NUREG-1781

CFD Analysis of 1/7th Scale

Steam Generator Inlet Plenum

Mixing During a PWR Severe

Accident

U.S. Nuclear Regulatory Commission

Office of Nuclear Regulatory Research

Washington, DC 20555-0001
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NUREG-1781

CFD Analysis of 1/7th Scale

Steam Generator Inlet Plenum

Mixing During a PWR Severe

Accident

Manuscript Completed: September 2003

Date Published: October 2003

Prepared by

C.F. Boyd, K Hardesty

Division of Systems Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001
ABSTRACT

Computational fluid dynamics (CFD) is used to predict steam generator inlet plenum mixing

during a severe accident scenario in a pressurized water reactor. Comparisons are made to

117th scale data. Qualitatively, the code predicts the experimental flow patterns and mixing

phenomena. Quantitatively, comparisons are made with key temperatures, mass flows, and

mixing parameters. The best estimate prediction is generally within 5% of the reported values.

Key temperature predictions are within a few degrees K of the test data. Boundary conditions

applied to the model include the hot leg inlet mass flow and temperature as well as the tube

secondary side temperature and heat transfer. The mass averaged temperature of the flow

entering the tubes is predicted to within 1 degree of the experimental data. The mass flow

through the tube bundle is predicted to within 0.5% of the data. The number of hot tubes is

overpredicted by 7 tubes out of the 216 total. The mixing fraction and the recirculation ratio,

both important mixing parameters, are predicted to within 5% of the data. These predictions

provide confidence in the code and modeling approach. The secondary side heat transfer

coefficient is determined to be the dominant governing parameter.

iii
CONTENTS

Abstract ... ... ...............

Executive Summary ...............

Foreword .....................

1 Introduction ................

2 Computational Fluid Dynamics (CFD) . .

3 Physical Model Description .

3.1 Hot Leg .

3.2 Inlet and Outlet Plenum ......

3.3 Steam Generator Tubes.

3.4 Steady State Test Description . . .

3.5 Scaling Parameters .........

4 CFD Model Development.

4.1 Finite Volume Mesh

4.2 Boundary Conditions ........

4.2.1 Tube Model . ..... . .

4.2.2 Velocity Inlet Conditions .

4.3 Material Properties .........

4.4 Turbulence Modeling .......

4.5 Solution Convergence ......

4.6 Grid Independence ........

5 Completed Predictions .

5.1 Summary of Assumptions and Limitz

6 Results ..................

6.1 Best Estimate Results ......

6.2 Hot Leg Prediction ...... . .

6.3 Nozzle Region Predictions . ...

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6.4 Inlet Plenum Flows ............ ............ . . . . . . . . . .. . 19

V
CONTENTS (continued)

Page

6.5 Tube Bundle Flows ............................. 19

6.6 Sensitivity Study Results .. . .. . .. .. .. . . . . . . . . . . . . 20

6.6.1

6.6.2

6.6.3

6.6.4

6.6.5

6.6.6

Summary

References

Inlet Temperature Sensitivity ....................

H-ot Leg Inlet Mass Flow (Inlet Velocity) Sensitivity.

Turbulence Model Sensitivity ....................

Tube Sheet Entrance Pressure Loss Sensitivity ..........

Tube Flow Viscous Loss Sensitivity .................

Tube Heat Transfer Coefficient Sensitivity .............

Appendix

7

8

A Appendix A

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Figures

Overview of Natural Circulation Flow Pattern ....................

Cross Section of inlet Plenum, Hot Leg, and Tube Sheet ..............

Computational Mesh .................................

Boundary Between Hot and Cold Tubes .......................

Hot Leg Temperature Prediction and Data (x = -0.566 m) .............

Hot Leg Temperature Contours and Velocity Profiles ...............

Path Lines on Symmetry Plane of Inlet Plenum ..................

Contours of Turbulence Intensity on Symmetry Plane of Inlet Plenum .......

Normalized Temperature Contours on Symmetry Plane of Inlet Plenum.

Velocity Vectors on Vertical Planes Normal to Symmetry Plane ..........

Temperature Contours on Horizontal Planes in Inlet Plenum ...........

21

21

22

22

23

23

25

27

A-i

28

28

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31

31

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33

vi
CONTENTS (continued)

Page

12. Temperature Contours on Vertical Planes Parallel to Symmetry Plane .... . . 34

13. Temperature Contours on Horizontal Plane 1 Inch Above Tube Sheet Entrance . 35

14. Histogram of Normalized Hot Temperatures 1 Inch Above Tube Sheet Entrance . 35

15. Predicted Temperature Contours on Model Symmetry Plane . . . . . . . . . . . . 36

Tables

1. SF6 Properties (2.07 MPa, 300 psia) ...... . . . . . . . . . . . . . . . . . . 37

2. Summary of Boundary Conditions ........ . . . . . . . . . . . . . . . . . 37

3. Assumptions and Limitations ......... . .. . . .. . . .. . . .. . . . . 38

4. Comparison of Test Data (SG-S3) with FLUENT Predictions ..... . . . . . . . 39

5. Boundary Conditions for Sensitivity Studies . . . . . . . . . . . . . . . . . . . . . 40

6. Summary of Sensitivity Study Results ....... . . . . . . . . . . . . . . . . . 41

vii
EXECUTIVE SUMMARY

This report describes the first step in a new analysis of steam generator inlet plenum mixing

using computational fluid dynamics (CFD).

Inlet plenum mixing is one of the important parameters governing the degree of thermal

challenge to steam generator tubes during postulated severe accidents in pressurized-water

reactors (PWRs). The NRC has implemented a steam generator action plan to confirm the

robustness of risk-informed licensing decisions and to reduce modeling uncertainties and

improve the technical basis for future licensing requests. One objective of this plan is to

investigate the time-dependent thermal-hydraulic conditions in the hot leg and steam generator.

This research will ultimately lead to a reduction in the uncertainties in modeling these conditions.

One aspect of this research involves using state-of-the-art CFD techniques to predict inlet

plenum mixing. The first step in this process is to evaluate the modeling technique using

existing experimental data at 1/7t scale.

There are two significant benefits from comparing computed predictions with experimental data.

First, the applicability of the modeling technique is established through a comparison with the

test data. This provides a level of confidence in the modeling approach, which will ultimately be

applied to full-scale steam generators under a variety of conditions not explicitly covered by the

available tests.; The second benefit from these predictions is clarifying specific aspects of the

experimental data. The 1/7 scale data serve as a primary source of information about the

thermal-hydraulic conditions in the hot leg and steam generator during severe accident natural

circulation conditions. The data, however, consist only of thermocouple measurements at a

limited number of locations. Details of the mixing behavior are not available. The CFD

predictions provide three-dimensional results for velocity, temperature, turbulence, and other

flow parameters over the entire domain of the hot leg and inlet plenum. These predictions

provide insights into the flow and mixing behavior that were previously unavailable from the

limited experimental measurements.

A best estimate analysis is completed using boundary conditions derived from a specific test

(SG-S3) at 1f7th scale. A high-quality computational mesh is developed that represents the key

features of the test facility. The FLUENT 6.0 CFD code is used for the analysis. Qualitatively,

the predictions show all of the experimentally observed flow features in the hot leg and steam

generator regions. Predicted features such as the sloping interface in the hot leg, the relative

sizes of the hot and cold flow regions, and the path and size of the inlet plenum plume are

consistent with the experimental observations. The global natural circulation flow pattern is also

well predicted by the CFD code.

The test data indicate a significant temperature reduction between the locations of the last hot

leg thermocouple and the first set of inlet plenum thermocouples encountered by the hot plume.

This temperature reduction occurs as the flow travels through the nozzle region of the hot leg,

where no measurements are available and the flow pattern is unknown. The predictions also

indicate a significant amount of mixing in this region. The specific flow pattern responsible for

this significant mixing is clearly evident in the CFD predictions. Cold flow returning to the hot leg

from the inlet plenum intersects the hot stream exiting the hot leg, resulting in significant mixing

at this location. This result results in a better understanding of the experimental result.

ix
The key mixing parameters predicted are generally within 5% of the measured values. Key

temperature predictions are typically within a few degrees of the experimental data. The most

significant predicted values are associated with the tube bundle temperatures and mass flows.

These predictions essentially match the test data. The predicted average temperature entering

the tube bundle is within 1 degree Kelvin of the reported test result. The tube bundle mass flow

prediction is within 0.5% of the experimental value. The ability to predict these two key

parameters establishes confidence in the modeling technique. The predicted shape and

location of the hot tube region match the data. Seven more tubes (out of 216 tubes in the

bundle) are predicted to carry hot flow than were observed experimentally.

One benefit of the CFD predictions is the ability to determine tube-to-tube variations. The data

include tube entrance temperatures for 25% of the tube bundle, providing a limited indication of

the tube-to-tube variation. The 3 dimensional predictions for temperatures and mass flows

provide a complete description of the tube-to-tube variations and provide a means to fill in the

gaps where no data exists.

A series of sensitivity studies are completed to establish the stability of the model and the impact

of major modeling assumptions. Key input parameters are systematically varied to determine

the governing phenomena. The secondary side heat transfer coefficient is determined to be the

dominant governing parameter with respect to the key mixing parameters. The variations

observed also explain a key feature of the data at 1 /

7th scale that has raised questions in

previous investigations. Specifically, the data result in significant variations in the mixing

parameters between the steady state and transient tests. The sensitivity studies indicate that

these differences are due to the differences in the secondary side heat transfer rate. This

finding helps to focus the efforts to reduce the uncertainty associated with the prediction of

severe accident natural circulation phenomena.

These results demonstrate the applicability of the CFD technique for this type of analysis and

provide detailed insights into the existing data. The results are a first step towards the goal of

completing CFD analysis of full-scale steam generators under a variety of conditions not

specifically addressed by the test data. These conditions include the effect of tube leakage and

the effect of geometrical differences in inlet plenum geometry. The predictions at 1/7m scale are

a necessary step. The agreement with the test data provides confidence in the modeling

approach and assumptions that will be used at full-scale conditions.

x
FOREWORD

Steam generator tube integrity during severe accidents is a critical safety issue. Tube failure

during these accidents results in a containment bypass with the associated radioactive release

to the environment. Altematively, failures of other reactor coolant system (RCS) components

prior to the tube failure leads to a depressurization of the RCS and an elimination of the threat to

the tubes. Existing predictions indicate that the time for RCS failure at locations such as the hot

leg or surge line connection is very close to the predicted time of tube failure. It is necessary to

identify and reduce uncertainties in these predictions to improve the agency's ability to assess

the likelihood of steam generator tube failures during severe accidents.

Thermal-hydraulic analysis of the RCS provides the temperature and pressure conditions that

challenge the RCS components and the steam generator tubes. Temperature of the steam in

the tubes is influenced significantly by three-dimensional mixing behavior in the steam generator

inlet plenum region. System codes such as SCDAP/RELAP5 do not implicitly model this mixing.

