Computers & Fluids 63 (2012) 128–134
Contents lists available at SciVerse ScienceDirect
Computers & Fluids j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p fl u i d
Two-dimensional CFD simulation of magnetorheological fluid between two fixed parallel plates applied external magnetic field Engin Gedik a,⇑, Hüseyin Kurt b, Ziyaddin Recebli a, Corneliu Balan c a
Faculty of Technology, Karabuk University, TR-78050 Karabuk, Turkey Faculty of Engineering, Karabuk University, TR-78050 Karabuk, Turkey c Faculty of Energetica, University Politehnica of Bucharest, RO-060042 Bucharest, Romania b
a r t i c l e
i n f o
Article history: Received 5 May 2011 Received in revised form 21 March 2012 Accepted 10 April 2012 Available online 21 April 2012 Keywords: Magnetorheological fluid Valve mode CFD Magnetic field effect
a b s t r a c t This paper presents a two-dimensional Computational Fluid Dynamics (CFDs) simulation for the steady, laminar flow of an incompressible magnetorheological (MR) fluid between two fixed parallel plates in the presence of a uniform magnetic field. The purpose of this study is to develop a numerical tool that is able to simulate MR fluids flow in valve mode and determine B0, applied magnetic field effect on flow velocities and pressure distributions. A uniform transverse external magnetic field is applied perpendicular to the flow direction. The equations governing the steady flow of an incompressible MR fluid are implemented in the commercial code Ansys 14.0 Fluent which is a flexible CFD code based on finite volume approach. The governing differential equations describing the flow between parallel plates under magnetic field are solved numerically by using Fluent MHD module based on solving the magnetic induction equation method. The external applied magnetic field, B0, takes values between 0 and 1.5 T with 0.5 T step size, was applied to determine B0 effects on fluid flow. The numerical solutions for velocity and pressure distributions were obtained for different magnetic fields. It was observed that increase in B0 leads to decrease flow velocity. Results, obtained from numerical study was plotted graphically and disgusted in the present paper. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.
1. Introduction MR fluids based on metal micro-particles in a carrier liquid are controllable fluids which can be referred to the family of smart materials [1]. The metal particles of these fluids are usually made of carbonyl iron, powder iron, or iron/cobalt alloys to achieve a high magnetic saturation and water, some hydrocarbons, glycol and silicone oil are generally employed as the carrier liquid depending upon the requirements for the application to be considered [2,3]. Under a normal state, MR fluid behaves like an ordinary Newtonian fluid with a given viscosity. When exposed the magnetic field to fluid the metal particles are guided by the magnetic field to form a chain like structure and it becomes semi-solid state. The field-induced transition of these smart fluids from the liquid to a semi-solid state is fast and reversible [3]. This chain-like structure restricts the motion of the fluid and therefore changes the rheological behavior of the fluid [2–7]. The field-dependent rheological changes in MR fluids are primarily observed as a significant increase in the yield shear stress of the fluids, which can be continuously controlled by the intensity of applied magnetic field [8]. Interest in MR fluids arises from their ability to provide simple, quiet, rapid-response ⇑ Corresponding author. Tel.: +90 370 4338200; fax: +90 370 4338204. E-mail address:
[email protected] (E. Gedik).
