flow as a Function of the Axial Cell or z-Direction. ......................... 4-4

Figure 19 TRACE-PARCS Coupled Simulation Steady State Power 2D Distribution. ........... 4-5
x
xi

TABLES

Page

Table 1 Simulation Time (Hours) as a Function of the Chosen Model................................ 1-2

Table 2 Number of Components in the Shape Model......................................................... 2-3

Table 3 Number of Junctions in the Shape Model.............................................................. 2-4

Table 4 Face Cell Properties in x-Direction in the Shape Model. ....................................... 2-7

Table 5 Face Cell Properties in y-Direction in the Shape Model. ....................................... 2-7

Table 6 Face Cell Properties in z-Direction in the Shape Model. ....................................... 2-8

Table 7 Single Junction Properties in x-Direction in the Split Model................................. 2-11

Table 8 Face Cell Properties in x-Direction, Cartesian Vessel in the Cylindrical Model.... 2-15

Table 9 Face Cell Properties in y-Direction, Cartesian Vessel in the Cylindrical Model.... 2-15

Table 10 Face Cell Properties in z-Direction, Cartesian Vessel in the Cylindrical Model.... 2-16

Table 11 Cylindrical Vessel Properties. ............................................................................. 2-17

Table 12 Axial Connections for both Vessels in the Cylindrical Model. .............................. 2-18

Table 13 Sideways Connections for both Vessels in the Cylindrical Model. ....................... 2-19

Table 14 Number of Components in the Cylindrical Model. ............................................... 2-19

Table 15 Number of Junctions in the Cylindrical Model...................................................... 2-20

Table 16 Comparison Plot Summary. .................................................................................. 4-1
xii
xiii

EXECUTIVE SUMMARY

Three new fully 3D models for TRACE code are presented in this document. They model the 

reactor core using 3D vessel components. Therefore, they could be used to simulate 

asymmetrical phenomena in the core regardless of the phenomenon implication, either thermalhydraulic or neutronic.

First, the Shape model is presented. It uses only one cartesian vessel with null flow area 

fraction on corner cells. Thus, the resulting shape resembles the radial mapping. The bypass is 

modeled using outermost cells and its flow area fraction is modified accordingly. The second

model is named Split model. This model, similar to Shape model, makes use of several 

cartesian vessels. These vessels are joined sideways to resemble the radial mapping. Finally, 

the third model uses one cartesian vessel similar to that of the Shape model but without bypass. 

Besides, a cylindrical vessel is coupled to the cartesian vessel. The cylindrical vessel has two 

radial cells. The innermost represents the bypass and the outermost cell represents the 

downcomer. The cylindrical vessel is also discretized into three different theta sectors. One cold 

and hot leg is attached to each theta sector.

Due to the 3D cross flow represented in these models, the bypass flow strongly fluctuates along 

the axial axis (z-direction). An iterative method is developed for automatic adjustment of the 

bypass flow. Finally, a model-to-model comparison is made in section 4. Several thermalhydraulic variables are compared with a traditional 1D model. The 1D model is also based on 

TRACE.

As a recommendation, when 3D feature is desired to model the core in TRACE, the Cylindrical 

model is advisable. This is the result of a trade of considering computational effort, realistic 

behavior and number of components used.
xiv
xv

ABBREVIATIONS

PWR Pressurized Water Reactor

NRC Nuclear Regulatory Commission

SNAP Symbolic Nuclear Analysis Package
xvi
xvii

NOMENCLATURE

Next, a list of all variables used is provided. Besides, a description and the source for each 

model are also shown. The source could be an equation, table, nuclear plant data, expert 

analyzer or simulation result. The variable is not used for a certain model if its source is shaded.

Variable Description Shape Split Cylind

φt Assembly fraction for each theta sector Eq 23

Ain System inlet area Eq 1 Eq 1 Eq 21

Aout System outlet area Eq 2 Eq 2 Eq 22

cpowr Power fraction for each heat structure in assembly cells Eq 4 Eq 4 Eq 4

cpowrby Power fraction for each heat structure in bypass cells Eq 5 Eq 5

cpowrby

t Power fraction for each heat structure in bypass cells for each 

theta sector Eq 27

fa Assembly flow area Plant Plant Plant

faby Bypass flow area Plant Plant Plant

fadc Downcomer flow area Plant

fabreak

t Break flow area for each theta sector Eq 24

fafill

t Fill flow area for each theta sector Eq 24

FAFa Flow area fraction in a-direction for cylindrical vessel Tab 11

FAFr Flow area fraction in r-direction for cylindrical vessel Tab 11

FAFt Flow area fraction in t-direction for cylindrical vessel Tab 11

FAFx Flow area fraction in x-direction for cartesian vessel Tab 4 Tab 4 Tab 8

fafx Flow area fraction in x-direction for assembly cells Expert Expert Expert

fafx,by Flow area fraction in x-direction for bypass cells Eq 12 Eq 12

FAFy Flow area fraction in y-direction for cartesian vessel Tab 5 Tab 5 Tab 9

fafy Flow area fraction in y-direction for assembly cells Expert Expert Expert

fafy,by Flow area fraction in y-direction for bypass cells Eq 13 Eq 13

FAFz Flow area fraction in z-direction for cartesian vessel Tab 6 Tab 6 Tab 10

fafz Flow area fraction in z-direction for assembly cells Eq 15 Eq 15 Eq 15

fafz,by Flow area fraction in z-direction for bypass cells Eq 14 Eq 14

Flowby Bypass mass flow Sim Sim Sim

Flowby

* Theoretical bypass mass flow Plant Plant Plant

Flowerror Bypass mass flow maximum acceptable error Expert Expert Expert

Flowfill

t Inlet mass flow for each theta sector Eq 25

Flowtot Total inlet mass flow Plant Plant Plant

FVOL Volume fraction for cylindrical vessel Tab 11

fvol Volume fraction Eq 16 Eq 16 Eq 16

fvolk Volume fraction for each axial level for assembly cells Eq 17 Eq 17 Eq 17

fvolby

k Volume fraction for each axial level for bypass cells Eq 18 Eq 18

Hby Power fraction that heats directly the bypass Expert Expert Expert

HDa

r=1 Hyd. diameter in a-direction for cylindrical vessel (bypass) Eq 34

HDa

r=2 Hyd. diameter in a-direction for cylindrical vessel Eq 35
xviii

(downcomer)

