EXPLORING THE USE OF COMPUTATIONAL FLUID DYNAMICS

TO MODEL A T-JUNCTION

NERS 590-2 – Project Report

University of Michigan – Professor Manera

15th August, 2014

Douglas Kripke

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1. INTRODUCTION

Nuclear power plants involve thermal mixing in T-junctions where hot and cold fluid

flows combine. Resulting time and spatial temperature fluctuations have historically caused pipe

failure in nuclear power plants via local thermal fatigue (Ogawa, 2005). Thus, much work has

been done regarding T-junctions such as experimental measurements and computation fluid

dynamics (CFD). CFD can take the form of direct numerical simulations (DNS), large eddy

simulations (LES), and reynolds-averaged Navier-Stokes (RANS) models, each of which use

different numerical methods and assumptions to solve the Navier-Stokes equations (NSE). With

regard to T-junctions, the thermal striping phenomenon is often characterized by the diameter

and flow velocity ratios of the main to branch pipe. Analysis seeks to determine the magnitude,

frequency, and impact region of the temperature fluctuations (Naik-Nimbalkar, 2010). This

stress on the pipe wall can then be combined with knowledge of the pipe’s material properties,

thickness, and restraint conditions to evaluate the T-junction’s longevity (Kamide, 2009). The

work of Ingarashi et at. (2003), Ogawa et at. (2005), and Kamide et at. (2009) all used the same

equipment in their water experiments, which had a ninety degree T-junction, a main to branch

diameter ratio of three, and a cold branch flow combining with a main flow 15°C warmer.

Temperature and velocity distributions were measured to characterize the flow field and

temperature fluctuations. This project will compare the use of the realizable and standard k-ε

RANS models in STAR-CCM+ to replicate the velocity field of experimental measurements of

water in a T-junction.

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2. PREVIOUS WORK

Extensive water experiments have been performed on a T-junction with a main pipe

diameter of 150 mm and a branch pipe diameter of 50 mm by Igarashi, Ogawa, Kamide, and

others (see references). Water in the main pipe was heated to 321 K and traveled 2.7 m

horizontally before reaching the 90° tee. Water in the branch pipe was heated to 306 K and

traveled 0.5 m upwards before reaching the tee. Temperature measurements were obtained with

a movable thermocouple tree as depicted in figure 1. The thermocouple tree contained 15

thermocouples (0.25 mm in diameter each) in the radial direction of the main pipe. The tree was

capable of rotating axially and shifting horizontally to yield measurements throughout the main

pipe with an accuracy of less than ±0.2 K.

Figure 1: Temperature measurement set-up (Ogawa, 2005)

Velocity measurements were obtained with a particle image velocimetry (PIV) system as

shown in figure 2. This system employs a laser, camera, computer, a timing controller, and

nylon powder (diameter ~30 µm) injected into the pipe as a tracer particle. With this system,

velocity measurement error was less than 0.04 m/s (Igarashi, 2003). Velocity measurements

were obtained with isothermal conditions, and the buoyancy force was determined negligible

with a main pipe velocity greater than 0.1 m/s by Igarashi et al. (2002).

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Figure 2: Velocity measurement set-up from Igarashi et al. (2003) left and Ogawa et al.

(2005) right

It was discovered that the flow of the jet exiting from the branch pipe could be predicted

by a momentum ratio MR of the main to branch flow velocity V according to table 1 as

𝑀𝑅 =𝑀𝑚

𝑀𝑏 (1)

with

𝑀𝑚 = 𝐷𝑚𝐷𝑏𝜌𝑚𝑉𝑚2 (1a)

𝑀𝑏 =𝜋

4𝐷𝑏

2𝜌𝑛𝑉𝑏

2 (1b)

Table 1: Momentum Ratio classification of flow pattern in T-junction

Range Branch Behavior

Impinging Jet MR < 0.35 jet impinges the opposite sidewall of the main pipe

Deflecting Jet 0.35 < MR < 1.35 jet flows through the central part in the main pipe

