Annals of Nuclear Energy 60 (2013) 432–438

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Annals of Nuclear Energy

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Numerical simulation of thermal stratification in an elbow branch pipeof a tee junction with and without leakage q

0306-4549/$ - see front matter � 2013 The Authors. Published by Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.anucene.2013.04.011

q This is an open-access article distributed under the terms of the CreativeCommons Attribution-NonCommercial-No Derivative Works License, which per-mits non-commercial use, distribution, and reproduction in any medium, providedthe original author and source are credited.⇑ Corresponding author. Tel.: +86 10 64417994.

E-mail address: likesurge@sina.com (T. Lu).

T. Lu a,⇑, H.T. Li a,b, X.G. Zhu a

a School of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, Chinab China Nuclear Power Engineering Co., Ltd., Beijing 100840, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 5 December 2012Received in revised form 12 April 2013Accepted 15 April 2013Available online 19 June 2013

Keywords:Numerical simulationThermal stratificationElbow branch pipeTeeLeakage

Thermal stratification can cause thermal fatigue of the piping system of a nuclear power plant. One of theregions most at risk of suffering from thermal fatigue is a small elbow pipe branching off from the mainpipe of the coolant loop for the drain or letdown system in the chemical and volume control system(CVCS). This work focuses on a fundamental description of the thermal stratification caused by turbulentpenetration and buoyancy effects in the elbow branch pipe using large-eddy simulations (LESs). The LESresults for the normalized temperature, mean temperature, and root-mean square (RMS) temperaturewere found to be in good agreement with the available experimental data which confirms that LES canpredict the thermal stratification in a closed elbow branch pipe where cold fluids are stagnant. Subse-quently, the flow and heat transfer were numerically predicted using LES when leakage occurred inthe elbow branch pipe. The numerical results show that the thermal stratification region is pushedtowards the horizontal part and may remain there for a long time for a leakage ratio of 1%. However, ther-mal stratification is quickly eliminated for a leakage ratio of 5%, although there is a higher power spec-trum density (PSD) of the temperature in the early stages of the leakage. It may be concluded that asmall leakage ratio can result in the elbow branch pipe being at high risk of thermal fatigue caused bythermal stratification.

� 2013 The Authors. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Thermal stratification or striping is of significant importance innuclear power plants because it can lead to transient temperaturefluctuations at the adjacent pipe walls which may result in thermalfatigue and failure of the pipe. In a previous review Iida (1992)noted that serious fatigue failures have occasionally been experi-enced in piping systems, pumps, and valves. The causes of fatiguefailures can be divided into two categories: mechanical-vibration-induced fatigue and thermal-fluctuation-induced fatigue. Bycomparison of the stresses due to thermal shock and thermal strat-ification, Miksch et al. (1985) concluded that the cracks observedwere in essence caused by thermal stratification. Tenchine (2010)suggested that piping thermal stratification or mixing is one of sev-eral thermal hydraulic challenges which progressively increasewith the power and the size of a sodium cooled nuclear reactor.Thermal fatigue incidents occurring in a tee piping system are

susceptible to turbulent temperature mixing effects. A Europeanstudy of the thermal fatigue evaluation of piping systems has beeninitiated, including assessment of the fatigue significance of turbu-lent thermal mixing effects in piping systems and identification ofthe significant fatigue parameters (Metzner and Wilke, 2005).

Thermal stratification or striping can be predicted using compu-tational fluid dynamics (CFD) simulations as well as measuredexperimentally. Turbulent isothermal and thermal mixing phe-nomena have been numerically and experimentally investigatedby Frank et al. (2010). The isothermal case involved turbulent mix-ing of two water streams at the same temperature in a tee junctionin the horizontal plane to exclude any buoyancy effects, while thethermal case had a temperature difference of 15 �C between thehot and cold water in a tee junction in the vertical plane in orderto induce thermal striping phenomena. Experimental temperatureand velocity measurements and numerical simulations were car-ried out by Kamide et al. (2009) in order to study the thermalhydraulic aspects of thermal striping in a mixing tee. Dependingon the momentum ratio of the main pipe to the branch pipe(MR), flow patterns in the tee were classified into three groups:wall jet (MR > 1.35), deflecting jet (0.35 < MR < 1.35), and impingingjet (MR < 0.35). Tests to investigate the interaction between themain coolant piping and the stagnant attached lines by turbulence

Fig. 1. Physical model and numerical sampling locations.