HDr

r=1 Hyd. diameter in r-direction for cylindrical vessel (bypass) Eq 36

HDr

r=2 Hyd. diameter in r-direction for cylindrical vessel (downcomer) Eq 37

HDt

r=1 Hyd. diameter in t-direction for cylindrical vessel (bypass) Eq 38

HDt

r=2 Hyd. diameter in t-direction for cylindrical vessel (downcomer) Eq 39

HDx Hyd. diameter in x-direction for cartesian vessel Tab 4 Tab 4 Tab 8

hdx Hyd. diameter in x-direction Expert Expert Expert

HDy Hyd. diameter in y-direction for cartesian vessel Tab 5 Tab 5 Tab 9

hdy Hyd. diameter in y-direction Expert Expert Expert

HDz Hyd. diameter in z-direction for cartesian vessel Tab 6 Tab 6 Tab 10

hdz Hyd. diameter in z-direction for assembly cells Plant Plant Plant

hdz,by Hyd. diameter in z-direction for bypass cells Plant Plant Plant

KR

by Bypass friction factor r-direction Expert Expert Expert

KZ

by Bypass friction factor z-direction Expert Expert Expert

KFACa Friction factor in a-direction for cylindrical vessel Tab 11

KFACr Friction factor in r-direction for cylindrical vessel Tab 11

KFACt Friction factor in t-direction for cylindrical vessel Tab 11

KFACx Friction factor in x-direction for cartesian vessel Tab 4 Tab 4 Tab 8

kfacx Friction factor in x-direction Expert Expert Expert

KFACy Friction factor in y-direction for cartesian vessel Tab 5 Tab 5 Tab 9

kfacy Friction factor in y-direction Expert Expert Expert

KFACz Friction factor in z-direction for cartesian vessel Tab 6 Tab 6 Tab 10

kfacz Friction factor in z-direction in assembly cells Expert Expert Expert

kfacz,by Friction factor in z-direction in bypass cells Expert Expert Expert

kfacz,dc Friction factor in z-direction in downcomer cells Expert Expert Expert

ncells Number of cells Eq 6 Eq 6 Eq 28

nchan Number of fuel assemblies Plant Plant Plant

nchan

t Number of fuel assemblies for each theta sector Expert

ncomp Number of components in the system Eq 7 Eq 19 Eq 40

nsjunc Number of single junction components Tab 14

njunc Number of junctions in the system Eq 8 Eq 20 Eq 41

nt

Number of theta sectors in cylindrical vessel, typically same 

as recirculation loops Expert

nx Number of cells in x-direction for cartesian vessel Plant Plant Plant

ny Number of cells in y-direction for cartesian vessel Plant Plant Plant

nz

Number of cells in z-direction for cartesian vessel (axial 

levels) Expert Expert Expert

P(x,y,z) 3D power distribution Plant Plant Plant

rdx Number of fuel rods per heat structure in assembly cell Plant Plant Plant

rdxby Number of fuel rods per heat structure in bypass cell Eq 3 Eq 3

rdxby

t Number of fuel rods per heat structure in bypass cell for each 

theta sector Eq 26

Xby Length in x-direction for bypass cell Eq 10 Eq 10

Xcell Length in x-direction for assembly cell Plant Plant Plant

Xr Radial discretization for cylindrical vessel Eq 30

Yby Length in y-direction for bypass cell Eq 11 Eq 11
xix

Ycell Length in y-direction for assembly cell Plant Plant Plant

Yt Theta discretization for the cylindrical vessel Eq 31

Z Axial discretization for the cartesian vessel Expert Expert Expert

Za Axial discretization for the cylindrical vessel Eq 29

zbreak Level for break connection, Cylindrical model only Expert

zfill Level for fill connection, Cylindrical model only Expert

1-1

1. INTRODUCTION

Most of the thermal-hydraulic nuclear plant models, using nuclear codes such as TRACE or 

RELAP5, are discretized in one dimension. This is because large amount of cells are needed to 

model the whole plant, and thus the matrices to be solved are big. However, in order to take 

advantage of the increasing computational power, it seems that the next logical step is to use 

3D spatial discretization. So far, TRACE is one of the few thermal-hydraulic codes that uses 3D 

components [1]. The vessel component is fully discretized in 3D and the thermal-hydraulic 

equations solved accordingly.

In this study, 3D vessel components, either cartesian, cylindrical or a combination, were used to 

model a nuclear reactor core. This is where the most important phenomena in a nuclear power 

plant occur. Therefore, the use of a 3D core can improve the result accuracy and highlight 

phenomena that were not simulated properly in a 1D core. For example, cross-flow, instabilities 

and in general asymmetric phenomena either in the thermal-hydraulic or neutronic phase.

It must be said that few studies using 3D vessels to model the reactor core where found [3], [4]

and [5]. Thus, this publication pretends to summarize and increase the available core modeling

knowledge. Three different models were developed to simulate a 3D reactor core. The different 

features of these models are explained deeply in chapter 2. Next, the three models are 

presented:

• Shape model. It uses only one cartesian vessel in which the corner cells have null 

volume to shape it as shown in the reactor radial mapping.

• Split model. It uses several cartesian vessels with different sizes and attached 

sideways to shape them as shown in the reactor radial mapping.

• Cylindrical model. It uses one cartesian vessel for the core (also with some null 

volume cells) and a cylindrical vessel that models the bypass (inner radial cell) and 

the downcomer (outer radial cell). The cylindrical vessel is also discretized in the 

theta direction.

All different models have been tested against a TRACE 1D model, resulting in a good 

agreement. Among the different models, all 3D models stand out by their capability to capture 

asymmetric phenomena triggered by the thermal-hydraulic and/or the neutronic code. These 

models provide realistic simulation results when these phenomena occur in the reactor core, 

and thus, they are suitable for core instability studies. Among the 3D models, the Cylindrical 

model is the recommended option because its similarity to a real nuclear reactor (reflector and 

downcomer), and because it has been tested for different scenarios.

Table 1 shows the simulation time, in hours, as a function of the model and the simulation state. 

As can be seen, for fast calculation the traditional TRACE 1D model beats the other models. 

However, the 3D calculation component is lost, therefore, if one wants to include 3D calculation, 

the best choice is the Cylindrical model. Cylindrical model takes a little bit longer than the Shape 

model, but it is more realistic. Furthermore, it must be said that the Split model, despite its good 

agreement with other models, always takes much longer calculation times. For the transient 

simulation, a control rod insertion was simulated with quite short time steps and a total 

simulation time of 100 seconds.
1-2

Model Components SSA CSS CTR Total time

Traditional 1D 363 0.03 0.05 1.63 1.71

Shape 731 0.63 1.78 7.68 10.09

Split 2713 3.11 15.14 127.97 146.22

Cylindrical 2589 1.07 1.79 11.87 14.73

Table 1 Simulation Time (Hours) as a Function of the Chosen Model.