Mixing coefficients are pre-determined based mainly on a limited set of experiments at 1/7t

scale. The experimental data provide valuable information but are limited in scale and range of

application. For instance, the effects of tube leakage and inlet plenum geometry variations on

the inlet plenum mixing cannot be assessed from the experiments. The Office of Research

(RES) has been using state-of-the-art computational fluid dynamics (CFD) to study a variety of

safety issues. CFD provides a tool for predicting the steam generator inlet plenum mixing under

a wide variety of conditions. The first step in the application of CFD to the steam generator inlet

plenum mixing issue is an assessment of the tool against the existing 1/7m scale data.

This report describes the completion of a detailed analysis of steam generator inlet plenum

mixing at 1/7't scale using CFD. The goal is to confirm the applicability of CFD for this type of

analysis and to enhance the NRC's understanding of the phenomena governing steam

generator inlet plenum mixing. The analysis supports the NRR user need request related to

steam generator severe accident response dated September 7, 2000. This request and

subsequent related issues are incorporated into the agency's Steam Generator Action Plan

(memorandum from Samuel Collins and Ashok Thadani to William Travers, May 11, 2001). The

steam generator action plan is intended to confirm the robustness of risk-informed licensing

decisions and to reduce modeling uncertainties and improve the technical basis for future

licensing requests.

The successful completion of this work represents an important milestone in the thermalhydraulic analysis of the RCS. The predictions agree well with the experimental results and the

applicability of the method for this type of analysis is established. This results provide a level of

confidence in the succeeding full-scale predictions under a variety of conditions lThe full-scale

work is being documented separately). In addition, the understanding of the 1/7 scale data has

significantly improved due to the detailed predictions of the mixing phenomena in regions where

no data are available. Assumptions and limitations of this analysis are outlined in Table 3.

Farouk Eltawila, Director

Division of Systems Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

xi
1 INTRODUCTION

The Nuclear Regulatory Commission (NRC) has implemented a steam generator action plan' to

address tube integrity issues. This plan includes tasks to predict steam generator inlet plenum

mixing during a severe accident scenario using computational fluid dynamics (CFD). The

sequence of interest in this study is a station blackout that leads to a loss of secondary side

cooling and a loss of primary inventory. As the core is uncovered, natural circulation of

superheated steam carries heat to structures, including the upper reactor vessel, hot leg, and

steam generator tubes. In the scenario considered, the loop seals are filled with water and full

loop circulation is blocked. A countercurrent natural circulation flow pattem, as illustrated in

Figure 1, is expected during this phase of the accident.

This scenario leads to a failure in the primary coolant loop. The thermal-hydraulic details

determine whether this failure occurs in the reactor coolant piping (within containment) or in the

steam generator tubing (with a leak path to the outside of containment). Steam generator inlet

plenum flow and mixing phenomena play a significant role in determining the temperature of the

steam that enters the tubes. A lack of mixing allows high temperature steam to enter the tubes

and consequently reduces the time before tube failure. Significant inlet plenum mixing reduces

the temperature of the hot steam entering the tubes. This increases the time before tube failure,

making it more likely that some other component in the system will fail first. If another

component fails (e.g., the surge line), the system will depressurize into the containment and the

threat to the tubes will be eliminated. A tube rupture represents a bypass of containment and a

potential radioactive release to the environment. Therefore, it is important to accurately predict

when the tubes (and other components) are expected to fail. Inlet plenum mixing is one

parameter needed for this prediction. Background information on many aspects of severe

accident-induced steam generator tube rupture can be found in NUREG/CR-6285 2 and NUREG157O.3

The thermal-hydraulic modeling of this severe accident scenario is typically performed with

lumped parameter codes such as SCDAP/RELAP5 or MELCOR. The efficiency gained by the

coarse nodilization of this approach makes it feasible to predict the transient behavior of the

entire reactor coolant system over extended periods of time. A limitation of these models is a

reliance on predetermined flow-field and mixing parameters to address any 3 dimensional flow

phenomena including the steam generator inlet plenum flows during the countercurrent natural

circulation phase of the transient. The primary source of data for the inlet plenum mixing

parameters during this type of natural circulation flow comes from experiments in a

Westinghouse 117 h scale test facility.4

The NRC is interested in mixing parameters under a variety of full-scale conditions not explicitly

covered in the experimental tests. Full-scale experiments are not practical. The NRC plans to

use CFD to predict mixing parameters at conditions not explicitly covered by the experiments.

First, the applicability of the technique will be established using the 117h scale test data. This

initial evaluation is the subject of this report. With confidence established in the technique at

1/7h scale, full-scale simulations under a variety of conditions will be evaluated in future work.

1
2 COMPUTATIONAL FLUID DYNAMICS (CFD)

The FLUENT (version 6.0) CFD code is used to predict the inlet plenum mixing and the natural

circulation flows. FLUENT is a commercially available, general-purpose CFD code capable of

solving a wide variety of fluid flow and heat transfer problems. The code solves the Reynoldsaveraged Navier-Stokes equations on a finite volume mesh. The Navier-Stokes equations

represent the mass, momentum, and energy conservation equations for a continuous fluid.

Reynolds averaging creates the need for turbulence modeling to account for the turbulent

diffusion of momentum and energy. The FLUENT code provides several turbulence modeling

options. Unstructured meshing capabilities allow the code to be applied to complex geometries.

Commercial CFD codes such as FLUENT are widely used in many industries today and are

commonly used to predict mixing phenomena.

Each of the steps in a CFD analysis can influence the predicted results and should be

considered. The basic steps involve describing the physical model; defining the CFD model

domain, boundary conditions, and models; validating the solution; and completing sensitivity

studies. When considering CFD predictions, the analyst must consider the assumptions and

limitations of each step in the process. Further details on the fundamentals of CFD are found in

the introductory text by Anderson.5

3
3 PHYSICAL MODEL DESCRIPTION

The physical model description is based upon a Westinghouse 1/7 t scale test facility.4

This facility is designed to study the natural circulation phenomena during the severe accident

scenario illustrated in Figure 1. The outlet pipe from the steam generators, the loop seal, and

the cold legs are not included in the test facility since they do not participate in this scenario.

Sulfur hexafluoride (SF6) is-used as the working fluid to make the scale of the facility closer to

the prototype.

The 117' scale facility is based upon the Indian Point 2 nuclear power plant, which has a

Westinghouse model 44 steam generator. However, the steam generator of the 11 7th scale

facility does not have full geometric similarity with the prototype. For example, the scaled facility

has a total of 216 tubes to represent the 3260 tubes of a full-scale model 44 steam generator. In

addition, the orientation of the hot leg relative to the inlet plenum is different. The 11 71h scale

facility has a hot leg oriented in a vertical plane normal to the divider plate that separates the

inlet and outlet plenums. This orientation of the hot leg makes the steam generator symmetric.

The hot leg nozzle of the model 44 steam generator, on the other hand, is oriented

approximately 30 degrees from a vertical plane normal to the divider plate. This design does not

have a symmetry plane. The effect of geometric variations will be studied in future work.

Scaling arguments and background for the 1/7th scale facility are given in Reference 3.

The Westinghouse 1t7t scale facility simulates the primary system of interest for one-half of a

four-loop Westinghouse pressurized water reactor (PWR). The reactor vessel is cut in half and

attached to two hot legs that lead to a right and left steam generator. Electrical heating provides

the power to the core. The entire system is insulated. Cooling water around the upper vessel

and the steam generator tubes provides the only significant heat removal during the steady state

tests. A diagram of the hot legs, inlet plenum, and the start of the tube bundle is given in Figure

2 for the left steam generator. A coordinate system is attached to the steam generator to help

define the model (see Fig. 2). The origin is centered on the tube sheet face. The y-axis points

up and is parallel to the tubes. The x-axis, which is parallel to the hot leg axis, points away from

the vessel. The z-axis is obtained from the right hand rule. A CFD model is created for one hot

leg and steam generator. Components included in the model are briefly described below to

provide some detail of the features that impact the current study.

3.1 Hot Leg

The hot legs are 0.10226 m (4.026 in.) inner diameter pipes with a 0.762 m (30 in.) centerline

length from the exit of the vessel upper plenum to the entrance of the steam generator inlet

plenums. The end of the pipe has a 45-degree radius elbow prior to entering the steam

generator. The length of this elbow is 0.127 m (5 in.) on the centerline.

This hot leg is instrumented in three areas as noted by the small black dots on Figure 2. Four

thermocouples are positioned on the vertical centerline near the entrance and exit to the hot leg.

Each thermocouple is reported to be at the centroid of a section that represents one-fourth of the

total pipe flow area. Near the center of the hot leg, six thermocouples are positioned on a

vertical centerline. These thermocouples are spaced 0.00635 m (0.25 in.) apart, with three

above and three below the horizontal centerline. Due to a limited data system capacity, all of the

hot leg thermocouples are not recorded for the test considered in this report.

5
3.2 Inlet and Outlet Plenum

The inlet and outlet plenums are also shown in Figure 2. Each plenum consists of a 0.2413 m

(9.5 in.) inner radius hemisphere attached to a 0.04115 m (1.62 in.) long vertical cylindrical

section that attaches the lower hemisphere to the tube sheet. The center point of the

hemispherical section is 0.04115 m (1.62 in.) below the tube sheet face. The plenum outer wall

thickness is 0.0127 m (0.5 in.). Furthermore, a 0.0127 m (0.5 in.) divider plate separates the

inlet and outlet plenums. The tube sheet forms the upper boundary of the inlet and outlet

plenum.

3.3 Steam Generator Tubes

The test facility tube bundle consists of 216 U-shaped tubes with a 0.007747 m (0.305 in.) inner

diameter and a 0.009525 m (0.375 in.) outer diameter. They are anchored into a 0.1143 m (4.5

in.) thick tube sheet that caps off the inlet and outlet plenums. The tubes are arranged in a

0.02064 m (0.8125 in.) triangular pitch array. The average tube length is 2.499 m (98.403 in.)

and the overall bundle height is 1.124 m (56.06 in.) from the bottom face of the tube sheet. The

average U-bend radius is 0.1014 m (3.994 in.).

Nearly one-fourth of the tubes, 51, are instrumented with a thermocouple positioned either

0.0254 m or 0.127 m (1 in. or 5 in., respectively) from the tube entrance. These thermocouples

are used to determine whether the tube carries hot or cold fluid.

3.4 Steady State Test Description

A single steady state test, referred to as test SG-S3, is used to evaluate the performance of the

CFD model. These data are assumed to represent a snapshot of the quasi-steady transient

behavior. During steady state testing, a steady power is applied to the core. Continuous water

cooling of the vessel upper plenum and the steam generator tubes removes the core power.

The hot leg and steam generator plenums are completely insulated and assumed adiabatic. For

the purposes of this study, the scaled reactor vessel provides a steady flow of heated SF8 into

the hot leg and receives the returning cooled SF6 from the steam generator. Only the hot leg

and steam generator are considered. The steam generator tube bundle is covered with a steel

cylinder and cooling water is pumped past the outside of the tubes to provide the heat removal

capacity. The mass flow rate and temperature rise of the cooling water is measured and used to

determine the amount of power leaving the tube bundle. This power, along with available

average flow temperature measurements, is used to obtain the hot leg and tube bundle mass

flow rates. The tests are run continuously until the measured data are steady.

