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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, February 7, 2020 - 12:00 to 12:50

Location:

STAG 160

Event Link:

Guest Speaker:

Institution:

OSU Mechanical Engineering

Abstract:

Particle-laden fluid flows, wherein a large number of small size particles are dispersed in a fluid, often undergoing turbulent motions, are widely encountered in nature, biological and industrial applications. These flows are commonly modeled using an Euler-Lagrange (EL) approach wherein the governing equations of the fluid phase are solved in an Eulerian fixed framework. The dynamics of the particles is modeled using Newton's second law of motion by tracking their centroids as Lagrangian point-particles (PP). This approach requires closures to estimate various fluid forces, such as drag, lift, added mass etc., acting on the particles. These closures are based on the ‘undisturbed velocity’ field, that is by definition, the field that is not influenced by the particles. However, when the two phases are two-way coupled, particles disturb the fluid phase, and this ‘undisturbed’ velocity is no longer available. The unavoidable use of such a disturbed velocity filed in particle force calculations can result in erroneous predictions by as much as 100%.

In this talk, using simple analytical and empirical expressions, a novel correction scheme is developed to recover the undisturbed velocity field at the location of particles from the available disturbed field. This model and the developed framework are general and applicable to range of flows that are unbounded or bounded by the no-slip walls. The model is first applied to some canonical test cases, for which analytical solutions are available. Then, its effect on a particle-laden turbulent channel flow is discussed against available experimental data. Significant improvements are achieved that enable the model to be potentially substituted for the current expensive particle-resolved techniques. The developed approach has significant implications on a range of particulate flows such as spray atomization, coal combustion, sediment transport, cloud formation, and cavitating bubbly flows.