A final comment must be made before explaining how to reproduce the 3D models. Due to the 

fact that the core is modeled using 3D components, which are connected node to node, the 

bypass mass flow has a strong variation along the way through the vessel (axial axis). This 

occurs because the bypass cells and fuel assembly cells have different volume, and thus the 

fluid flows freely among them. Therefore, the bypass friction factor has to be adjusted at each 

node, axially and radially. Furthermore, for the Cylindrical model, because it could have several 

theta sectors, it has to be adjusted among the different theta sectors. This is a tedious task, 

even for expert users. However, an iterative process to adjust the bypass friction factor for each 

level and each sector is presented in Chapter 3. It was proved to work successfully in all 

models. All three 3D models are explained in Chapter 2. Finally, in Chapter 4 the 3D models are

compared against a traditional TRACE 1D model for the same nuclear reactor.
2-1

2. MODEL DESCRIPTION

2.1 Shape model

The whole core is modeled by means of only one cartesian vessel. This element provides the 

cross-flow between each fuel assembly node and between fuel assemblies and reflector area. 

This is an improvement over 1D models. The flow area fraction within this vessel is modified so 

the external shape is consistent with the reactor radial mapping, see Figure 1.

Figure 1 Cartesian Vessel Radial Cut, White Cells have Zero Flow Area Fraction, Gray 

Cells Represent Fuel Assembly Cells and Blue Cells Represent Bypass Cells.

Hereafter a list of main features and components used to build the Shape model is provided.

- There is only one cartesian vessel that represents the whole core, both the assemblies 

and the bypass. In the same axial level, each cell corresponds to one fuel assembly, 

thus, there is not any fuel assembly collapsed.

- The bypass is modeled using the outermost vessel nodes. The bypass node flow area 

fraction is modified so the sum of all bypass nodes areas is equal to the real bypass 

area.

- One heat structure is associated with each cell representing fuel assemblies and cells 

representing the bypass.

- One power component heats all heat structures.

- It is not possible to connect the fill or break component directly with a plenum, thus onecell big pipes are used between them. Moreover, several one-cell pipes are used to 

connect both plenums with each cell -fuel assemblies or bypass- at both ends of the 

cartesian vessel.
2-2

See Figure 2 for a simplified Shape model (5x5 vessel), sketch using SNAP tool [2].

Figure 2 Shape Model Sketch, Simplified 5x5 Vessel.

The flow area into the system, Ain, is defined as the sum of the inlet flow area over all fuel 

assemblies, nchan, Eq. (1). The same logic is used for the system outlet area, Aout, Eq. (2).

AAiiii = � ffffff

zz=1

cchaaaa

ff=1

(1)

AAoooooo = � ffffff

zz=

cchaaaa

ff=1

(2)

Where ffffff

zz is the fuel assembly flow area at a certain axial node, z. The index variable f goes 

over all fuel assembly modeled.

These areas are assigned to the fill/break, inlet/outlet one-cell big pipe, and inlet/outlet plenum 

components. The inlet and outlet one-cell big pipes are set vertically and have zero friction 

factor values.

One cylindrical heat structure is associated to each fuel assembly. They have zero flux as inner 

surface boundary condition (heat structure center), and their outer surface is coupled to the 

associated cartesian vessel cell. The number of fuel rods for each fuel assembly is given by the 

fuel assembly manufacturer. This is introduced in TRACE using the surface multiplier variable 

(rdx). The bypass cells are heated by means of a heat structure per cell. Heat structures 

coupled to bypass cells are not modeled as fuel rods, variable nofuelrod equal 1.The surface 

multiplier for each heat structure in a bypass cell, rdxby, is given by Eq. (3); and its power 

fraction is set equal to the bypass power fraction, Eq. (5).

rrrrrrbbbb = 1

nnrrrr rrrrrr

� rrrrrrff

cchaaaa

ff=1

(3)
2-3

Where

nreflec is the number of cells representing the bypass, and

rdxf is the number of fuel rods per fuel assembly f.

All heat structures are powered by a single power. The total reactor power, prompt heat and the 

3D nodal power distribution (P(x,y,z)) are supplied by the power plant, With these data, the axial 

power distribution (normalized to one) for each heat structure in core cells can be calculated. 

The power fraction for each heat structure, cpowr (fuel assemblies) and cpowrby (for bypass) is

calculated with the following formulas:

cccccccc = PP( , yy, zz)

1 − HHbbbb

nn cc

(4)

cccccccc bbbb = HHbbbb

nn cc

(5)

Where

Hby is the power fraction that heats directly the bypass, and

ncells is the number of cells representing fuel assemblies plus the number of cells 

representing the bypass, Eq. (6).

nn cc = nn haa + nnrrrr rrrrrr (6)

The total number of components, ncomp, for Shape model is detailed in Table 2. It can be 

expressed as in Eq. (7).

Component Quantity

Fill 1

Break 1

Plenum 2

Big pipe 2

Power 1

Cartesian vessel 1

Heat structure ncells

Pipe inlet vessel ncells

Pipe outlet vessel ncells

Table 2 Number of Components in the Shape Model.

nn cccc = 7 + nnvv + 3 · nn cc (7)

The same can be done with the total number of junctions, njunc, for Shape model, see Table 3

and Eq. (8).
2-4

Junction from Junction to Quantity

Fill Inlet big pipe 1

Inlet big pipe Lower plenum 1

Lower plenum Lower small pipe ncells

Lower small pipe Cartesian vessel ncells

Cartesian vessel Upper small pipe ncells

Upper small pipe Upper plenum ncells

Upper plenum Outlet big pipe 1

Outlet big pipe Break 1

Table 3 Number of Junctions in the Shape Model.

nnjj = 4 + 4 · nn cc (8)

According to the vessel component in TRACE, all cells have the same dimension. Let the 

variables Xcell and Ycell be the fuel assembly dimensions, given by the manufacturer, and thus 

the vessel unitary cell dimensions (blue straight-line cell in Figure 3). Nonetheless, the volume 

of a cell representing a fuel assembly does not need to be the same as the volume of a cell 

representing the bypass. This can be solved modifying the flow area fraction. If the total bypass 

flow area is faby, the flow area for one bypass cell is faby/nreflec. Let the variables Xby and Yby be

the sides that define the flow area for one bypass cell, (green dashed line cell in Figure 3). Note 

that there is no shrink in the z-direction.
2-5

Figure 3 Cell Representing the Bypass Dimensions in a Cartesian Vessel.

