# Induced flow in a T-junction

Pressurized Water Reactors is connected to a large number of auxiliary lines in which the fluid is usually colder than in the main pipe. Most of the time, the mass flow rate is small in the part of the auxiliary line located between the main circuit and the first valve. Hence, this zone might show temperature fluctuations if hot fluid coming from the main pipe is recirculating due to the shear at the junction. Previous analyses in Robert (1992) have shown that the swirl power in the dead leg is directly affected by the Reynolds number in the main pipe and by geometric details of the junction, whereas the influence of thermal effects is comparatively negligible. This is the reason why the application challenge proposed here focuses on the isothermal study of this flow : the motivation, for safety reasons, is to understand and be able to model the hydraulic behavior of auxiliary lines connected to the primary circuit of Pressurized Water Reactors.

The height of the recirculation zone is the key Design or Assessment Parameter (DOAP).

## Best Practice Advice for the AC

Key Fluid Physics

A high Reynolds number developed turbulent flow is maintained in the main pipe while very small incoming mass flow rates are imposed in the auxiliary pipe (or ‘dead leg’) of the T-junction. In such a configuration, a vortex is generated at the junction. Due to the shear, the flow is recirculating in the dead leg. The symmetry of this recirculation with respect to the plane including the axes of the two pipes may break down, then a swirling flow extends along the dead legs.

The key parameters are the precise design of the T-junction and the mass flow rate in the auxiliary line.

Application Uncertainties

The uncertainties are essentially the following:

• The details of the T-junction geometry are known but seem to have quite a large impact on the swirl developing in the dead leg; hence, they constitute a source of uncertainties

• The precise determination of the limits of the swirling zone remains difficult and depends on the technique used, for experiments as well as for computations.

• No determination of measurement errors are available

Computational Domain and Boundary Conditions

The computational domain represents the geometry described in Figure 1 with the same sharp-edged junction as in the experiments. This was crucial since this parameter is of major importance with respect to the height of the recirculation zone.

The pipe lengths have been chosen to minimize the size of the numerical model so as maximize the grid refinement.

The inlet of the main pipe has been placed relatively near from the junction to reduce the size of the numerical model. Hence, special attention is necessary for the determination of inlet boundary conditions.

The outlet needs to be sufficiently far away from the junction to prevent any recirculating structure from crossing it.

The height of the auxiliary pipe needs to be large enough to prevent the corkscrew pattern from reaching its top.

Figure 1 : Computational domain.

At the inlets (main pipe and auxiliary pipe), Dirichlet conditions are used for all transported variables.

In the main pipe, the incoming flow is supposed to be fully developed. Hence, the mean velocity and turbulent quantities were obtained from preliminary periodic pipe computations with the same bulk velocity and the same cross-section.

For the auxiliary pipe, due to the very small flow-rates, it is not necessary to describe so accurately the incoming flow. The mean velocity was taken constant and turbulent quantities were estimated from usual experimental laws for the friction velocity.

In fully developed pipe flows with zero-roughness, and for Reynolds numbers Re (based on the bulk velocity VA and the hydraulic diameter D) ranging between 5,000 and 30,000, the friction velocity ut can be determined from ${\displaystyle u_{t}=V_{A}((0.3164/Re^{0.25})/8)^{0.5}}$ The turbulent kinetic energy k can then be estimated from ut as k = ut2/0.3 and the dissipation as ε = ut3/(0.42D0.1).

At the outlet (main pipe), zero gradient conditions were applied for all transported variables.

Wall functions were used at solid walls.

Discretisation and Grid Resolution

• The overall precision of the discretisation is first order in time and second order in space. Second order precision in space seemed important, especially for the second moment closure model.

• Convergence in space has been checked for k-epsilon and Reynolds Stress Model simulation by using three different grids (100000, 400000 and 1500000 cells).

Physical Modelling

• The swirling flow characteristics encountered in this application does not seem to be captured properly with a k-epsilon model, whereas a Reynolds stress modelling provides results in better agreement with experimental data.

Recommendations for Future Work

• Find a documented UFR related to this AC

• More calculations would be required using different codes, so as to judge of the dependence to the code, the discretisation and the model implementation.

• Calculations should be carried out on even more refined grids, to ensure that convergence has been reached, even with Reynolds stress model.

• Large Eddy simulation shall be tried on this configuration

• Computation with different T-junction geometries are also of interest

• A more detailed experimental determination of the corkscrew height would be interesting