E-Journal of Advanced Maintenance Vol. 6-4 (2015) 118-130
Japan Society of Maintenology

A Review of Evaluation Methods Developed for Numerical Simulation of
the Temperature Fluctuation Contributing to Thermal Fatigue of a
T-junction Pipe
Akira NAKAMURA1,*, Yoichi UTANOHARA1, Koji MIYOSHI1 and Naoto KASAHARA2
1
2

Institute of Nuclear Safety System, Inc., 64 Sata, Mihama-cho, Mikata-gun, Fukui 919-1205, JapanThe University of Tokyo, School of Engineering, 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan

ABSTRACTThis paper reviews the current status of numerical simulation evaluation methods for evaluation of thermal
fatigue in a T-junction pipe and identifies future research items to enhance the methods. The influencing factorsof numerical simulation methods on the evaluation of temperature fluctuation near a wall are discussed. Thenthe mechanism of thermal fatigue and the numerical simulation evaluation methods are described, and theinfluencing factors such as turbulence models, differencing schemes, computational meshes and inlet conditions
are discussed. Some recent models LES, SAS, and combined models are examined to assess fluid temperaturefluctuation. Differencing schemes and mesh fineness are important to keep the accuracy of calculations.
Regarding boundary conditions, the inlet flow conditions, velocity profile and velocity perturbation, influence
the temperature fluctuation.
KEYWORDS

ARTICLE INFORMATION

thermal fatigue, thermal stress, temperature fluctuation, numericalsimulation, T-junction pipe, thermal striping

Article history:
Received 8 May 2014
Accepted 17 July 2014

1.

Introduction

Thermal fatigue cracking may initiate at a T-junction pipe where high and low temperature fluids
flow in and mix. Temperature fluctuation caused by fluid mixing propagates in the pipe wall, and thetemperature distribution generates thermal stress. The pipe cracking may be caused by this stress if it
is bigger than the fatigue limit. These successive phenomena are called thermal fatigue. Damages ofpipes due to thermal fatigue have been reported in [1][2]. To prevent thermal fatigue, better
understanding of mixing and the temperature fluctuation mechanism and sophisticated evaluation
methods of temperature and stress distributions in the pipe wall are needed. There are many researchchallenges indeed because thermal fatigue, as composite phenomena, lies between thermal hydraulic,mechanical and material problems. Thermal fatigue is one of the major degradation mechanisms thatmust be considered in nuclear power plant aging management and researchers at the Institute of
Nuclear Safety System, Inc. (INSS) have conducted many research studies concerned with evaluationof thermal fatigue. INSS has been contracted by the Japan Nuclear Regulation Authority to be a partof the Japan Aging Management Program on System Safety (JAMPSS). Through this program,thermal fatigue research studies have been driven by the partnership of various research organizations
including the Japan Atomic Energy Agency (JAEA), universities and plant manufacturers, and byinternational information exchanges especially between experts in Japan and France.
At mixing areas of the nuclear power plant piping systems, there are possibilities for occurrenceof high-cycle thermal fatigue by temperature fluctuation. If a piping system is exposed to unavoidable
temperature difference to maintain plant conditions, this risk of fatigue cracking by temperaturefluctuation is not negligible. Evaluation methods of thermal fatigue are important when plant aredesigned to prevent fatigue cracking. Many research and development projects in this field have beenplanned and are being conducted worldwide and their results have been reported at international
conferences and in academic journals of nuclear engineering and thermal hydraulics.
*

Corresponding Author, E-mail: a-naka@inss.co.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

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A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction pipe

