Date of Award

Spring 2014

Degree Type


Degree Name

Master of Science (MS)


Aeronautics and Astronautics

First Advisor

Tom I-P Shih

Committee Member 1

Gregory Blaisdell

Committee Member 2

Li Qiao


Flows with particles play an important role in a number of engineering applications. These include trajectories of droplets in sprays in fuel-injected-reciprocating-piston and gas-turbine engines, erosion of materials due to particle impact on a surface, and deposition of materials on surfaces by impinging droplets or particles that could solidify or bond on impact. For these applications, it is important to understand the forces that act on the particles so that their trajectories could be predicted.

Considerable work has been done on understanding the forces acting on spherical particles, where the Reynolds numbers (Rep ) based on the particle diameter and the relative speed between the particle and the fluid is less than unity. When Rep is larger than unity and when the particle is accelerating or decelerating, the added-mass effect and the Basset forces are not well understood.

In this study, time-accurate numerical simulations were performed to study laminar incompressible flow induced by a single non-rotating rigid spherical particle that is accelerated or decelerated at a constant rate in an initially stagnant fluid, where the unsteady flow about the spherical particle is resolved. The Rep studied range from 0.01 to 100, and the acceleration number (Ac ), where A c is the square of the relative velocity between the particle and the fluid divided by the acceleration times the particle diameter studied was in the range 2.13×-7 < |Ac |< 21337. Results obtained show the added mass effect for Rep up to 100 has the same functional form as those based on potential theory where the Rep is infinite and creeping flow where Rep is less than unity. The Basset force, however, differs considerably from those under creeping flow conditions and depends on Rep and the acceleration number (Ac ). A model was developed to provide the magnitude of the added-mass effect and the Basset force in the range of Rep and Ac studied. Results obtained also show the effect of unsteadiness to become negligible whenAc reaches 80.