T. Lu et al. / Annals of Nuclear Energy 60 (2013) 432–438 433

penetration have been carried by Kim et al. (1993), and a loadingdefinition for thermal striping was proposed.

Large-eddy simulations (LESs) are a very popular way of pre-dicting flow details such as velocity, temperature, and vortex. Bothcollision and co-current thermal striping in a mixing tee have beennumerically simulated by Hu and Kazimi (2006) using LES solvedby the commercial CFD code FLUENT. Numerical results of normal-ized mean and fluctuation temperatures were compared withexperimental measurements. The mixing in tee junctions madeof different materials with different pipe wall thicknesses wereinvestigated by Kuhn et al. (2010) using different LES subgrid scale(SGS) models in order to identify the influence of the SGS on thesimulation results, and the results were also compared with avail-able experimental data. Their study showed the ability of LES toaccurately predict thermal fluctuations in turbulent mixing. Tem-perature fluctuations in a mixing tee were simulated by Lu et al.(2010) in FLUENT using the LES with the Smagorinsky–Lilly (SL)SGS model with consideration of buoyancy effects. Their numericalresults were in good agreement with the available experimentaldata, showing the validity of the LES model for predicting the mix-ing of hot and cold fluids in a mixing tee junction. The temperaturefluctuations and structural response of coolant piping at a mixingtee were investigated using LES by Lee et al. (2009). Their studyshowed that the temperature difference between the hot and coldfluids in a tee junction and the enhanced heat transfer coefficientdue to turbulent mixing are the dominant factors affecting thethermal fatigue failure of a tee junction.

In a nuclear power plant, several small pipes branch off fromthe main pipe of the coolant loop, with a temperature of 300 �Cand a velocity of 10 m/s in the drain or letdown system in thechemical and volume control system (CVCS). These pipes are oftenbent and connected to a closed valve (Ourmaya et al., 2006). Theturbulence of the main pipe flow usually initiates a perturbationflow in the elbow branch pipe and hot water penetrates into it.In addition, the fluid in the elbow is relatively stagnant and at alow temperature. Thermal stratification may arise if the perturba-tion momentum and buoyancy remain in dynamic balance in a re-gion where the hot fluid is above the cold fluid.

This work focuses on a fundamental description of the thermalstratification caused by turbulent penetration and buoyancy effectsusing large-eddy simulations (LES), for the two cases where leak-age of the elbow branch pipe does and does not occur. Firstly,based on the experimental model and flow parameters in the liter-ature (Ourmaya et al., 2006), the LES for the case without leakageof the closed elbow branch pipe was completed. Then the numer-ical results of the transient temperature were compared with theexperimental data to confirm that LES has the capability to predictthe temperature fluctuations. After validation of the numericalsimulations, LES for other cases with leakage of the elbow branchpipe were performed in order to predict extent of penetration ofhot water into the horizontal part of the elbow branch pipe.

2. Mathematical model and numerical simulations

As shown for the model in Fig. 1 (Ourmaya et al., 2006), at thebeginning hot water at temperature of 65 �C and velocity of 6 m/sflows in the top main rectangular channel, with cross-section of60 mm � 10 mm, which is connected to an elbow branch pipe ini-tially filled with stagnant cold water at temperature of 15 �C. Thebore of the elbow pipe is 43 mm, which is similar to that of the2 in branch pipe in a nuclear power plant. The details of geometryand flow parameters can be found in reference (Ourmaya et al.,2006). As a consequence of turbulence at the tee junction, mixingbetween hot and cold water occurs and may propagate downwardsin the vertical – and even in the horizontal – part of the elbow

branch pipe. Consequently, thermal stratification occurs with thefluctuating interface between hot and cold water, which resultsin the elbow branch pipe being at risk of thermal fatigue.

