Body Force Density in the Elastic Dielectric

1971 ◽  
Vol 49 (1) ◽  
pp. 9-12 ◽  
Author(s):  
J. Grindlay ◽  
A. Redlack
Keyword(s):  
Angular Momentum ◽  
Equation Of State ◽  
Body Force ◽  
Integral Condition ◽  
The Body ◽  
Force Density ◽  
Material Symmetry ◽  
Integral Conditions ◽  
Body Force Density ◽  
Elastic Dielectric

The laws of conservation of linear and angular momentum are shown to impose certain integral conditions on the body force density in an elastic dielectric which is in static equilibrium.An equation of state, quadratic in the variables Di, Di;j, Ei, Ei;j, is postulated for the body force density. In the case of nonpiezoelectric cubic material symmetry it is found that, within the quadratic approximation, the integral condition imposed by the law of conservation of linear momentum is satisfied only if the body force of this form vanishes.

Singular Integral Equation Method for Interaction Between Elliptical Inclusions

1998 ◽  
Vol 65 (2) ◽  
pp. 310-319 ◽  
Author(s):  
Nao-Aki Noda ◽  
Tadatoshi Matsuo
Keyword(s):  
Boundary Conditions ◽  
Integral Equations ◽  
Singular Integral ◽  
Body Force ◽  
Numerical Solutions ◽  
Singular Integral Equations ◽  
Integral Equation Method ◽  
The Body ◽  
Force Density ◽  
Cauchy Type

This paper deals with numerical solutions of singular integral equations in interaction problems of elliptical inclusions under general loading conditions. The stress and displacement fields due to a point force in infinite plates are used as fundamental solutions. Then, the problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknowns are the body force densities distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. To determine the unknown body force densities to satisfy the boundary conditions, four auxiliary unknown functions are derived from each body force density. It is found that determining these four auxiliary functions in the range 0≦φk≦π/2 is equivalent to determining an original unknown density in the range 0≦φk≦2π. Then, these auxiliary unknowns are approximated by using fundamental densities and polynomials. Initially, the convergence of the results such as unknown densities and interface stresses are confirmed with increasing collocation points. Also, the accuracy is verified by examining the boundary conditions and relations between interface stresses and displacements. Randomly or regularly distributed elliptical inclusions can be treated by combining both solutions for remote tension and shear shown in this study.

Swirling recirculating flow an a liquid-metal column generated by a rotating magnetic field

1987 ◽  
Vol 185 ◽  
pp. 67-106 ◽  
Author(s):  
P. A. Davidson ◽  
J. C. R. Hunt
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Liquid Metal ◽  
Secondary Flow ◽  
Body Force ◽  
The Body ◽  
Rotating Magnetic Field ◽  
Force Balance ◽  
Centripetal Acceleration ◽  
Axial Variation

In this paper we consider theoretical and experimental aspects of axisymmetric, swirling flow which is generated in a column of liquid metal by a rotating magnetic field. Two cases are discussed, one in which there is no axial variation in the stirring force, and one where the body force is restricted to a relatively short length of the column. The latter case is of considerable practical interest in continuous casting.One-dimensional stirring, where the swirl is independent of z and θ, is well understood. The magnetic body force is balanced by shear, all inertial forces being zero (except for the centripetal acceleration). However, in two-dimensional axisymmetric stirring, the axial variation in swirl drives a strong secondary poloidal flow. The principal local force balance is between the magnetic torque and inertia. The body force spins up the fluid as it passes through the forced region and the secondary flow sweeps this angular momentum into the unforced region. Consequently, the size and distribution of the swirl is controlled by the secondary flow.The role of wall friction is considered and shown to control the length of the recirculating eddy. An approximate solution of the inviscid equations of motion, based on the angular momentum integral, is derived for the flow in the forced region. This is compared with the results of numerical experiments.The analysis predicts that the swirl velocity scales on {B(σ/ρω)½}ωR, has a maximum at the bottom of the driven region, and penetrates an axial distance of the order ℝR away from the forced region. (For turbulent flow the Reynolds number ℝ must be based on an effective eddy viscosity.) All these features were reproduced experimentally.

Modeling and Analyzing of Electrowetting Using Electromagnetic Body Force Density and Surface Tension

2011 ◽  
Vol 47 (5) ◽  
pp. 946-949 ◽  
Author(s):  
Tan Il Sung ◽  
Hong Soon Choi ◽  
Young Sun Kim ◽  
Il Han Park
Keyword(s):  
Surface Tension ◽  
Body Force ◽  
Force Density ◽  
Body Force Density

scholarly journals Computational Modeling of Vortex Generators for Turbomachinery

2002 ◽  
Author(s):  
R. V. Chima
Keyword(s):  
Computational Models ◽  
Body Force ◽  
Secondary Flows ◽  
The Body ◽  
Vortex Generators ◽  
Force Model ◽  
Suction Surface ◽  
Near Surface ◽  
Compressor Rotor ◽  
Surface Particle

In this work computational models were developed and used to investigate applications of vortex generators (VGs) to turbomachinery. The work was aimed at increasing the efficiency of compressor components designed for the NASA Ultra Efficient Engine Technology (UEET) program. Initial calculations were used to investigate the physical behavior of VGs. A parametric study of the effects of VG height was done using 3-D calculations of isolated VGs. A body force model was developed to simulate the effects of VGs without requiring complicated grids. The model was calibrated using 2-D calculations of the VG vanes and was validated using the 3-D results. Then three applications of VGs to a compressor rotor and stator were investigated: 1. The results of the 3-D calculations were used to simulate the use of small casing VGs used to generate rotor preswirl or counterswirl. Computed performance maps were used to evaluate the effects of VGs. 2. The body force model was used to simulate large partspan splitters on the casing ahead of the stator. Computed loss buckets showed the effects of the VGs. 3. The body force model was also used to investigate the use of tiny VGs on the stator suction surface for controlling secondary flows. Near-surface particle traces and exit loss profiles were used to evaluate the effects of the VGs.

Sign in / Sign up

Export Citation Format

Share Document