3.5 Scaling Parameters

The test series utilized a heavy gas, sulfur hexaflouride (SF6 ), to increase certain scale

parameters to improve the representation of full-scale behavior. SF8 has a density near 100

kg/M3 at the test conditions. Two important parameters are noted below. For test SG-S3, the

Rerolds number in the hot leg, based upon the hot stream velocity and pipe radius, is over 6 x

10 . At full-scale conditions, the Reynolds number is in the range of 105. The Grashof number,

a measure of the effect of buoyancy on the hot plume in the inlet plenum, is 8 x 1011 in the test

facility and estimated at 5 x 1012 for full-scale conditions. The Richardson number, a measure of

the ratio of the buoyancy to inertial forces on the plume, is approximately 2 x 102 for both the

6
1/7' scale data and the full-scale conditions. The magnitudes of these important parameters

from the 1/7t scale test are at or near the magnitude estimated for the full-scale plant. The 1If7

test is expected to be a good representation of full-scale behavior based on these limited

considerations. Other factors, such as thermal radiation and geometric factors, are not

considered here. A complete review of the scaling for the Westinghouse 1/7 th scale tests is

contained in Appendix B and C of NUREG/CR-62853.

7
4 CFD MODEL DEVELOPMENT

The physical geometry and conditions described above are represented on a finite volume mesh

on which the governing Navier-Stokes equations are discretized and solved. The model is

developed for the FLUENT version 6.0 unstructured CFD code.

To save computer resources, the symmetry of the hot leg and steam generator is utilized. Only

half of the physical model is meshed and a vertical symmetry plane is established through the

hot leg and steam generator. Due to poor convergence with the steady state solver, a transient

solver is applied with steady boundary conditions to obtain a steady solution. The principal

features of the CFD model are summarized below:

transient Reynolds-averaged Navier-Stokes solution with steady boundary conditions

-vertical symmetry plane through hot leg and steam generator

Reynolds stress turbulence model (2n order) with nonequilibrium wall functions

full buoyancy effects on turbulence (as defined in FLUENT code)

temperature-dependent thermal properties (SF6 as working fluid) at constant pressure

gravity

500,000+ finite volume cells (hexagonal mesh)

segregated solver with 2d order differencing on momentum and energy

porous media model representing 216 individual steam generator tube flow paths

Significant modeling attributes and assumptions are further described below.

4.1 Finite Volume Mesh

The finite volume mesh, shown in Figure 3, consists of over half a million hexagonal elements.

In the bulk of the mesh, the cell aspect ratio is limited to 2 except for the tube bundle. In the

tubes, the cell aspect ratio ranged from 1 at the tube sheet to nearly 5 along straight sections of

tube. Cell skew is minimized through careful grid spacing and the use of the hexagonal

elements. Growth rate between neighboring cells is limited to 20% with few exceptions. The

majority of the cells in the hot leg and plenums are of the same approximate dimensions. The

hot leg is meshed with 26 cells along a diameter and the inlet plenum contains approximately 60

cells along a radius.

4.2 Boundary Conditions

Boundary conditions are applied at the walls (both internal and external), the inlet, and the outlet.

All walls use a no-slip condition for the momentum equations with zero surface roughness. In

addition, all walls are adiabatic with the exception of the tube walls above the tube sheet. The

vertical midplane of the steam generator and hot leg is modeled as a symmetry plane. The

vessel end of the hot leg is split into two faces to facilitate an inflow and outflow boundary. A

60/40 split based on height is used. This ratio comes from experimental observations. The 60%

region on top is where hot gas enters the hot leg from the vessel (velocity inlet condition). The

lower 40% of the hot leg pipe end provides an exit for the cooled gas returning to the vessel

(pressure outlet condition). The boundary conditions of the hot leg and tube bundle are

determined based on the experimentally observed energy balance. These conditions are

described in more detail below.

9
4.2.1 Tube Model

Directly modeling the 216 tubes from the Westinghouse 1/7t scale facility is not practical. This

approach requires a model with millions of cells. This size model is impractical for simulations

on typical computers in the year 2002. Computational mesh requirements are estimated in the

range of tens of millions of computational cells for full-scale steam generators with thousands of

individual tubes. To reduce the mesh requirements and to facilatate practical solutions, a

simplified tube bundle model is developed that maintains the flow and heat transfer

characteristics of the actual tube bundle with significantly fewer computational cells.

In the FLUENT model, square tubes with a larger cross section are used to represent the

individual tubes of the Westinghouse facility. Individual flow paths and tube heights are

preserved. A porous media option is used in the FLUENT model throughout the tube region.

This approach provides a set of modeling coefficients (porous model inputs) that are used to

preserve pressure loss and heat transfer characteristics of the tubes even though the cross

section is not prototypical. The porous media approach and use of square tubes significantly

reduce the meshing requirements needed to compute the tube flows. The square tube cross

section is easier to mesh with the hexagonal elements. A single cell can be used to accurately

define the cross section. A round tube requires many cells to adequately define the shape of the

cross section. The porous media approach also eliminates the need to resolve the tube wall

boundary layer sheer stresses and the tube sheet flow reduction pressure loss.

The tube model is validated by looking at one individual tube in detail. A prototypical round tube

is discretized with nearly one million cells to study the heat transfer and pressure drop

characteristics in great detail. The results are used to define the coefficients used in the

equivalent square, porous media tube with 4000 cells. The porous coefficients are adjusted in

the FLUENT code to ensure the porous tube approximation reproduces the prototypic tube

characteristics over a wide range of conditions. This approach does not accurately resolve flow

in individual tubes but does provide a realistic upper boundary condition for the inlet (and outlet)

plenum where the mixing of interest takes place. The principal attributes of the tube bundle

modeled with this approach are the pressure drop at the tube entrance, the flow (viscous) losses

within the tubes, the heat losses from the tubes, and the buoyancy driving forces. Tube bundle

mass are governed by a balance between the viscous (and inertial) pressure losses and the

buoyancy driving force. The inputs to this model are defined to preserve this balance and result

in an appropriate tube bundle mass flow. Further details on the tube bundle modeling approach

are outlined in Appendix A.

4.2.2 Velocity Inlet Conditions

The velocity inlet covers a region that represents the upper 60% (based upon height) of the

vessel end of the hot leg. It is assumed that the flow coming from the reactor vessel is well

mixed and at a uniform temperature and velocity. Further details of the velocity and temperature

profiles for flow coming from the vessel are unknown. Sensitivity studies indicated that the flows

at the inlet plenum end of the hot leg are not significantly affected by changes in the inlet velocity

profile at the vessel end of the hot leg. The uniform velocity and temperature boundary

conditions applied at the vessel end of the hot leg are considered a reasonable assumption.

Specific values for the inlet temperature and velocity are determined to match the reported hot

leg temperature and mass flow from the data.

10
4.3 Material Properties

The working fluid is sulfur hexafluoride (SF6). Fluid properties are obtained from graphs and

tables in Reference 4. Since the steady state tests are conducted at fixed pressure, properties

are specified as temperature dependent only. The properties used in the analysis of test SG-S3

are listed in Table 1. The FLUENT code uses linear interpolation on temperature to find the

thermal properties from the table.

4.4 Turbulence Modeling

Two turbulence models are used for the results cited in this report. Second order Reynolds

stress modeling (RSM) is used for all predictions with the exception of a sensitivity that uses the

first order, isotropic RNG k-epsilon model. Detailed experimental data, not available from the

Westinghouse tests, are needed to fully validate and justify the selection of the turbulence

model. The second order RSM turbulence model is considered to be the most appropriate

model available in the FLUENT code. The RSM model does not assume isotropic turbulence

like the two-equation k-epsilon type models. Full buoyancy effects on the turbulence model are

applied and nonequilibrium wall functions are used. Details of the turbulence models are

beyond the scope of this report.

4.5 Solution Convergence

Steady state solutions are obtained using a transient solver with steady boundary conditions.

Initially, each case is run using the steady state solver to obtain a rough solution that serves as

the initial condition for the transient solver. The transient solver is used until a steady solution is

obtained. Solution convergence is monitored in several ways. First, solution residuals are

monitored at each time step to ensure they have dropped sufficiently. In addition, several

temperatures and velocities are monitored in key areas. These monitored prediction points

asymptotically approach steady values as the solution nears convergence. Finally, an overall

mass and energy balance is monitored for convergence.

4.6 Grid Independence

A complete grid independence study is not performed due to the physical scale of the model. A

high-quality mesh is used for this analysis to minimize any grid affects on the results. In

addition, second order differencing is used to reduce numerical diffusion. Qualitative information

on grid independence is given below for completeness.

The final grid for this study contains over 500,000 finite volume cells. In the process of

constructing the grid, over 15 separate grids were created and tested. The final grid is a

compilation of the lessons learned during this process. Grid optimizations include optimized

node density for wall functions and verification of grid independence in the tube bank. The final

mesh is created using all hexagonal elements with grid stretching and skew minimized. In

regions of high gradients or transitions, the cell aspect ratio is kept very close to 1. Mesh size is

reduced at the walls to accommodate the wall functions. Transitions away from the walls are

limited to growth rates between 5 and 20%.

11
Although a full grid independence study is not completed, a high degree of confidence in the

quality of the mesh is obtained from localized grid studies, from the high-quality mesh, and

ultimately from the accurate prediction of the experimental results.

12
5 COMPLETED PREDICTIONS

Test SG-S3 is selected from the set of lIW 7 scale tests. It is one of the higher temperature and

power tests available. Initially, a best estimate case is completed to provide a direct comparison

of the predictions with the test data. The boundary conditions applied are determined from the

data. Next, a set of sensitivity studies is completed on some of the major modeling input

assumptions. This is done to establish the sensitivity of the results to variations in some of the

input parameters. Sensitivity studies reported here include variations of the hot leg inlet

temperature, hot leg mass flow, turbulence model, tubesheet entrance pressure drop, viscous

losses in the tube bundle, and tube heat transfer characteristics. The boundary conditions used

in the FLUENT model for these predictions are summarized in Table 2.

Additional sensitivity studies on modeling options such as the turbulent wall treatment, buoyancy

effects on turbulence, finite differencing schemes, solution algorithms, and mesh quality were

also completed. These studies helped to ensure the solution is stable and not unduly affected

by simple modeling assumptions. No significant variations were observed for these unreported

sensitivity studies. The studies are noted here only to document that they were considered.

Predictions completed in this study focused on the left steam generator from the facility because

the reported mixing parameters and other key variables from the test came from this side.

Significant asymmetries between the left and right steam generator data make quantitative

comparisons of the predictions with the right side data problematic. The asymmetries are

probably caused by the 40% difference in the cooling flow rates applied to the left and right

steam generators during the steady state testing.

5.1 Summary of Assumptions and Limitations

The completed CFD predictions give valuable insights into the three-dimensional natural

circulation flows in the hot leg and the primary side of the steam generator. However, the final

results are dependent upon the modeling assumptions and limitations of the approach. To

facilitate a better understanding of the predicted results, a partial list of assumptions and

limitations is given in Table 3. These limitations should be considered to gain a better

understanding of the results.

