Direct Numerical Simulation (DNS) of Suspensions in Spatially Varying Electric Fields

2007 ◽  
Author(s):  
M. Janjua ◽  
S. Nudurupati ◽  
P. Singh ◽  
I. Fischer ◽  
Nadine Aubry
Keyword(s):  
Rigid Body ◽  
Electric Fields ◽  
Lagrange Multiplier ◽  
Numerical Scheme ◽  
Rigid Body Motion ◽  
Solid Particles ◽  
Lagrange Multiplier Method ◽  
Body Motion ◽  
Multiplier Method ◽  
Point Dipole

We have developed a numerical scheme to simulate the motion of dielectric particles in uniform and nonuniform electric fields. The particles are moved using a direct simulation scheme in which the fundamental equations of motion of fluid and solid particles are solved without the use of models. The motion of particles is tracked using a distributed Lagrange multiplier method (DLM) and the electric force acting on the particles is calculated by integrating the Maxwell stress tensor (MST) over the particle surfaces. One of the key features of the DLM method is that the fluid-particle system is treated implicitly by using a combined weak formulation where the forces and moments between the particles and fluid cancel, as they are internal to the combined system. The flow inside the particles is forced to be a rigid-body motion using the distributed Lagrange multiplier method. The MST is obtained from the electric potential, which, in turn, is obtained by solving the electrostatic problem. In our numerical scheme the Marchuk-Yanenko operator-splitting technique is used to decouple the difficulties associated with the incompressibility constraint, the nonlinear convection term, and the rigid-body motion constraint. A comparison of the DNS results with those from the point-dipole approximation shows that the accuracy of the latter diminishes when the distance between the particles becomes comparable to the particle diameter, the domain size is comparable to the diameter, and also when the dielectric mismatch between the fluid and particles is relatively large.

Direct Simulation of Electrorheological Suspensions Subjected to Spatially Nonuniform Electric Field

2002 ◽  
Author(s):  
J. Kadaksham ◽  
P. Singh ◽  
N. Aubry
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Lagrange Multiplier ◽  
Dipole Approximation ◽  
Nonuniform Electric Field ◽  
Lagrange Multiplier Method ◽  
Body Motion ◽  
Multiplier Method ◽  
Point Dipole ◽  
Time Step

A numerical method based on the distributed Lagrange Multiplier method (DLM) [2,8] is developed for direct simulations of electrorheological (ER) liquids subjected to spatially varying electric fields. The flow inside particle boundaries is constrained to be rigid body motion by the distributed Lagrange multiplier method. The point-dipole approximation [6] is used to model the electrostatic forces acting on the polarized particles. The code is verified by performing a convergence study that shows that the results are independent of mesh and time step sizes. In a spatially nonuniform electric field the particles move to the regions where the magnitude of electric field is locally maximum when the particle permittivity is greater than that of the liquid. On the other hand, when the particle permittivity is smaller than that of the liquid the particles move to the regions of local minimum of electric field.

Direct Numerical Simulations (DNS) of Particles in Spatially Varying Electric Fields

2014 ◽  
Author(s):  
Edison C. Amah ◽  
Pushpendra Singh ◽  
Mohammad Janjua
Keyword(s):  
Electric Fields ◽  
Numerical Scheme ◽  
Particle System ◽  
Particle Diameter ◽  
Solid Particles ◽  
Body Motion ◽  
Point Dipole ◽  
Electric Force ◽  
Combined System ◽  
Splitting Technique

A numerical scheme is developed to simulate the motion of dielectric particles in uniform and nonuniform electric fields of a micro fluidic device. The particles are moved using a direct simulation scheme in which the fundamental equations of motion of fluid and solid particles are solved without the use of models. The motion of particles is tracked using a distributed Lagrange multiplier method (DLM) and the electric force acting on the particles is calculated by integrating the Maxwell stress tensor (MST) over the particle surfaces. One of the key features of the DLM method is that the fluid-particle system is treated implicitly by using a combined weak formulation where the forces and moments between the particles and fluid cancel, as they are internal to the combined system. The MST is obtained from the electric potential, which, in turn, is obtained by solving the electrostatic problem. In our numerical scheme the Marchuk-Yanenko operator-splitting technique is used to decouple the difficulties associated with the incompressibility constraint, the nonlinear convection term, the rigid-body motion constraint and the electric force term. A comparison of the DNS results with those from the point-dipole approximation shows that the accuracy of the latter diminishes when the distance between the particles becomes comparable to the particle diameter; the domain size is comparable to the diameter; and also when the dielectric mismatch between the fluid and particles is relatively large.

