Nondimensional Analysis of Electrorheological and Magnetorheological Dampers Using a Herschel-Bulkley Constitutive Model

Aerospace ◽  
2003 ◽  
Author(s):  
Norman M. Wereley
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Constitutive Model ◽  
Yield Stress ◽  
Flow Mode ◽  
Damping Capacity ◽  
Bingham Plastic ◽  
Field Dependent ◽  
Local Shear ◽  
Local Shear Stress

Quasisteady modeling of linear stroke flow mode magnetorheological (MR) and electrorheological (ER) dampers has focused primarily on the utilization of the Bingham-plastic constitutive model to assess performance metrics such as damping capacity. In such Bingham-plastic MR (or ER) flows, the yield stress of the fluid, τy, is activated by applying magnetic (or electric) field. The Bingham-plastic model assumes that the material is in either (1) a preyield condition where the local shear stress is less than the yield stress, τ < τy, or (2) a postyield condition, where the local shear stress is greater than the yield stress, τ > τy, so that the material flows with a constant postyield viscosity. The objective of this paper is to analyze the damping capacity of such a controllable MR or ER damper in the situation when the field dependent fluid exhibits postyield shear thinning or thickening behavior, that is, the postyield viscosity is a function of shear rate. A Herschel-Bulkley model with a field dependent yield stress is proposed, and the impact of shear rate dependent viscosity on damping capacity is assessed. Key analysis results—velocity profile, shear stress profile, and damping coefficient—are presented in a nondimensional formulation that is consistent with prior results for the Bingham-plastic analysis. The nondimensional analysis formulated here clearly establishes the Bingham number as the independent variable for assessing flow mode damper performance.

Nondimensional Analysis of Electrorheological and Magnetorheological Dampers Using a Herschel-Bulkley Constitutive Model

2003 ◽  
Author(s):  
Norman M. Wereley
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Constitutive Model ◽  
Yield Stress ◽  
Flow Mode ◽  
Damping Capacity ◽  
Bingham Plastic ◽  
Field Dependent ◽  
Local Shear ◽  
Local Shear Stress

Quasisteady modeling of linear stroke flow mode magnetorheological (MR) and electrorheological (ER) dampers has focused primarily on the utilization of the Bingham-plastic constitutive model to assess performance metrics such as damping capacity. In such Bingham-plastic MR (or ER) flows, the yield stress of the fluid, τy, is activated by applying magnetic (or electric) field. The Bingham-plastic model assumes that the material is in either (1) a preyield condition where the local shear stress is less than the yield stress, τ < τy, or (2) a postyield condition, where the local shear stress is greater than the yield stress, τ > τy, so that the material flows with a constant postyield viscosity. The objective of this paper is to analyze the damping capacity of such a controllable MR or ER damper in the situation when the field dependent fluid exhibits postyield shear thinning or thickening behavior, that is, the postyield viscosity is a function of shear rate. A Herschel-Bulkley model with a field dependent yield stress is proposed, and the impact of shear rate dependent viscosity on damping capacity is assessed. Key analysis results — velocity profile, shear stress profile, and damping coefficient — are presented in a nondimensional formulation that is consistent with prior results for the Bingham-plastic analysis. The nondimensional analysis formulated here clearly establishes the Bingham number as the independent variable for assessing flow mode damper performance.

scholarly journals Flow Mode Magnetorheological Dampers with an Eccentric Gap

2014 ◽  
Vol 6 ◽  
pp. 931683 ◽  
Author(s):  
Young-Tai Choi ◽  
Norman M. Wereley
Keyword(s):  
Constitutive Model ◽  
Mr Damper ◽  
Flow Mode ◽  
Rectangular Duct ◽  
Damping Force ◽  
Bingham Plastic ◽  
Mr Dampers ◽  
Annular Gap ◽  
Field Dependent ◽  
Viscous Field

This paper analyzes flow mode magnetorheological (MR) dampers with an eccentric annular gap (i.e., a nonuniform annular gap). To this end, an MR damper analysis for an eccentric annular gap is constructed based on approximating the eccentric annular gap using a rectangular duct with a variable gap, as well as a Bingham-plastic constitutive model of the MR fluid. Performance of flow mode MR dampers with an eccentric gap was assessed analytically using both field-dependent damping force and damping coefficient, which is the ratio of equivalent viscous field-on damping to field-off damping. In addition, damper capabilities of flow mode MR dampers with an eccentric gap were compared to a concentric gap (i.e., uniform annular gap).

