Sludge can be considered as a two-phase mixture in which the water is the continuous phase, and the sludge is the dispersed phase.

Drift flux model assumes that the primary source of slip between the phases is gravitational settling of the dispersed phase.

*driftFluxFoam* solver is developed by Brennan’s PhD thesis [1] based on mixture model approximation (former *settlingFoam*). In this model, only one continuity equation and one momentum equation are solved for the mixture. In other words, the two-phases in drift flux model are treated as a single fluid mixture in which the velocity, pressure and the density of individual phases are replaced by a single property of the mixture.

The two phases are defined by following equation:

The mixture density is defined as:

And the velocity of the mixture is defined by:

The subscripts *c*,*d*, and *m* stands for continuous, dispersed and mixture phase, respectively. The *driftFluxFoam* is a transient solver for two incompressible fluids treated as a single mixture. The solver is based on Pimple algorithm and can handle larger time steps and does not reply on under-relaxation.

The available viscosity models for this solvers are Bingham plastic, plastic and slurry viscosity model. To read about the implemented models for *driftFluxFoam* solver, refer to [2]. To understand the non-Newtonian models in OpenFOAM and how to implement a customized non-Newtonian model, see this tutorial.

Here, we use this solver to simulate the 2D flow of water jet nozzle to observe the penetration length in the channel full of sludge. The water depth is 5 m and the length of the channel is 20m. The jet flow of 180m^{3}/h is introduced at the middle of the channel (velocity 1 m/s). The nozzle diameter is 0.5 m and the sludge volume phase fraction is 0.001. In this model, k-ε turbulent model considering of buoyancy term is taken into account. Buoyancy is exchange between the potential energy of the flow and the turbulent kinetic energy. The presence of dispersed phase produce modifications in the structure of turbulence. Brennan (2001) showed that adding the buoyancy term, modifies the flow field, modifies the turbulent viscosity and improves the accuracy of the simulation.

It is worthwhile to note that this is a sample of using *drfitFluxFoam* solver to show one application of this solver. In practice, this simulation should be performed in 3D to capture full details of the model.

The sludge is modeled by Bingham plastic non-Newtonian model.

It is worth to mention that the drift flux model is not valid for large particles such as coarse sand or the particles that changes their phase status.

**Lynet engineering AS** has experience of designing jet pumps employed in dredging technology. We perform the basic calculations with our designed calculations sheets and analyse/optimize the design with CFD modelling.

More references to read:

1. Brennan, D. (2001). *The numerical simulation of two phase flows in settling tanks* (Doctoral dissertation, Imperial College London (University of London)).

2. Medina, M. E. V. (2019). *Secondary settling tanks modeling: study of the dynamics of activated sludge sedimentation by computational fluids dynamics* (Doctoral dissertation, Université de Strasbourg).