The flow area fraction is defined as the ratio between the real flow area in cell (green area) and 

the geometry cell area (blue area). In order to obtain the flow area fraction a relationship 

between bypass cell dimensions (green) and fuel assembly cell dimensions (blue) must be 

established. We assume the following relation, Eq. 9.

XXbbbb

YYbbbb

= XX

YY

→ XXbbbb = YYbbbb

XX

YY (9)

As explained before, the flow area for one bypass cell is faby/nreflec.and Xby and Yby are the sides 

that define the flow area for one bypass cell. Thus, the quantity XbyYby is also the flow area for 

one bypass cell. If both quantities are compared, as in Eq. 10, a new relation is obtained.

XXbbbb · YYbbbb = ffffbbbb

nnrrrr rrrrrr

→ XXbbbb = ffffbbbb

nnrrrr rrrrrr

1

YYbbbb

(10)

Combining Eq. (9) and Eq. (10).

YYbbbb = �YY

XX

ffffbbbb

nnrrrr rrrrrr

(11)

Finally, the bypass flow area fraction, fafby, in all three dimensions can be obtained as follows, 

Eq. (12) to Eq. (14). Because there is no shrink in the z-direction, both the real length and cell 

length in z-direction are equal and they cancel each other. In Eq. (14), relationship defined in 

Eq. (10) is used.

Xby

Ycell

Yby

Xcell

y

z

x

faby/nreflec
2-6

ffffffxx,bbbb = YYbbbbZZ

YY ZZ = YYbbbbYY (12)

ffffff ,bbbb = XXbbbbZZ

XX ZZ = XXbbbbXX (13)

ffffffzz,bbbb = XXbbbbYYbbbb

XX YY = ffffbbbb/nnrrrr rrrrrrXX YY (14)

The flow area fraction for a fuel assembly cell can be calculated as shown in Eq. (15). Note that 

the quantity XcellYcell (assembly total area) is bigger than the fuel assembly flow area, fa, 

because the structures inside the assembly block a fraction of the total area. Thus the flow area 

fraction for a fuel assembly cell must be smaller than one.

ffffffzz = ffff

XX YY (15)

Once the flow area fraction is obtained, the main properties for the x-direction face cells in the 

cartesian vessel can be calculated according to Table 4. Note that because the wet perimeter is 

unknown, the hydraulic diameter is assumed to be equal to the flow area. Same conclusions 

can be applied to the y-direction.

Three different situations can be found: reflector-reflector, reflector-fuel assembly and fuel 

assembly-fuel assembly. The expert analyst must introduce the fuel assembly friction factors, 

whereas the friction factors for the bypass cells (in x and y-direction) can be adjusted iteratively, 

see Chapter 3. The same can be seen in Table 6 for the z-direction face properties.
2-7

Cells Property Value

Flow Area Fraction (FAFx) fafx,by

Hydraulic Diameter (HDx) Yby·Z

Friction Factor (KFACx) 0

Flow Area Fraction (FAFx) fafx,by

Hydraulic Diameter (HDx) Yby·Z

Friction Factor (KFACx) kfacx,by

Flow Area Fraction (FAFx) 1

Hydraulic Diameter (HDx) Ycell·Z

Friction Factor (KFACx) 0.5·(kfacx1+ kfacx2)

Table 4 Face Cell Properties in x-Direction in the Shape Model.

Cells Property Value

Flow Area Fraction (FAFy) fafy,by

Hydraulic Diameter (HDy) Xby·Z

Friction Factor (KFACy) 0

Flow Area Fraction (FAFy) fafy,by

Hydraulic Diameter (HDy) Xby·Z

Friction Factor (KFACy) kfacy,by

Flow Area Fraction (FAFy) 1

Hydraulic Diameter (HDy) Xcell·Z

Friction Factor (KFACy) 0.5·(kfacy1+ kfacy2)

Table 5 Face Cell Properties in y-Direction in the Shape Model.

Reflector Reflector

Fuel

Assembly Reflector

Fuel

Assembly

Fuel

Assembly

Reflector Reflector

Fuel

Assembly Reflector

Fuel

Assembly

Fuel

Assembly

1 2

1 2
2-8

Cell Property Value

Flow Area Fraction (FAFz) fafz,by

Hydraulic Diameter (HDz) hdz,by

Friction Factor (KFACz) kfacz,by

Flow Area Fraction (FAFz) fafz

Hydraulic Diameter (HDz) hdz

Friction Factor (KFACz) kfacz

Table 6 Face Cell Properties in z-Direction in the Shape Model.

There is only one property defined in the cell center (not in the cell faces), it is the volume 

fraction. However, since there is no shrink in the z-direction, see Figure 3, the volume fraction is 

the same as the flow area fraction in z-direction, see Eq. (15) and Eq. (16).

ffff ff = ffff · ZZ

XX YY · ZZ = ffffXX YY = ffffffzz (16)

Moreover, the flow area fraction is obtained at cell face, but the volume fraction must be 

calculated at the cell center, thus a linear interpolation is applied. See Eq. (17) for fuel assembly 

volume fraction and Eq. (18) for bypass volume fraction. Index k represents the axial cell index.

ffff ff

kk = 1

2 �ffffffzz

kk + ffffffzzkk+1

� (17)

ffff ffbbbb

kk = 1

2 �ffffffzz,bbbb

kk + ffffffzz,bbbbkk+1

� (18)

As seen in Figure 2, in order to connect the vessel inlet/outlet to the lower/upper plenums, onecell pipes for each vessel cell is used (with the exception of the null flow area fraction cells,

white cells in Figure 1). It is important to know that it is not possible to define properties in the 

first vessel axial face in TRACE. Thus, the properties for the first/last cell face are set to zero. 

Instead, its properties are set in the one-cell pipe before/after the vessel. All the one-cell pipes 

are set vertically, their length is set to 1 m and their friction factors and hydraulic diameters are 

set equal to the first/last fuel assembly cell associated, as explained in Table 6. All the inlet 

connections are set at the bottom cell side (-Z in bottom level). Whereas all the outlet 

connections are set at the upper cell side (+Z in upper level).

Reflector

Fuel

Assembly
2-9

2.2 Split model

Hereafter a list of main features and components used to build the Split model is provided.

- Several cartesian vessel are used. They represent the whole core, both the assemblies 

and the bypass. In the same axial level, each cell corresponds to one fuel assembly, 

thus, there is not any fuel assembly collapsed.

- The different cartesian vessels are joined sideways using single junctions node-to-node 

in all axial levels, thus the external shape is consistent with the reactor radial mapping.