In France, the Électricité de France (EDF) developed an original evaluation method [3] forthermal fatigue to investigate the root cause of leakage in the residual heat removal system of theCivaux nuclear power plant Unit No.1 that occurred in 1998. Pasutto et al. [4] and Chapuliot et al. [5]examined the effect of upstream piping on thermal fatigue that had occurred in Civaux. These groups
used the computational fluid dynamics (CFD) code Code_Saturne developed by EDF and the
CAST3M code developed by Commissariat à l’Énergie Atomique (CEA), respectively, and they tried
numerical simulation with the Smagorinsky model in large eddy simulation (LES). To obtain thevalidation data of thermal stress and to observe the temperature fluctuation mechanism in a T-junction
pipe, CEA, EDF and AREVA conducted temperature measurement experiments in a pipe wall [6] andtemperature distribution visualization experiments [7] using FATHER and FATHERINO facilities.
The heat transfer coefficient from water to the pipe wall was measured in [7][8] by a coefh sensor
installed in the FATHER T-junction. Kuhn et al. [9] calculated the temperature distribution using
Fluent code to compare temperature measured by infrared rays through a thin brass pipe in
FATHERINO. Howard and Pasutto [10] investigated the effect of modeling on temperaturefluctuation using Code_Saturne and some approaches such as LES Smagorinsky, LES Dynamic and
WALE. But the best approach to evaluate temperature fluctuation is still unknown.
OECD/NEA conducted some international benchmark research studies [11][12] to improve
developed temperature evaluation methods using CFD. Vattenfall Research and Development in
Sweden measured the distribution of flow velocity and temperature in a T-junction. Other research
institutes used CFD calculations at experiment conditions to compare results and to show
reproducibility of time-averaged velocity and root-mean-square of velocity [13][14][15]. The
difference in CFD methods against temperature fluctuation was not well clarified [12] for the reason
that temperature fluctuation data were limited.
JAEA conducted a series of T-junction experiments called the “water experiment on fluid mixing
in T-pipe with long cycle fluctuation” (WATLON)[16], and categorized flow patterns based on the
momentum ratio of inlet velocities between main and branch pipes. The assessments of temperaturefluctuation through the measurement of water temperature [16] and wall temperature [17] were alsodone. Tanaka et al.[18] developed an original code MUGTHES and tried to calculate the wall jet
condition in WATLON. Tanaka and Oshima [19] tried to calculate the impinging jet condition in
WATLON using LES. Coste et al. [20] simulated the WATLON experiment by the TRIO-U code of
CEA and by the AQUA code of JAEA. From the simulations they observed the effect of upstream
conditions and mesh fineness on the calculated time-averaged or fluctuation of flow velocity andtemperature. Nakamura et al. [21] compared calculated temperature fluctuation by detached eddy
simulation (DES) in the commercial CFX code to temperature fluctuation in WATLON.
To assess the thermal fatigue of a T-junction pipe, the “Guideline for Evaluation of High-Cycle
Thermal Fatigue of a Pipe” [22] established by the Japan Society of Mechanical Engineers (JSME) is
used in Japan. This guideline aims to assess thermal striping at mixing tees and thermal stratification
at closed-end branch pipes. JAMPSS supported a research project on thermal fatigue to enhance thisguideline. The objectives of this project [23] are (1) clarification of thermal loads by fluid temperaturechange and failure mechanism; (2) proposal of rational evaluation methods for the JSME guideline;(3) development of numerical simulation methods of thermal fatigue phenomena; and (4) study offailure probability evaluation methods for plant system safety. The present authors of this review
conducted benchmark works using CFD codes in the JAMPSS-supported research project, andobtained some results of simulation methods to evaluate temperature fluctuation.
In order to assess thermal fatigue, local temperature fluctuation in the wall must be known.
Numerical simulations for such an assessment need to use time-variable simulations instead of steadystate simulations which are usually used in ordinary design or performance assessment. The modelingof turbulence and higher-order differencing schemes of an advection term are needed in unsteadysimulation to evaluate accurate time variation. And an accurate temperature distribution near the wallis also needed to treat heat transfer from water to the wall. Some practicable results are being obtained
these days to balance accuracy with the efforts of making these large calculations.
The current status of simulation methods and future research items to enhance the evaluation ofthermal fatigue in a T-junction pipe are discussed in this review.

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A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction pipe

2. Evaluation method development for temperature fluctuation in a T-junction
2.1. Temperature fluctuation mechanism and numerical simulation methods
The thermal load and cracking failure mechanism at a mixing zone of hot and cold fluids can be
decomposed into elemental processes as indicated in Fig.1 [23]. Dominant issues during the loading
process are temperature fluctuation and its attenuation. When hot and cold fluids mix, (A) vortices
generate temperature fluctuation in the main flow. (B) Fluctuation propagates to the boundary layer offlow. (C) Next, the fluctuation in the layer is transferred to the structure surface. (D) The fluctuationon the surface then propagates through the pipe wall by heat conduction and generates thermal stressby the constraint of pipe structure. In (E) the repetition of thermal stress initiates high cycle fatigue
cracking.
Some influencing factors on cracking in processes (A) to (D) are shown on the right side of Fig.1.
They are: (1) convection and turbulence mixing of flow in the main flow and boundary layer; (2)molecular diffusion and unsteady heat transfer in the viscous sublayer; and (3) attenuation oftemperature gradient in the pipe material by the heat conduction. These three factors influence thethermal load. In addition, factor (4) multi-axial load and random stress amplitudes affect crack
initiation and propagation.
Among the factors described above, (1) to (3) are typical of thermal fatigue caused by fluid
temperature fluctuation. Thermal stress range is inhomogeneous along the axial and circumferential
directions in a pipe. The stress amplitude range is inhomogeneous along the pipe thickness direction.
These are the characteristics of thermal fatigue due to the fluid mixing. It is, therefore, important toassess the crack initiation location and to evaluate crack propagation rate or suppression in the depth
direction.
Process

