Stochastic models are used to predict various outcomes of a system by utilising random perturbations on pre-determined variables.   As many processes are not deterministic, stochastic models can be used to give the probability of a certain result.   This use of probability can be used, for example, to model the Brownian motion of particles or fluid parcels, and has previously been used to predict diffusion in oceanography, propagation of atmospheric pollutants, and dissipation of odours.   To construct deterministic models for complex flow systems is challenging and computationally demanding.   Stochastic models use a simplified structure instead, greatly reducing computational cost, whilst predicting complex flow characteristics.   We propose a Lagrangian stochastic approach to model liquid and particle trajectories in a multiphase stirred vessel system.   In a Lagrangian stochastic model (LSM), fluid or particle positions are advanced in space over a given time step and are subject to random perturbations.   Depending on the order of the model (zeroth, first, second), different flow parameters (position, velocity, acceleration) are affected by this random increment.   The random increment is defined by the Wiener process and the LSM, a data-driven model, utilises a velocity flow field extracted from Lagrangian experimental trajectory data.

Experiments were conducted to obtain 3D Lagrangian data of two-phase particle-liquid systems in a mechanically agitated vessel, using a unique technique of positron emission particle tracking (PEPT).  In PEPT, radiolabelled particles are used as flow followers and tracked in 3D space and time through positron detection.  Thus, each component in a multiphase particle-liquid flow can be labelled and its behaviour observed.  Compared with leading optical laser techniques (e.g. LDV, PIV), PEPT has the enormous and unique advantage that it can image opaque fluids, and fluids inside opaque apparatus with comparable accuracy.  The suspension of coarse monomodal glass particles of various sizes in water at concentrations up to 40 wt% was studied using a wide range of impeller rotation speeds to achieve turbulent flow at high impeller Reynolds numbers \>10^5^.  The experimental Lagrangian trajectory data obtained were used to construct Eulerian flow fields to describe the behaviour of each phase under different flow conditions and to extract the velocity data required to drive a LSM.  

The main benefit of such a method is its predictive capability.  Thus, experiments are conducted over a range of impeller speeds and the results obtained can be used to construct the two-phase flow field corresponding to any arbitrary impeller speed.   Furthermore, the amount of data required to drive the LSM is relatively small.  For example, PEPT data measured over a duration of 5 min can be used to faithfully construct multiphase Lagrangian trajectories that are hours long.

The predictive capability of different order LSMs was evaluated and the first order LSM was the most suitable for this type of flow.  The LSM was also compared to numerical computational fluid dynamics (CFD) simulations.   Trajectories predicted by LSM showed good agreement with both Eulerian-Eulerian and Eulerian-Lagrangian simulations.  Unlike numerical Eulerian-Eulerian or Eulerian-Lagrangian methods, LSMs are not computer intensive, however, and long Lagrangian trajectories can be generated in a relatively short time.


A Data-Driven Stochastic Model for the Analysis of Complex Two-Phase Particle-Liquid Flows

Division / Sponsors: 
Heat Transfer Division (HTD), Fluids Engineering Division (FED)

Heat Transfer Summer Conference
Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2020/volume/83709

18th International Conference on Nanochannels, Microchannels, and Minichannels
Paper Proceedings: https://asmedigitalcollection.asme.org/ICNMM/ICNMM2020/volume/83693

Fluids Engineering Division Summer Meeting
Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2020/volume/83716

HT-ICNMM2020 - Virtual Conference, SHTC - Virtual Conference, FEDSM2020 - Virtual Conference

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