Multiphase Flows for Aerospace Applications – Online Short Course 3 May 2027 - 26 May 2027 Online

CLASS 1 — Introduction to Multiphase Flows
Instructor: Suhas S. Jain | 2 Hours
This lecture establishes the fundamental physical and mathematical concepts required for the remainder of the course. Participants will be introduced to the definition and classification of multiphase flows, including gas–liquid, liquid–liquid, and fluid–particle systems involving droplets, bubbles, films, particles, and sprays. Representative aerospace applications will include aircraft icing, fuel injection and atomization, propulsion and combustion, particle-laden high-speed flows, shock–droplet and shock–particle interactions, and phase-change processes.

The lecture will introduce the physics of fluid interfaces, including surface tension, interfacial energy, the Young–Laplace pressure jump, and interfacial stress conditions. Important nondimensional parameters—including the Reynolds, Weber, Capillary, Ohnesorge, Bond/Eötvös, Stokes, and Mach numbers—will be discussed in the context of identifying dominant physical mechanisms. Canonical multiphase phenomena such as droplet and bubble deformation, breakup, coalescence, and interfacial instabilities will also be introduced. The session will conclude with an overview of governing conservation equations and the major approaches used to model multiphase flows, including sharp- and diffuse-interface formulations, interface-tracking and interface-capturing methods, and Eulerian and Lagrangian descriptions.

CLASS 2 — Diffuse-Interface Methods for Multiphase Flows
Instructor: Suhas S. Jain | 2 Hours
This lecture introduces the mathematical foundations, numerical formulation, and practical application of diffuse-interface methods for multiphase flows. The distinction between sharp- and diffuse-interface descriptions will first be established, followed by the mathematical representation of interfaces using phase indicators and order parameters. Free-energy-based approaches, phase-field formulations, and governing equations such as the Cahn–Hilliard and Allen–Cahn equations will be introduced together with their coupling to the Navier–Stokes equations.

Particular attention will be given to the representation of surface tension and interfacial stresses, interface thickness, numerical resolution, and the treatment of large density and viscosity contrasts. Conservative and non-conservative formulations will be compared, with emphasis on mass and momentum conservation. The lecture will also examine boundary conditions, wetting, interface curvature, breakup and coalescence, and the ability of diffuse-interface methods to naturally accommodate changes in interface topology. The advantages, limitations, and appropriate applications of these methods will be discussed through representative multiphase-flow examples.

CLASS 3 — Volume-of-Fluid Methods for Multiphase Flows
Instructor: Olivier Desjardins | 2 Hours
This lecture covers the fundamental concepts and practical numerical considerations associated with Volume-of-Fluid (VOF) methods, one of the most widely used approaches for simulating flows with deforming fluid interfaces. Participants will learn how interfaces are represented using volume fractions and how the volume-fraction field is transported through the computational domain. Geometric and algebraic VOF approaches will be discussed, with particular attention to interface reconstruction techniques such as piecewise-linear interface construction.

The lecture will address the calculation of interface normals and curvature, representation of surface tension, balanced-force formulations, and the origins and mitigation of spurious or parasitic currents. Conservation of mass and momentum, consistent transport schemes, and treatment of large density and viscosity ratios will be emphasized. Additional topics will include breakup and coalescence, adaptive mesh refinement, grid-resolution requirements, and the tradeoffs among numerical accuracy, robustness, and computational expense. Applications to droplets, liquid jets, atomization, and turbulent multiphase flows will illustrate the capabilities and limitations of modern VOF approaches.

CLASS 4 — Experimental Methods for Multiphase Flows: Low- and High-Speed Diagnostics
Instructor: Jacob McFarland | 2 Hours
This lecture introduces experimental techniques for studying multiphase flows across low- and high-speed regimes. Participants will examine experimental design, generation and characterization of droplets and particles, and practical considerations such as optical access, calibration, spatial and temporal resolution, and reproducibility. Low-speed diagnostics will include phase Doppler particle analysis (PDPA) for measurements of droplet size and velocity, together with other representative techniques for dispersed-phase characterization.