interfaces between electronic controls and mechanical systems. Those MR fluids, which have the potential to change radically the way electromechanical devices are designed and operated, has long been recognized [9]. MR fluid technology has been used in various engineering applications such as shock absorbers, clutches, brakes, polishing devices, actuators, hydraulic valves, exercise equipment, seismic dampers [2,6] and military suspension systems [1,3,10]. These fluids are usually applied in three modes [2,10]. First one is MR fluid operating in valve mode, with fixed magnetic poles, may be appropriate for hydraulic controls, servo valves, dampers, and shock absorbers. Chooi and Oyadiji [11] have studied design, modeling and testing of MR dampers using analytical flow solutions with valve mode. Grunwald and Olabi [4] have studied experimentally design and built of MR valve and orifice. They have also studied a parametrical analysis with magnetic simulations of MR valve and orifice. Carlson and Spencer [12] have studied MR fluid (MRF) dampers for semi-active seismic control. Milecki [13] described and studied a semi-active controllable fluid damper. The damper employs a MR fluid that changes its properties in the presence of a magnetic field. The direct-shear mode with a moving pole, in turn, would be suitable for clutches and brakes, chucking/locking devices, dampers, breakaway devices and structural composites is the second. Based on the particular characteristic of a MR fluid, a rapid, reversible
0045-7930/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compfluid.2012.04.011
E. Gedik et al. / Computers & Fluids 63 (2012) 128–134
129
Nomenclature B B0 b E J V P D H q x
total magnetic field (T) applied external magnetic field (T) induced magnetic field (T) electrical field intensity vector (V/m) electrical current density vector (A/m2) velocity vector (m/s) pressure gradient (Pa) electric induction field (C/m2) magnetic induction field (A/m) electric charge density (C/m3) coordinate (m)
and dramatic change in its rheological properties produced by the application of an external magnetic field, a simple disk type MR fluid damper operating in shear flow mode was studied by Zhu [14]. A performance evaluation of an automotive MR brake design with a sliding mode controller was investigated by Park et al. [15]. Li and Du [16] have designed and fabricated a new MR brake prototype. The rheological properties of MR fluids, in particular the dynamic yield stress, were experimentally investigated based on a Bingham plastic model. The working principles of the MR brake were analyzed and discussed in the paper. Sukhwani and Hirani [17] have studied high-speed MR brakes. The third one is squeeze mode which can be used in some small-amplitude vibration dampers applications. Zhang et al [18] has investigated theoretically and experimentally squeezestrengthen effect in MR fluids. Yan et al. [19] have studied MR fluids on glass polishing technology. Jang et al. [20] has proposed a new behavioral model for MR fluid under a magnetic field using Lekner summation method. The resulting stress functions of the proposed model were transformed rapidly into convergent functions using the Lekner summation method. Finally, the characteristics of the stiffened MR fluid under a magnetic field were investigated using the transformed functions. Flow of a MR fluid through different types of porous media was investigated both theoretically and experimentally by Kuzhir et al. [21]. Bajkowski et al. [22] has studied a lumped mass model for a damper filled with a MR fluid. Frictional and temperature effects were described, analyzed and simulated numerically in their papers. Balan et al. [23] has studied experimental investigations and rheological characterizations in magnetic and electric fields of liquids based on water in crude oils emulsions, added with ferrofluids. Recebli and Kurt [24] have studied analytically steady two-phase fluid flows under the effects of magnetic and electrical fields in circular pipes. The unsteady flow of two phase fluid flows in circular pipes presence of magnetic and electrical field has also been investigated numerically in our previous work [25]. In this paper, we have investigated laminar flow of an incompressible MR fluid between two fixed parallel plates in the presence of a uniform magnetic field applied perpendicularly to the flow direction. The MR fluid based on iron micro-particles in a carrier liquid was investigated numerically by using Fluent MHD module based on magnetic induction equation solver method. The magnetic field induction, B0, take values between 0 and 1.5 T with 0.5 T step size, was applied externally in order to determine magnetic field effects on fluid flow. Steady, laminar, incompressible MR fluid flow was investigated by using valve mode which is described in details at Section 3. By using this mode, the problem geometry was designed and created in Gambit 2.3.16 program, and then it was imported the Ansys 14.0 Fluent for two-dimensional numerical computations. The numerical solutions for velocity and pressure distributions were obtained for different magnetic
y t
coordinate (m) time (s) dynamic viscosity (kg/ms) kinematic viscosity (m2/s) electric permittivity (F/m) magnetic permeability (H/m) density (kg/m3) electrical conductivity (1/X m) shear stress (Pa) shear rate (1/s)
g m e0 le q r s c
fields values. It was observed that increase in B0 leads to increase yield stress and consequently decrease of flow velocity. 2. Rheological behaviors of MR fluids Rheology has been properly defined as the study of the flow and deformation of materials, with special emphasis being usually placed on the former [26]. Viscosity is the most important physical property of fluids. There are two ways to express the viscosity. They are either dynamic viscosity or kinematic viscosity. Dynamic viscosity is defined by:
g¼
s c
ð2:1Þ
where s is shear stress (N/mm2) and c is share rate (1/s). Kinematic viscosity is defined by:
m¼
g q
ð2:2Þ
where q is density (kg/m3). Fluids obeying Newton’s law, where the value of g is constant, are known as Newtonian fluids. If g is constant, the shear stress is linearly dependent on velocity gradient. Fluids in which the value of g is not constant are known as non-Newtonian fluids. A Newtonian fluid is one for which the viscosity although varying with temperature and pressure does not vary with deformation rate or time; nor does such a liquid display any elastic properties. A non-Newtonian fluid is one whose flow curve (shear stress versus shear rate) is nonlinear or does not pass through the origin, i.e. where the apparent viscosity, shear stress divided by shear rate,
Fig. 1. Types of time-independent flow behavior.