(B)

(C)

(D)

Fluid
Temperature
Tf

Hot Fluid

Time

Hot Fluid TH

Cold Fluid TC

SurfaceTemperature
Ts
Thermal Stress σ(A)Cold Fluid(A) Temp.fluctuation in
main Flow(B) Temp.fluctuation inboundary layer

Time

ThermalFatigueTime(C) Temp.fluctuation on
structural surface(D) Stress fluctuation inside
structure(E) Fatigue crack initiationand propagation

Influence factors(1)Turbulent
diffusion in fluid(2) Heat transfer fromfluid to structure(3) Heat conduction
and constraint in
structure(4) Multi-axial
random loads andmaterial
characteristics

Fig.1 Thermal load and cracking mechanism at a mixing zone of hot and cold fluids [23]The JSME guideline mentioned in Sec. 1 was established for pipe designing. It prescribes theevaluation flowchart on the left side of Fig.2, and it uses the experiment database of temperaturefluctuation measured in the main flow. The main data included in this guideline are the measured
non-dimensional temperature fluctation near the T-junctions in the conditions covering light water
nuclear power plants piping. The authors in this paper think that this database is not efficient to assess
the most affected area of thermal load. Additional evaluation methods of thermal stress distribution
are needed when the fatigue cracks are examined by ultrasonic testing. The authors have made efforts

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A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction pipe

to develop new detailed evaluation methods using numerical simulations shown in the flowchart on
the right side of Fig.2.
Evaluation flowchart by
JSME guideline

Evaluation flowchart using
numerical simulations

Temperature time series(Database of experiments)

Water temperature
calculated by CFD code

Temperature amplitudes andoccurrence frequencies

Thermal stresscalculated by FEM code

Thermal stress
Thermal stress amplitudes
and occurrence frequencies

Detailed
evaluation
methodFatigue damage factor

Initiation of fatigue cracks

Crack propagation analysis

Fig.2 The evaluation flowchart of thermal fatigue prescribed by JSME guideline and the evaluation
flowchart using numerical simulations

Efforts to reproduce temperature fluctuation in a mixing area by CFD codes were conducted
before the JSME guideline was established and some cases appeared in it[22]. Recent years have beenmarked by the speed-up and memory of computers, and the effects of mesh fineness or the turbulencemodel were investigated as described the following sections. It is necessary to understand what modelor approach for treating turbulence is appropriate to reproduce temperature fluctuation because eachcan affect the flow patterns related to the fluctuation mechanisms. The influence of turbulence models
will be discussed in the next section. It is also important to check total evaluation accuracy which
depends on the wall temperature distribution in order to evaluate thermal stress caused by thetemperature fluctuation in the pipe. The unsteady heat transfer was higher than the steady one fromsome experimental results described in the guideline, but the accuracy of modeling of turbulence near
the wall or boundary conditions was not investigated well. This point is the future work and is notdescribed in this paper. Other approaches such as LES with very fine meshes to capture turbulent
eddies near the wall or direct numerical simulation (DNS) may show good results but their calculation
time and power are unrealistic [23].
Before showing the calculated results, the experiment that was the target of simulations describedin this paper is shortly mentioned here. A benchmark work [24] was conducted in the
JAMPSS-supported research project mentioned in Sec. 1 in order to select a better evaluation methodfrom many combinations of simulation methods and calculation conditions. Some of these results aredescribed in the next section in relation to factors influencing the numerical simulation. The target of
this benchmark was WATLON test results with the wall jet condition [16]. The test conditions are
summarized in Fig.3. The inlet temperatures of main and branch pipes were 48 and 33 °C,
respectively. Flow rates in each pipe were 1.46 and 1.0 m/s, respectively. Figure 3(a) shows theconfiguration of the acrylic resin pipe used as the test section. The temperature fluctuation and its
distribution in the main flow were measured by thermocouples at the mixing area. The modeled area
for the CFD calculation was determined as Fig.3(b).