Wall Jet MR > 1.35 jet is bent to main pipe wall

where D is the diameter, ρ is the density, and the subscripts m and b denote the main and branch

pipe respectively. The velocity V was calculated from the cross section average. The

momentum ratio characterizes the flow after the mixing in a T-junction as either a wall jet,

deflecting jet, or impinging jet as seen in figure 3. As long as the momentum ratio of equation 1

is conserved, Kamide et al. (2009) showed that different fluid temperatures and velocities will

yield the same normalized temperature and velocity distributions. Velocities were normalized by

the main branch velocity, and temperatures were normalized as

𝑇∗ =𝑇−𝑇𝑏

𝑇𝑚−𝑇𝑏 (2)

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Figure 3: Visual classification of flow pattern in T-Junction (Kamide, 2009)

A deflecting jet has the least thermal impact on the wall, and thus the other conditions are

of greater interest. Igarashi et al. (2003) tested two cases identified in table 2. Ogawa et al.

(2005) studied the effects of a pipe bend leading into a T-junction. And Kamide et al. (2009)

tested a multitude of different velocities and characterized the temperature fluctuation intensity.

The 2003 and 2009 studies compared experimental data to an in-house CFD code. Naik-

Nimbalkar et al. (2010) did a literature review and comparison of the aforementioned studies.

Table 2: Test Conditions

Vm Vb 𝑀𝑅

Case 1: Wall Jet 1.46 m/s 1 m/s 8.1

Case 2: Impinging Jet 0.23 m/s 1 m/s 0.2

The work by Igarashi et al. (2003) used the velocity distributions to obtain time averaged

streamlines in vertical and horizontal cross sections of the pipe as seen in figure 4. The dominant

momentum of the fluid from the main pipe overtakes and entrains the branch pipe flow in a

spatially confined mixing region near the branch inlet. The branch pipe jet is bent downwards

with vortices formed in the wake region below. An alternating vortex is formed in the wake

region, resulting in the mirror twin vortices seen in the time averaged horizontal cross section,

which interestingly bares resemblance to the well-studied turbulent flow past a circular cylinder.

The main inlet fluid in the top half of the pipe accelerates around the mixing zone. Figure 5

shows the vertical and horizontal velocity components on a vertical line at the pipe length

Z=0.5Dm (with Z=0 set at the intersection of the main pipe with the axis of the branch pipe).

This velocity distribution and one at Z=1Dm will be the subject of replication for this CFD study.

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Figure 4: Measured time-averaged streamlines for the wall jet case 1 (Igarashi, 2003) with

velocity normalized to the branch pipe flow

Figure 5: Wall jet temperature and velocity profile for a vertical line at Z=0.5Dm (Igarashi 2003)

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3. CFD MODELING

In order for turbulence models to be valid, it must first be determined that the flows

involved are indeed fully turbulent. The Reynolds number for a Newtonian fluid like water can

be readily calculated as

𝑅𝑒 =𝜌𝑣𝐷𝐻

𝜇 (2)

Table 3 shows the appropriate density and viscosity for the experimental inlet conditions.

Reynolds numbers of 382,639 and 66,406 were obtained for the main and branch pipe,

respectively. Thus, the flows are fully turbulent and the use of turbulent models validated.

Table 3 Inlet water properties for Reynolds number calculation

DH (m) v (m/s) T (°C) ρ (kg/m3) μ (kg/m∙s) Re

Main Pipe 0.15 1.46 48 988.92 5.66×10-4 382,639

Branch Pipe 0.05 1.00 33 994.76 7.49×10-4 66,406

The simulation will exclude temperature specifications and solve for steady state

conditions. Ideally, a segregated temperature model would be used with temperature dependent

density and dynamic viscosity. However, the temperature difference between the pipes was set

to zero (isothermal conditions) for experimental velocity measurements (Kamide, 2009), and the

added analytical benefit of solving for the steady state temperature distribution is not worth the

additional computational resources required. The water study does not specify the isothermal

temperature used for the velocity measurements. It will therefore be assumed that the water is at

48°C with a constant density and dynamic viscosity of 988.92 kg/m3 and 5.66×10-4 kg/m∙s.