130
E. Gedik et al. / Computers & Fluids 63 (2012) 128–134
Fig. 3. MR fluid flow between two parallel plates.
Fig. 2. Behavior of an idealized, Bingham model, MR fluid in the presence of an applied magnetic field B as a function of shear rate.
is not constant at a given temperature and pressure but is dependent on flow conditions such as flow geometry and shear rate [27]. Typical relationships between shear rate and shear stress with flow curves on linear scales for various types of fluid behavior are shown in Fig. 1. The rheological properties of smart controllable fluids such as electro rheological and MR fluids depend on concentration and density of particles, particle size and shape distribution, properties of the carrier fluid, additional additives, applied field, temperature and other factors [28]. MR Fluids are a class of smart materials whose rheological properties (e.g. viscosity) may be rapidly varied by applying a magnetic field [29]. The essential feature of the MR fluids is that they can reversibly change their states from a Newtonian fluid to a semi-solid or even a solid with controllable dynamic yield stress within a few milliseconds, when they are subjected to a controlled magnetic field [30,31]. Normally, in the field-off state, are liquid with a viscosity 0.1–1 Pa s. However, when a magnetic field is applied, the soft magnetic particles acquire a dipole moment and align with the external field to form fibrous columns or aggregates. These columns must be deformed and broken for the suspension to flow giving rise to a yield stress that is a function of the magnetic flux density [32–34]. In steady state rheology, this type of flow is commonly modeled as a Bingham fluid [35–41] with a magnetic-field dependent yield stress s0(B),
sðc; BÞ ¼ s0 ðBÞ þ gp c for s > s0
ð2:3Þ
c ¼ 0 for s > s0
ð2:4Þ
where s is the shear stress, gp is the plastic viscosity, and c is the shear rate. The behavior of MR fluid is summarized by the graph of s versus c shown in Fig. 2. 3. Description of the problem Let us consider the problem of a steady, laminar flow of a MR fluid between two fixed parallel plates in the xy-plane along the x-direction, see Fig. 3. MR fluids can be used in three principal modes of operation: valve mode (pressure driven flow), direct shear mode, and squeeze mode. In valve mode, the two magnetic poles are fixed, and a pressurized flow of MR fluid moves between them as illustrated in Fig. 4. Here, MR fluid flows through a flow channel and a magnetic field is applied transverse to the flow direction. The yield stress that develops in the fluid establishes a pressure threshold for any
Fig. 4. Valve modes for MR fluids [36].