Quasi-Steady Herschel-Bulkley Analysis of Magnetorheological Dampers With Preyield Viscosity

Aerospace ◽  
2005 ◽  
Author(s):  
Sung-Ryong Hong ◽  
Shaju John ◽  
Norman M. Wereley
Keyword(s):  
Yield Stress ◽  
Power Law ◽  
Performance Metrics ◽  
Dynamic Range ◽  
Fluid Velocity ◽  
Constitutive Behavior ◽  
Flow Mode ◽  
Damping Capacity ◽  
Mr Fluid ◽  
Bingham Plastic

A magnetorheological (MR) fluid, modeled as a Bingham-plastic material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Based on viscometric measurements, such a Bingham-plastic model is an idealization to physical magnetorheological behavior, albeit a useful one. A better approximation involves modifying both the preyield and postyield constitutive behavior as follows: (1) assume a high viscosity preyield behavior over a low shear rate range below the yield stress, and (2) assume a power law fluid (i.e., variable viscosity) above the yield stress that accounts for the shear thinning behavior exhibited by MR fluids above the yield stress. Such an idealization to the MR fluid’s constitutive behavior is called a viscous-power law model, or a Herschel-Bulkley model with preyield viscosity. This study develops analytical quasi-steady analysis for such a constitutive MR fluid behavior applied to a flow mode MR damper. Closed form solutions for the fluid velocity, as well as key performance metrics such as damping capacity and dynamic range (ratio of field on to field off force). Also, specializations to existing models such as the Herschel-Bulkley, the Biviscous, and the Bingham-plastic models, are shown to be easily captured by this model when physical constraints (idealizations) are placed on the rheological behavior of the MR fluid.

Rheology and structure of blood suspensions

1964 ◽  
Vol 19 (1) ◽  
pp. 127-133 ◽  
Author(s):  
S. E. Charm ◽  
W. McComis ◽  
G. Kurland
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Yield Stress ◽  
Structural Model ◽  
Cell Suspensions ◽  
Rate Curve ◽  
Red Cell ◽  
Shear Rates ◽  
Straight Line ◽  
Rate Plot

A structural model developed for kaolin suspensions was applied to blood in order to determine the structure and strength of the red cell suspensions. The yield stress of red cell suspensions determined in settling experiments agreed with the yield stress determined from shear stress-shear rate information employing Casson's equation. Theoretical considerations indicate that the shear stress-shear rate curve for blood should approach a straight line. This was found to be true at shear rates above 40 sec-1. The slope of this line was predicted from calculations based on sedimentation experiments and a modified Einstein's equation. The data suggest that the curvature of the shear stress-shear rate plot at low shear rates is due to aggregates of cells which break down under increasing shear rate, resulting finally in individual flocs. It is suggested that a floc consists of one to four cells with adhering plasma. The aggregate was calculated to have twice as much plasma associated with it as does a floc. However, the size of the aggregate could not be determined since the number of flocs associated with an aggregate could not be determined. shear stress-shear rate curve; red cell floc; red cell aggregate; sedimentation rate; blood viscosity and flow Submitted on February 28, 1963

Roughness Influence on Turbulent Flow Through Annular Seals

1994 ◽  
Vol 116 (2) ◽  
pp. 321-328 ◽  
Author(s):  
Victor Lucas ◽  
Sterian Danaila ◽  
Olivier Bonneau ◽  
Jean Freˆne
Keyword(s):  
Surface Roughness ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Flow ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Mixing Length ◽  
Local Shear ◽  
Wall Shear ◽  
Local Shear Stress

This paper deals with an analysis of turbulent flow in annular seals with rough surfaces. In this approach, our objectives are to develop a model of turbulence including surface roughness and to quantify the influence of surface roughness on turbulent flow. In this paper, in order to simplify the analysis, the inertial effects are neglected. These effects will be taken into account in a subsequent work. Consequently, this study is based on the solution of Reynolds equation. Turbulent flow is solved using Prandtl’s turbulent model with Van Driest’s mixing length expression. In Van Driest’s model, the mixing length depends on wall shear stress. However there are many numerical problems in evaluating this wall shear stress. Therefore, the goal of this work has been to use the local shear stress in the Van Driest’s model. This derived from the work of Elrod and Ng concerning Reichardt’s mixing length. The mixing length expression is then modified to introduce roughness effects. Then, the momentum equations are solved to evaluate the circumferential and axial velocity distributions as well as the turbulent viscosity μ1 (Boussinesq’s hypothesis) within the film. The coefficients of turbulence kx and kz, occurring in the generalized Reynolds’ equation, are then calculated as functions of the flow parameters. Reynolds’ equation is solved by using a finite centered difference method. Dynamic characteristics are calculated by exciting the system numerically, with displacement and velocity perturbations. The model of Van Driest using local shear stress and function of roughness has been compared (for smooth seals) to the Elrod and Ng theory. Some numerical results of the static and dynamic characteristics of a rough seal (with the same roughness on the rotor as on the stator) are presented. These results show the influence of roughness on the dynamic behavior of the shaft.

