# Evaluation AC3-02

**Induced flow in a T-junction**

**Application Challenge 3-02** © copyright ERCOFTAC 2004

**Comparison of Test data and CFD**

Figure 4 compares the length of vortex penetration obtained by numerical simulation with experimental measurements. The length of the vortex penetration has been determined numerically by visualizing the time-averaged velocity field obtained in different planes of the dead leg. This method is consistent with the way the experiments were carried out. It is also important to note that experiments and calculations were conducted by the same team, thus making comparisons easier and less subject to interpretation errors. The results for three different flow rates are presented. Significant improvement is obtained when refining the mesh.

The prediction of the vortex penetration in the dead leg using Reynolds stress model on the finest mesh is in very good agreement with the experiments. The differences between medium and fine meshes illustrate the necessity to use very fine grids with the Reynolds stress model. It might be necessary to perform yet another simulation on an even finer mesh to achieve full grid independence.

With the k-epsilon model, on the contrary, the computed vortex penetration is not satisfactory, even on the finest mesh. Moreover, the very small difference between the results obtained on medium and fine meshes indicates that the use of even more refined meshes would be unlikely to bring significant improvement.

Figure 4

Length of vortex penetration for different flow rates in the auxiliary pipe. Comparison between Reynolds stress model (SMC) and k-ε model. Coarse, medium and fine meshes have been used.

Figure 5 presents the rotation velocity at different sections in the auxiliary pipe obtained by both numerical and experimental simulations. According to tests by Robert (1992), the power of the rotation velocity into the auxiliary line is very sensitive to geometric details of the T-junction (in particular, depending on the type of junction, sharp or rounded edge). Small differences between the mock-up geometry and the numerical mesh could generate differences on the rotation velocity. To validate independently the vortex decay in the auxiliary line, numerical and experimental results are compared using dimensionless quantities. The rotation velocities obtained from numerical and experimental simulations are scaled by the corresponding rotation velocities near to the T-junction taken at H/D = 3. Using Reynolds stress model, the vortex decay is very close to the experimental result. On the contrary, it is overestimated with the k-epsilon.

Figure 5

Maximum rotation velocity scaled by the corresponding value at the section H/D=3. Comparison between Reynolds stress model (SMC), k-epsilon results and experimental data

Figure 6 and Figure 7 help to visualize the flow features. They represent the vortex penetration in the dead leg for VA/VM = 0.25 % (k-epsilon and Reynolds Stress Model respectively). The positive vertical velocity component is displayed in black and the negative in gray: black trajectories represent fluid particles coming from the main pipe and gray trajectories represent the fluid particles coming from the top of the auxiliary pipe. Velocity vectors are plotted at three different sections of the auxiliary pipe H/D=2, 5 and 7 from the results of fine, medium and coarse meshes.

Figure 6

k-epsilon prediction of vortex penetration in the dead leg - VA/VM = 0.25 %.

Figure 7

Reynolds stress model prediction of vortex penetration in the dead leg - VA/VM = 0.25 %.

5. CONCLUSIONS RECOMMENDATIONS AND FUTURE WORK

Numerical calculations performed on the T-junction with coarse (100 000), medium (400 000) and fine (1 500 000) meshes were used to test the influence of the grid. The results illustrate that a thorough mesh refinement is necessary before trying to draw conclusions from any numerical simulation. Indeed, on too coarse a mesh, results from the Reynolds stress model might turn out to be significantly worse than those obtained with a k-epsilon model.

The numerical results obtained with the Reynolds stress turbulence model on the finest mesh confirm the presence of the swirling flow structure observed experimentally in the dead leg. On the other hand, with the k-epsilon eddy viscosity model, the vortical penetration in the dead leg is not satisfactorily reproduced. This demonstrates that Reynolds stress modeling might be a very interesting alternative to less sophisticated turbulence models such as k-epsilon, especially to capture swirling flows.

The quantitative prediction of swirling flows (and resulting temperature fluctuations) in such configurations remains difficult, especially if one considers for example the sensitivity of the vortex penetration to details of the T junction.

Moreover, the unsteady characteristics of the flow tends to make extensive studies (both numerical and experimental) costly and relatively tedious to carry out.

Other CFD simulations, with a new version of ESTET, and with a more recent EDF code, are still to be achieved.

**References**

Deutsch E., Méchitoua N., Mattéi J.D., (1996) "Flow simulation in piping system dead legs using second moment closure and k-epsilon model", *Proc. 6th International Symposium on Turbulence Modelling and Measurements*, September 8-10, Tallahassee, Florida, USA.

Deutsch E., Montanari P., Mallez C., (1997) "Isothermal study of the flow at the junction between an auxiliary line and primary circuit of pressurised water reactors", *Journal of hydraulic Research Vol. 35, No. 6, 799-811*.

Launder B. E., Spalding D. B. (1974) "The numerical computation of turbulent flows." *Comp. Methods in Applied Mech and Eng., 3, 269-289*.

Launder B. E. (1989) "Second-moment closure : present...and future." *intl J. Heat Fluid Flow 10, 282-300*.

Méchitoua, N, J.D. Mattéi, D. Garréton, B. Chaumeton, (1994) "Three Dimensional Flow and Combustion Modelling of a Laboratory Gas Turbine Combustor." *International Symposium on Turbulence, Heat and Mass Transfer*, August 8-11, Lisbon, Portugal.

Robert M. (1992) "Corkscrew flow pattern in piping system dead legs" *NURETH-5*, September, Salt Lake City, USA.

© copyright ERCOFTAC 2004

Contributors: Frederic Archambeau - EDF - R&D Division

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