ME 537
Multiphase Flows
Class time: Mon Wed 10:00-11:20 MEB234


Professor Alberto Aliseda
office: MEB 306
tel: 543-4910
office hours: Tu, Th 9:30-10:30 or by appointment

Course description Lecture Notes
Syllabus Textbook Grading Homework Exams

Course Description

  This course is designed to provide students with a strong background on 
fundamental fluid mechanics the necessary understanding of the dynamics
of multiphase flow to carry out research in their area of interest. Particular
emphasis will be placed on bubble and particle dynamics, including
sediment transport, cavitation, atomization and other environmental and
industrial processes. 
Although we will cover both Eulerian-Eulerian (two fluid) models and
Eulerian-Lagragian (discrete particles) models, most of the material
concentrates on the study of a discrete phase (particles, droplets or
bubbles) in a continuous phase. Topics will include Basset-Boussinesq-
Oseen equation of motion for a particle in a non-uniform flow, particle
interactions with turbulence, inertial clustering, cavitation and bubble
dynamics, droplet breakup, collisions and coalescence,  and surface tension

Lecture Notes

Two Fluid Formulation: Conservation of Mass, Momentum and Energy for multiple immiscible phases.

Flow Around a Spherical Particle. Stokes Flow, Oseen Correction.

Hydrodynamic Forces on a Spherical Particle in a Nonuniform (Turbulence) Flow.

Dynamics of Particles in Turbulent Flows.

Deformation of Bubbles and Particles.

Droplet Breakup.

Bubble Dynamics. The Rayleigh-Plesset Equation.


Turbulence Modification by Particles.

Reading Assignments

Eulerian-Eulerian Framework to understand Multiphase Flows and modeling of interphase coupling. Crowe et al. "Handbook of Multiphase Flow", 2006. Chapter 13.

Batchelor's Book Chapter: Flow around a sphere, including Stokes, Oseen and Hadamard-Rybczynski solutions for flow around spheres with no-slip and free-slip (fluid-filled sphere) boundary conditions.

Maxey and Riley: Equation of Motion for a small rigid sphere in a nonuniform flow. Physics of Fluids Vol 26, issue 4, 1983

Multiphase Interactions. Crowe et al. "Handbook of Multiphase Flow", 2006. Chapter 12. In particular, section 12.6: Turbulence Modulations by Particles

Bubble Deformation and Collapse. Christopher Brennen. "Fundamentals of Multiphase Flow" 1st Edition, 2009. Chapter 4.


Homework #1. Explain the use of a Two-Fluid Formulation to describe the motion of small spherical bubbles in a turbulent flow.
Paper to read: "Direct Numerical Simulations of Bubble-Laden Turbulent Flows Using the Two-Fluid Formulation". Druzhinin and Elghobashi. Physics of Fluids 1998. Vol 10, pp. 685; doi: 10.1063/1.869594

Homework #2. Describe the dynamics of small spherical particles in turbulent flows from the following two papers:
Paper #1: "The motion of small spherical particles in a cellular flow field". M. Maxey, 1987, Physics of Fluids, 30, 7.
Paper #2: "Chaotic Dynamics of Particle Dispersion in Fluids". L.P. Wang, M. Maxey, T.D. Burton, D.E. Stock, 1992, Physics of Fluids A, 4, 8

Homework #3. Study the influence of particles in the turbulence characteristics of the carrier flow. Read and discuss the following two papers:
Paper #1: "On the two way interaction between homogeneous turbulence and small solid particles: Turbulence Modification", by S. Elghobashi and G.C. Truesdell, 1993, Physics of Fluids A, 5. (7).
Paper #2: "Classification of turbulence modification by dispersed spheres using a novel dimensionless number" by T. Tanaka,  and J.K. Eaton, Phys. Rev. Let. 101, (11), 114502, 2008.


Midterm Exam. Published on Nov 2, Friday, at 8 am, it is due on Nov 4, Sunday, at 5 pm.

Final Exam. Published on Dec 12, Wednesday, at 12:30 am, it is due on Dec 14, Friday, at 8 pm.


Introductions, syllabus, course administration.                                       Week 0
Stokes flow around a spherical particle and Oseen correction.              Week 1
Equation of motion for a small spherical particle in a
non-uniform flow, the Basset-Boussinesq-Oseen equation.   
Week 2
Other forces exerted by the carrier flow on a bubble/droplet/particle
immersed in it. Saffman Lift, Bjerknes force, thermophoresis, etc.  
Week 3

Particle dynamics. Inertial effects.                                                             Week 4                                                   

Two Fluid Models.                                                                                      Week 5

Turbulence modulation by particles.                                                       
Week 6
Droplet/bubble deformation and breakup.                                              Week 7
Bubble dynamics.                                                                                       Week 8    

Cavitation.                                                                                                   Week 9

Droplet collisions and coalescence.                                                           Week 10


The required texts for this course are:

        1. Crowe, C.T. “Multiphase Flow Handbook”. Taylor & Francis, Boca Raton, Fl. 2006.
        2. Brennen, C.E.”Fundamentals of Multiphase Flow”, Cambridge University Press, New York, 2005.
        3. Weber, M. E., Clift, R., Grace, J. R. “Bubbles, Drops, and Particles”, Dover Books, New York, NY. 2013.


Homework               20%        
Personal Project       40%
Midterm                  15%
         Final                        25%

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