Inlet pipe boundaries will be set with a fully developed velocity flow profile created from

a separate pipe simulation. For the main pipe, the water experiment had an inlet velocity profile

and turbulent intensity profile shown in figure 6. The asymmetry of the distribution is very

curious. The entry length of the experiment was 18Dm (for engineering applications 10D is

usually considered sufficient), so the flow should have been fully developed. Further

investigation into literature found the velocity profile to be nearly identical to the classical case

of developed flow in a square channel with three smooth walls and one rough (Gretler, 1994).

This could have occurred accidentally in the experiment from nylon powder used in PIV

measurements depositing along the bottom of the pipe. An attempt was made to replicate this

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Figure 6: Velocity and fluctuation intensity distributions

at the inlet prior to the tee (Kamide, 2009)

distribution with the wall roughness increased along the bottom of an infinite pipe. However, the

obtained distribution was symmetric. Alternatively, the one-dimensional experimental profile

was fed into a pipe simulation and extracted after a pipe length of one meter to obtain a two-

dimensional profile as seen in figure 7. This will be used in the T-junction simulation as the

main pipe inlet velocity profile (via an XYZ table). For the branch pipe, an infinite pipe of the

same diameter was modeled with periodic boundary conditions. The fully-developed velocity

profile was extracted and will be used in the T-junction simulation for the branch pipe inlet. The

T-junction will have a simple split-flow outlet.

The CFD results will be found using the realizable and standard k-ε models with two-

layer y+ wall treatment. A segregated rather than coupled model will be used to save on

computational requirements. Figure 8 shows some additional physics assumptions selected.

The free-stream turbulent intensity ratio was measured (see figure 6) to be 8.76% and will be set

as such for all simulations. For the inlet simulations, the turbulence length scale was set to the

appropriate hydraulic diameter. The T-junction simulation will have a length scale of 7% the

main pipe’s diameter and a turbulent velocity scale of 1.46 m/s. Careful meshing and monitoring

will ensure wall y+ values remain between 30 and 100 as required by the wall treatment of the

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Figure 7: Main branch inlet velocity developed in two-dimensions (left) from the one-

dimensional velocity profile of the water experiment (right)

model. The pipe wall will be set to adiabatic, no-slip, and smooth.

The T-junction domain was set around measurement lines at Z=0.5Dm and Z=1Dm as

small as possible to minimize computational requirements. From figure 4, the time-averaged

wake vortex occurs within a pipe length of 1Dm after the tee. Therefore, as seen in figure 9, the

pipe inlets were created directly at the tee meeting point, and the pipe extends a length of 1Dm.

This domain is not sufficient, however, to negate entrance and exit effects. To account for this, a

mesh extrusion will be used on every boundary extending the inlets by 25 mm and the outlet by

150 mm as is the topic of the following

section.

Figure 8: Physics assumptions used for the CFD analysis

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Figure 9: CAD representation of the T-junction model domain showing the main and branch

inlet (left) and outlet (right). The origin is at the intersection of main and branch pipe axes, the

y-axis is in the vertical direction, and the main pipe extends to Z=1Dm

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4. MESH DEVELOPMENT

All mesh studies used the standard k-ε model with the physics parameters described in

the previous section.

Branch Pipe Inlet Simulation

An infinite pipe simulation was used to generate a fully developed flow for the branch

pipe inlet. The infinite pipe was created with the same diameter (50 mm) and a pipe length of

0.1 m with periodic boundary conditions. The surface re-mesher and polyhedral mesh were

selected due to their known efficiency in sub-diving a region. Two prism layers were included,

and the prism layer thickness was set to an absolute value of 0.003 m. This thickness yielded

desirable wall y+ values of around 50 for each mesh size. The solution was considered

converged when the residuals stabilized with each iteration. Table 4 shows the results of the

mesh convergence study.

The optimum base size was 0.005 m. The fully developed velocity profile converged

between base sizes 0.008 m and 0.005 m as seen in figure 10. Thus, the smallest independent

base size was determined to be the best. For this base size, figure 11 shows the residual

convergence, figure 12 shows the mesh itself, and figure 13 shows the obtained velocity profile.

