Variable Order Modeling of Diffusive-convective Effects on the Oscillatory Flow Past a Sphere
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- 1 September 2008
- journal article
- research article
- Published by SAGE Publications in Journal of Vibration and Control
- Vol. 14 (9-10), 1659-1672
- https://doi.org/10.1177/1077546307087397
Abstract
This work advances our understanding of the drag force acting on a particle due to the oscillatory flow of a viscous fluid with finite Reynolds and Strouhal numbers. The drag force is is determined using the novel concept of variable order (VO) calculus, where the order of derivative can vary with the parameters and variables, according to the dynamics of the flow. Using the VO formulation we determine: (i) The region of validity of Tchen's equation for oscillatory flow, (ii) the region where the order of the derivative is fractional but constant, and (iii) the region where the strong non-linearity of the flow requires a variable order derivative to account for the increased complexity of the flow.Keywords
This publication has 14 references indexed in Scilit:
- A computational stream function method for two-dimensional incompressible viscous flowsInternational Journal for Numerical Methods in Engineering, 2005
- An experimental study on stationary history effects in high-frequency Stokes flowsJournal of Fluid Mechanics, 2004
- On the viscous motion of a small particle in a rotating cylinderJournal of Fluid Mechanics, 2002
- Application of Dynamic Fractional Differentiation to the Study of Oscillating Viscoelastic Medium With Cylindrical CavityJournal of Vibration and Acoustics, 2002
- Spherical Particle Motion in Harmonic Stokes FlowsAIAA Journal, 2001
- General solution of the particle momentum equation in unsteady Stokes flowsJournal of Fluid Mechanics, 1998
- On the equation for spherical-particle motion: effect of Reynolds and acceleration numbersJournal of Fluid Mechanics, 1998
- Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds numberJournal of Fluid Mechanics, 1992
- Equation of motion for a small rigid sphere in a nonuniform flowPhysics of Fluids, 1983
- III. On the motion of a sphere in a viscous liquidPhilosophical Transactions of the Royal Society of London. (A.), 1888