For incompressible flow, the filtered Navier–Stokes and energyequations can be written as (Ndombo and Howard, 2011)

@q@tþ @qui

@xi¼ 0 ð1Þ

@qui

@tþ @quiuj

@xj¼ � @p

@xi� q0bðT � T0Þg

þ @

@xjðlþ ltÞ

@ui

@xjþ @uj

@xi

� �� �ð2Þ

@qT@tþ @qTuj

@xj¼ @

@xj

kcp

@T@xj� qT 00u00j

!ð3Þ

Here w represents the implicit filtering operation on the flowvariable, to the grid and w00 is the subgrid part of the flow variable,and q, b, l, lt, k, and cp represent the density, thermal expansioncoefficient, molecular viscosity, turbulent viscosity, thermal con-ductivity, and specific heat capacity, respectively.The effect of theunresolved scale on the resolved scale in the above equations isrepresented by the subgrid scale (SGS) stress, which is modeledusing the eddy viscosity hypothesis. In this work, the Smagorin-sky–Lilly model is used for the turbulent viscosity, and is given by

lt ¼ qL2s jSj

2 ð4Þ

where Ls is the mixing length for the subgrid scales. Ls and jSj arecomputed using

Ls ¼minðkd;CsV1=3Þ ð5Þ

jSj ¼ffiffiffiffiffiffiffiffiffiffiffiffi2SijSji

qð6Þ

Sij ¼12

@ui

@xjþ @uj

@xi

� �ð7Þ

where k is the von Karman constant of 0.42, d is the distance to theclosest wall, Cs is the Smagorinsky constant, and V is the volume ofthe computational cell.

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Mean temperature of experiment Mean temperature of simulation RMS temperature of experiment RMS temperature of simulation

T*

5%10%

0.04

0.05

0.06

0.07

0.08

0.09

0.10

T*R

MS

434 T. Lu et al. / Annals of Nuclear Energy 60 (2013) 432–438

Fully-developed velocity profiles in both the main rectangularchannel and the elbow branch pipe calculated using the steadyReynolds stress model (RSM) were used as the inlet velocity condi-tions. The steady fields of the RSM were set as the initial conditionof the rectangular channel for the LES calculations. A stagnantvelocity field and temperature of 15 �C were initially set for the el-bow branch pipe at the beginning of the LES.

The LES simulations were performed with different meshes andfinally the case with about 1.8 million cells was selected as the gridindependent model. A constant time step of 5 ms was used for thesimulations. The total simulation time for the mixing process was

0 50 100 150 200 250 3000.75

0.80

0.85

0.90

0.95

Experiment (Oumaya et al., 2006) Simulation

T ∗

t / s

(a)

0 50 100 150 200 250 300

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

T ∗

t / s

Experiment (Oumaya et al., 2006) Simulation

(b)

0 50 100 150 200 250 3000.200.250.300.350.400.450.500.550.600.650.70

T ∗

t / s

Experiment (Oumaya et al., 2006) Simulation

(c) Fig. 2. Comparison between numerical and experimental data for the normalizedtemperature in the plane of y = 0 mm: (a) h = 43�; (b) h = 47; and (c) h = 51�.

42 43 44 45 46 47 48 49 50 51 520.2

0.3

θ/ 0

0.02

0.03

Fig. 3. Comparison between numerical and experimental results for the normalizedmean and RMS temperatures at different angles.

300 s. Taking a leakage ratio of either 1% or 5% of the main channelflow rate, LES was conducted for a leakage beginning at the 300th sand lasting 50 s. To correspond to the experimental measurements,the temperatures close to the wall (1 mm) at angles from 43� to 65�in the plane of y = 0 mm were recorded at time intervals of 5 ms.