fluid flow. Varying the magnetic field allows one to vary this pressure threshold, thus creating a controllable and proportionate valve mechanism without the need for moving mechanical parts. Examples of valve mode devices include servo-valves, dampers, shock absorbers and actuators [36]. Typically, in these devices, a piston moves back and forth in a tubular housing that is filled with MR fluid. The MR fluid is forced to pass through an orifice in or around the piston. The pressure drop developed in such devices based on valve mode is generally assumed to result from the sum of a viscous component DPg and a field dependent induced yield stress component DPs. This pressure drop may be approximated by [42,43]:
DP ¼ DPg þ DPs ðBÞ ¼
12g2g csy ðBÞL þ g g3w
ð3:1Þ
where L, g and w are the length, gap and width of the flow channel between the fixed poles respectively, Q is the volumetric flow rate, g is the viscosity with no applied field and sy is the yield stress developed in response to an applied field B. The parameter c is a function of the flow velocity profile and has a value ranging from a minimum value of 2 (for DPs/DPg less than 1) to a maximum value of 3 (for DPs/DPg greater than 100) [44]. The fundamental equations governing the steady motion of an incompressible MR fluid under magnetic field between two parallel plates are:
rV ¼0 @V þ ðV rÞV ¼ rP þ gDV þ ½J B @t
q
ð3:2Þ ð3:3Þ
where q is the density, V the velocity vector, P the pressure, g is the viscosity, J the current density, B the total magnetic field, B = B0 + b, B0 and b the applied and induced magnetic field respectively. The two non-conducting plates are located at the y = ±5 mm planes and extend from x = 0 to 300 mm. Both upper and lower plates are stationary. The fluid flow between two plates under the influence of constant pressure gradient dP/dx is in the x
E. Gedik et al. / Computers & Fluids 63 (2012) 128–134
131
is the electric charge density. The induction fields H and D are defined as:
H¼
1
l
B
D ¼ eE
Fig. 5. Sketch of the problem.
direction. The model geometry has been separated three zones, fluid upstream, magnetic zone and fluid downstream respectively. The magnetic field has been applied on middle part (c part in Fig. 5) of the geometry throughout the y direction as shown in Fig. 5. The magnetic field induction, B0, take values between 0 and 1.5 T with 0.5 T step size, have been applied to determine B0 effects on MR fluid flow. The fluid properties used in numerical computations are as follows: q = 2380 kg/m3, g = 0.042 kg/ms, le = 4 h/m, P = 500 Pa. The coupling between the fluid flow field and the magnetic field can be understood on the basis of two fundamental effects: the induction of electric current due to the movement of conducting material in a magnetic field, and the effect of Lorentz force as a result of electric current and magnetic field interaction. In general, the induced electric current and the Lorentz force tend to oppose the mechanisms that create them. Movements that lead to electromagnetic induction are therefore systematically broken by the resulting Lorentz force. Electric induction can also occur in the presence of a time-varying magnetic field. Electromagnetic fields are described by Maxwell’s equations:
rB¼0
ð3:4Þ
r B ¼ le J
ð3:5Þ
ð3:9Þ ð3:10Þ
where l and e are the magnetic permeability and the electric permittivity, respectively. For sufficiently conducting media such as liquid metals, the electric charge density q and the displacement current @D are customarily neglected. While studying the interaction @t between flow field and electromagnetic field, it is critical to know the current density J due to induction. Generally, two approaches may be used to evaluate the current density. One is through the solution of a magnetic induction equation; the other is through solving an electric potential equation [45]. In this paper we used to magnetic induction equation in order to solve the problem. In the next section, we present the numerical method used to solve the above problem. 4. Numerical procedure In this paper, we have studied numerically flow of a MR fluid between two fixed parallel plates. The solution of the governing equations describing the flow is solved numerically under the initial and boundary conditions by using Fluent MHD module based on the magnetic induction equation method. Second order upwind was selected to solve momentum equation, Bx and By magnetic induction in the MHD module. Constant material physical properties were defined. The magnetic induction equation is derived from Ohm’s law and Maxwell equations. The equation provides the coupling between the flow field and the magnetic field. In general, Ohm’s law that defines the current density is given by;
J ¼ rE
ð4:1Þ
where r is the electrical conductivity of media. For fluid velocity field V in a magnetic field B, Ohm’s law takes the form:
@B rE¼ @t
ð3:6Þ
rD¼q
ð3:7Þ
From Ohm’s law and Maxwell’s equation, the induction equation can be derived as:
ð3:8Þ
@B 1 2 þ ðV rÞB ¼ r B þ ðB rÞV @t lr
rH¼Jþ
@D @t
where B (Tesla) and E (V/m) are the magnetic and electric fields respectively, le is the magnetic permeability, H and D are the induction fields for the magnetic and electric fields respectively, q (C/m3)
J ¼ r½E þ V B
ð4:2Þ
ð4:3Þ
The flow is considered steady, laminar, incompressible, developed in a 2D planar configuration, the parallel plate geometry being created with the pre-processor Gambit. A mesh converged
Fig. 6. Mesh converged study.