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A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction pipe

18Dm

Dm=150mmA

10Db
y

A-A viewAθ

Db=50mmz(a) Test section of WATLON

325mm

775mm

48℃,
1.46m/s
100mm

Dm = 150mm
33℃,
1.0m/sDb = 50mm(b) Computational region of the test section
Fig.3 Test section and wall jet flow conditions of WATLON [16]2.2. Factors influencing numerical simulation
2.2.1. Turbulence models
The turbulence model is one of a important factor influencing the reproduction of thetemperature fluctuation caused by the vortices downstream from a T-junction. Reynolds-averaged
Navier-Stokes (RANS) models have a lot of application experience in steady state simulations, but
few in unsteady simulations including temperature time-variable fluctuation. Turbulence models havetheir applicable conditions in the computational meshes and the boundary conditions etc. The effect of
turbulence models on temperature fluctuation was necessary to be checked using same meshes andconditions.
To check the effect of turbulence models, computational meshes were prepared, therefore, as
shown in Fig.4 for the modeled area described in Sec.2.1. This mesh and the same boundary
conditions were used in different calculations with some turbulence models. Figure 5 [24] shows
typical calculated results obtained by Fluent 12 with LES Dynamic SGS. Two other RANS models,the SST and RSM models, could not reproduce any temperature fluctuation in the mixing area. Figure
6 shows the fluid temperature fluctuation intensity at 1mm from the wall in the circumferential
direction, 0.5Dm and 1.0Dm downstream from the junction point. The temperature fluctuation intensity
calculated by DES showed underestimation at 0.5Dm, but the LES Dynamic SGS did not both at
0.5Dm and 1.0Dm. Here Dm is the inner diameter of the main pipe, Tm and Tb are the inlet temperaturesof main and branch pipes, respectively, the vertical axis is the non-dimensional standard deviation of
the temperature at 1mm from the wall (Trms / (Tm - Tb) = Tstd*), θ is the circumferential direction shownin Fig.4(c), and z is the flow direction distance from the cross point of the main and branch pipe axes.

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A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction pipe

Adiabatic wall

Outletyxz(b) Side view and length of the pipe

Vm = 1.46 m/s

Vb = 1.0 m/s(c) Side view from inlet of the mainpipe(a) Total mesh and boundary conditions

θ(e) Detail of the inlet(d) Detail at the T-junction

Fig.4 Computational meshes for WATLON T-junction [24](a) Temperature at t = 13.0s(b) Temperature fluctuation intensity
Fig.5 Instantaneous temperature and temperature fluctuation intensity downstream from the T-junction
calculated by Fluent 12 with LES Dynamic SGS [24]123A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction piper ' = 1mm

0.3

WATLONFLUENT-12, LES, Dynamic SGS
FrontFlow/Red, LES, Cs=0.1
CFX-11, DES

0.2

Trms / (Tm -Tb )Trms / (Tm -Tb )

0.3

0.1

0

r ' = 1mm
WATLONFLUENT-12, LES, Dynamic SGS
FrontFlow/Red, LES, Cs=0.1
CFX-11, DES

0.2

0.1

0
-90

-60

-30

0

30

θ [deg]

60

90

-90

-60

-30

0

θ [deg]

30

60

90

(a) z = 0.5Dm(b) z = 1.0Dm
Fig.6 Fluid temperature fluctuation intensity in circumferential direction downstream
from the T-junction [24]. Open circles are the measured value in WATLON [16].