For high-speed multiphase flows, the lecture will discuss shadowgraphy and laser-induced fluorescence (LIF), focusing on what each method measures, how data are interpreted, and the challenges of rapidly evolving interfaces and dispersed phases. Examples will illustrate diagnostic selection, synchronization, measurement uncertainty, and complementary use of experimental methods to support physical interpretation and numerical-model validation.

CLASS 5 — Primary Atomization and Sprays
Instructor: Olivier Desjardins | 2 Hours
This lecture focuses on the physical processes governing primary atomization and the evolution of sprays in aerospace applications. Topics include liquid-jet and sheet instability, ligament formation, droplet breakup, and the development of fuel sprays. The roles of turbulent flow, combustion, and phase change will be considered in understanding spray formation and behavior in propulsion systems.

The lecture will connect high-fidelity simulation, predictive modeling, and experimental investigation of atomization and sprays. Participants will examine numerical representations of liquid interfaces and spray dynamics, modeling assumptions and limitations, and the types of experimental observations used to evaluate predictions. Representative examples will highlight the challenges of connecting interface-resolved physics to engineering-scale spray models.

CLASS 6 — Interactive Session: Low-Speed Multiphase Flows
Instructor: Jacob McFarland | 2 Hours
This interactive session brings together computational and experimental perspectives on low-speed multiphase flows. Participants will compare representative numerical approaches, discussing the differences in interface treatment, modeling assumptions, resolution requirements, and the information each method can provide. Illustrative example codes or results may be used where suitable.

Using representative experimental observations and simulations, the group will discuss how to compare quantities consistently, interpret discrepancies, and identify sources of numerical and measurement error. Sprays may serve as an example problem. The session will conclude with an open discussion of current scientific and practical challenges in predictive low-speed multiphase-flow modeling and measurement.

CLASS 7 — High-Speed Multiphase Flows: Droplet Breakup and Impingement
Instructor: Christoph Brehm | 2 Hours
This lecture examines high-speed multiphase-flow phenomena, with particular emphasis on droplet deformation, breakup, and impingement. Participants will consider the effects of compressibility, shocks, aerodynamic loading, relative phase motion, and surface interactions on droplet response. Relevant physical timescales and nondimensional parameters will be used to interpret the dominant regimes; phase-change effects may be discussed where relevant.

The lecture will integrate simulations, models, and experiments used to investigate high-speed droplets and dispersed phases. Topics include numerical treatment of compressible multiphase interactions, representation of breakup and impingement, experimental diagnostics, and tradeoffs between physical fidelity, computational cost, and model applicability. Aerospace examples will connect the underlying physics to practical flow conditions.

CLASS 8 — Interactive Session: High-Speed Multiphase-Flow Problems
Instructor: Christoph Brehm | 2 Hours
The final interactive session focuses on critical interpretation of high-speed multiphase-flow predictions. Participants will compare representative numerical methods and their assumptions, then examine computational results alongside experimental measurements and theoretical expectations. Example data, potentially including droplet-breakup test cases, may be used to explore agreement and differences among approaches.

Participants will discuss possible causes of discrepancies, including modeling approximations, numerical resolution, initial and boundary conditions, experimental uncertainty, and interpretation of observed quantities. Through guided discussion, they will propose ways to diagnose errors and improve comparisons, identify current challenges, and synthesize lessons from the course on connecting multiphase-flow physics, numerical modeling, and experimental evidence.

COURSE DELIVERY AND MATERIALS

• The course lectures will be delivered via Zoom. Access to the Zoom classroom will be provided to registrants near to the course start date.
• All sessions will be available on-demand within 1-2 days of the lecture. Once available, you can stream the replay video anytime, 24/7.
• All slides will be available for download after each lecture. No part of these materials may be reproduced, distributed, or transmitted, unless for course participants. All rights reserved.
• Between lectures during the course, the instructor(s) will be available via email for technical questions and comments.