13
6 RESULTS

The results of this study demonstrate that the FLUENT code has the potential to predict the

natural circulation behavior in the hot leg and steam generator during this type of severe

accident scenario. Qualitatively, the code predicts the flow pattern with specific characteristics

that are observed from the test series. 'Quantitatively, predicted key parameters are in good

agreement with the data. The best estimate prediction is described in detail followed by a

discussion of the sensitivity studies.

6.1 Best Estimate Results

The results include specific data and integral parameters that are compared with the

experimental data.4 Detailed three-dimensional (3D) predictions of variables are also provided

to aid in the understanding of the phenomena. The integral features of the predictions are most

useful for assessing inputs to 1 D system codes that are used to predict plant behavior during

this type of transient. Features such as recirculation ratio, mixing fraction, and tube flow

fractions are used to set up simplified inlet plenum mixing models. Table 4 shows significant

parameters computed from the CFD results, compared to the experimental data for test SG-S3.'

Generally speaking, these predicted parameters are in good agreement with the experimental

results and are generally assumed to fall within the experimental uncertainty. Individual items

are discussed below.

Heat Loss at Tubes. Predicted total tube heat loss is 3.7% above the experimentally reported

value. Experimental tube bundle heat loss is determined from a secondary side coolant mass

flow rate and temperature rise measurements for this coolant. The experimental uncertainty of

the temperature and mass flow measurements and of other system heat losses is not available.

The CFD code computes the total tube heat loss as an integral of heat flux over the surfaces of

each tube. From a 15t law of thermodynamics analysis, the predicted tube inlet and outlet

temperatures and the tube bundle mass flow govern this value. The predicted temperature drop

in the tube bundle is 35.3K (63.5 OF). For a given tube bundle mass flow, one degree (K)

difference in the temperature drop changes the total tube heat loss prediction by 3%. The 3.7%

difference between the prediction and the measured value is considered insignificant in light of

the assumed experimental uncertainty.

# Hot Tubes vs. # Cold Tubes. Seven additional tubes are predicted to carry hot flow compared

to the reported value. This difference is equal to 3.2% of the total number of tubes (216) in the

bundle. Figure 4 illustrates the predicted boundary between the hot (upward) flow tubes and the

cold return flow tubes on a horizontal plane 1 inch (0.0254 m) above the entrance to the tube

sheet. The predicted boundary line is typically within one tube of the measured boundary and

the general location and shape of the tube boundary are consistent. A review of the complete

set of experimental results demonstrates a variation in the tube flow split ratio larger than the

difference observed here. These predicted results are considered good in light of these

experimental variations.

The experimental results appear to be biased towards reporting too many hot tubes. This bias, if

corrected, further increases the difference between the prediction and the experiments. The

flow in a tube, hot or cold, is determined by a temperature measurement made 1 inch (0.0254

* or 5 inch for some tubes

15
m) above the inlet plenum inside the tube. Temperatures close to the secondary side

temperature indicate the tube carries cold return flow. Temperatures above the secondary side

temperature are assumed to indicate hot (upward) flow. Approximately 25% of the tubes are

instrumented. Some type of judgment is used to assign the tubes with no thermocouple to either

a hot or cold flow status. The unmeasured tubes that are positioned directly between a hot and

cold tube are assumed to carry hot flow. This biases the result towards a higher number of hot

tubes. If one assumes that tubes between a hot and cold tube carry cold flow, the number of hot

tubes for test SG-S3 is only 49. This represents a reduction of 26 tubes or 12% of the total

tubes in the bundle. It is suggested that the midpoint, 62 hot tubes, of these values may

represent the total number of hot tubes for this test. Assuming 62 hot tubes increases

overprediction by the CFD model to 9% of the tubes in the bundle. The CFD predictions

determine hot and cold flow tubes based upon the velocity profiles 1 m (39.4 inches) above the

inlet plenum. The results are not influenced by interpretation since each tube is considered.

Th, Hot Lea. The hot leg hot-flow temperature is predicted to be 4.3 'C below the experimentally

observed value. The predicted value can be controlled by the inlet boundary conditions. It is not

adjusted to match the experimental value because of differences in the approaches used to

obtain this value. The experimental hot leg hot-flow temperature is obtained from a single

thermocouple reading located on the center of the upper quarter flow area of the hot leg near the

steam generator end of the pipe (x = -0.292 m, -11.5 in.). Based on the CFD predictions, this

point is not at a temperature equal to the mass averaged hot leg hot-flow temperature. The

predicted hot leg hot-flow temperature is obtained as a mass averaged integral of the forward

flow in the hot leg on a vertical plane near the mid-point of the pipe (x = -0.56 m, -22 in.).

Figure 5 illustrates the temperatures in the hot leg used to obtain the value for Th. The

continuous curve represents the CFD prediction on the centerline of the pipe between the lower

and upper wall. The predictions indicate that the return flow is at a relatively uniform

temperature of approximately 353.2 K on the bottom half of the pipe. The upper portion of the

pipe contains the hot flow. The vertical line at a temperature of 428.1 K represents the mass

averaged temperature of this forward flow. The diamond (single point) on the plot indicates the

measured result (432.5 K). The predicted temperature at the location of the thermocouple is

approximately 442 K. This indicates a predicted temperature higher than the measurement.

The limited available data in the hot leg do not allow for refinement of the hot leg hot-flow

prediction. The predicted value is considered acceptable in light of the potential uncertainty in

the measured value. The measurement uncertainty is affected by the large temperature

gradient expected in the region of the thermocouple. A vertical temperature gradient of 4 to 5 0C

per millimeter (206 0F/in.) is predicted at this location. In addition, the single thermocouple

measurement is unlikely to be equal to the mass averaged temperature. Detailed velocity and

temperature profiles, unavailable from the tests, are needed to assess the measurement.

Tr, Hot Lea. The average temperature of the cold return flow in the hot leg is predicted to be

about 6.7 K lower than the measured value. Measured values are obtained from the average

value of two thermocouples positioned in the lower half of the hot leg near the steam generator

end. The return temperature is observed and predicted to be very uniform. An average vertical

temperature gradient of approximately 0.1 0C per millimeter is predicted in this region. The

predicted hot leg cold-flow temperature is obtained as a mass averaged integral of the return

flow in the hot leg on a vertical plane near the midpoint of the pipe (x = -.56 m, -22 in.).

16
m. Hot Lea. Mass flow in the hot leg is predicted to be 2.3% below the reported value.' This

value can be adjusted with the hot leg inlet boundary conditions. The value is considered in

good agreement and needs no adjustment in light of the suspected experimental uncertainties.

The computed mass flow is obtained from an integral of the hot flow near the center of the hot

leg (x = -.56 m, -22 in.). The experimental mass flow rate is estimated from the hot leg

temperature measurements and the tube bundle energy loss. Tube bundle heat transfer is

obtained from measurements of the secondary side coolant mass flow and its associated

temperature rise. A steady state 1 d law of thermodynamics analysis is used to obtain the tube

bundle energy loss. An additional It law analysis is used to obtain the hot leg mass flow from

the tube bundle heat loss and the measured values of Th and Tc. This indirect means of

obtaining the hot leg mass flow is expected to result in a measurement uncertainty significantly

above the 2.3% difference in the predicted value. The uncertainty is not estimated in the data

report.

T11, T. Tubes. The temperature of the hot flow entering the tubes, Tht, is predicted to be within 1

degree of the measured value. Tube entrance temperatures are a primary result of this analysis.

The hot flow, after significant mixing in the inlet plenum, is predicted to have essentially the

same temperature as in the experiment as it enters the tube bundle. This result is very - -

encouraging for the prospects of predicting inlet plenum mixing with CFD. The cold-tube return

flow temperature, Tct, is essentially equal to the secondary side temperature.. This value is

established as a boundary condition to match the data exactly.

Tube temperatures in the experiments come from thermocouples located within the tubes 1 inch

(0.0254 m) or 5 inches (0.127 m) above the tube entrance. Approximately 25% of the tubes are

instrumented. The downflow measurements are essentially equal to the secondary side

temperature. This fact makes the up and down flow tubes easy to distinguish. All of the hot

thermocouples are identified and a simple average is used to determine the experimental hotflow temperature entering the tube bundle (TN). FLUENT predictions of the temperature

entering the tube bundle are obtained from a mass weighted integral over the upward flow

region at an elevation 1 inch above the tube sheet entrance.

mt Tubes. Mass flow through the tube bundle is predicted to be within 1 % of the experimental

value. The agreement lends credibility to the modeling approach used for the tube bundle. The

predicted mass flow is obtained from an integral of the mass flux over the region of upward flow

in the bundle. This integral is completed 1 m (39.4 in.) above the tube sheet. Experimentally,

the tube bundle mass flow is determined from a steady state 1st law of thermodynamics analysis.

The tube bundle heat loss and the tube entrance and exit temperatures are used to find the

mass flow rate.

mrn (recirculation ratio). The ratio of the tube bundle mass flow to the hot leg mass flow defines

the recirculation ratio. The predicted ratio is about 2.5% above the experimentally reported

value. The prediction is considered to be within the experimental uncertainty.

f (mixing fraction). The mixing fraction, f, is defined as the fraction of hot leg (hot) flow that

mixes with the cold return flow in the inlet plenum. The formulation for f is given in an associated

report6 (Ebeling-Koning et al., 1990) along with a diagram of flow patterns used to define f. The

predicted mixing fraction is 4.7% below the reported value. The formulation given in Reference

6 is used with the CFD predictions to determine the mixing fraction even though the assumptions

made to define f may not be ideal. Although the result is very sensitive to small changes in the

tube bundle hot flow temperature, the prediction is very consistent with the data.

17
6.2 Hot Leg Prediction

The hot leg flow consists of an accelerating hot flow stream traveling from the vessel to the

steam generator along the top one-half to one-third of the hot leg flow area. Cooler gas returns

from the steam generator to the vessel through the lower portion of the hot leg. The flow

remains very stratified in the hot leg region. Figure 5 shows the vertical temperature profile at a

location near the center of the hot leg. The hot flow occupies the upper 40% of the hot leg

(based on height). A large vertical temperature gradient is predicted in the lower portion of the

hot flow. The cold return flow temperatures are much more uniform, as shown on the lower

portion of the curve. These predictions agree qualitatively with the experimental observations

and limited measurements in the hot leg as noted in Reference 2 (p. D-1 6).

Figure 6 illustrates temperature contours on the hot leg symmetry plane. The uniform cold return

flow region is clearly seen on the bottom of the pipe. Vertical profiles of the velocity on the

symmetry plane are inset on the figure at two locations (x = -.56 m and x = -.292 m). These

profiles illustrate the acceleration of the hot flow as it approaches the steam generator. As the

flow accelerates, the hot flow area is reduced. The flow is predicted to continue accelerating

into the nozzle region with a peak velocity reached just beyond the nozzle exit (in the inlet

plenum). The flow retains a high degree of stratification throughout the hot leg. Temperature

contours on a hot leg cross section at x = -0.56 m (-22 in.) illustrate the high degree of thermal

stratification.