As described in the previous section, Pasutto et al.[4] and Chapuliot et al. [5] investigated themixing area of the residual heat removal system in Civaux Unit 1 using CFD with LES Smagorinsky.
Howard and Pasutto [10] investigated the effect of modeling on temperature fluctuation using
Code_Saturne and some approaches such as LES Smagorinsky, LES Dynamic and WALE.
OECD/NEA conducted some international benchmark research studies, but the difference of CFD
methods against temperature fluctuation was not clarified well [12] due to the limited temperaturefluctuation data. In these papers, no best approach was established to evaluate temperature fluctuation.
A modeling constant Cs in the Smagorinsky model should be assigned when this model is used in
LES. Nakamura et al. [25] compared some Cs values using the CFX code with LES Smagorinsky, but
did not found an appropriate number from Cs = 0.05 to 0.25 because the calculated temperaturefluctuations shown in Fig.7 were underestimated.
r ' = 1mm, z = 0.5Dm

0.3

Trms /(Tm - Tb )0.4

WATLON
CFX-11,LES,Cs=0.05
CFX-11,LES,Cs=0.10
CFX-11,LES,Cs=0.15
CFX-11,LES,Cs=0.20
CFX-11,LES,Cs=0.25

r ' = 1mm, z = 1.0Dm
WATLON
CFX-11,LES,Cs=0.05
CFX-11,LES,Cs=0.10
CFX-11,LES,Cs=0.15
CFX-11,LES,Cs=0.20
CFX-11,LES,Cs=0.25

0.3

Trms /(Tm - Tb )

0.4

0.2
0.1
0

0.2
0.1
0

-90

-60

-30

0

θ [deg]

30

60

90

-90

-60

-30

0

θ [deg]

30

60

90

(a) z = 0.5Dm(b) z = 1.0Dm
Fig.7 Fluid temperature fluctuation intensity in circumferential direction downstream
from the T-junction calculated by the CFX code using LES Smagorinsky [25].
Open circles are the measured value in WATLON [16].

Frank et al. [26] calculated a series of OECD/NEA benchmark simulations using the CFX codewith the SST model and BSL-RSM model (these are RANS), DES and scale-adaptive simulation(SAS). They reported good estimation of time-averaged and fluctuation intensity in flow velocity, but
the temperature fluctuation was not compared well. Toth and Aszodi [27] tried a series of OECD/NEA
benchmark simulations using the CFX code with the approaches LES-WALE, SAS-SST, and
DES-SST. They reported fluid temperature fluctuation intensity at 1mm from the wall by these three
approaches. The LES-WALE, with a differencing scheme of the advection term as a central (CD) andbounded central (BCD) for the momentum and energy equations, was reported to show bigger
temperature fluctuations than experiments because of numerical instability. SAS-SST used a special
treatment called zonal LES which changed turbulence modeling in some zones; upstream anddownstream zones of the main pipe used the SAS and the T-junction zone used the LES. Gritskevich

124

A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction pipe

et al.[28] also tried a series of OECD/NEA benchmark simulations using Fluent code with theapproaches SAS, Delayed DES, and Embedded LES. They reported SAS with BCD could not capture
the temperature fluctuation well, but the Embedded LES gave better results.
2.2.2. Differencing schemes for momentum and energy equations
As previously described about Tosh and Aszodi [27], the differencing schemes of the advection
term for the energy equation are known to influence the calculation accuracy. And some schemes
show unstable in flow field or temperature field. Qian and Kasahara [29] and Qian et al. [30] tried
some calculations in WATLON condition described in Sec.2.2.1 using FrontFlow/Red code with LES
Smagorinsky and LES Dynamic. They used hybrid (HB, a combination of 1st order upwind 1UD and2nd order central 2CD) differencing scheme of the advection term for the momentum equation, andtried some schemes for the energy equation. They reported the 2nd order total variation diminishing(TVD) scheme was better than the 1UD or HB of the advection term for the energy equation.
Nakamura et al.[25] examined the differencing scheme of the advection and diffusion terms for theenergy equation under the conditions of the LES Dynamic in the CFX code and the 2CD scheme of
the advection term for the momentum equation. Figure 8 shows calculated temperature fluctuation
intensities. Some cases of the diffusion schemes (SDS) gave numerical instability. The use of 2nd order
upwind (higher upwind, 2UD) of the advection term and 2CD of the diffusion term for the energy
equation were better able to suppress instability and to maintain the accuracy.
According to these latest studies, the use of the central (CD) scheme or bounded central (BCD)
scheme of the advection term for the momentum equation and the use of 2nd order upwind (2UD)
scheme or 2nd order total variation diminishing (TVD) scheme are efficient. Further investigation isrequired to ascertain the best combination of differencing schemes for the momentum and energy
equations in consideration of other numerical conditions including turbulence models and meshfineness.
WATLON
CFX-12,Dynamic,SDS=1
CFX-12,Dynamic,SDS=2
CFX-12,Dynamic,SDS=3
CFX-12,Dynamic,SDS=4
CFX-12,Dynamic,SDS=5
CFX-12,Dynamic,SDS=6
CFX-12,Dynamic,HigherUpwindr ' = 1mm, z = 0.5Dm