Dynamics of Electrorheological Suspensions Subjected to Spatially Nonuniform Electric Fields

2004 ◽  
Vol 126 (2) ◽  
pp. 170-179 ◽  
Author(s):  
J. Kadaksham ◽  
P. Singh ◽  
N. Aubry
Keyword(s):  
Electric Field ◽  
Pressure Gradient ◽  
Lagrange Multiplier ◽  
Critical Value ◽  
Nonuniform Electric Field ◽  
Lagrange Multiplier Method ◽  
Multiplier Method ◽  
Point Dipole ◽  
Time Duration ◽  
Time Step

A numerical method based on the distributed Lagrange multiplier method (DLM) is developed for the direct simulation of electrorheological (ER) liquids subjected to spatially nonuniform electric field. The flow inside particle boundaries is constrained to be rigid body motion by the distributed Lagrange multiplier method and the electrostatic forces acting on the particles are obtained using the point-dipole approximation. The numerical scheme is verified by performing a convergence study which shows that the results are independent of mesh and time step sizes. The dynamical behavior of ER suspensions subjected to nonuniform electric field depends on the solids fraction, the ratio of the domain size and particle radius, and four additional dimensionless parameters which respectively determine the importance of inertia, viscous, electrostatic particle-particle interaction and dielectrophoretic forces. For inertia less flows a parameter defined by the ratio of the dielectrophoretic and viscous forces, determines the time duration in which the particles collect near either the local maximums or local minimums of the electric field magnitude, depending on the sign of the real part of the Clausius-Mossotti factor. In a channel subjected to a given nonuniform electric field, when the applied pressure gradient is smaller than a critical value, the flow assists in the collection of particles at the electrodes, but when the pressure gradient is above this critical value the particles are swept away by the flow.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

2014 ◽  
Vol 228 (16) ◽  
pp. 2985-2991 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong ◽  
Xiuyun He
Keyword(s):  
Rigid Body ◽  
Single Mode ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Reference Guide ◽  
Revolute Joints ◽  
Operation Modes ◽  
Straight Line ◽  
Motion Stage ◽  
Motion Mode

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

Computation of Nonlinear Response of Hydraulically Actuated Structures

1997 ◽  
Author(s):  
T. D. Burton ◽  
C. P. Baker ◽  
J. Y. Lew
Keyword(s):  
Rigid Body ◽  
Flexible Structures ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Beam ◽  
Test Bed ◽  
Ode Models ◽  
Hydraulically Actuated ◽  
Pressure Dynamics ◽  
Low Order

Abstract The maneuvering and motion control of large flexible structures are often performed hydraulically. The pressure dynamics of the hydraulic subsystem and the rigid body and vibrational dynamics of the structure are fully coupled. The hydraulic subsystem pressure dynamics are strongly nonlinear, with the servovalve opening x(t) providing a parametric excitation. The rigid body and/or flexible body motions may be nonlinear as well. In order to obtain accurate ODE models of the pressure dynamics, hydraulic fluid compressibility must generally be taken into account, and this results in system ODE models which can be very stiff (even if a low order Galerkin-vibration model is used). In addition, the dependence of the pressure derivatives on the square root of pressure results in a “faster than exponential” behavior as certain limiting pressure values are approached, and this may cause further problems in the numerics, including instability. The purpose of this paper is to present an efficient strategy for numerical simulation of the response of this type of system. The main results are the following: 1) If the system has no rigid body modes and is thus “self-centered,” that is, there exists an inherent stiffening effect which tends to push the motion to a stable static equilibrium, then linearized models of the pressure dynamics work well, even for relatively large pressure excursions. This result, enabling linear system theory to be used, appears of value for design and optimization work; 2) If the system possesses a rigid body mode and is thus “non-centered,” i.e., there is no stiffness element restraining rigid body motion, then typically linearization does not work. We have, however discovered an artifice which can be introduced into the ODE model to alleviate the stiffness/instability problems; 3) in some situations an incompressible model can be used effectively to simulate quasi-steady pressure fluctuations (with care!). In addition to the aforementioned simulation aspects, we will present comparisons of the theoretical behavior with experimental histories of pressures, rigid body motion, and vibrational motion measured for the Battelle dynamics/controls test bed system: a hydraulically actuated system consisting of a long flexible beam with end mass, mounted on a hub which is rotated hydraulically. The low order ODE models predict most aspects of behavior accurately.

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