6.3 Nozzle Region Predictions

The nozzle region plays a significant role in the overall mixing behavior of the system. This is a

region of complex flow topology and high thermal and velocity gradients. Significant mixing

begins to occur in the nozzle region. This region is at an intersection between the hot and cold

flow streams. The hot stream is exiting the hot leg and entering the inlet plenum. The cooler

return flow is trying to enter the hot leg and-flow towards the vessel. Path lines on the symmetry

plane are shown in Figure 7. The hot flow vectors accelerate through the nozzle and flow

directly to the tube sheet. Cold return flow intersects the hot plume right at the nozzle exit. This

intersection of two streams is indicated on Figure 7. The return flow appears to form a

stagnation point on the hot plume with part of the flow becoming entrained into the rising plume

and part of the flow entering the hot leg. Inlet plenum flows, described in the next section,

further clarify this behavior.

This complex flow behavior significantly increases the level of turbulence in the flow. Figure 8

shows the contours of turbulence intensity on the symmetry plane in the nozzle and inlet plenum

region. Turbulence intensity reaches a local maximum at the intersection of the nozzle and the

inlet plenum. This location corresponds to the region where the two streams intersect

highlighted in Figure 7. The significant result of this complex flow is the resultant mixing of the

hot plume as evidenced by the reduction in plume temperature. Figure 9 shows normalized

temperature contours in the nozzle and inlet plenum region. The hottest temperatures remain in

the range between 1.2 and 1.3 for the entire hot leg length. Significant temperature reduction

begins to occur at the junction between the nozzle and the inlet plenum. The isotherms are very

close together in this region. The normalized temperature is reduced to 0.55 just below the tube

sheet entrance. These data are consistent with experimental observations that indicate a

significant temperature reduction close to the nozzle region. It is noted that the normalized

18
temperature for the mass averaged hot leg hot flow is 1.0. Peak hot leg temperatures are higher

than this mass averaged value.

6.4 Inlet Plenum Flows

The steam generator inlet plenum is the region associated with the mixing phenomena of

interest in this study. As noted earlier, this mixing begins to occur significantly in the nozzle

region. The hot plume leaving the nozzle rises quickly through the inlet plenum and impacts the

face of the tube sheet. Part of this flow enters the tube bundle and flows to the outlet plenum of

the steam generator. Another portion of this flow stagnates and turns radially outward from the

point of intersection. This behavior is similar to a stagnation flow on a porous surface. The flow

that remains in the inlet plenum flows radially towards the inlet plenum walls. The flow on the

symmetry plane is shown in the path lines of Figure 7. There are significant mixing flows in

planes perpendicular to the symmetry plane. Figure 10 shows flow vectors on three vertical

planes normal to the symmetry plane. As the hot plume intersects the tube sheet, flow is

directed towards the walls of the inlet plenum and then down and around the spherical walls.

Flows from both sides intersect at the bottom of the inlet plenum and are directed upward again.

This behavior explains the upward flow paths evident over much of the inlet plenum symmetry

plane in Figure 7. Two large recirculation regions are formed in the inlet plenum as shown in

Figure 10.

The plume spreading is minimal until the plume intersects the tube sheet and spreads out in all

directions. Figure 11 shows temperature contours on three horizontal (y) planes. The y

coordinate value of each plane is noted on the figure along with the relative locations of the

plane within the inlet plenum. The lower plane (y = -5.5 in.) shows the region of the plume just

above the elevation of the nozzle. The plume is very small and the remainder of the inlet plenum

is at a significantly lower temperature. In the next plane shown, y = -2 in., the plume

temperature is reduced but the plume is still occupying only a small region of the inlet plenum.

The upper plane is located just 0.25 inches below the tube sheet. At this elevation, the plume

has impacted the tube sheet and is spreading in all directions. The region of impact is identified

by the hottest temperature zone at the center. The extent of the spreading can be clearly seen

at this level. The spreading layer is pushed downward by the returning flow from the outlet

plenum and the hot layer drops below the 0.25 inch level shown in the top plane.

Similar behavior is illustrated in Figure 12 in vertical planes parallel to the symmetry plane.

Three planes are shown with z coordinates of 0, -2, and -5.5 inches. Temperature contours on

the symmetry plane, z = 0, show the path of the plume and the spreading of the hot flow as it

encounters the tube sheet. On a plane just 2 inches away, the plume is not evident. The hot

layer near the tube sheet is the only evidence of the hot plume. The colder return flow from the

tubes enters the inlet plenum and is entrained by the inlet plenum flows. Some of this return

flow is evident by the cooler temperatures at the upper most portion of the plane at z = -5.5

inches.

6.5 Tube Bundle Flows

Part of the tube bundle carries hot flow from the inlet to the outlet plenum. The remaining tubes

carry the cooler return flow back to the inlet plenum. The hot tubes loose their heat to the

secondary side coolant at a rate that reduces the hottest tubes to temperatures near the

secondary side temperature by the time the flow reaches the top of the tube bundle. Beyond this

19
point, the forward flow and the return flow tubes are at a temperature equal to the secondary

side coolant. This is consistent with the test setup but does not represent prototypical behavior.

Figure 4 (adapted from Reference 6) shows the boundary between the hot and cold tubes. The

CFD results overpredict the number of hot tubes by more than 3%. Generally speaking, the

predicted region of hot tubes is consistent with the data and the wider range of experimental

observations. Figure 13 shows the temperature contours on a horizontal plane 1 inch above the

tube sheet entrance. The hot tube region is clearly visible on the figure. The cold tubes, with

black contours, are all at a uniform temperature equal to the secondary side coolant

temperature. Some cold tubes on the boundary between the hot and cold tubes show a small

amount of hot gas in a portion of the tube region. These tubes had a small return flow velocity

and hot gas penetrated into the tubes a small distance as indicated in the figure. This is

probably the result of the tube modeling approach that utilized tubes of increased cross sectiont

to simplify the mesh requirements.

A peak temperature is found at the center of the hot tube region in Figure 13 and the

temperature drops off from that point. To quantify the temperature variations in the hot flow

tubes, a histogram is created to show the relative number of tubes within a series of temperature

ranges. Figure 14 gives the percentage of tubes in the tube sheet that fall into specific

normalized temperature ranges. Temperatures are normalized by the total temperature

difference between the hot leg hot-flow temperature (Th) and cold tube return flow temperature

(Tr). The normalized scale ranges from 0 to 1 and is broken down into 20 ranges (5% each).

The center point of each region is indicated on the horizontal axis. Only hot flow tubes are

shown on the histogram and the tube percentages are based upon the total number of tubes in

the bundle. The summation of the value for each range equals 38%. The data indicate that the

normalized temperature entering the tube sheet fall within the normalized temperature range of

0.15 - 0.55. The largest group of tubes, just over 10% of the total, falls in a normalized

temperature band centered on 0.375 (range from .35 - .40). Only 2.3% of the tubes fall into the

highest range between 0.5 and 0.55. These maximum values demonstrate the effectiveness of

the inlet plenum mixing for reducing the temperature of the hot gas reaching the tube bundle.

Figure 15 shows temperature profiles for the entire symmetry plane of the model. The hot gas in

the tube bundle approaches the secondary side temperature prior to reaching the top of the tube

bundle. This is consistent with the experimental observations from the steady state tests.

These temperature observations from the test program were used to establish the rate of heat

transfer from the tube bundle model. Appendix A should be reviewed for details of the approach

used to model the tubes.

6.6 Sensitivity Study Results

Sensitivity studies are completed to quantify the effect of variations in the input parameters to

look for values where uncertainty can significantly affect the solution. Table 5 lists the conditions

used for the sensitivity studies. Solution sensitivities are considered for variations of the hot leg

inlet temperature, hot leg inlet velocity, turbulence model, tubesheet pressure drop, viscous tube

losses, and the tube external heat transfer coefficient. Specific results from the sensitivity

studies are listed in Table 6. Each sensitivity study prediction results in the same general flow

behavior as the base case outlined above. No fundamental changes in the flow structure are

t See Appendix A.

20
predicted. Specific values for flow variables and mixing parameters are affected by the

variations in the input parameters and will be quantified. Table 6 lists the values predicted for

specific parameters along witM an indication of the change in the value in relation to the base

case result. Each of the sensitivity studies is discussed in more detail below.

6.6.1 Inlet Temperature Sensitivity

The inlet temperature sensitivity is completed with the temperature at the hot leg inlet set to

432.45 K (318.7 OF). All other modeling options and input parameters are equivalent to the base

case described earlier. This inlet temperature is 15 K (28 OF) lower than the base case boundary

condition. Generally speaking, this analysis does not reveal a significant sensitivity. The flow

patterns and most of the predicted parameters in Table 6 are very close to the base case

prediction. The variations predicted are consistent with the change made to the boundary

conditions.

The largest change, other than the obvious hot leg temperature reduction, is the 13 % reduction

in the tube bundle heat loss. This reduction results from the combination of a reduced tube

bundle mass flow and a reduced tube bundle entrance temperature. Tube bundle entrance

temperature, Tht, is predicted to be 2.9 K (5.2 OF) below the base case result. The 2.9 K drop in

the entrance temperature reduces the total temperature drop for the tube flows by 8.2%

compared to the base case. Tube bundle heat loss is proportional to this temperature drop and

the tube bundle mass flow. Tube bundle mass flow is reduced by 5.9%. A drop in the tube

bundle mass flow is expected due to the lower temperatures and resulting lower buoyancy

forces.

The 15K (28 0F) temperature drop at the boundary results in a 10.3 K (18.5 OF) drop in the mass

averaged hot leg temperature. There is apparently less hot leg mixing and entrainment in the

lower temperature case. At the tube sheet entrance, the temperature reduction is only 2.9 K (5.2

°F), as noted earlier. This does not appear to be a significant reduction given the 15 K decrease

at the boundary. The results look more consistent in dimensionless form. Using reference

temperatures specific to each case, the dimensionless tube entrance temperature for the base

case is 0.391 and for this sensitivity study the result is 0.405. These values are within 3.6% of

each other.

6.6.2 Hot Leg Inlet Mass Flow (Inlet Velocity) Sensitivity

The hot leg inlet mass flow is increased by 20% for this sensitivity. The increase is achieved by

increasing the inlet velocity by 20% without changing the inlet temperature. The general

behavior of the system is similar to that described earlier for the base case. In general, the

higher velocities in the hot leg resulted in increased mass flows throughout the system.

The hot leg mass flow predicted at the middle of the pipe increases by 11.4%. The higher

velocity in the hot leg results in additional flow reversal (entrainment). Some of the increased

mass flow reverses in the hot leg and flows back towards the vessel prior to reaching the steam

generator. Some limited additional analysis, not reported here, indicates that further increases

in the inlet velocity result in ever-increasing amounts of flow reversal in the hot leg with little or no

increase in the net mass flow to the inlet plenum. These higher velocity inlet conditions are

reaching the countercurrent flow limitations for this model.