0.5

0.4

Trms / (Tm - Tb )Trms / (Tm - Tb )

0.4
0.3
0.2
0.1
0

WATLON
CFX-12,Dynamic,SDS=1
CFX-12,Dynamic,SDS=2
CFX-12,Dynamic,SDS=3
CFX-12,Dynamic,SDS=4
CFX-12,Dynamic,SDS=5
CFX-12,Dynamic,SDS=6
CFX-12,Dynamic,HigherUpwindr ' = 1mm, z = 1.0Dm

0.5

0.3
0.2
0.1
0

-90

-60

-30

0

θ [deg]

30

60

90

-90

-60

-30

0

θ [deg]

30

60

90

(a) z = 0.5Dm(b) z = 1.0Dm
Fig.8 Fluid temperature fluctuation intensity in circumferential direction downstream
from the T-junction calculated by CFX using Dynamic SGS and some numerical schemesof advection and diffusion term for the energy equation [25]. The parameter SDS means the combinationof scalar diffusion schemes of the diffusion term for the energy equation[25] modified to obtain thestability in CFX code. Open circles are the measured value in WATLON[16].

2.2.3. Computational meshes
To obtain thermal stress, it is necessary to capture an adequate temperature distribution in thepipe wall. Many recent CFD codes can solve for the fluid temperature (advection and diffusion) andthe solid temperature (heat conduction), coupled to each other. The right flowchart in Fig.2
presupposes this coupled simulation. It is well known that the mesh discretization changes accuracy of
the CFD. For the evaluation of thermal stress, meshes alter not only the fluid temperature fluctuation
intensity but also heat transfer and heat conduction of a pipe if CFD is applied to this evaluation flow.
In the first step, the mesh width should be checked in the flow simulation.
Utanohara et al.[31][32] investigated the mesh effect on temperature fluctuation based on ASME

125

A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction pipe

V&V guideline [33] using the Fluent 12 with LES Dynamic. Figure 9 shows the four meshes with themesh element numbers from 0.09 to 1.35 million. Figure 10(a) shows the calculated temperaturefluctuation intensity compared with WATLON [16], and the open circles in Fig.10(b) shows the samevalue at θ = 30 deg extracted from (a) against the mesh width h in the circumferential direction. The
closed square in Fig.10(b) is the Richardson extrapolated value estimated by the grid convergenceindex method in ASME V&V 20. If the width h was less than 4mm, which meant the mesh number
was more than 0.24 million, the calculated intensities are almost same as the extrapolated one thatmeans the virtual value using an ideally fine mesh. The maximum intensity when h was less than
4mm shown in Fig.10(a) evaluated as more than in the experiment which means on the safe side forthermal stress evaluation.
Nakamura et al. [34][35] calculated temperature fluctuation in the pipe wall using the LES withfine mesh near the wall surface. This method treated heat transfer without the wall function or othermodeling near the wall. They located the first mesh of the fluid near the wall surface under theviscous layer and calculated the energy equation coupled with fluid and solid. They reported thatvortex shedding frequency was dominant in their calculation although the observed frequencies werevortex shedding of some Hz and had a longer period in the experiment [17].

OutletAdiabatic wallyxz(a) 1.35 million cells(cross section 5280 cells)(b) 0.66 million cells(cross section 3328 cells)

Vm = 1.46 m/s

Vb = 1.0 m/s(e) Modeled area and boundary conditions
Vm = 1.46 ms/(c) 0.24 million cells(a) 0.09 million cells(cross section 1676 cells)(cross section 832 cells)
Fig.9 Computational mesh for grid dependency evaluation [31]126

A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction pipe
0.34

1.35 milz = 0.5 D m

0.24 mil

0.2

r ' = 1 mm
z = 0.5 D m
θ = + 30°

0.32

0.66 milT rms / (T m - T b)

0.3

Trms / (Tm -Tb )WATLONr ' = 1mm

0.09 mil

0.1

0.30

Extrapolated value

0.28
0.26
0.24

0

0.22
-90

-60

-30

0

30

60

90

0.0

θ [deg](a) Fluid temperature fluctuation intensity(z = 0.5 Dm, 1mm from the wall). Opencircles are the measured value in
WATLON[16].