- The bypass is modeled using the outermost vessel nodes resulting from all cartesian 

vessels joined. The bypass node flow area fraction is modified so the sum of all bypass 

nodes is equal to the real bypass area.

- One heat structure is associated with each cell representing fuel assemblies and cells 

representing the bypass.

- One power component heats all heat structures.

- It is not possible to connect the fill or break component directly with a plenum, thus onecell big pipes are used between them. Moreover, several one-cell pipes are used to 

connect both plenums with each cell –fuel assemblies or bypass- at both ends in the 

cartesian vessel.

See Figure 4 for a simplified Split model (5x5 vessel without lateral junctions), sketch using 

SNAP tool [2].

Figure 4 Split Model Sketch, Simplified 5x5 Vessel.
2-10

Essentially, the Split model could be explained with the same equations as the Shape model. 

However, there are multiple cartesian vessels, see Figure 5 as an example, each color is a 

different vessel. These vessels are connected sideways by means of single junctions, see 

Figure 4. These are equivalent to pipe components but with no volume, thus only using a face 

as a connection. One single junction is set for each vessel cell that is next to a different 

cartesian vessel. Moreover, this is repeated for each axial level. The result is that the number of 

components and junctions increases drastically, as can be seen in Table 1.

1

3

8 9

7 5 4 6

10 11

2

Figure 5 Cartesian Vessel Distribution in the Split Model (Size and Shape).

The axial connections are defined as explained previously for the Shape model. Besides, all 

single junctions (sideways junctions) are connected to two different cartesian vessels, either in 

the x-direction (±X) or the y-direction (±Y). Single junctions are set horizontally and its length is 

set to 0.1 m, other properties for x-direction single junctions can be seen in Table 7. Same

conclusions can be extrapolated for the y-direction single junctions. Again, three different 

situations can be found: reflector-reflector, reflector-fuel assembly and fuel assembly-fuel 

assembly.
2-11

Cells Property Value

Flow Area xcell·Z·fafx,by

Hydraulic Diameter xcell·Z·fafx,by

Friction Factor 0

Flow Area xcell·Z·fafx,by

Hydraulic Diameter xcell·Z·fafx,by

Friction Factor kfacx,by

Flow Area xcell·Z

Hydraulic Diameter xcell·Z

Friction Factor 0.5·(kfacx1+ kfacx2)

Table 7 Single Junction Properties in x-Direction in the Split Model.

The number of total components, Eq. (19), and total junctions, Eq. (20), are similar to that of the 

Shape model, Table 2 and Table 3. However, the number of vessels, nvessels, has been 

increased and the single junctions, nsjunc, must be added to the count.

nn cccc = 7 + nnvv + 3 · nn cc + nn · nnzz (19)

nnjj = 4 + 4 · nn cc + 2 · nn · nnzz (20)

Where nz is the number of axial levels or cells in the z-direction for a given vessel.

Reflector Reflector

Fuel

Assembly Reflector

Fuel

Assembly

Fuel

Assembly

1 2
2-12

2.3 Cylindrical model

Hereafter a list of main features and components used to build the Cylindrical model is provided.

- There is only one cartesian vessel that represents only the fuel assemblies (not the 

bypass). In the same axial level, each cell corresponds to one fuel assembly, thus, there 

is not any fuel assembly collapsing.

- One cylindrical vessel with two radial nodes is modeled. The innermost node represents 

the core bypass and the outermost simulates the downcomer.

- The cylindrical vessel has nz+2 axial levels, nz equally distributed as the cartesian vessel 

plus two additional axial levels representing the upper and lower plenum.

- The cylindrical vessel could be discretized in the theta direction to model different theta

sectors.

- To establish the theta connection, a mapping between fuel element and its theta sector 

is needed.

- One break component is connected to each downcomer theta sector (outer radial node 

in the cylindrical vessel). The connections are established at a certain axial level, zbreak.

Each break is connected to a different theta sector. Similarly, several fill connections are 

established at a lower level, zfill.

- One heat structure is coupled with each cell representing a fuel assembly within the 

cartesian vessel. Besides, one heat structure is associated with each bypass theta

sector in the cylindrical vessel.

- The heat transfer between bypass and downcomer (reactor barrel) is modeled through a 

heat structure -with no fuel rods- coupled to the inner/outer radial cell of the cylindrical 

vessel.

- One power component heats all heat structures coupled with fuel assemblies and 

bypass cells. The heat structure simulating the reactor barrel is not heated by the power 

component. It has convection boundary conditions at both sides.

- It is not possible to connect the fill or break component directly to the cylindrical vessel, 

thus one-cell big pipes are used between them.

- In order to connect both vessels, single junctions are used in the axial connections. See 

Table 12 for axial connection information.

- Moreover, both vessels are also connected sideways at all levels, one-cell pipes are 

used. See Table 13 for radial connection information. Single junctions cannot be used as 

sideways junctions for the Cylindrical model, see Figure 8.

- There is not any plenum component in the Cylindrical models.
2-13

See Figure 6 (left) for an example of a cylindrical vessel discretized into three theta sectors.

Figure 6 (right) is an example of the mapping between fuel assemblies and theta sectors.

Figure 6 Left: Cylindrical Vessel (Radial Cut) with Three Theta Sectors. Right: Cartesian 

Vessel with the Fuel Assembly-Theta Sector Association.

See Figure 7 for a simplified Cylindrical model (5x5 vessel without lateral junctions), sketch 

using SNAP tool [2].

Figure 7 Cylindrical Model Sketch, Simplified 5x5 Vessel.

R=1

R=2 φ = 1

φ = 2 φ = 3
2-14

As it can be seen, there is not any independent component representing the plenums (they are 

included in the cylindrical vessel) in the Cylindrical model. The inlet and outlet flow area for the 

cylindrical vessel have different definitions compared to previous models, see Eq. (21) and Eq. 

(22).

AAiiii = ZZ(zzff ) · 2ππ�ffffdd + ffffbbbb

ππ

(21)

AAoooooo = ZZ(zzbb ) · 2ππ�ffffdd + ffffbbbb

ππ

(22)

Where

fadc is the downcomer flow area,

faby is the bypass flow area,

zfill is the axial level where the fill component is connected,

zbreak is the axial level where the break component is connected, and

Z(k) is the cell height for a given axial level (k).

Since there are several fills and breaks, the flow area for each fill or break component, fafill

t and 

fabreak

t

, is the inlet/outlet flow area times the sector fraction or theta fraction, see Figure 6 (right)

and Eq. (24). If nchan is the total number of fuel assemblies and nchan

t is the number of fuel 

assemblies in each theta sector, the theta fraction, φt, is defined as in Eq. (23). Similarly, the 

flow through each fill, Flowfill

t

, can be obtained with Eq. (25).