Table 4 Mesh convergence study for branch inlet

Base Size (m) Vertices Vmax (m/s) Iterations Time (s)

0.02 8,691 1.1189 600 32

0.015 17,584 1.1371 869 68

0.01 19,424 1.139 1159 97

0.009 19,466 1.1387 962 80

0.008 19,593 1.1431 1042 86

0.007 19,632 1.1416 1121 93

0.006 19,588 1.141 1136 94

0.005 19,981 1.1438 1166 100

0.004 41,381 1.1646 1529 210

0.003 49,062 1.176 1705 270

0.0025 111,614 1.1908 2481 824

0.002 180,333 1.1825 2653 1389

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Figure 10 Velocity profile versus base size for the branch inlet mesh convergence study

Figure 11 Branch inlet residual convergence with a base size of 0.005 m

1.11

1.12

1.13

1.14

1.15

1.16

1.17

1.18

1.19

1.2

0 0.005 0.01 0.015 0.02 0.025

max

imu

m v

elo

city

base size (m)

(m/s

)

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Figure 12 Branch inlet mesh with a base size 0.005 m (left) and y+ wall values (right)

Figure 13 Branch inlet velocity profile

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Main Pipe Inlet Simulation

As discussed previously, a standard infinite pipe simulate failed to create a main pipe

inlet profile to match the experimental data of figure 6. Instead, the one-dimensional

experimental profile was fed into a pipe of the same diameter and length of one meter to obtain a

two-dimensional profile more similar to the experiment than an infinite pipe simulation. An

extruder mesh extended the pipe from 0.1 m to 1 m in length. A mesh convergence study found

a prism layer thickness of 0.0025 m and a base size of 0.01 m to be optimal. Figure 14 shows the

mesh, and figure 15 shows the velocity profile.

Figure 14 Main inlet mesh with a base size 0.01 m (left) and y+ wall values (right)

Figure 15 Main inlet velocity profile

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T-junction Simulation

As discussed earlier, the main CAD domain of figure 9 will be extended with a mesh

extruder. The inlets will be extended by 25 mm each for a single layer, and the outlet will be

extended by 150 mm with 5 layers. This should negate any entrance or exit effects while

minimizing computational requirements for a finer mesh. Two prism layers were included, and

the prism layer thickness was set to an absolute value of 0.002 m. This thickness yielded

desirable wall y+ values of around 50 for each mesh size but with local variations between 5 and

160 near the branch pipe inlet. A trimmer mesh was used for the bulk of the pipe. The solution

was considered converged when the residuals stabilized with each iteration. Table 5 shows the

results of the mesh convergence study.

The optimum base size was 0.0025 m. The maximum and minimum velocity were

relatively base size independent between the base sizes 0.7 m and 0.0025 m, and so the smaller

base size was deemed the best. For this base size, figure 16 shows the residual convergence and

figure 17 shows the mesh itself and wall y+ values. It was impossible to achieve y+ values

between 30 and 100 for the whole wall with a constant prism layer thickness, however the

majority of the wall region did remain in this range.

Table 5 Mesh convergence study for the T-junction

Base Size (m) Vertices Vmin (m/s) Vmax (m/s) Iterations Time (s)

0.01 8,691 -0.1788 1.9057 186 9

0.007 15,555 -0.3234 1.8963 153 14

0.005 29,449 -0.2960 1.9078 200 34

0.003 71,496 -0.2583 1.9020 293 128

0.0025 101,612 -0.3197 1.9053 397 249

0.002 167,483 -0.4242 1.9699 344 373

0.00125 434,053 -0.4361 1.9299 721 2284

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Figure 16 T-junction residual convergence with a base size of 0.0025 m

Figure 17 T-junction mesh with a base size 0.0025 m (left) and y+ wall values (right)

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5. RESULTS

With the mesh size established in the previous section, a comparison could be made

between the experimental data, the standard k-ε model, and the realizable k-ε model. A visual

inspection can be seen in the vertical and horizontal streamlines of figures 18 and 19 and is

useful for a qualitative comparison. Both models clearly captured the wall jet behavior of the T-

junction in which the wall jet is bent downwards by the main pipe flow with a wake region

below the jet and an accelerated flow above the jet. The realizable model appears to have a

sharper particle trajectory in the wake region than the standard model, and neither of the

streamlines captured the vertical time-averaged vortex. The horizontal streamlines both captured

the horizontal time-averaged twin vortices, though the standard model shows a convergence of

the flow around the vortices at a shorter pipe length than the realizable model.

