1 Copyright © 2012 by ASME Proceedings IMECE2012 2012 ASME International Mechanical Engineering Congress and Exposition November 9-15, 2012, Houston, Texas, USA IMECE2012-85404 DYNAMICS OF PLUG ZONES IN ELASTO-PLASTIC UNSTEADY FLOW IN CIRCULAR TUBES Mario F. Letelier Department of Mechanical Engineering University of Santiago of Chile mario.letelier@usach.cl Dennis A. Siginer Department of Mechanical Engineering University of Santiago of Chile dsiginer@hotmail.com Juan L. Ahumada Department of Mechanical Engineering University of Santiago of Chile jl.ahumada.v@gmail.com Juan S. Stockle Department of Mechanical Engineering University of Santiago of Chile Juan.stockle@usach.cl ABSTRACT Purely oscillatory flow of an elasto-plastic fluid in round tubes is analyzed. A combined linear Maxwell-Bingham model is used to characterize the fluid behavior. INTRODUCTION A mathematical model is presented to analyze laminar parallel unsteady flow in round tubes when the fluid embodies both elastic and plastic properties. In most applications of magnetically induced plasticity such as dampers [1, 2], a base Newtonian fluid is seeded with iron particles that, as a whole, reacts to imposed magnetic fields and develops yield stress that depends both on the iron concentration and on the field strength [1]. We assume that the base fluid is viscoelastic, a condition that phenomenologically should increase the variety of responses when the flowing fluid is subjected to magnetic effects. In this analysis elastic effects are represented by means of a single mode linear Maxwell model with relaxation time λ. When λ=0 the standard case of a Newtonian base fluid is recovered. This study may be useful in the design of damping devices in which it is required to program piston displacements in order to damp out big and sudden loads. In this case it is assumed that the damper`s base fluid is viscoelastic and that plasticity is induced via magnetorheological stresses. In damping systems it is necessary to control the damping rate, which requires the determination of the plug zones in the flow to get accurate computations. The analysis shows that the interplay of elasticity and plasticity leads to unusual patterns of flows, in which more than one solid zone may exist. Criteria for determining plug radii when both elasticity and plasticity are present are presented. The required consistency of the equation of motion and constitutive equation is also analyzed, since in oscillatory flow of plastic fluids inconsistencies may arise when the yield stress and the oscillatory pressure gradient are out of phase. The analytical procedure herein employed is an extension of previous work of the authors [3, 4]. Analytical expressions for the velocity field and for the rate of flow are obtained for the specific case of a purely oscillatory flow, which is a special case of a wide family of flows that can be studied with this procedure. The selected case has some characteristics that make it relevant, such as the nature of plug zones when the flow reverses due to the imposed oscillating pressure gradient. ANALYSIS Under the assumption of laminar, parallel, incompressible and unsteady flow in a circular tube, the equation of motion, in terms of stress, is given by (1) in which w is the axial velocity, t is time, (r, z) are cylindrical coordinates, ρ is the density and P is the piezometric pressure. The Maxwell-Bingham fluid can be described by a combined linear model,