Modelling of Poly-Disperse Multiphase Flows with an Euler-Euler Approach
by J. Carneiro, V. Kaufmann, Y. Liao and Wolfgang Polifke
Motivation
Sprays as well as bubbly flows are regarded as multiphase flows consisting of a large number of particles, which can be either liquid or gaseous and are dispersed in a continuous fluid. This dispersion increases the phase interface area significantly, which has a strong effect on the momentum and energy transfer between the phases. Therefore the sizes and distribution of the particles influence the physics and chemistry of many processes such as combustion engines, spray combustion, steam generators, aerated stirred vessels, nuclear reactors etc.
A calculation of these processes is very demanding due to the high numerical effort, as it normally requires a high resolution in time and space. Furthermore it is very difficult to consider the whole characteristic of a dispersed multiphase flow in a calculation.
The goal is to develop a model, in the context of an Euler-Euler formulation, which decreases the numerical effort and enables the simultaneous implementation of various multiphase flow phenomena, e.g. coalescence, break-up, evaporation, etc. In a former project this has been done by E. Gharaibah for dispersed bubbly flows calling the model 'Moments Model', cp. [1]. In the current projects the 'Moments Model' will be enhanced for sprays and bubbly flows considering demixing due to the size dependence of particle velocity and flow regime transition.
The 'Moments Model'
The 'Moments Model' discretises the particle size distribution and solves its population balance within a preprocessing step. Therefore the particle size distribution is represented by a number density function, which can be expressed mathematically, e.g. by a clipped Gaussian function. This function is parameterised by three moments, which are mean value, variance and the volume fraction of the particles. The results of the population balance equation are saved in lookuptables for a reasonable range of influencing flow parameters.
In the CFD program additional transport equations for two moments (mean value and variance) are solved for the dispersed phase beside the common set of governing equations for each phase. The link between the preprocessor and the CFD is achieved by flow parameters influencing the droplet size distribution on the one hand, and by source terms for the transport equations on the other hand. The sources are calculated directly from the lookup-tables, which makes the procedure more efficient, cf. Figure 1.
Outlook
Several issues regarding the further development of the moments model remain to be investigated.
- The numerical stability of the coupled system as well as a revision of the form of the transport equations for the moments are currently carried out.
- The demixing of big and small particles is a challenge for the conventional Euler-Euler approach. Up to now the fact that particles with different sizes have different velocities, the so called "poly-celerity", has not been considered in the moments model. In order to account this effect an additional source term for the transport equations shall be introduced.
- Furthermore the model will be enhanced regarding the flow regime transition in bubbly flows. Herefore geometry as well as phase independent formulations for the calculation of the interfacial area have to be found. The general applicability of the model is seen in the fields of sprays and thermohydraulic flows including phase change.
Selected Publications
[1] Gharaibah E., Polifke W. (2004) A Numerical Model of Dispersed Two Phase Flow in Aerated Stirred Vessels based on Presumed Shape Number Density Functions. Ed. Sommerfeld M., Bubbly Flows, Springer Verlag, 2004, 295-305