21
The increase in the hot leg velocity does not affect the path of the rising hot plume. Buoyancy

forces still dominate the plume behavior. The plume is predicted to rise through the inlet plenum

on essentially the same trajectory as in the base case. The number of hot flow tubes in the

bundle and the pattern of hot tubes is unchanged. The increased hot leg mass flow increases

the mass averaged temperature in the hot leg by over 5 K (9 0F). This increase in temperature

increases the buoyancy forces in the inlet plenum and accounts for the 7.7% increase in the

tube bundle mass flow. The increase in the tube bundle mass flow is not quite as large as the

increase in the hot leg flow and the resulting recirculation ratio is 3.4% below the base case

prediction. The mass averaged temperature entering the tubes is 3.2 K (5.8 OF) higher than the

base case. This value results in an averaged dimensionless temperature entering the tubes of

0.404. This value is consistent with the base case and inlet temperature sensitivity study

discussed earlier.

6.6.3 Turbulence Model Sensitivity

The second order Reynolds stress turbulence model is selected for this analysis for the reasons

stated earlier in this report. This decision is not based upon a detailed analysis of the flowfield

since these data are not available from the experiment. To quantify the effect that the choice of

the turbulence model can have, the base case is modified to use a first order k-epsilon type

turbulence model. The RNG k-epsilon turbulence model is used along with full buoyancy effects

and nonequilibrium wall functions to remain consistent with the base case.

Qualitatively, the results and flow patterns are similar. The predicted parameters are generally

within 5% of the base case. One notable exception is the mixing fraction that is over 12% higher

than the base case. K-epsilon type turbulence models have a tendency to overmix under many

conditions and it is suspected that this characteristic is evident in these results. This particular

model also predicted significantly more lower tube recirculation. In a small portion of the tubes,

hot gas enters the tubes and rises for a short time before some of it is cooled and returns directly

to the inlet plenum. It is assumed that this phenomenon occurs due to the large tube cross

sections associated with the tube bundle modeling approach. This phenomenon is not expected

to occur in the experiments due to the small tube cross sections associated with the facility. This

type of recirculation can help increase the tube bundle heat loss. A detailed analysis of the

effects of the turbulence modeling approach is beyond the scope of this report.

6.6.4 Tube Sheet Entrance Pressure Loss Sensitivity

The simplified tube model used for this analysis assumes the tube sheet entrance pressure drop

is proportional to the local flow velocity squared. The tube bundle model and this relationship

are described in Appendix A. For this sensitivity study, the tube entrance pressure drop

coefficient is increased by 25%. For a given flow velocity, this change creates a tube bundle

entrance pressure drop 25% higher than the base case. This results in no significant variation

in the predicted results. Key mixing parameters are within 2% of the base case results. This

increase in the pressure drop decreased the tube bundle flows by only 2.2%. Tube bundle

entrance pressure drop accounts for only a fraction of the total pressure drop for flow through

the tubes. Most of the total pressure drop comes from the viscous (shear) losses to the tube

wall. This sensitivity study demonstrates that a small amount of uncertainty in the tube entrance

pressure loss coefficient does not significantly impact the overall solution.

22
6.6.5 Tube Flow Viscous Loss Sensitivity

The tube bundle modeling approach defined in Appendix A relies on coefficients to model the

viscous pressure drop for flow in individual tubes. This sensitivity study increases these

coefficients by 25% over the base case. The most significant change is a 10.7% reduction in the

tube bundle mass flow and a related 9.2% drop in the recirculation ratio. This result is not

surprising since the resistance to flow in the tube bundle is predominantly made up from the tube

flow viscous losses. Surprisingly, the number of hot tubes and other parameters are not

significantly affected by this change in the tube bundle flow resistance. Fortunately, tube flow

viscous losses for single-phase flow are predicted with a relatively low level of uncertainty. The

results of this sensitivity study provide confidence that small uncertainties in the tube flow

viscous loss determination do not adversely affect the overall results.

6.6.6 Tube Heat Transfer Coefficient Sensitivity

The heat transfer coefficient on the outside of the tubes (secondary side boundary condition) is

changed for a pair of sensitivity studies related to this important parameter. The results indicate

that this boundary condition plays a significant role in the determination of the mixing parameters

of interest. This is the only sensitivity study completed that affects the predicted number of hot

tubes. In addition, the largest changes in the recirculation ratio and the mixing fraction result

from these changes. The heat transfer coefficient on the tube secondary side is predicted to be

a key parameter governing the flow and mixing behavior of this type of scenario.

Heat transfer coefficients in complex geometries are difficult to determine without detailed

experiments. Natural circulation flows on the secondary side of the tubes are assumed to be

complex in nature. There is a potential for large uncertainties in the secondary side heat transfer

coefficients. The results of this sensitivity study indicate that an effort should be made to reduce

the uncertainty in the secondary side heat transfer coefficients used for this type of modeling

approach due to the significant impact these conditions have on the predicted mixing

parameters.

The base case utilized a heat transfer coefficient of 250 W/m2-K on the outer surface of each

tube. This value cannot be compared directly to the experimental heat transfer coefficient due to

the nature of the tube bundle model. This value is established, along with other tube bundle

thermal properties, to provide an equivalent rate of heat loss from the tubes. Sensitivity studies

are completed with the heat transfer coefficient set to 5000 and 100 W/m2-K. The 5000 W/m2-K

case is chosen to be large enough to effectively set the tube outer wall temperature to the

secondary side temperature. The value of 100 W/m2-K reduces the heat transfer coefficient by

a factor of 2.5.

The first interesting result is the effect these changes have on the net tube bundle heat loss.

The heat loss decreases when the heat transfer coefficient is increased. Tube bundle heat loss

increases when the heat transfer coefficient is decreased. The tube bundle flows help explain

the differences in the tube bundle heat loss. The increased heat transfer coefficient results in

the tube flows reaching the secondary side temperature over a shorter length of tube. This

results in a shorter column of hot gas that provides the buoyancy driving force. A small tube

bundle mass flow is the result. Likewise, the decreased heat transfer coefficient results in a

larger vertical column of hot gas that produces a larger buoyancy driving force. The tube bundle

mass flow is increased in this case. For a given temperature change, the tube bundle heat loss

is proportional to the tube bundle mass flow rate. Tube bundle mass flow rates changed by an

23
average of 16.8% for these sensitivity studies. The resulting average change in the recirculation

ratio is 14.8%.

The number of hot tubes changed as a result of the changes in the heat transfer rate. More

tubes carried hot flow in the case where the heat transfer coefficient is decreased. It is

suggested that the reduced heat transfer rate, and the resulting reduction in the tube bundle

mass flow, cause the rising hot plume in the inlet plenum to spread further when it intersects the

tube sheet. This increased spreading is suspected to be the cause of the increase in the

number of hot tubes. The flow pattern of the plume intersecting the tube sheet is a combination

of a stagnation flow and a penetrating flow. If the tube bundle flows are retarded due to a

smaller buoyancy force, the amount of penetrating flow is reduced and the stagnation flow

pattern (spreading) is enhanced. The mixing fraction relates to the portion of the flow from the

hot leg that mixes into the inlet plenum without directly penetrating into the tubes. This increase

in the mixing fraction for the case with increased heat transfer is consistent with the analogy of

the stagnation and penetrating flows. Increases in the buoyancy driving force make it easier for

the rising hot plume to penetrate into the tube bundle and therefore result in decreases in both

the number of hot tubes and the mixing fraction.

24
7 SUMMARY

The best estimate prediction at lI7t" scale demonstrates the applicability of the modeling

approach used along with the FLUENT CFD code to predict severe accident natural circulation

flow and mixing parameters in the steam generator inlet plenum. Best estimate predictions are

qualitatively consistent with the experimental observations. The overall flow pattern and

behavior are correctly predicted. Quantitative comparisons demonstrate the capability to predict

key mixing parameters for this type of scenario. A series of sensitivity studies demonstrates that

the solution is not adversely affected by the uncertainty in key modeling parameters and

boundary conditions. The most significant modeling input is predicted to be the secondary side

heat transfer coefficient. This input parameter has a significant impact on the three key mixing

parameters (# hot tubes, mixing fraction, and recirculation ratio). It is suggested that the

secondary side heat transfer is the key boundary condition that must be well defined in order to

carry out this type of modeling. The qualitative and quantitative agreement between the data

and the predictions confirms the applicability of the FLUENT code to predict the severe accident

natural circulation flow and mixing behavior in the hot leg and steam generator. There are no

foreseen limitations for applying this technique to similar scenarios beyond the range of the

existing experimental data.

25
8 REFERENCES

1. Memorandum on the steam generator action plan from Ashok Thadani and Samuel

Collins to William Travers, dated May 11,2000.

2. P. D. Bayless et al., 'Severe Accident Natural Circulation Studies at the INEL,"

NUREG/CR-6285, INEL-94/0016, February 1995.

3. SGTR Severe Accident Working Group, "Risk Assessment of Severe Accident-Induced

Steam Generator Tube Rupture," NUREG-1570, March 1998.

4. Westinghouse Electric Corporation, "Natural Circulation Experiments for PWR HighPressure Accidents," Research Project 2177-05, Final Report, August 1993.

5. J. D. Anderson, Computational Fluid Dynamics: The Basics with Applications,

McGraw-Hill Series in Mechanical Engineering, McGraw Hill, 1995.

6. D. B. Ebeling-Koning et al., "Steam Generator Inlet Plenum Mixing Model For Severe

Accident Natural Circulation Conditions," 1990 ASME Winter Meeting, Dallas, Texas.

27
PreUaurizer

Reactor

Vessel

Steam

Generator

Inlet

Plenum

Hot Log L°oo

Blocd

Figure 1. Overview of Natural Circulation Flow Pattern

Figure 2. Cross Section of Inlet Plenum, Hot Leg, and Tube Sheet

i Seal

ked

28
SG-S3 000utle 000 0 outlet side

0000000 0~ 0 0 0 00 0000

0 00000000000000000

000000 0OE0000000000000

/000000 00 0 00 000 0 0 00 0 00 0\

000.000 000G0 00 O00000 00~0

oooooooooo. 1Y ooooo

ooo0ooo ooooo6o O 00OOO0

00000009,000000000000000

00@000 00 O OO !OG WO® O O O .0

. __ OOO. _ _ (DI0_ .IOO 

o o o o o jO o6 o 0-. o o Omi Ot O oo o

0 GOWO0 -. 4T:o0E)!0 0e .00-

O 0sb00 G0E0 It cro O 0 @2,0>,9-0 eo ioleosido @ o

\ ooo c oo oo oo

o so saS23i si <304ild o@,0 We

999*datz, -- n pre(

Figure 3. Computational Mesh Figure 4. Boundary Between Hot and Cold Tubes

-0.19 -

-0.20 -

-0.21 -

-0.22 -I

-0.23 -

-0.24 -

-0.25 -

-0.26 -

-0.27 -

-0.28 -

-0.29 -

. .. . ...... ~~~~~~~~~~~~~~~~~~~~~. . .. . ................... ..... ......... .