φφ = nn haa

nn haa (23)

ffffff = AAiiii · φφ

ffffbb = AAoooooo · φφ (24)

FF ff = FF · φφ (25)

This flow area is applied to the fill/break flow area and its attached one-cell pipe. In contrast to 

Shape model, the one-cell big pipes are set horizontally and their friction factors are zero. The 

one-cell big pipes are connected to the cylindrical vessel at inlet and outlet levels (zfill and zbreak),

one to each theta sector and to the outer radial cell (+R).

The heat structures and power component are defined similarly to those of the previous models. 

Heat structures have zero flux as the center boundary condition. Their outer surface is coupled 

with the associated hydraulic cell. Including the heat structures associated to each bypass theta

sector (innermost radial cell at cylindrical vessel). The characteristics of the fuel rods for each 

fuel assembly are given by the manufacturer. As in the Shape model, the surface multiplier in 

each heat structure in a bypass cell must be defined. For the Cylindrical model, it is given by Eq.

(26).
2-15

rrrrrrbbbb = φφ � rrrrrrff

cchaaaatt

ff=1

(26)

The heat structure modeling the barrel between the downcomer and the core bypass has no 

power associated. Its thickness is set equal to the barrel thickness and the chosen material is 

stainless steel 304. All other heat structures are powered by a single power component. The 

power distribution is defined as in the previous model. However, to calculate the power fraction 

that reaches the bypass heat structures Eq. (27) is used. This time, ncells variable is defined as 

Eq. (28).

cccccccc bbbb = HHbbbb

nn cc

φφ nn (27)

nn cc = nn haa + nn (28)

Where Hby is the power fraction that heats directly the bypass, and φt, is defined in Eq. (23). The 

number of theta sectors is represented by nt.

The properties for the cartesian vessel cell face in the x-direction and y-direction can be seen in 

Table 8 and Table 9. The same properties for the cell face in the z-direction can be seen in 

Table 10. In comparison to the previous models, now only one situation is possible: fuel 

assembly–fuel assembly.

Cells Property Value

Flow Area Fraction (FAFx) 1

Hydraulic Diameter (HDx) Ycell·Z

Friction Factor (KFACx) 0.5·(kfacx1+ kfacx2)

Table 8 Face Cell Properties in x-Direction, Cartesian Vessel in the Cylindrical Model.

Cells Property Value

Flow Area Fraction (FAFy) 1

Hydraulic Diameter (HDy) Xcell·Z

Friction Factor (KFACy) 0.5·(kfacy1+ kfacy2)

Table 9 Face Cell Properties in y-Direction, Cartesian Vessel in the Cylindrical Model.

Fuel

Assembly

Fuel

Assembly

Fuel

Assembly

Fuel

Assembly

1 2

1 2
2-16

Cell Property Value

Flow Area Fraction (FAFz) fafz

Hydraulic Diameter (HDz) hdz

Friction Factor (KFACz) kfacz

Table 10 Face Cell Properties in z-Direction, Cartesian Vessel in the Cylindrical Model.

Regarding the cylindrical vessel, as mentioned, it has two additional axial levels to simulate the 

lower/upper plenum. The height of these additional levels is the same as the first/last axial 

levels height in the cartesian vessel. Spatial discretization for the cylindrical vessel, a-direction 

(axial), r-direction (radial) and t-direction (theta), can be seen in Eq. (29) to Eq. (31).

ZZaa = [ ZZ(1), ZZ(1), Z(2), ... , Z(nn ), ZZ(nn ) ] (29)

XXrr = ��ffffbbbb

ππ , �ffffbbbb + ffffddππ � (30)

YY = 360

nn haa aa

nn haa

(31)

Where

faby is the bypass flow area,

fadc is the downcomer flow area,

Z(i) is the vessel cell height for axial level i, and

nchan

t is the number of fuel assemblies in the t

th theta sector.

Fuel

Assembly
2-17

Other properties, such as flow area fraction and friction factor, can be seen in Table 11.

Property Value

Bypass (r=1) Downcomer (r=2)

Flow Area Fraction Radial (FAFr) see comment below 0

Flow Area Fraction Theta(FAFt) 1 1

Flow Area Fraction Axial (FAFa) 1 see comment below

Volume Fraction (FVOLa) 1 1

Friction Factor Radial (KFACr) 0 0

Friction Factor Theta (KFACt) 0 0

Friction Factor Axial (KFACa) kfacz,by kfacz,dc

Table 11 Cylindrical Vessel Properties.

The flow area fraction in radial direction for the first and last axial levels, Eq. (32), is set to 1.

These cells simulate the lower and upper plenum, and thus the fluid must flow from the bypass 

to the downcomer and vice versa.

FF FFrr

zz = 1 if zz is 1 or nn , 0 otherwise (32)

The flow area fraction in axial direction for the downcomer (outer radial cell in the cylindrical 

vessel) between the zfill and zbreak is set to zero. However, the expert analyst could set this value 

to a specified flow area fraction, faffill2break. Thus, the inlet fluid could flow directly upwards 

through the downcomer and directly to the outlet without cooling the core, Eq. (33). This 

behavior is more realistic. Nonetheless, studies have shown that faffill2break near 10-3 leads to 

convergence and stability problems.

FF FFaa

zz = ffffffff 2bb if zzff < zz < zzbb , 1 otherwise (33)

The hydraulic diameter for both radial cells can be expressed as in Eq. (34) to Eq. (39).

HHHHaa

rr=1 = h bbbb (34)

HHHHaa

rr=2 = h dd (35)

HHHHrr

rr=1 = ZZ · 2ππ · φφ �ffffbbbb

ππ (36)

HHHHrr

rr=2 = ZZ · 2ππ · φφ �ffffbbbb + ffffdd

ππ (37)

HHHH rr=1 = ZZ�ffffbbbb

ππ (38)
2-18

HHHH rr=2 = ZZ�ffffbbbb + ffffdd

ππ (39)

In order to connect both vessels, single junctions are used in the axial connections. All single 

junctions are set vertically. Their friction factors and hydraulic diameters are set equal to the 

first/last fuel assembly cell associated, as explained for Shape model in Table 6 (fuel assembly 

situation). The axial connections between both vessels must be set according to Table 12, 

otherwise the fluid does not flow correctly. To establish the theta connection a mapping between

fuel elements and its theta sector is needed, see Figure 6 (right). The mapping for the upper 

and lower connections could be different. Please bear in mind that the axial level in the 

cylindrical vessel is referred to a maximum level of nz+2 (because of the two additional levels,

upper and lower plenums).

