Toroidal equilibrium of rotating plasma with adiabatic constraints

A numerical technique, alternative to Grad's well-known ADM method has been proposed to deal with the slow adiabatic evolution of a toroidal plasma with flow. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. Implications for the problem of bifurcation due to nonlinearity of the governing equations are discussed. In the case of field-aligned sub-Alfvénic flow the system is in the second elliptic regime if β <A2/(1 – A2) at the magnetic axis, where A is the Mach Alfvén number of the flow. Super-Alfvénic flows do not satisfy the local firehose stability criterion.

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Kinematics and Dynamics of a Parallel Manipulator With Woven Joints

14th Biennial Conference on Mechanical Vibration and Noise: Vibrations and Dynamics of Robotic and Multibody Structures ◽

10.1115/detc1993-0143 ◽

1993 ◽

Author(s):

Hyunsok Pang

Keyword(s):

Lagrange Multipliers ◽

Kinematic Analysis ◽

Inverse Kinematics ◽

Parallel Manipulator ◽

Inverse Dynamics ◽

Numerical Technique ◽

Vector Analysis ◽

Kinematics And Dynamics ◽

Governing Equations ◽

Numerical Examples

Abstract Presented is an analysis of the kinematics and the inverse dynamics of a proposed three DOF parallel manipulator resembling the Stewart platform in a general form. In the kinematic analysis, the inverse kinematics, velocity and acceleration analyses are performed, respectively, using vector analysis and general homogeneous transformations. An algorithm to solve the inverse dynamics of the proposed parallel manipulator is then presented using a Lagrangin technique. In this case, it is found that one should introduce and subsequently eliminate Lagrange multipliers in order to arrive at the governing equations. Numerical examples are finally carried out to examine the validity of the approach and the accuracy of the numerical technique employed. The trajectory of motion of the manipulator is also performed using a cubic spline.

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On Suddenly Expanding Non-Isothermal Pipe Flows of a Bingham Fluid

10.1115/imece1999-1226 ◽

1999 ◽

Author(s):

Khaled J. Hammad

Keyword(s):

Heat Transfer ◽

Newtonian Fluid ◽

Transfer Problem ◽

Numerical Technique ◽

Complex Nature ◽

Brinkman Number ◽

Governing Equations ◽

Heat Transfer Characteristics ◽

Flow And Heat Transfer ◽

Pipe Expansion

Abstract The non-isothermal laminar flow of the Bingham non-Newtonian fluid through a sudden pipe expansion is investigated. The governing equations of conservation of mass, momentum and energy are solved using the finite-difference numerical technique. The effects of non-dimensional yield stress, Reynolds number, Prandtl number and Brinkman number on the flow and heat transfer characteristics are studied. The obtained results indicate the complex nature of the present non-Newtonian fluid flow and heat transfer problem and reveal new features not encountered in the case of Newtonian fluids.

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Toroidal plasma configuration with non-planar magnetic axis

Journal of Plasma Physics ◽

10.1017/s0022377800001975 ◽

1984 ◽

Vol 32 (2) ◽

pp. 179-196

Author(s):

Hussain M. Rizk

Keyword(s):

Cross Section ◽

Ohmic Heating ◽

Circular Cross Section ◽

Magnetic Axis ◽

Toroidal Plasma ◽

Mhd Equilibrium ◽

Special Cases ◽

Magnetic Surfaces ◽

Plasma Configuration ◽

The Ideal

The ideal MHD equilibrium, stability, classical diffusion, effective thermal conductivity, and Ohmic heating of a zero-shear toroidal plasma configuration with a single non-planar magnetic axis of variable torsion and curvature are investigated. The plasma has a circular cross-section through which a longitudinal current density with arbitrary profile flows. In this type of magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. This magnetic toroidal configuration is of a stellarator type with a non-planar magnetic axis. The present work also covers as special cases tokamak and a magnetic toroidal plasma configuration with a magnetic axis of arbitrarily modulated curvature.

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Magnetic well and Mercier stability of stellarators near the magnetic axis

Journal of Plasma Physics ◽

10.1017/s002237782000121x ◽

2020 ◽

Vol 86 (5) ◽

Author(s):

Matt Landreman ◽

Rogerio Jorge

Keyword(s):

Stability Criterion ◽

Arbitrary Shape ◽

Small Distance ◽

Magnetic Axis ◽

Design Approach ◽

Ideal Condition ◽

Independent Variables ◽

Neoclassical Transport ◽

Major Radius ◽

Magnetic Well

We have recently demonstrated that by expanding in small distance from the magnetic axis compared with the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate the magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the ‘inverse expansion’ in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene and Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

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Flow over a non-uniform sheet with non-uniform stretching (shrinking) and porous velocities

Advances in Mechanical Engineering ◽

10.1177/1687814020909000 ◽

2020 ◽

Vol 12 (2) ◽

pp. 168781402090900

Author(s):

Aftab Alam ◽

Dil Nawaz Khan Marwat ◽

Saleem Asghar

Keyword(s):

Boundary Layer ◽

Differential Equations ◽

Viscous Flow ◽

Ordinary Differential Equations ◽

Excellent Agreement ◽

Arbitrary Shape ◽

Realistic Model ◽

Governing Equations ◽

Surface Geometry ◽

Shrinking Surface

Viscous flow over a porous and stretching (shrinking) surface of an arbitrary shape is investigated in this article. New dimensions of the modeled problem are explored through the existing mathematical analogies in such a way that it generalizes the classical simulations. The latest principles provide a framework for unification, and the consolidated approach modifies the classical formulations. A realistic model is presented with new features in order to explain variety of previous observations on the said problems. As a result, new and upgraded version of the problem is appeared for all such models. A set of new, unusual, and generalized transformations is formed for the velocity components and similarity variables. The modified transformations are equipped with generalized stretching (shrinking), porous velocities, and surface geometry. The boundary layer governing equations are reduced into a set of ordinary differential equations (ODEs) by using the unification procedure and technique. The set of ODEs has two unknown functions f and g. The modeled equations have five different parameters, which help us to reduce the problem into all previous formulations. The problem is solved analytically and numerically. The current simulation and its solutions are also compared with existing models for specific value of the parameters, and excellent agreement is found between the solutions.

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Numerical Simulation of Laminar Confined Impinging Jet in a Composite Channel

Heat Transfer: Volume 1 ◽

10.1115/ht2008-56248 ◽

2008 ◽

Author(s):

Marcelo J. S. de Lemos

Keyword(s):

Porous Layer ◽

Control Volume ◽

Numerical Technique ◽

Simple Algorithm ◽

Local Distribution ◽

Governing Equations ◽

Stagnation Region ◽

Volume Method ◽

Material Porosity ◽

Macroscopic Equations

This work shows numerical results for a jet impinging onto a flat plane covered with a layer of a porous material. Porosity of the porous layer is varied in order to analyze its effect on the local distribution of Nu. Macroscopic equations for mass and momentum ae obtained based on the volume-average concept. The numerical technique employed for discretizing the governing equations was the control volume method with a boundary-fitted non-orthogonal coordinate system. The SIMPLE algorithm was used to handle the pressure-velocity coupling. Results indicate that inclusion of a porous layer decreases the peak in Nu avoiding excessive heating or cooling near the stagnation region.

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