FLUENT Prediction ............... ... ...... .... . ........ ... ....... ... I ..../

mass averaged ...... temperature for ... test data

flow .~~hot from FLUENT(425K

... .......... ~~~~~~~~~~~~...... ; ........ ..... . ... .. ....

prediction (428.1 K) . ( .

~~~~~~~~~~~~~~~~~~~~~~~~... . . ..... .... .

Test SGS3; vertical profile in hot leg .. . ....... ... .. . .. ......... . ..... ..

o

-1 - ---] - -- I - I I I I

350 360 370 380 390 400 410 420 430 440 450

temperature (K)

Figure 5. Hot Leg Temperature Prediction and Data (x = -0.566 m)

29
hot leg cross section

450 T (K)

439

inlet

plenum

171-

r-!

-! 1

- 1,

, 1 .2. -

428

417

406

395

384

373

362

351

340

at x= -0.56 m I

L X ~~~~~x = -0.56 m x = -0.292 m

I . i

test SG-S3 hot leg symmetry plane

predicted temperature contours _ velocity profiles,

on pipe centerline

Figure 6. Hot Leg Temperature Contours and Velocity Profiles

significant mixng

at stream intersection

Figure 7. Path Lines on Symmetry Plane of Inlet Plenum

30
17.6 %

15.9

"I I

14.1

. we .6 12.3

! 88

7.1

5.3

3.5

1.8

0.0

Figure 8. Contours of Turbulence Intensity on Symmetry Plane of Inlet Plenum

Figure 9. Normalized Temperature Contours on Symmetry Plane of Inlet Plenum

31
velocity vectors

length proportional

to velocity magnitude

~- z

- .-.

- --.. ...

* ***-*r- - - -- .

-. J* 

x -4 inch (-. 1016

-+= -- t-\s, * 

)'

KL

x=-6 inch (-O.1524 m) Liz

Figure 10. Velocity Vectors on Vertical Planes Normal to Symmetry Plane

32
v = -0.25 inch (-0.0064 m)

v = -55 inch (-0.1397 m)

Figure 11. Temperature Contours on Horizontal Planes in Inlet Plenum

33
z = 0 (symmetry plane) X= ,'-I -r~ &W1

z = -2 inch (-0.0508 ml

I,

450 K

439

428

417

406

395

384

373

362

351

340

Figure 12. Temperature Contours on Vertical Planes Parallel to Symmetry Plane

34
387

T (K)

382

;,,t372 /1i

367 7,

-362

352

347

342

Figure 13. Temperature Contours on Horizontal Plane 1 Inch Above Tube Sheet Entrance

1 2 -- - -

Normalized T

T' = (T-TEt)(Th-Tjt)

10 -

Predicted Values

.0 8 -8 ______________- ---- Te = 337.85 K

Th =428.11 K

o 4-- -_ -1 _ - _ - - _ - - _ - ._ -. -___________--

0 KEI- T T _T

N A (0 . N1" N" A N" .N P. N N QC Q v- ' IF' ft ! V A 4 4N, ('I (0 N.1

a o' a' a a a o' o' 'o ao o' ao o' o o'

r (Normalized Temperature Range)

Figure 14. Histogram of Normalized Hot Temperatures 1 Inch Above Tube Sheet Entrance

35
447

436

425

414

403

392

381

i370359

Figure 15. Predicted Temperature Contours on Model Symmetry Plane

36
Table 1. SF6 Properties (2.07 Mpa, 300 psla)

T density T Cp T k T viscosity

(K) (kgm 3) (K) (J/kg-K) (K) (Wlm-K) (K) (Pa-s)

333.3 132.9 333.2 832.3 313 .016522 312 1.79 e-05

3472 122.7 355.4 822.3 323 .017041 472 2.35 e-05

361.1 114.9 377.6 826.9 330 .016781

388.9 102.7 444.3 864.6 353 .018598

416.7 94.3 393 .020414

444.4 86.9 473 -. 024220

Table 2. Summary of Boundary Conditions

Input Boundary Condition SG-S3

Fluid SF6, 300 psia

Inlet Velocity (m/s) 0.1045

Inlet Temperature (K) 447.45

Secondary Side Temperature (K) 337.85

Heat Loss Region Tubes Only

37
Table 3. Assumptions and Limitations

Assumptions Notes/Limitations

porous tube model The model is developed to reproduce mass flow and heat

loss characteristics of bundle. Velocity is atypical due to

an increased flow area. Return flow velocity is low. The

impact of the different return velocity has not been

assessed. Heat transfer is augmented by increasing the

thermal conductivity within the tubes to make up for the

increased cross section. Isotropic thermal conductivity

also affects conduction in flow direction.

grid density sufficiency A rigorous grid sensitivity study is not attempted.

inlet boundary conditions Boundary conditions are determined to match the mass

and energy balance from the limited data available. No

direct velocity measurements are available and a single

temperature measurement provides the mass averaged

temperature.

adiabatic plenum divider plate The steel plate separating the inlet and outlet plenums is

assumed adiabatic. A limited sensitivity study, not

documented in this report, suggests that the heat loss

across this plate is only 1% of the total tube bundle heat

loss.

adiabatic tube sheet The nearly 4-inch thick steel tube sheet, which supports

the tubes and separates the cooling water from the hot

inlet plenum, is assumed to be adiabatic. The effect of

this assumption is not assessed.

all tubes receive to the same No information is given about the secondary side cooling

cooling of the tubes other than an inlet and outlet temperature, a

calculated mass flow rate, and a few measurements of

temperature in the tubes at the top of the bundle. Tubes in

the center of the bundle may or may not be cooled as

effectively as tubes on the exterior of the bundle. The

CFD model assumes each tube is subjected to the same

conditions at all locations. Heat transfer is a significant

governing parameter. The implications of this

simplification have not been assessed.

symmetry model This assumption could limit the potential physical

oscillations of the buoyant plume in the inlet plenum.

38
Table 4. Comparison of Test Data (SG-S3) with FLUENT Predictions

Parameter Westinghouse FLUENT Difference

17th Test Data* Prediction

Heat Loss at Tubes (kW) 3.56 3.69 3.7 %

# Hot Tubes 75 82 7 tubes (3.2%)

# Cold Tubes 141 134 -7 tubes

Th Hot Leg (average Hot T (C)) 159.3 155 -4.3 0C

T, Hot Leg (average Cold T (C)) 86.8 80.1 -6.7 0C

m Hot Leg (mass flux (kgls)) .06 .0586 -2.3 %

Tbt Tubes (average Hot T (C)) 100.8 100 -0.8 0C

T~t Tubes (average Cold T (C)) 64.7 64.7 0

mt Tubes (mass flux (kg/s)) 0.12 0.1206 0.5 %

rnmr (recirculation ratio) 2.01 2.06 2.5 %

f (mixing fraction 2

) 0.85 0.81 -4.7 %

* Permission to use this EPRI Licensed Material is granted by EPRI.

39
Table 5. Boundary Conditions for Sensitivity Studies

Sensitivity Study hot leg inlet hot leg turbulence tube tube flow bundle

temperature inlet model entrance viscous loss heat

velocity pressure coefficients transfer

T*,, (K) drop coefficient

Vi, (m/s) coefficient (I/m; /ml2) (W/m 2K)

Base Case 447.45 0.1045 RSM 45.06 (137.9; 250

9.09E+09)

Inlet Temperature 432.45 - -

reduced by 15 K

Hot Leg Mass Flow - 0.1254

Increased 20%_

Turbulence Model - - RNG -

lower order model

Tube Entrance - - - 56.325

Pressure Drop

increased 25%

Viscous Tube Loss - - - - (172.4;

increased 25% 1.14E+07)

Tube Heat Transfer - - - 5000

increased coefficient

Tube Heat Transfer - - - 100

decreased coefficient

40
Table 6. Summary of Sensitivity Study Results

Inlet hot leg inlet turbulence tube sheet viscous tube tube heat tube heat

base case temperature mass flow model entrance flow loss transfer transfer

parameter (-15 deg) (+ 20%) (e RNG) loss (+25%) (+25%) (h = 5000) (I = 100)

heat loss at tubes (kW) 3.69 3.21 4.33 3.85 3.58 3.53 3.85 (% difference) (-13%) (+17.3%) (+4.3%) 3.69 (-3%) (4.3%) (4.3%)

# hot tubes (difference) 82 82 82 82 82 82 88 (+ 6) 81 (- 1)

Th - hot leg (CC) 155 144.7 160.1 153 155.2 156.4 157 153 (difference (0C)) (-10.3) (+5.1) (-2) (+0.2) (+1.4) (+2) (-2)

T, - hot leg (

0C) 79.8 81.8 76.8 80.6 82.9 84 76.6 (difference (

0

C))80.1 (-0.3) (+1.7) (-3.3) (+0.5) (+2.8) (+3.9) (-3.5)

m - hot leg (kg/s) 0.0589 0.0653 0.0601 0.0585 0.0577 0.0573 0.0598 (% difference) 0.0586 (+0.5%) (11.4%) (+2.6%) (-0.2%) (-1.5%) (-2.2%) (+2.0%)

Tht - tubes (CC) 97.1 103.2 97.3 100.6 102.7 100.1 96.8 (difference (

0

C))100 (-2.9) (+3.2) (-2.7) (+0.6) (+2.7) (+0.1) (-3.2)

T, - tubes (

0C) 64.7 64.7 64.7 64.7 64.7 64.7 64.7 64.7

ml - tubes (kg/s) 0.1135 0.1299 0.1173 0.1191 0.1077 0.1028 0.1433 (% difference) 0.126 (-5.9%) (+7.7%) (-2.7%) (-2.2%) (-10.7%) (-14.8%) (+18.8%)

mt/mr - recirculation 1.93 1.99 1.95 *2.04 1.87 1.79 2.4 ratio (% difference) 2 (-6.3%) (-3.4%) (-5.3%) (-1.0%) (-9.2%) (-13.1%) (+16.5o%)

f - mixing fraction 2 0.82 0.79 0.91 0.80 0.93 0.77 (% difference) 0.81 (+1.2%) (-2.5%) (+12.3%) (-1.2%) 0.81 (+14.8%) (4.9%)
APPENDIX A

STEAM GENERATOR TUBE MODEL

POROUS MEDIA APPROACH

A.1 BACKGROUND

The computational fluid dynamics (CFD) analysis documented in this report uses a

porous media approach to model each steam generator tube. This approach is used to

reduce the amount of computer resources required to model the tubes. The overriding

goal of the CFD model is to determine inlet plenum mixing phenomena. The tube

bundle is a boundary condition for the inlet plenum. The tube bundle model must

provide an appropriate tube bundle mass flow and pressure boundary condition such

that the inlet plenum flows are well represented. Tube bundle flows result from a

balance between the buoyancy driving forces and the inertial and viscous pressure loss

terms. The modeling approach used here seeks to provide a model to reproduce each

of these characteristics with a minimal number of nodes.

Modeling the tubes directly is estimated to require 8 million cells. This makes a detailed

study impractical. To simplify the mesh, each tube is modeled as a rectangular channel

and is defined as a porous medium. The porous media formulation in the FLUENT CFD

code provides a means of modeling the pressure drop at the tube sheet inlet and the

shear flow viscous losses along the tube with simple algebraic relations. In addition,

porous material properties can be established to provide the desired heat transfer

characteristics. Resolution of the tube boundary layers and tube entrance effects is

unnecessary. The rectangular cross section is used to further reduce the mesh

requirements since many hexagonal elements are needed to accurately define a circular

cross section.

Three different models, available within the FLUENT modeling formulation, are relied on

to establish the tube bundle model. One model, Equation A-1, applies a volume-based

source term to the momentum equation to simulate the pressure loss through a porous

region. This model is used to represent the viscous flow losses along the tubes.

dP = D .,uV + C 2 pV IVJ * A-1

dx 2

The first term in Equation A-1 represents viscosity-dominated losses and the second