Cylindrical vessel Cartesian vessel

Axial level Direction Axial level Direction

Lower plenum 1 +Z 1 -Z

Upper plenum nz + 2 -Z nz +Z

Table 12 Axial Connections for both Vessels in the Cylindrical Model.

For sideways connections one-cell pipes are used. Single junctions cannot be used as sideways

junctions for the Cylindrical model because TRACE does not allow more than one single 

junction to be connected to the same target cell and the same direction. See Figure 8.

 *****************

 ** warning ** *****************

Connections in the same plane in one vessel are not in the same 

plane of the other vessel

 ***************** ** warning **

 *****************

Vessel 10, junction 3070201 is inconsistent with Vessel 10, 

junction 1110201

Figure 8 Error if Single Junctions are used as Sideways Connections.

Sideways pipes are set horizontally and its length is set to 0.1 m. Connections are set for every 

axial level and every single cell between the outermost cartesian vessel cells and the inner 

radial cell in the cylindrical vessel (i.e. between all orange faces in Figure 6 -right- and the 

center orange point in Figure 6 -left-). Again, the theta connections are determined by the fuel 

element-theta sector mapping. The lateral connections are summarized in Table 13.
2-19

Cylindrical vessel Cartesian vessel

Axial level Radial cell Direction Axial level Direction

2, 3, ... nz+1 1 -R 1, 2, ... , nz ±X or ±Y

Table 13 Sideways Connections for both Vessels in the Cylindrical Model.

The other properties for the sideways connections are the same as explained in Table 7

(reflector – fuel assembly situation) for the Split model.

The total number of components for the Cylindrical model is detailed in Table 14, and expressed 

in Eq. (38).

Component Quantity

Fill nt

Break nt

Big pipe 2·nt

Power 1

Cartesian vessel 1

Cylindrical vessel 1

Heat structure bypass nt

Heat structure barrel nt

Heat structure fuel nchans

Lower Single Junction nchans

Upper Single Junction nchans

One-cell pipes 2·nz·(nx-2+ny-2)

Table 14 Number of Components in the Cylindrical Model.

nn cccc = 1 + nnvv + 6 · nn + 3 · nn haa + 2 · nnzz · (nnxx − 2 + nn − 2) (40)
2-20

The same can be done with the total number of junctions for Cylindrical model Table 15 and Eq.

(41).

Junction from Junction to Quantity

Fill Inlet big pipe nt

Inlet big pipe Cylindrical vessel nt

Cylindrical vessel Outlet big pipe nt

Outlet big pipe Break nt

Cylindrical vessel Lower single junction nchan

Lower single junction Cartesian vessel nchan

Cartesian vessel Upper single junction nchan

Upper single junction Cylindrical vessel nchan

Cartesian vessel Sideways one-cell pipe 2·nz·(nx-2+ny-2)

Sideways one-cell pipe Cylindrical vessel 2·nz·(nx-2+ny-2)

Table 15 Number of Junctions in the Cylindrical Model.

nnjj = 4�nn + nn haa + nnzz · (nnxx − 2 + nn − 2)� (41)

Where nx and ny are the number of cells in the cartesian vessel in x and y-directions 

respectively.
3-1

3. BYPASS FLOW ADJUSTMENT

An iterative process to adjust the bypass flow is developed [3]. The process modifies the bypass 

friction factor until the specified theoretical flow value is reached. In Figure 9 a flow chart for the 

friction factor iterative process is presented.

Figure 9 Bypass Friction Factor Adjustment Iteration Process.

Generate 

Input

Run Simulation

Read Flowby(i,z)

Abs (Flowby(i,z)-Flowby

*

) < Flowerror YES

NO

END

K

z

by(i,z)=Kzby(i-1,z)· [ Flowby(i-1,z) / Flowby

*

]

2

If Kz

by(i,z) < 1 & Flowby(i-1,z) < Flowby

*

K

R

by(i,z-1)=K

R

by(i-1,z-1) · 4

i = i + 1

Restart

3D model (vessel)?

NO YES
3-2

Where:

i: iteration count

z: axial node

Flowby

*

: theoretical bypass flow

Flowby(i,z): simulation bypass flow

Flowerror: maximum acceptable error

K

z

by(i,z): bypass friction factor (axial)

K

R

by(i,z): bypass friction factor (radial)

The iteration process starts generating the input deck and running the simulation. The resulting 

bypass flow, Flowby, is read and compared with the theoretical bypass flow, Flowby*

. If the 

difference is small enough (smaller than Flowerror), the iteration process ends. Otherwise it 

applies a correction for the axial bypass friction factor, KZ

by, for each axial level (1D and 3D 

models). Only for 3D models, it is also possible to apply a radial bypass friction factor, KR

by,

correction for each axial level.

The correction for the axial bypass friction factor is proportional to the square ratio of the last 

obtained bypass flow and the theoretical flow (for each axial level). However, imagine that a 

certain bypass friction factor is small (say less than 1) and the resulting bypass flow is less than 

the theoretical bypass flow. In this case, the desired increase in bypass flow cannot be archived 

decreasing the friction factor anymore. Thus, the radial bypass friction factor at the immediate 

inferior level is increased by a factor of four. As a result, less flow will escape the bypass radially 

in the immediate inferior level and it will flow axially upwards.

The iteration process is carried out until the absolute error is satisfied. The error, Flowerror, is 

obtained comparing the bypass flow, for the last iteration step, with the theoretical bypass flow. 

For each new iteration step, a restart file is created. Thus, a restart is run with the considerable

decrease in the simulation time. Once the friction factors are adjusted for the steady state 

simulation (SSA), the process is repeated for the coupled (with PARCS) steady state simulation 

(CSS). By default the initial guess for the CSS simulation is the converged value for the SSA. 

However, if the expert analyzer requests it, a new guess for the CSS simulation could be 

introduced. Once the CSS simulation is converged, the coupled transient simulation is run (CSS 

converged friction factors are used). See Figure 10.

Traditional 1D models do not have cross flow, thus the bypass flow is constant with height. 

Nevertheless, 3D vessel models simulate the cross flow for the whole core. The cross flow 

exists between reflector area and fuel assemblies, and also among fuel assemblies. Therefore, 

in 3D models, because of the cross flow, the bypass flow strongly fluctuates along the axial axis. 

