Turbulence modelling in buoyant flows

The project aims at the validation of numerical models in Computational Fluid Dynamics (CFD) codes suitable for the description of turbulent mixing in Pressurised Water Reactors under the impact of fluid density gradients.
In nuclear reactor safety research, fluid mixing induced by buoyancy effects is relevant for
  • Boron dilution issues, when lower borated water with different temperature mixes with the ambient water in the reactor pressure vessel
  • Pressurised thermal shock scenarios, when cold emergency cooling water is injected into the reactor and gets in contact with the vessel wall
  • Containment analysis, when in the case of severe accidents hot hydrogen and steam mix with the containment atmosphere.
While commercial CFD codes in general can treat buoyancy effects e.g. within the Boussinesq approximation, there are defeciencies in the modeling of buoyancy driven turbulence. Usual turbulence models assume isotropic turbulence, while buoyancy induces anisotropy. In the project, higher order turbulence models have been developed which take into account for that anisotropy. Buoyancy generated source and dissipation terms are introduced into the balance equations for the turbulent energy was proposed. The buoyancy induced source term is proportional to the Reynolds flux . Additional balance equations for  and for the fluctuation product  are solved. The source term can be included into type turbulence models as well as into Reynolds stress models.
The models are validated against experiments at the VeMix test facility.

VeMix test facility

The VeMix test facility has a simple geometry and is set up to ensure that the gravity force acts along the significant length scale. Plexiglas units were used to allow observation of flow patterns that are generated.
The configuration of the VeMix test facility is a vertical parallel plane channel, which is rectangular in form. The facility (Fig 1) was assembled from 5 plexiglass units with an inlet nozzle and an outlet nozzle unit. In the horizonthal part, stratified water trap with fluid of higher (below) and lower (above) density is prepared. Into this water trap, fluid with higher density is intoduced through the inlet nozzle. The inlet flowrate can modified over the range 0.1-1.8 [l/ s] to give different inlet momentum force magnitudes. The density difference was varied between 0-10% by adding sucrose to modify the magnitude of the buoyancy forces. The ranges of these flow conditions allowed the development of different flow patterns or regimes according to characteristic non-dimensional numbers.
The internal Richardson number is a non-dimensional number, which dependent on the flow condition could be used to qualitatively define two flow regime, which were observed in the vessel:
The internal Richardson number is the ratio between the buoyancy and the momentum forces, which is given by:

where is density difference of the fluids, v - characteristic velocity in the VeMix vertical channel, the characteristic length, which defines the thickness of the layer between the heavy and light waters, distance from the base of the VeMix test facility up to the boundary between the heavy and light waters, distance from the base of the VeMix test facility up to the lower surface of the inlet nozzle, g acceleration due to gravity.

  •  regime of flow falling jet patterns Fig 2 . The gravity force acts along the vertical axis and is significantly stronger than momentum forces driven by inlet flowrate. The jet drops near to the wall below the inlet nozzle.
  • the transition regime between the horizontal and falling jet patterns. The gravity and momentum forces are in near equilibrium and the resulting flow pattern strongly depends on the force ratio. In this regime it is not easy to predict the flow pattern observed.
  • regime of flow horizontal jet patterns Fig 3. The momentum force driven by input flowrate is stronger than gravity force, which results in the formation of a horizontal jet. The horizontal jet influences the transient mixing behaviour, as oscillation waves are formed on interface between the heavier water and the lighter water.

A new Surface Wire Mesh Sensor (SWMS) developed at HZDR was installed in one of the vertical sections of VeMix. It makes possible to obtain density distribution with high resolution in space and time based on electrical conductivity measurement. A comparison of the SWMS data with calculated density distribution in the test section is shown on Fig 4. The regime of flow horizontal jet pattern is very clealyr see in regions below the inlet nozzle.


This project is funded by the German Federal Ministry of Economics and Technology under contract numer 150 1287.