Uploaded byHamed Hoorijani
Multiphase models
The document provides an overview of multiphase models, focusing on Eulerian-Eulerian and Lagrangian particle methods, particularly the Two-Fluid Model (TFM) and the mixture model. It explains the mathematical foundations and applications of these models in modeling interactions between multiple phases, including liquids, gases, and solids. The mixture model is presented as a simplified alternative to the full multiphase model, suitable for various applications like sedimentation and particle-laden flows.
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Multiphase models
- 1. Introduction to Multiphase ModelsFirstPart Hamed Hoorijani M.Sc. Student At the university of Tehran Linked :linkedin.com/in/hamed-hoorijani/ : Hamed Hoorijani Hoorijani@ut.ac.ir Hoorijani.h@gmail.com July 2019
- 5. Multiphase models • Eulerian-EulerianModels • Lagrangian Particle Methods VOF Mixture TFM BD MD DEM QM QM+MD DPD …
- 7. TFM model(Two-Fluid Model) •The Eulerian multiphase allows for the modeling of multiple separate, yet interacting phases. • The phases can be liquids, gases, or solids in nearly any combination. • An Eulerian treatment is used for each phase, in contrast to the Eulerian-Lagrangian treatment that is used for the discrete phase model.
- 8. TFM Main Equations VolumeFraction Equation Conservation Equations
- 9. TFM Main Equations Conservationof Momentum
- 10. TFM Main Equations Conservationof Momentum Conservation of Energy Equations:
- 11. TFM Main Equations Fluid-FluidMomentum Equations Fluid-Solid Momentum Equations
- 12. TFM Main Equations InterphaseExchange Coefficients particulate relaxation time For the model of Schiller and Naumann
- 13. • The mixturemodel is a simplified multiphase model that can be used in different ways. • It can be used to model multiphase flows where the phases move at different velocities, but assume local equilibrium over short spatial length scales. • It can be used to model homogeneous multiphase flows with very strong coupling and phases moving at the same velocity and lastly, the mixture models are used to calculate non-Newtonian viscosity. • The mixture model can model phases (fluid or particulate) by solving the momentum, continuity, and energy equations for the mixture, the volume fraction equations for the secondary phases, and algebraic expressions for the relative velocities. • Typical applications include sedimentation, cyclone separators, particle-laden flows with low loading, and bubbly flows where the gas volume fraction remains low. Mixture Model
- 14. The mixture modelis a good substitute for the full Eulerian multiphase model in several cases: 1. A full multiphase model may not be feasible when there is a wide distribution of the particulate phase 2. when the interphase laws are unknown or their reliability can be questioned. A simpler model like the mixture model can perform as well as a full multiphase model while solving a smaller number of variables than the full multiphase model. The mixture model allows you to select granular phases and calculates all properties of the granular phases. This is applicable for liquid-solid flows Mixture Model
- 15. Mixture Main Equations ContinuityEquation Momentum Equation
- 16. Mixture Main Equations MomentumEquation
- 17. Mixture Main Equations EnergyEquation Relative (Slip) Velocity and the Drift Velocity
- 18. Mixture Main Equations Relative(Slip) Velocity and the Drift Velocity Volume Fraction Equation for the Secondary Phases
- 19. Mixture Main Equations GranularProperties Kinetic Viscosity Collisional Viscosity Since the concentration of particles is an important factor in the calculation of the effective viscosity for the mixture, we may use the granular viscosity to get a value for the viscosity of the suspension. The volume weighted averaged for the viscosity would now contain shear viscosity arising from particle momentum exchange due to translation and collision. Gidaspow Syamlal
- 20. Mixture Main Equations GranularTemperature Solids Pressure
- 21. VOF Model(Volume ofFraction) • Appropriate for flow where Immiscible fluids have a clearly defined interface. • Shape of the interface is of interest • Typical problems: • Jet breakup • Motion of large bubbles in a liquid • Motion of liquid after a dam break (shown at right) • Steady or transient tracking of any liquid-gas interface • Inappropriate for: • Flows involving small (compared to a control volume) bubbles • Bubble columns
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