3. Results and discussion

The normalized mean temperature and normalized tempera-ture fluctuation intensity are used to describe the time-averagedtemperature and time-averaged temperature fluctuation intensity.The normalized temperature is defined as

T� ¼ T � Tcold

Thot � Tcoldð8Þ

where T is the instantaneous temperature, Tcold is the temperatureof the cold fluid, and Thot is the temperature of the hot fluid. Thenormalized mean temperature is

T� ¼ 1N

XN

n¼1

T� ð9Þ

where N is the total number of sampling times.The normalized temperature fluctuation intensity is given by

the root-mean square (RMS) of the temperature

Fig. 4. Velocity vector contoured by temperature at the 300th s in the plane ofy = 0 mm.

T. Lu et al. / Annals of Nuclear Energy 60 (2013) 432–438 435

T�RMV ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

Xn¼1

NðT� � T�Þ2

rð10Þ

3.1. Validation of numerical results for the case without leakage

Fig. 2 shows a comparison between numerical and experimen-tal results for the normalized temperature (Ourmaya et al., 2006)

Fig. 5. Velocity vector contoured by temperature at different leak

at different angles in the plane of y = 0 mm when the elbow branchpipe is stagnant Although the numerical results are not alwaysconsistent in time with the experimental data, most of time thetemperature fluctuation of the numerical results is very close tothat of the experimental data.

The normalized mean temperatures and the normalized RMStemperatures at different angles are shown in Fig. 3. The normal-ized mean temperature decreases with increasing angle, which

age times in the plane of y = 0 mm (a–c) l = 1%; (a0–c0) l = 5%.

436 T. Lu et al. / Annals of Nuclear Energy 60 (2013) 432–438

means the average temperature in the top of the bent part is higherthan that in the bottom. However, the normalized RMS tempera-ture at an angle of 47� is the largest among the three points, whichmeans that the point at an angle of 47� has the largest temperaturefluctuation intensity. For the normalized mean temperature, theabsolute error of the numerical result is in the range of �5% ofthe experimental data. For the normalized RMS temperature, theabsolute error of the numerical result is in the range of �10% ofthe experimental data except for the point at an angle of 51� wherethe absolute error is �33%. To large extent, the numerical resultsfor both the normalized mean and RMS temperatures are in goodagreement with the experimental data, which validates LES as ameans of predicting the temperature fluctuation in an elbowbranch pipe due to turbulent penetration and buoyancy effects.Since the LES were successfully validated, the flow and heat trans-fer were numerically simulated for the case of leakage from theelbow branch pipe.

3.2. With leakage from the branch pipe

The horizontal part of the branch elbow pipe connects a valve ina nuclear power plant, leakage might occur in the valve. Whenleakage occurred, the leakage ratio of the elbow branch pipe tothe main pipe is defined by

l ¼ Q branch outlet

Q main inletð11Þ

where Qbranch outlet is the outlet flow rate of the elbow branch pipeand Qmain inlet is the inlet flow rate of the main pipe.

3.2.1. Velocity vectors and temperature contoursFig. 4 shows the velocity vector contoured by the temperature

at the 300th s for the case without leakage. At the 300th s, hotwater penetrates into the vertical part of the elbow branch pipedue to the turbulence and can even reach the bent part. In the bentpart thermal stratification occurs as a consequence of the dynamicinterface of the hot fluid over the cold fluid because the turbulencemomentum decreases with the penetration depth and it remains inbalance with the buoyancy. If the thermal stratification phenome-non continues, the bent part is at risk of thermal fatigue. Althoughthere is zero flow rate at the end of the elbow branch pipe, there issome circulation in the horizontal part of the elbow branch pipedue to the turbulence penetrating from the main pipe. If leakagefrom the elbow branch pipe occurs, the thermal stratification inter-face will shift down the horizontal part. In our study of elbowbranch pipe leakage ratios of l = 1% or 5% beginning at the

0 5 10 15 20 25 30 35 40 45 500.0

0.2

0.4

0.6

0.8

1.0

Angel at elbow θ=0°θ=45°θ=50°θ=55°θ=60°θ=65°

T*

t /s(a)

Fig. 6. Changes in normalized temperature with leakage time in the bent part o

300th s, we take the velocity and temperature as shown in Fig. 4as the initial conditions.