1.0

2.0

3.0

4.0

grid size h [mm]

5.0

6.0

7.0

(b) Grid dependency of fluid temperature fluctuation
intensity. Open circles are the calculated value shownin the left figure where z = 0.5 Dm, θ=30°, 1mm fromthe wall. Closed square is the extrapolated value
based on ASME V&V 20 [33].

Fig.10 Fluid temperature fluctuation intensity downstream from the T-junction
calculated by Fluent 12 with LES Dynamic SGS and some grids [32]2.2.4. Inlet flow conditions
The shapes of piping in power plants are complex and there are elbows typically upstream from a
T-junction that the thermal fatigue may occur. Elbows make the turbulent uneven flow and influence
the temperature fluctuation. It is future works to introduce the piping complexity into the numericalsimulation of temperature fluctuation evaluation. Even if a experiment was done with the straight pipe
condition upstream from a T-junction, the velocity profile and turbulence at the inlet of main andbranch pipes in the numerical simulation influence the temperature fluctuation.
Utanohara et al. [32] investigated the effect of inlet conditions when they calculated somecombinations of inlet flow shown in Fig.11(a), including the velocity profile and velocity perturbationin the radial direction for main and branch pipe inlets. Figure 11(b) compares the temperaturefluctuation intensities in these combined conditions with WATLON. The case with the inlet conditions
that both inlets had the same velocity profile and perturbation had a larger intensity than any othercases with combinations of the flat profile or no perturbation.

0.24 mil
Perturbation only inthe main pipe
Prof Noperturb
profile without
perturbation
Noprof Noperturb
Flat profile without
perturbation
Prof Perturb
Profile with
perturbation

Perturbation
ProfileMain
1/n-thpower law○
1/n-thpower law×
Flat

Branch1/n-thpower law×
1/n-thpower law×
Flat

Perturbation

××

1/n-thpower law○

1/n-thpower law○

ProfilePerturbation
ProfileProfilePerturbation

WATLON
0.24 mil
ProfPerturb
ProfNoperturb
NoprofNoperturb

r ' = 1mm

0.3

Trms / (Tm -Tb )Case

z = 0.5 D m

0.2

0.1

0
-90

-60

-30

0
θ [deg]3060(b) Fluid temperature fluctuation intensity(z = 0.5 Dm, 1mm from the wall)Fig.11 Fluid temperature fluctuation intensity downstream from the T-junction
calculated by Fluent 12 with LES Dynamic SGS and inlet conditions[32](a) Simulation conditions of inlets

127

90

A. Nakamura, et al./ A review of evaluation methods
developed for numerical simulation of the temperature fluctuation
contributing to thermal fatigue of a T-junction pipe

3.

Conclusion

This paper reviewed the current status of evaluation simulation methods for thermal fatigue in a
T-junction pipe and identified future research items to enhance the evaluation methods. In Sec.2.2,
some factors influencing numerical simulation methods of temperature fluctuation near the pipe wall
were discussed. LES with Dynamic provided better temperature fluctuation intensities with someturbulence models. In addition, expanded models from SAS or DES that change turbulence modelingbetween divided zones in the CFD modeled area have been developed and were described here. Somepapers reported that differencing schemes were needed to keep stability and accuracy of thetemperature field; these included the 2nd order central or hybrid differencing schemes for the
momentum equation, and the 2nd order upwind or 2nd order TVD scheme for the energy equation. The
mesh fineness was investigated to find its effect on fluid temperature fluctuation, and a rough standard
to reproduce it on the safe side was found. But more research studies are needed to evaluate heattransfer from the fluid to the wall. Regarding upstream conditions, the calculated temperaturefluctuation could be larger when the velocity profile and velocity perturbation were set at both inlets
of the T-junction than where there was a flat profile or no perturbation.
These results will contribute to setting a standard method to evaluate thermal stress using
numerical simulations. For the future, it is necessary to investigate temperature fluctuation
mechanisms at a T-junction and validate the method against these mechanisms. New experimental
data are required for the validation data.

Acknowledgements
This work has been performed as a part of the Japan Aging Management Program on System
Safety (JAMPSS) sponsored by Nuclear Regulation Authority (NRA). The authors also express theirappreciation for many discussions with thermal fatigue research committee members, including
Hiroshi Ikeda, Shaoxiang Qian, Masaaki Tanaka and Hitoshi Nakamura who were members of thebenchmarking studies described in this paper.

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