scholarly journals Viscoplastic Couette Flow in the Presence of Wall Slip with Non-Zero Slip Yield Stress

Materials ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 3574 ◽  
Author(s):  
Yiolanda Damianou ◽  
Pandelitsa Panaseti ◽  
Georgios C. Georgiou
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Yield Stress ◽  
Couette Flow ◽  
Wall Slip ◽  
Threshold Value ◽  
Bingham Plastic ◽  
Navier Slip ◽  
Angular Velocities ◽  
Slip Yield Stress

The steady-state Couette flow of a yield-stress material obeying the Bingham-plastic constitutive equation is analyzed assuming that slip occurs when the wall shear stress exceeds a threshold value, the slip (or sliding) yield stress. The case of Navier slip (zero slip yield stress) is studied first in order to facilitate the analysis and the discussion of the results. The different flow regimes that arise depending on the relative values of the yield stress and the slip yield stress are identified and the various critical angular velocities defining those regimes are determined. Analytical solutions for all the regimes are presented and the implications for this important rheometric flow are discussed.

scholarly journals Stress-gradient Coupling in Glacier Flow: IV. Effects of the “T” Term

1986 ◽  
Vol 32 (112) ◽  
pp. 342-349 ◽  
Author(s):  
Barclay Kamb ◽  
Keith A. Echelmeyer
Keyword(s):  
Shear Stress ◽  
Coupling Theory ◽  
Longitudinal Stress ◽  
Longitudinal Flow ◽  
Stress Gradients ◽  
Flow Coupling ◽  
Flow Response ◽  
Longitudinal Variations ◽  
Local Shear ◽  
Local Shear Stress

AbstractThe “T term” in the longitudinal stress-equilibrium equation for glacier mechanics, a double y-integral of ∂2τxy/∂x2 where x is a longitudinal coordinate and y is roughly normal to the ice surface, can be evaluated within the framework of longitudinal flow-coupling theory by linking the local shear stress τxy at any depth to the local shear stress τB at the base, which is determined by the theory. This approach leads to a modified longitudinal flow-coupling equation, in which the modifications deriving from the T term are as follows: 1. The longitudinal coupling length is increased by about 5%. 2. The asymmetry parameter σ is altered by a variable but small amount depending on longitudinal gradients in ice thickness h and surface slope α. 3. There is a significant direct modification of the influence of local h and α on flow, which represents a distinct “driving force” in glacier mechanics, whose origin is in pressure gradients linked to stress gradients of the type ∂τxy/∂x. For longitudinal variations in h, the “T force” varies as d2h/dx2 and results in an in-phase enhancement of the flow response to the variations in h, describable (for sinusoidal variations) by a wavelength-dependent enhancement factor. For longitudinal variations in α, the “force” varies as dα/dx and gives a phase-shifted flow response. Although the “T force” is not negligible, its actual effect on τB and on ice flow proves to be small, because it is attenuated by longitudinal stress coupling. The greatest effect is at shortest wavelengths (λ 2.5h), where the flow response to variations in h does not tend to zero as it would otherwise do because of longitudinal coupling, but instead, because of the effect of the “T force”, tends to a response about 4% of what would occur in the absence of longitudinal coupling. If an effect of this small size can be considered negligible, then the influence of the T term can be disregarded. It is then unnecessary to distinguish in glacier mechanics between two length scales for longitudinal averaging of τb, one over which the T term is negligible and one over which it is not.Longitudinal flow-coupling theory also provides a basis for evaluating the additional datum-state effects of the T term on the flow perturbations Δu that result from perturbations Δh and Δα from a datum state with longitudinal stress gradients. Although there are many small effects at the ~1% level, none of them seems to stand out significantly, and at the 10% level all can be neglected.The foregoing conclusions apply for long wavelengths λh. For short wavelengths (λ h), effects of the T term become important in longitudinal coupling, as will be shown in a later paper in this series.

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