132
E. Gedik et al. / Computers & Fluids 63 (2012) 128–134
Table 1 Mesh parameters.
5. Results and discussion
Mesh no.
Mesh size
Element number
Velocity (m/s)
Mesh 1 Mesh 2 Mesh 3 Mesh 4 Mesh 5
1.5 mm 1 mm 0.5 mm 0.25 mm 0.15 mm
1386 3000 12,000 48,000 133,866
0.3640 0.3725 0.3732 0.3734 0.3734
study has been done to ensure that the velocity at the center of two parallel plates under B0 = 0 T situation is converged. Several mesh size of the geometry is performed. The velocity responses for various mesh size are shown in Fig. 6 with course and finer mesh. The analysis is run with ever increasing mesh density until there is no significant difference from one run to another. It shows that the velocity is increasing for smaller mesh size and became almost constant after mesh size 0.25 mm. Mesh parameters used for the mesh converged study is given Table 1. In this simulation, we used a standard element size of 0.25 mm (Mesh 4 in Table 1) in order to perform the basic meshing procedure. The geometry is considered to be planar, 48,000 hexahedra type element and 98,646 nodes were used for the solution. The problem was modeled numerically using CFD Ansys 14.0 Fluent commercial code.
In this paper, the flow of MR fluid between two fixed parallel plates under the influence of magnetic field was examined at valve mode. Solution of the continuity, momentum which includes electromagnetic force equations was conducted with CFD package program, Ansys 14.0 Fluent. The Fluent program employs finite volumes approach for the solution of selected equations. Fluent MHD Module and magnetic induction method was utilized to solve the problem. Results obtained from solutions were plotted graphically and discussed below. Results were obtained for two different flow models in this study. These are: the situation with no magnetic field (B0 = 0 T) is for Newtonian flow and for non-Newtonian flow in the existence of magnetic field. Magnetic field was applied in area c on the plate in order to determine the behavior of MR fluid under the influence of magnetic field. Mean velocity profiles of flow in areas l(2), l(1), l(0), l(+1) and l(+2) was drawn and given in Fig. 7. The velocity profile is symmetric with respect to the mid-plane because the flow between parallel fixed plates is steady. In this figure, l(2) and l(+2) represent the lines in areas where magnetic field is not applied, whereas l(1), l(0), l(+1) represent the entry, middle and exit parts of the area which magnetic field was applied respectively. Maximum velocity value reached on each line
Fig. 7. Velocity profiles of l(2), l(1), l(0), l(+1) and l(+2).
E. Gedik et al. / Computers & Fluids 63 (2012) 128–134
133
Fig. 8. Contours of velocity magnitudes for different B values.
Fig. 10. Velocity distributions along the flow.