Fig. 5 shows the velocity vector contoured by temperature withdifferent leakage ratios of the elbow branch pipe at different leak-age times. In the initial stage of the leakage, as shown in Fig. 5a anda0, the thermal stratification interface goes ahead from the bentpart to the horizontal part. The advancing speed for the case ofl = 5% is faster than that for l = 1%. With the progress of the leakage,as shown in Fig. 5b and b0, there is a slight difference in the distri-butions of the thermal stratification interface for the two differentleakage ratios. The thermal stratification interface of the case witha leakage ratio of l = 1% looks more horizontal than that for l = 5%.The mixing of cold and hot fluids of the case of a leakage ratio ofl = 5% is stronger than that for l = 1% because in the former casethe fluid produces a stronger secondary flow when passing thebent part. The larger leakage ratio has a bigger turbulence momen-tum which overcomes the buoyancy. At the 50th s, as shown inFig. 5c and c0, the temperature distributions are obviously different.For a leakage ratio of l = 1%, the cold fluid is distributed in the bot-tom of the horizontal part while the hot fluid occupies the top dueto the buoyancy as shown in Fig. 5c. However, for a leakage ratio ofl = 5%, the situation is the opposite of that for l = 1%. Although thecold fluids occupy the top of the horizontal part, the temperaturedifference between the top and the bottom is very small due tothe stronger turbulence for a leakage ratio of l = 5%, as shown inFig. 5c0.

3.2.2. Normalized temperature changesFig. 6 shows the normalized temperature changes with different

leakage ratios in the bent part of the elbow. For the case with smal-ler leakage ratio of l = 1% as shown in Fig. 6a, the normalized tem-peratures at angles of 0–55� increase to almost unity, which is thenormalized temperature of the hot fluid in the main pipe in thefirst 10 s of leakage, while the normalized temperature at an angleof 60� increases unevenly to 1 at around the 47th s. Moreover, thenormalized temperature at an angle of 65� almost retains the tem-perature of the cold fluid in the first 45 s and then increases slowly.For a larger leakage ratio of l = 5%, as shown in Fig. 6a0, the normal-ized temperatures in the bent part quickly and smoothly increaseto 1 in the first 5 s and the bent part becomes full of the hot fluidfrom the main pipe. A comparison of the results for the two differ-ent leakage ratios suggests that lower leakage ratios more readilygive rise to thermal stratification.

Fig. 7 shows the normalized temperature changes at differentlocations of the horizontal part for different leakage ratios. Thesituation for the horizontal part is similar to that for the bent part.

0 1 2 48 500.0

0.2

0.4

0.6

0.8

1.0

T∗

t /s

Angel at elbow θ=0°θ=45°θ=50°θ=55°θ=60°θ=65°

(a’) f the elbow branch pipe in the plane of y = 0 mm: (a) l = 1%; and (a0) l = 5%.

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

T*

t / s

x=-0.125 z= -0.41 z= -0.42 z= -0.43 z= -0.44 z= -0.45

0 2 4 48 50

0.0

0.2

0.4

0.6

0.8

1.0

t / s

T*

x=-0.125 z= -0.41 z= -0.42 z= -0.43 z= -0.44 z= -0.45

(a) (a’)

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

t / s

T*

x=-0.5 z= -0.41 z= -0.42 z= -0.43 z= -0.44 z= -0.45

0 2 4 6 8 10 12 14 16 18 48 50

0.0

0.2

0.4

0.6

0.8

1.0

t / s

T* x=-0.5

z= -0.41 z= -0.42 z= -0.43 z= -0.44 z= -0.45

(b) (b’) Fig. 7. Normalized temperature changes with leakage time in the horizontal part of the elbow branch pipe in the plane of y = 0 mm: (a) and (b) l = 1%; (a0) and (b0) l = 5%.

