Chongqing University of Technology

About: Chongqing University of Technology is a education organization based out in Chongqing, China. It is known for research contribution in the topics: Microstructure & Alloy. The organization has 5199 authors who have published 4205 publications receiving 35954 citations. The organization is also known as: Chongqing Institute of Technology.

Viscoplastic Flow of the MR Fluid in a Cylindrical Valve

Abstract: Bingham viscoplastic model is used to describe the constitutive behavior of Magnetorheological (MR) fluids subject to an applied magnetic field. Based on Navier-Stokes’ equation, a theoretical analysis of the effect of the applied magnetic field on the viscoplastic flow in a cylindrical valve is presented. The expressions for the velocity in viscoplastic flow are derived. The results indicate that the volumetric flow rate can be continuously adjusted by an external magnetic field. With the increase of the applied magnetic field the yield boundary gets closer to the two cylindrical surfaces, and the restriction of flow is increased. Introduction MR fluids are suspensions of micron-sized, magnetizable particles in a carrier fluid such as synthetic oil and silicone oil, which are regarded as the intelligent materials that respond to an applied magnetic field with a change in their rheological properties. Upon application of a magnetic field, the polarization between two induced dipoles causes the suspended particles in the MR fluids to form a chain-like microstructure aligned with the direction of the applied magnetic field. The magnetic chain structure restricts the movement of the MR fluids, thereby changing the rheological properties of the suspension. These fluids exhibit a viscoplastic behavior with yield strength. Thus the viscoplastic MR fluids have the properties of both viscosity and plasticity. Altering the strength of an applied magnetic field will precisely control the yield stress of the fluid. Based on the mechanical properties, these MR fluids can be used in brakes and clutches [1,2]. An MR valve is a device that uses the MR fluid flowing through a cylindrical orifice. In order to understand the flow behaviors and the yield characteristics of MR fluid in MR valve, in this paper, the viscoplastic flow of MR fluid in a cylindrical valve is investigated theoretically. Based on Navier-Stokes’ equation, the effect of the applied magnetic field on the viscoplastic flow of an MR fluid between two fixed cylinders is analyzed to locate the yield boundary that separates viscous flow and viscoplastic flow. The expressions for the velocity and the volumetric flow rate in viscoplastic flow are derived to provide a theoretical foundation for the design of MR valve. Rheological behavior of MR fluids In the absence of an applied magnetic field, MR fluids exhibit a Newtonian fluid behavior. Upon application of a magnetic field, the behavior of the controllable fluids is often represented by Bingham viscoplastic model. The flow is governed by Bingham’s equations [3]: Key Engineering Materials Online: 2004-10-15 ISSN: 1662-9795, Vols. 274-276, pp 969-974 doi:10.4028/www.scientific.net/KEM.274-276.969 © 2004 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific.net. (Semanticscholar.org-13/03/20,17:14:19) γ η τ σ & + = B rz for B rz τ σ ≥ (1) 0 = γ& for B rz τ σ < (2) where rz σ is the shear stress, η is the viscosity of MR fluid , and γ& is the fluid shear strain rate. rz σ is the absolute value of rz σ , and B τ is the yield stress developed in response to an applied magnetic field. Bingham model shows that without the applied magnetic field the yield stress of material equals zero, and MR fluid exhibits the characteristics of a conventional Newtonian fluid. When the magnetic field is applied, MR fluid exhibits the characteristics of Bingham viscoplasticity. For the flow field at B rz τ σ ≥ , MR fluid flows with a viscosity η . For the flow field at B rz τ σ < , the MR material behaves like a solid. Operating principle The operational principle is that the yield stress of MR fluids in the valve can be controlled by application of an external magnetic field. It can be classified as the constant flow valve in which the difference in pressure through the valve can be continuously controlled when the volumetric flow rate is constant, and the constant pressure valve in which the volumetric flow rate through the valve can be precisely controlled when the difference in pressure is constant. The characteristics of the MR valve are that the inner and outer cylinders don’t move in relation to each other, and the annular gap is constant. When the MR fluid flows through the gap, altering the strength of the magnetic field permits continuous control of the valve’s volumetric flow rate or the pressure drop. Flow analysis In order to derive the equation of the fluid flow between two cylinders, the following assumptions are given: the fluid is incompressible and experiences steady-state flow. There is no flow in circumferential and radial direction. The gradient of the pressure in radial direction is zero. Fig.1 shows the axial flow of an MR fluid in the annular gap between two fixed cylinders. In the cylindrical coordinate system ( z r , ,θ ), assume the distribution of the velocity of the flow is: Outer cylinder Inner cylinder MR fluid Coil-assembly Magnetic flux