Fig. 9. Static pressure distributions for B = 0, 0.5, 1, 1.5 T.
at the center of plate (y = 0.005 m) has been obtained as 0.373 m/s. On the other hand, depending on increasing magnetic field, the decrease in velocity can be clearly seen from the figure. In this figure, maximum velocity values calculated in l(2), l(1), l(0), l(+1) and l(+2) areas are 0.307, 0.295, 0.293, 0.278 and 0.303 m/s respectively at B0 = 0.5 T situation. Velocity values at the same points turned out to be 0.176, 0.160, 0.143, 0.138, and 0.174 m/s for B0 = 1 T situation; and 0.098, 0.086, 0.075, 0.073, and 0.098 m/s for B0 = 1.5 T situation. The increase of magnetic field strength caused decrease in velocity values of flow. At all values of magnetic field, the largest decrease in velocity became at l(+1) point in the area c. Due to the impact of magnetic field strength in the area c, small decreases in flow velocity occurred in other areas as well (a, b, d, e). In Fig. 8 the contour graphs of mean velocity values of Newtonian flow (B0 = 0 T) and non-Newtonian flow at increasing B0 values up to 1.5 T can be seen. As it can be clearly seen from the figure, the increase in magnetic field strength leads to decrease of flow velocity values. Maximum velocity decreases for non-Newtonian flow was found as 0.073 m/s at B0 = 1.5 T; 0.14 m/s at
B0 = 1 T; and 0.28 m/s at B0 = 0.5 T. In Newtonian flow situation, the flow preserved its velocity value as 0.373 m/s throughout the plate. A constant pressure gradient, dP/dx was applied in the x-direction. In Fig. 9 static pressure distribution is shown for different magnetic field values. While the pressure drop was changing linearly at B0 = 0 T situation, it decreases suddenly in the area where magnetic field was applied. As it can be seen from the figure, the pressure drop changes depend on the increase in the magnetic field. The largest decrease in pressure occurred at B0 = 1.5 T situation. The pressure drop is changed from 350 Pa to 120 Pa on the magnetic field zone and the pressure curve of the flow which is away from the applied magnetic field zone becomes linear again. Fig. 10 provides the mean velocity distributions that occurred throughout the plate at the center of plates (x = 0–0.3 m y = 0.005 m) so that the velocity changes along the flow with and without magnetic field can be clearly seen. In this figure the velocity value was found as 0.373 m/s for B0 = 0 T, whereas in non-Newtonian fluid flow model velocity values decrease depending on the applied magnetic field. These decreases were larger in the area where magnetic field was applied, whereas they were smaller in the areas where magnetic field was not applied. In area c, where magnetic field was applied, the decrease in velocity values becomes 25.4%, 63.4% and 80.6% at B0 = 0.5, 1 and 1.5 T respectively.
134
E. Gedik et al. / Computers & Fluids 63 (2012) 128–134
6. Conclusion In this study, the flow of MR fluid between two fixed parallel plates under the influence of magnetic field has been examined numerically using CFD code. Magnetic field was applied perpendicular to the flow. The flow was steady, laminar, viscous and incompressible. The fluid flow between two plates under the influence of constant pressure gradient dP/dx is in the x direction. In the present study, analysis were done and compared for two different flow models of MR fluid, namely Newtonian (without magnetic field) and non-Newtonian (under magnetic field). Analysis for non-Newtonian fluid flow was conducted applying magnetic induction equation method in Fluent MHD module. From the results of this analysis, various plots were obtained and presented in the charts taking into consideration of flow velocity and pressure distributions. In addition to that, the study exhibits the rheological behavior and magnetic characteristics of MR fluid flow in pressure driven flow mode. As a result, it