T. Lu et al. / Annals of Nuclear Energy 60 (2013) 432–438 437

For the case with a smaller leakage ratio of l = 1%, as shown inFig. 7a and b, the normalized temperature in the top of thehorizontal part increases more rapidly than in the bottom. More-over, the normalized temperature of the point of z = �0.45 isequal to the temperature of the cold water in the first 50 s of leak-age due to the buoyancy. As shown in Fig. 7a0 and b0, the normal-ized temperature in the case of the larger leakage ratio of l = 5%increases to almost unity in the first 16 s of leakage, which meansthat at this leakage ratio the horizontal part is full of hot waterfrom the main pipe after leakage for 16 s and the original coldwater in the elbow branch pipe has been lost. Comparison ofthe different leakage ratios indicates that thermal stratificationoccurs more readily, and lasts longer, for smaller the leakageratios.

0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

l=1% (y=0, θ=60°) l=5%, (y=0, θ=65°)

t/s

T∗

Fig. 8. Comparison of the normalized temperature variations for different leakageratios at the locations with the strongest temperature fluctuation intensity.

3.2.3. The power spectrum density of the temperature fluctuationFig. 8 shows a comparison of the normalized temperature

changes for different leakage ratios at the different locations withthe strongest temperature fluctuation intensity. The normalizedtemperature for the larger leakage ratio of l = 5% increases morerapidly than for the smaller one. The normalized temperature forthe smaller leakage ratio of l = 1% fluctuates during the leakage.Fig. 9 shows a comparison of the power spectrum density (PSD)of the temperature with the strongest fluctuation intensity for dif-ferent leakage ratios. In the first 5 s of the leakage, increasing leak-age ratios result in an increase in the PSD, but after 5 s, smallerleakage ratios lead to higher values of PSD. Although larger leakageratios can induce a higher PSD, the period of thermal stratificationis shorter. It can be concluded that with decreasing leakage ratios,

1 10 100

1E-18

1E-16

1E-14

1E-12

1E-10

1E-8

1E-6

1E-4

0.01

Pow

er S

pect

rum

Den

sity

[deg

C2

/HZ]

f/Hz

l=1% (Y=0, θ=60°) (From 0-50 second)l=5% (Y=0, θ=65°) (From 0-5 second)l=5% (Y=0, θ=65°) (From 5-50 second)

Fig. 9. Comparison of the power spectrum density of the temperature with thestrongest fluctuation intensity for different leakage ratios.

438 T. Lu et al. / Annals of Nuclear Energy 60 (2013) 432–438

the elbow branch pipe suffers from increasing risk of thermal fati-gue caused by thermal stratification.

4. Conclusions

As thermal stratification can result in thermal fatigue in the pipingsystem of a nuclear power plant, safety and integrity evaluations ofthe piping system have become an important issue. Because of thecomplication of the thermal stratification itself, the flow and heattransfer should be fundamentally understood. One of the regionsmost at risk of suffering from thermal fatigue is a small elbow pipebranched off from the main pipe of the coolant loop for the drain orletdown system in the chemical and volume control system (CVCS).This work focuses on a fundamental description of the thermal strat-ification caused by turbulent penetration and buoyancy effects usingLES. In the absence of leakage, the LES results are in good agreementwith the available experimental data, which validates the LES as ameans of predicting the thermal stratification occurring in the elbowbranch pipe. Given this validation of LES, the flow and heat transferwere numerically predicted when leakage occurred in the elbowbranch pipe. The numerical results show that, for a leakage ratio of1%, the thermal stratification region is pushed down the horizontalpart and may remain for a long time in the horizontal part. The ther-mal stratification dissipates rapidly at a leakage ratio of 5%, althoughin this case there is a larger power spectrum density of the tempera-ture in the early stage of the leakage. It can be concluded that withdecreasing leakage ratios, the elbow branch pipe suffers fromincreasing risk of thermal fatigue caused by thermal stratification.

Acknowledgements

This work was supported by the National Natural ScienceFoundation of China (Project No. 51276009) and National BasicResearch Program of China (Project No. 2011CB706900).

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