Publication Date


Document Type


First Advisor

Shelton, John (Professor)

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mechanical Engineering


Fluid dynamics--Mathematical models; Vortex-motion--Mathematical models


The lid-driven cavity is a canonical problem in the field of analytical and computational fluid dynamics, the system is comprised of a square domain of an incompressible fluid, where its upper lid has a specified velocity and the remaining wall boundaries are subjected to a fixed, no-slip, zero velocity constraints. There are numerous examples found in the literature that address the validation of the system's well known stable behavior, which includes a primary recirculating vortex, along with secondary corner vortices that are shown to be dependent on the Reynolds number. Additional literature has shown that when the system is extended, the velocity characteristics in the plane normal to this axis are symmetric along the axis parallel to the direction of flow. Determination of stability for these three-dimensional system can be defined as when the flow at the center of the cube along the vertical direction settles to a particular velocity over a given time period. It has been experimentally observed that as the Reynolds number increases to 3200 and 10000, the system velocity at this center point exhibits oscillatory unstable frequency behavior indicating there is a critical Reynolds number for where the flow characteristics transition from laminar to turbulent. Further studies have shown that two-dimensional system exhibits three-dimensional instability when perturbed by three-dimensional mathematical equations. Thus it is worth noting that in this study, Reynolds numbers of 100, 400, and 1000 will be evaluated to maintain stability and laminar flow. This transition point can be greatly affected due to the presence of particles of granular material acting as random perturbations in the system initially suspended in the domain and varying concentration. In this investigation, an open-source CFD software called OpenFOAM will be used to determine the effect of concentration of these suspended particles on the flow within a cavity and its stability. A Eulerian-Lagrangian approach is used here to describe the particle interaction and the primitive variables of the Navier-Stokes equations are used to solve for the liquid phase. The Lagrangian computational framework involves determination of various forces acting on the particle; including Hertzian contact from other interacting particles, Ergun-Wen drag and buoyancy. The details to be studied in this case will be the deviation of the velocity streamlines, the settling time, stability spectral frequency behavior and the velocity profile along the centerline of the system. The purpose of these studies and analyses will aid in the future findings of advantageous methodologies to determine how granular materials can be used to enhance desirable characteristics of fluid behaviors.


Advisors: John Shelton.||Committee members: Pradip Majumdar; Nicholas Pohlman.||Includes bibliographical references.||Includes illustrations.


viii, 70 pages




Northern Illinois University

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