was observed that the magnetic field applied to MR flow decreases its flow velocity depending on the increase of magnetic field. Such decreases occurred as 25.4%, 63.4%, and 80.6% at B0 = 0.5, 1 and 1.5 T situations respectively. It is found that the electromagnetic force is affecting the MR fluid flows and the magnetic field can give us to flow control ability of MR Fluids which needed operating process at valve mode. From our point of view, the presented study can be effectively used for computer simulation of MR fluids. In this present implementation, the method is limited to the simulation of steady, laminar flows. It should be pointed out that the CFD simulation described in this work can represent a useful starting point to investigate more complex problems, such as, three-dimensional unsteady flows. For this, the authors recently extended the current study to investigate both electrical and magnetic field effect on fluid flow in cylindrical pipe [46]. Acknowledgment The authors would like to thank the Scientific and Technological _ Research Council of Turkey (TUBITAK) for providing the financial supports for this study under the 110M030 project. References [1] Mazlan SA, Ekreem NB, Olabi AG. An investigation of the behavior of magnetorheological fluids in compression mode. J Mater Process Technol 2008;201:780–5. [2] Olabi AG, Grunwald A. Design and application of magneto-rheological fluid. Mater Des 2007;28:2658–64. [3] Engin T, Evrensel C, Gordaninejad F. Numerical simulation of laminar flow of water-based magneto-rheological fluids in micro tubes with wall roughness effect. Int Commun Heat Mass Transfer 2005;32:1016–25. [4] Grunwald A, Olabi AG. Design of magneto-rheological (MR) valve. Sensors Actuat A 2008;148:211–23. [5] Carlson JD, Catanzarite DM, Clair KA. Commercial magneto-rheological fluid devices. In: 5th Int conf on electro-rheological, magneto-rheological susp and associated tech, Sheffield, 10–14 July 1995. [6] Brigadnov IA, Dorfmann A. Mathematical modeling of magnetorheological fluids. Continuum Mech Thermodynam 2005;17:29–42. [7] He JM, Huang J. Magnetorheological fluids and their properties. Int J Modern Phys B 2005;19:593–6. [8] Hong SR, Wereley NM, Choi YT, Choi SB. Analytical and experimental validation of a nondimensional Bingham model for mixed-mode magnetorheological dampers. J Sound Vib 2008;312:399–417. [9] Laun HM, Gabriel C, Schmidt G. Primary and secondary normal stress differences of a magnetorheological fluid (MRF) up to magnetic flux densities of 1 T. J Non-Newtonian Fluid Mech 2008;148:47–56. [10] http://www.lord.com/Products-and-Solutions/Magneto-Rheological-(MR).xml. [11] Chooi WW, Oyadiji SO. Design, modelling and testing of magnetorheological (MR) dampers using analytical flow solutions. Comput Struct 2008;86:473–82.
[12] Carlson JD, Spencer BF. Magneto-rheological fluid dampers for semi-active seismic control. In: The proceedings of the 3rd int conf on motion and vib cont, Chiba Japan, September 1–6 1996. p. 35–40. [13] Milecki A. Investigation and control of magneto-rheological fluid dampers. Int J Mach Tools Manuf 2001;41:379–91. [14] Zhu C. A disk-type magneto-rheological fluid damper for rotor system vibration control. J Sound Vib 2005;283:1051–69. [15] Park ED, Stoikov LF, Suleman LA. A performance evaluation of an automotive magnetorheological brake design with a sliding mode controller. Mechatronics 2006;16:405–16. [16] Li WH, Du H. Design and experimental evaluation of a magnetorheological brake. Int J Adv Manuf Technol 2003;21:508–15. [17] Sukhwani VK, Hirani H. Design, development, and performance evaluation of high-speed magnetorheological brakes. Proc Inst Mech Eng, Part L: J Mater Des Appl 2008;222:73–82. [18] Zhang XZ, Gong XL, Zhang PQ. Study on the mechanism of the squeezestrengthen effect in magnetorheological fluids. J Appl Phys 2004;96:4. [19] Yan Y, Boseon