This is especially relevant in the Cylindrical model. Due to its theta sectors, friction factors could 

vary from one theta sector to another. This process was successfully used to adjust the bypass 

flow for all three models explained in previous chapters. As an example, in Figure 11, the 

bypass flow for a Cylindrical model with three theta sectors (dashed lines) is compared with a 

1D model (straight lines). The x-axis represents the axial cells (z-direction). The 1D model was 

built using pipes in RELAP5 code. In this case, a maximum absolute error of 5 kg/s was set.
3-3

Figure 10 Friction Factor Input Value for Different Simulation States.

Figure 11 Cylindrical Model with Three Theta Sectors, Bypass Flow in z-Direction.

SSA kfac

CSS

CTR

ckfac

kfac*

kfac* kfac: user friction factors

ckfac: user fric. fact. for CSS

kfac*: converged fric. fact.

 : user optional data

Until 

convergence

Until 

convergence

4-1

4. MODEL-TO-MODEL COMPARISON

In order to compare the 3D models, a traditional 1D model was created in TRACE. It has one 

pipe per fuel assembly (no collapsed model) and its heat structure associated. The bypass is 

modeled using a bigger pipe, also with a heat structure component. All pipes are connected to 

an upper and lower plenum. The boundary conditions in the fill and break components are the 

same as in the 3D models. See Figure 7 for a simplified traditional model (collapsed), sketch 

using SNAP tool [2].

Figure 12 Traditional Collapsed Model Sketch.

In Table 16 the summary for the compared variables is presented.

Variable distribution Figure

Moderator density 13

Mass flow 14

Moderator temperature 15

Fuel center temperature 16

Fuel surface temperature 17

Bypass mass flow (z-direction) 18

TRACE-PARCS power 19

Table 16 Comparison Plot Summary.
4-2

Figure 13 Moderator Density 3D Distribution.

Figure 14 Mass Flow 3D Distribution.

SSA PIPE MODEL Density distribution SSA SHAPE MODEL Density distribution

SSA SPLIT MODEL Density distribution SSA CYLINDRICAL MODEL Density distribution

SSA PIPE MODEL Flow distribution SSA SHAPE MODEL Flow distribution

SSA SPLIT MODEL Flow distribution SSA CYLINDRICAL MODEL Flow distribution
4-3

Figure 15 Moderator Temperature 3D Distribution.

Figure 16 Fuel Center Temperature 3D Distribution.

SSA PIPE MODEL Temperature distribution SSA SHAPE MODEL Temperature distribution

SSA SPLIT MODEL Temperature distribution SSA CYLINDRICAL MODEL Temperature distribution

SSA PIPE MODEL Fuel temperature distribution SSA SHAPE MODEL Fuel temperature distribution

SSA SPLIT MODEL Fuel temperature distribution SSA CYLINDRICAL MODEL Fuel temperature distribution
4-4

Figure 17 Fuel Surface Temperature 3D Distribution.

Figure 18 Bypass Mass Flow as a Function of the Axial Cell or z-Direction.

SSA PIPE MODEL Clad surface temperature distribution SSA SHAPE MODEL Clad surface temperature distribution

SSA SPLIT MODEL Clad surface temperature distribution SSA CYLINDRICAL MODEL Clad surface temperature distribution

5 10 15 20 25 30 35

z-cell

966

968

970

972

974

976

978

980

Mass Flow (kg/s)

SSA Mass Flow in Bypass

PIPE

SHAPE

SPLIT

CYLINDRICAL
4-5

Figure 19 TRACE-PARCS Coupled Simulation Steady State Power 2D Distribution.

2 4 6 8 10 12 14 16 18

x-cell

2

4

6

8

10

12

14

16

18

y-cell

CSS PIPE MODEL PARCS relative collapsed power distribution

2 4 6 8 10 12 14 16 18

x-cell

2

4

6

8

10

12

14

16

18

y-cell

CSS SHAPE MODEL PARCS relative collapsed power distribution

2 4 6 8 10 12 14 16 18

x-cell

2

4

6

8

10

12

14

16

18

y-cell

CSS SPLIT MODEL PARCS relative collapsed power distribution

2 4 6 8 10 12 14 16 18

x-cell

2

4

6

8

10

12

14

16

18

y-cell CSS CYLINDRICAL MODEL PARCS relative collapsed power distribution

5-1

5. CONCLUSIONS

System codes take the advantage of 1D component simulations to speed up the calculation 

time. Nevertheless, due to the improving computational hardware, more and more complicated 

models are computational affordable.

In this study, three different 3D models to simulate the reactor core are presented. This is an 

interesting work, mainly due to the scarce literature available regarding this issue. The first 

presented model is the Shape model, with only one cartesian vessel. The second model or Split 

model, with several cartesian vessels joined sideways. Finally, the third model is the Cylindrical 

model with a cartesian vessel and a cylindrical vessel with two radial cells, the bypass and 

downcomer. Moreover, an iterative process is designed to adjust the bypass flow for all models.

This iterative process modifies the bypass friction factors (axially and radially) until the desired 

bypass flow is archived. It is proved to be very helpful.

All three models are seen to be in perfect agreement against a traditional 1D model. All 3D 

models were built to resemble the counterpart 1D model. In this document the particularities 

regarding each model and problems encountered during its definition or simulation are 

explained in detail. The work done is expected to broaden the scarce related literature and, to 

serve as a basis for new 3D model developments and implementations.

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6. REFERENCES

[1] TRACE v5.0 User’s Manual. Volume 1: Input Specification. Nuclear Regulatory 

Commission.

[2] Symbolic Nuclear Analysis Package (SNAP). User's Manual. 2007.

[3] C. Mesado, R. Miró, T. Barrachina, G. Verdú. “Control rod drop transient: uncertainty 

and sensitivity analysis of thermal-hydraulic variables using a 3D model with TRACE 

V5.0P3/PARCS 3.0”. 16th International Topical Meeting on Nuclear Reactor 

Thermalhydraulics (NURETH-16), Chicago (IL), USA, 2015.

[4] C. Mesado, M. Garcia-Fenoll, R. Miró, T. Barrachina, G. Verdú. “Modelado de un PWR 

Mediante Componentes 3D”. 39a Reunión Anual de la SNE, Reus (Tarragona) España, 

25-27, September, 2013.

[5] C. Mesado, R. Miró, T. Barrachina, G. Verdú. “PWR Simulation using a 3D vessel with 

TRACE/PARCS”. International topical meeting on nuclear reactor thermal hydraulics 

(NURETH-15), Italy, 2013.







NUREG/IA-0460 Model 3D Cores for PWR Using Vessel Components in TRACEv5.0P3