term provides a higher order term. In three dimensions, the coefficients C and D are

matrices to allow for nonisotropic behavior.

The second model, Equation A-2, utilizes a surface-based source term to create a step

change in pressure. This equation is used to model the form losses that occur as flow

enters and exits the tubes at the tube sheet.

Ap = (L V + C2 2 pV2) m A-2

A-1
A final equation from FLUENT's porous model formulation is used to establish the

effective thermal conductivity, kff (Equation A-3).

keff = 4 -kf + (I - (D)ks A-3

This equation is used to enhance the heat transfer within the tubes to make up for the

increased tube cross section.

A.2 GEOMETRY

The tube bundle of the Westinghouse 1/7th scale facility2 consists of 216 U-shaped tubes

with a 0.007747 m (0.305 in.) inner diameter and a 0.009525 m (0.375 in.) outer

diameter. The tubes are anchored into a 0.1143 m (4.5 in.) thick tube sheet that caps off

the inlet and outlet plenums. Furthermore, the tubes are arranged into a 0.02064 m

(0.8125 in.) triangular pitch array. The average tube length is 2.499 m (98.403 in.) and

the overall bundle height is 1.124 m (56.06 in.) from the face of the tube sheet.

In the FLUENT model, rectangular cross section tubes and a porous media approach

are used to represent the individual tubes of the Westinghouse facility. Each tube

modeled in FLUENT represents the flow path and heat transfer characteristics for a

single tube in the 1t7th scale facility. Figure A-1 shows a section of tubes from the

Westinghouse 1/7t facility that are meshed directly and a corresponding section of the

tubes meshed for use with a porous media approach. The symmetric tube section

shown in Fig. A-1 a includes one complete tube in the center and four one-quarter-tube

sections at the comers. The porous media model of this section in Fig. A-1 b represents

the same region. In the final CFD model, the porous tubes were smaller and only

represented a single tube.

y

(a) (b)

Figure A-1. (a) Meshed Region of Westinghouse 1[7' Scale Round Tube Model

(b) Mesh used for Equivalent Porous Media Model

A-2
A.3 LOSS COEFFICIENT DETERMINATION

The loss coefficients needed in Equations A-1 and A-2 are determined from the detailed

model in Fig. A-1 a. Predictions for the viscous sheer loss along the tube, dpldk, and the

tube entrance and exit loss, Ap,:are determined from this model. 'Using ctp1dx and Ap

over a range of velocity and temperature values, the coefficients needed to define the

porous model (C, D, and C2) are found. The pressure drop at the tube sheet is directly

proportional to V2. For this reason, the parameter a is set to 10o2 to effectively reduce

the first term in Equation A-2 to 0. To check the results, dp dx and Ap are predicted

using a porous model (Fig. A-1 b) with the porous media coefficients coming from the

curve fits.

A pressure drop occurs as fluid enters the tubes and a slight recovery occurs as the fluid

exits. Modeling restrictions in FLUENT make it difficult to simulate this phenomenon.

The pressure change through the tube sheet is always negative in the porous model. To

model the pressure drops, a net pressure drop is'determined that includes the entrance

and exit effects. The pressure drop at the tube entrance and exit is then defined as half

the net pressure drop for a combined loss consistent with the expected behavior.

A.3.1 Viscous Loss Coefficients

The data used to define and validate the viscous loss coefficients are given in Table A-1.

Table A-1. Data for Determination of Viscous Loss Coefficients and Results

Fig. A-1 a Fig. A-1 b

Jv6pV 2 VinTin fzpV V

(mis) (K) (kgfm-s) (Pa-m) (dp'(dp

-...dx)ROUND dx ) POROUS

(Pa/m) (Pa/m)

0.03375 375.0 0.0591 6.716E-7 -13.8 -14.9

0.0675 375.0 0.2365 1.343E-6 -43.2 -45.5

0.1350 375.0 0.9459 2.687E-6 -158.0 -157.0

0.03375 315.0 0.0814 5.984E-7 -16.9 -17.0

0.0675 315.0 0.3257 1.1 97E-6 -53.5 -56.0

0.1350 315.0 1.303 2.394E-6 -200.0 _

For each boundary condition combination (Vi,, Ti,), the pressure gradient is predicted in

a round tube with a well-defined mesh (Figure A-la). A multidimensional curve fit of

(dp/dX)RoUND versus lpV 2 and I.V is used to fit Equation A-1. Coefficients C and D are'

found to be 137.9 and 9.0920E+6, respectively.: Using these values in a porous model,

Figure A-1b, the pressure gradients are predicted again and listed in the last column of

Table A-1. The results demonstrate that the porous tube model with relatively few cells

can accurately produce the viscous pressure drop within the tubes.

A.3.2 Form Loss Coefficient

FLUENT uses the porous jump coefficient, C2, of Equation A-2 to determine the inertial

losses of the porous media model. The input parameters and total pressure loss of the

tubes are listed in Table A-2 below.

A-3
Table A-2. Values Used To Determine Inertial Loss Coefficient

Vin Tin n 1⁄2pV2 APROUND APPOROUS

(mis) (K) (kg/m-s2) (Pa) (Pa)

0.03375 375.0 0.0591 -5.3 -4.95

0.0675 375.0 0.2365 -19.4 -21.5

0.1350 375.0 0.9459 -79.0 -86.0

0.03375 315.0 0.0814 -7.0 -7.20

0.0675 315.0 0.3257 -27.5 -29.5

0.1350 315.0 1.303 -108.0 1

In Table A-2, the total pressure drop through the tube is listed for both the round and

porous media tubes, APREND and AppoRouS, respectively. The data labeled ApRouND

come from the model shown in Fig. A-1 a. The model coefficient, C2, determined from

these data is 41.6. This porous coefficient is used to define the inertial loss in the

porous media tube model, Fig. A-1 b. The results are given as the last column in Table

A-2. The porous model is in good agreement with the data.

A.4 THERMAL PROPERTIES

Tube heat transfer characteristics are also considered for the porous media approach. A

porous tube with a relatively large cross section is used to represent each tube. The

larger cross-sectional area reduces the heat transfer effectiveness. Early attempts to

model the tubes with no heat transfer augmentation demonstrated that the heat transfer

from the tubes was too low even with an infinite heat transfer coefficient on the

secondary side. To boost the heat removal rate, the effective conductivity in the tubes is

increased (see Equation A-3).

The fluid phase thermal conductivity, k,, is defined by the temperature dependant fluid

properties of sulfur hexafluoride. The porosity of the medium, A, and the solid medium

thermal conductivity, ks, are inputs to the porous model that are used here to augment

the effective conductivity of the tubes. Data from the Westinghouse 1/7' scale facility

indicate that tube temperatures essentially reach the secondary side temperature as the

flow reaches the top of the tube bundle. Further details are not available. The porosity

and solid conductivity are adjusted to establish this experimentally determined condition.

The thermal conductivity and porosity of the solid medium in this report are 1.5 W/m2K

and 0.75, respectively. One other factor controlling the tube thermal behavior is the tube

external heat transfer coefficient. This is not part of the porous model but does play a

role. The heat transfer coefficient, h, is set to 250 W/m2-K for the external surfaces of

each of the tubes above the tube sheet.

A-4
NRC FORM 335 US. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

(249 (Asned by NRC. Add Vol, Supp., Rev,

320NR m1u2 BIBLIOGRAPHIC DATA SHEET * dd NrimIany)

(See hksuctaos on U* rveve)

2. TITLE AND SUBTITLE NUREG-1781

CFD Analysis of 1/7th Scale Steam Generator Inlet Plenum Mixing During a PWR Severe

Accident 3. DATE REPORT PUBLISHED

MONTH YEAR

October 2003

4. FIN OR GRANT NUMBER

S. AUTHOR(S) 6. TYPE OF REPORT

Christopher F. Boyd

Kelly Hardesty Technical

7. PERIOD COVERED (scua Dabs)

8. PERFORMING ORGANIZATION -NAME AND ADDRESS (NNRC. pivde~ Dsn. OfficoreRon. US MdearR etwyCnansb lad makig addrsss Incntaor

p-namend maAgadd.s&)

Divison of Systems Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

US Nuclear Regulatory Commission

Washington, DC 20555-0001

9. SPONSORING ORGANIZATION -NAME AND ADDRESS WHO~r " wnea bove-Jl~raorP~~e NRCI)Msi Offro rRegi U.S NudlerftulamoyCombb

and maft ad*sbJ

Same as above

10. SUPPLEMENTARY NOTES

11. ABSTRACT 200 *ds orles)

Computational fluid dynamics (CFD) is used to predict steam generator Inlet plenum mixing during a severe accident scenario

In a pressurized water reactor. Comparisons are made to 1/7th scale data. Qualitatively, the code predicts the experimental

flow patterns and mixing phenomena. Quantitatively, comparisons are made with key temperatures, mass flows, and mixing

parameters. The best estimate prediction Is generally within 5% of the reported values. Key temperature predictions are

within a few degrees K of the test data. Boundary conditions applied to the model Include the hot leg Inlet mass flow and

temperature as well as the tube secondary side temperature and heat transfer. The mass averaged temperature of the flow

entering the tubes Is predicted to within 1 degree of the experimental data. The mass flow through the tube bundle is predicted

to within 0.5% of the data. The number of hot tubes Is overpredicted by 7 tubes out of the 216 total. The mixing fraction and

the recirculation ratio, both important mixing parameters, are predicted to within 5% of the data. These predictions provide

confidence In the code and modeling approach. The secondary side heat transfer coefficient is determined to be the dominant

governing parameter.

1Z KEY WORDS/DESCRIPTORS ({ift oww orphrtses W*tw msamtsextesA xto mptA . 13. AVAJLABIUTY STATEMENT

severe accident unlimited

steam generator 14. SECURInY CLASSIFICATION

CFD - hs Page)

tubes unclassified

mixing

pressurized water reactor unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORMl 335 "C-8) TWs form ww electmnically procixed by Elite Federal FwM Im
L Printed

on recycled

paper

Federal Recycling Program
NUREG-1 781 CFD ANALYSIS OF 1/7TH SCALE STEAM GENERATOR INLET PLENUM MIXING

DURING A PWR SEVERE ACCIDENT

OCTOBER 2003

UNITED STATES

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

OFFICIAL BUSINESS