Simulation of Stirred Tank Hydrodynamics using mesh and meshless Methods

Smoothed particle Hydrodynamics (SPH) is a mesh-free method based on the lagrangian formulation, used in the simulation of fluid flow. SPH relies on the representation of the fluid domain as a set of particles, which interact within a prescribed range by means of weighting or smoothing functions. The use of weighted contributions rather than a linear system of equations, allows for massive parallelisation, taking advantage of recent developments in CUDA GPU technology to significantly reduce simulation times.
SPH offers many significant potential benefits in crystallisation simulations. These include the potential to explicitly model phenomena relating to the solid phase such as nucleation, growth and breakage. In particular, the SPH approach allows for advanced modelling of secondary nucleation based on such factors as particle velocity and impact angle, with direct linkage to experimentally determined particle-wall measurements. Lastly, SPH provides for superior tracking of interfaces in free surface flow, as commonly present in batch crystallisers, when compared to grid based techniques.
Application of SPH to crystallisation modelling first requires validation of hydrodynamics in a typical batch reactor vessel. In this paper, the hydrodynamics of a baffled stirred tank, driven by a rushton turbine at Re = 7300, are considered. Published LDA data for this configuration show highly three dimensional vortex flow structures with elevated turbulence levels close to the impeller. SPH turbulent flow calculations were performed using the Fluidix code. A large number of particles are required in order to produce SPH simulations of equivalent resolution to mesh based techniques. In this study, up to 30 million such particles were used.
Detailed comparison of the SPH phase resolved and phase averaged flow-field is made to published LDA data. Further comparison is made to Large Eddy Simulation (LES) and Reynolds averaged Navier-Stokes (RANS) calculations performed utilising the traditional mesh based approach. For both LES and RANS calculations, the transient sliding mesh procedure was adopted. The mesh used for the RANS calculations consisted of 241k nodes and 228k hexahedrons, while a uniform tetrahedral grid was utilised for the LES simulations consisting of 11 million elements. In the case of LES simulations, the WAL-E sub grid scale model was applied.
Phase averaged flow field data obtained from this study indicate that SPH allows for rapid prediction of the global mean flow, with marginally reduced accuracy when compared to the RANS simulations. The LES approach provides the closest match to experimental axial, radial and tangential velocity profiles [r/T=0.183, 0.25 & 0.317]. Similarly LES data for the dissipation of turbulence kinetic energy is shown to best match experimental data. Local flow information such as this can be vital for the prediction of chemical reactions, where mixing at the small scales can be the rate limiting phenomena.
While conventional mesh based simulation approaches provide the most accurate description of the complex turbulent flow of stirred tank reactor, the natural advantages of SPH in terms of scalability and its lagrangian nature retain it as an attractive proposition in crystallisation modelling.