For a more quantitative comparison, the axial (Z) and radial (Y) velocity profiles at a pipe

length of 0.5Dm and 1Dm were compared to the experimental data in figures 20 and 21. The

differences between the models is slight, but the realizable model seems to be an improvement

over the standard model. Both models are known to have difficulty in regions of flow separation

and high adverse pressure gradients. Flow separation occurs in the wake region indicated by a

reversal in the axial flow. Both models show flow separation occurring at a lower height in the

pipe and have particular difficulty along the wall. The model could have benefit from a smaller

prism layer along the wall in the wake region. The models did manage to capture the same

strong velocity gradient of the flow separation. Above the wall jet, both models show flow

acceleration, however the profile should have flattened out as it progressed through the pipe

which is better captured by the realizable model. The superiority of the realizable model is best

seen in the radial velocity of the wake region at a pipe length of 1Dm where the standard model

incorrectly calculates a positive velocity. On the top of the pipe, the boundary layer thickness

seems accurate but not the flow speed. Perhaps an alteration of the turbulent length scale or an

inclusion of pipe roughness could improve this inadequacy.

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Figure 18 Streamlines from a vertical cross-section showing the experimental data on top, the

standard model on the left, and the realizable model on the right with a shown pipe length of 1Dm

Figure 19 Streamlines from a horizontal cross-section viewed from the bottom of the tee

showing the experimental data on top, the standard model on the left, and the realizable model on

the right with a shown pipe length of 1Dm

Standard k-ε

Standard k-ε

Realizable k-ε

Realizable k-ε

1Dm

↓

1Dm

↓

1Dm

↓ 1Dm

↓

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Figure 20 Comparison of velocity distributions on a vertical line at a pipe length of 0.5Dm

Figure 21 Comparison of velocity distributions on a vertical line at a pipe length of 1Dm

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6. CONCLUSIONS

The standard and realizable k-ε models were used in STAR-CCM+ to successfully

replicate the behavior of water in a T-junction but with limited accuracy. The experimental data

was thorough and specified detailed information for the boundary conditions of the simulation,

but the strange shape of the main pipe velocity distribution was not fully explained and difficult

to replicate exactly. Mesh sizes were set as small as possible before the converged solution

became unstable. Wall y+ values were kept between 30 and 100 to the best ability of a constant

prism layer thickness throughout the pipe which suffered most in the wake region directly

following the branch inlet. Results show the same general trends as the experimental data, but

with shortcomings along the wall and in identifying the height of the wall jet. Tweaking of the

turbulent length scale for the T-junction model could help to improve its accuracy. The

realizable k-ε model showed slight improvement over the standard k-ε model especially in the

region downstream of the flow separation. Future work could seek to improve the accuracy of

the models through refining the mesh in the wake region, fine tuning the turbulent length scale,

and changing the roughness of the wall from smooth to that of PVC pipe. Furthermore, a

segregated temperature model could be included to add an additional level of model validation.

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REFERENCES

Igarashi, M., Tanaka, M., 2003. Study on fluid mixing phenomena for evaluation of thermal

striping in a mixing tee. In: Proceedings of the 10th International Toping Meeting on

Nuclear Reactor Thermal Hydraulics (NURETH-10), Korea.

Igarashi, M., Tanaka, M., Kawashima, S., Kamide, H., 2002. Experimental study on fluid mixing

for evaluation of thermal striping in T-pipe junction. In: Proceeding of ICONE10-22255,

Arlington USA

Kamide, H., Igarashi, M., Kawashima, S., Kimura, N., Hayashia, K., 2009. Study on mixing

behavior in a tee piping and numberical analyses for evaluation of thermal striping.

Nuclear Engineering and Design 239, 58-67.

Naik-Nimbalkar, V.S., Patwardhan, A.W., Banergee, I., Padmakumar, G., Vaidyanathan, G.,

2010. Thermal mixing in T-junctions. Chemical Engineering Science 65, 5901-5911.

Ogawa, H., Igarashi, M., Kimura, N., Kamide, H., 2005. Experimental study on fluid mixing

phenomena in T-pipe junction with upstream elbow. In: Proceedings for the NURETH-

11, France.