Two-phase flow

Two-phase flow

Two-phase flow is a 2nd semester elective specialised course held at University of Ljubljana, Slovenia.


2. semester - University of Ljubljana, Slovenia


Prof. B. Šarler, Assist. Prof. M. Perpar

Course Points (ECTS)


Contact Information

University of Ljubljana, Slovenia

Course Overview

Module objective

The fundamental goal of this study course is to acquaint the students with the basic characteristics of two-phase flows, with a special emphasis on liquid-gas (vapour) systems. The students will gain the ability to clearly and logically decompose the scales of complex technical systems from the viewpoint of two-phase flow. The subject matter is extremely important in a wide palette of traditional energy and process engineering disciplines, as well as for the new multi-disciplinary technologies in environmental science and mechatronics.

Knowledge outcome

Upon the successful completion of study obligations, the students will be able to:

  • understand the transport characteristics of two-phase fluids, with a special emphasis on the flow regimes defined by the phase interface surface;
  • determine a corresponding mathematical system, closed up with the constitutive relations of state, mechanical and energy relations;
  • select the appropriate model to solve problems by using modern software packages, employed as standard tools in the industrial and developmental environment.

The knowledge acquired in this course will especially benefit the students in solving the problems related to designing systems and devices using fluids as the medium for the transfer of energy or matter, or as the carrier medium between contact surfaces. It can be used in a variety of applications related to heat, lubrication and new product design in the discipline of mechanical engineering.

The theoretical knowledge assimilated in the course will be useful for various research and development and practical purposes in the field of power engineering, process engineering, tribology, and especially for designing new structures.

Syllabus outline

  • Complex system: enforced, designed or created hierarchy, variable two-phase system structures; objective: to obtain the knowledge about separating scales and defining the target function in multifunctional systems with multiple scales.
  • Laws of continuum physics for single-phase, single-component systems from the viewpoint of two-phase flow: laws of conservation; mechanistic approach, energy approach. Microfluidics: the advantages of using microsystems. The problems of modeling microsystems with two-phase flow: determination of viscous shear stress, slip at the wall, surface tension.
  • Modeling two-phase flow – one-dimensional description: the model of homogeneous flow: transport equations, the friction factor; stratified flow model: pressure drop; drift flux model: the influence of gravity for negligible shear stresses.
  • Liquid and gas (vapour) systems: flow regimes, pressure drop, phase fraction, two-phase flow instability. Boiling. Condensation. Cavitation.
  • Gas and solid particle systems: flow regimes in transport by pipes for low concentrations of solid particles, slurry transport. Fluidization. Sedimentation.

Monitoring of student progress

  • case studies
  • study workshops
  • laboratory exercises
  • written examination


[1] G.B. Wallis, One-dimensional Two-phase Flow, McGraw-Hill 1969.
[2] G. Hetsroni, Handbook of Multiphase Systems, Hemisphere, 1982– Selected chapters.
[3] C. E. Brennen: Fundamentals of Multiphase Flow, Cambridge University Press, 2005– Selected chapters.
[4] Crowe, C.T.: Multiphase Flows with Droplets and Particles. CRC Press, Boca Raton, Fla, 1998.
[5] J.R. Thome, Engineering Data Book III, Wolverine, eBook.
[6] B. J. Azzopardi, Gas-Liquid Flows, Digital Library, Begell House, eBook.