Particle-laden swirling flow

Application Challenge AC3-12 © copyright ERCOFTAC 2013

Key Fluid Physics

The introduced swirling flows are highly turbulent and as known, the turbulence structure is strongly anisotropic. Moreover, the flow is characterized by a central recirculation region and a flow separation in the pipe expansion. Mostly such kind of flows is not stationary, but exhibits some fluctuations of the vortex core (precessing). This effect also influences the particle behaviour which is manifested in the formation of particle ropes. These are caused by slight fluctuations of the particle-laden primary jet induced by the vortex precession. Eventually these ropes move spirally along the test section wall downward. As a consequence of the locally high particle concentration two-way coupling effects and also inter-particle collisions might become of importance.

Application Uncertainties

The flow geometry is relatively simple and can be accurately specified and discretised. The inlet conditions were measured 3 mm downstream of the exit of the inlet tubes so that the variation of the flow during the first 3 mm (i.e. from the exact geometrical exit) can be neglected. In previous calculations, as shown above, the particle size across the central tube inlet was specified according to that provided in Fig. 2 (i.e. no variation). The first measured profile reveals that a spatial variation of the particle size distribution at the exit can be neglected. Possibly however, the mean velocity and the rms values for the different particle size classes might be slightly different. It should be also kept in mind that the measurements were only done for one profile across the test section. Hence any asymmetries of the flow could bias the results.

Computational Domain and Boundary Conditions

Previous calculations, as shown above, have been done based on the two-dimensional axisymmetric conservation equations. As a matter of fact however the flow should be considered as fully three-dimensional and possibly the computations should be done using an unsteady approach in order to capture the slight precessing of the swirling vortex. This will also affect the particle behaviour and it is possible to numerically predict particle rope formation and dispersion (Lipowsky and Sommerfeld 2007, Sommerfeld et al. 2010).

Discretisation and Grid Resolution

For full three-dimensional calculations of the considered swirling flow at least 300,000 control volumes should be used when applying RANS methods. In the case of LES, the grid resolution should be much higher. Apte et al. (2003) have for example used 1.6 million hexahedral volumes.

For steady-state calculations several hundred thousands of particles should be sufficient. For unsteady simulations the number of considered particles needs to be higher in order to ensure good statistical averaging.

Physical Modelling

It is suggested to calculate the swirling flow either with a Reynolds-stress turbulence model (Lipowsky and Sommerfeld 2005) or applying LES. This has been done by Apte et al. (2003) using LES on an unstructured grid and applying the dynamic Smagorinsky model. For simulating the particle phase the Lagrangian approach was adopted accounting for drag and gravity only. Moreover two-way coupling was accounted for. For Case 1 introduced here an excellent agreement with all components of the measured gas and particle phase mean velocities as well as the rms velocities was obtained. Also the profiles of the particle number mean diameter were predicted reasonably well. A comparison with the measured stream-wise particle mass flux is not shown.

Due to the singularity at r = 0 in a cylindrical frame of reference, particle tracking should be done on a Cartesian coordinate system. In this formulation centrifugal and Coriolis forces should not appear. For the considered gas-solid system, added mass, pressure term and Basset force are negligible. Since the particles are relatively small, transverse lift forces (slip-shear and slip-rotation lift, see Sommerfeld et al. 2008) have not a very strong effect on the particle motion and the resulting concentration profiles (see Fig. 15 and Sommerfeld and Qiu 1993). Moreover, the model for predicting the instantaneous velocity seen by the particle has an essential effect on the computed particle dispersion. In this case an uncorrelated isotropic discrete eddy concept was used. This model could be improved by accounting for the anisotropy of turbulence using for example a Langevin model (Lipowsky and Sommerfeld 2005).

Recommendations for Future Work

The described test cases for particle-laden swirling flows provide very detailed measurements for air- and particle-phase properties. It would be interesting to see a comparison of steady and unsteady calculations as well as calculation results obtained with different turbulence closures, including LES. Moreover, in the case of rope formation (unsteady simulations) the effect of two-way coupling and inter-particle collisions should be evaluated.

Contributed by: Martin Sommerfeld — Martin-Luther-Universität Halle-Wittenberg