K, Shiguo H, Xing C. Glass polishing technology using MR fluids. J Rare Earths 2007;25:367–9. [20] Jang KJ, Seok BK, Lee MSJ. Behavioral model for magnetorheological fluid under a magnetic field using Lekner summation method. J Magn Magn Mater 2009;321:1167–76. [21] Kuzhir P, Bossis G, Bashtovoi V, Volkova O. Flow of magnetorheological fluid through porous media. Eur J Mech B/Fluids 2003;22:331–43. [22] Bajkowski J, Nachman J, Shillor M, Sofonea M. A model for a magnetorheological damper. Math Comput Model 2008;48:56–68. [23] Balan C, Broboana D, Gheorghiu E, Vekas L. Rheological characterization of complex fluids in electro-magnetic fields. J Non-Newtonian Fluid Mech 2008;154:22–30. [24] Recebli Z, Kurt H. Two-phase steady flow along a horizontal glass pipe in the presence of the magnetic and electrical fields. Int J Heat Fluid Flow 2008;29:263–8. [25] Gedik E, Kurt H, Recebli Z, Keçebasß A. Unsteady flow of two-phase fluid in circular pipes under applied external magnetic and electrical fields. Int J Ther Sci 2012;5:156–65. [26] Barnes HA. A handbook of elementary rheology. The University of Wales Institute of Non-Newtonian Fluid Mechanics; 2000. [27] Chhabra RP, Richardson JF. Non-Newtonian flow and applied rheology. 2nd ed. IChemE; 2008. [28] Jha S, Jain VK. Rheological characterization of magnetorheological polishing fluid for MRAFF. Int J Adv Manuf Technol 2009;42:656–68. [29] Kciuk M, Turczyn R. Properties and application of magnetorheological fluids. J Achieve Mater Manuf Eng 2006;18(1–2):127–30. [30] Guo D, Hu H. Nonlinear stiffness of a magneto-rheological damper. Nonlinear Dynam 2005;40:241–9. [31] Çesßmeci S ß , Engin T. Modeling and testing of a field-controllable magnetorheological fluid damper. Int J Mech Sci 2010;52:1036–46. [32] Barnes HA. The yield stress a review or ‘pamsa qei’ everything flows? J NonNewtonian Fluid Mech 1999;81:133–78. [33] Klingenberg DJ. Magnetorheology: applications and challenges. AIChE J 2001;47:246–9. [34] Deshmukh SS, McKinley GH. Rheological behavior of magnetorheological suspensions under shear, creep and large amplitude oscillatory shear (LAOS) flow. In: Proc XIVth int congr on rheology, Seoul, Korea, August 22–27 2004. [35] Genç S. Synthesis and properties of magnetorheological (MR) fluids. PhD thesis. University of Pittsburg; 2002. [36] Carlson DJ. Magnetorheological fluids. CRC Press; 2009. [37] Park JH, Park OO. Electrorheology and magnetorheology. Korea–Aust Rheol J 2001;13(1):13–7. [38] Wereley NM, Chaudhuri A, Yoo JH, John S, Kotha S, Suggs A, et al. Bidisperse magnetorheological fluids using Fe particles at nanometer and micron scale. J Intell Mater Struct 2006;17:393–401. [39] Mazlan SAB. The behaviour of magnetorheological fluids in squeeze mode. PhD Thesis. Dublin City University; 2008. [40] Bompos DA, Nikolakopoulos PG. CFD simulation of magnetorheological fluid journal bearings. Simul Model Pract Theory 2011;19:1035–60. [41] Jang KI, Min BK, Seok J. A behavior model of a magnetorheological fluid in direct shear mode. J Magn Magn Mater 2011;323:1324–9. [42] Phillips RW. Engineering applications of fluids with a variable yield stress. PhD thesis. Berkeley: University of California; 1969. [43] Abu-Ein SQ, Fayyad SM, Momani W, Al-Alawin A, Momani M. Experimental investigation of using MR fluids in automobiles suspension systems. Res J Appl Sci, Eng Technol 2010;2(2):159–63. [44] Jolly MR, Bender JW, Carlson JD. Properties and applications of commercial magnetorheological fluids. SPIE 5th annual int symp on smart struct and mater, San Diego, 15 March 1998. [45] Ansys 14. FLUENT documentation, FLUENT magnetohydrodynamics (MHD) module manual; 2011. [46] Gedik E, Kurt H, Recebli Z. 3D finite element solution of electrically conducting fluid flow in circular pipes under applied external magnetic and electrical field. Int J Numer Method Fluids, submitted for publication.
