scholarly journals Reevaluation of the Braginskii viscous force for toroidal plasma

2011 ◽  
Vol 77 (6) ◽  
pp. 829-841
Author(s):  
ROBERT W. JOHNSON
Keyword(s):  
New York ◽  
Velocity Profile ◽  
Qualitative Agreement ◽  
Pitch Angle ◽  
Transport Processes ◽  
Viscous Force ◽  
Plasma Discharges ◽  
Viscous Stress ◽  
Viscous Stress Tensor ◽  
Toroidal Plasma

AbstractThe model by Braginskii [1] (Braginskii, S. I. 1965 Transport processes in plasma. In: Review of Plasma Physics, Vol. 1 (ed. M.A. Leontovich). New York, NY: Consultants Bureau, pp. 205–311) for the viscous stress tensor is used to determine the shear and gyroviscous forces acting within a toroidally confined plasma. Comparison is made to a previous evaluation, which contains an inconsistent treatment of the radial derivative and neglects the effect of the pitch angle. Parallel viscosity contributes a radial shear viscous force, which may develop for sufficient vertical asymmetry to the ion velocity profile. An evaluation is performed of this radial viscous force for a tokamak near equilibrium, which indicates qualitative agreement between theory and measurement for impure plasma discharges with strong toroidal flow.

Mathematical Model Investigation of Far-Field Transport of Ocean-Dumped Sewage Sludge Related to Remote Sensing

1982 ◽  
Vol 14 (3) ◽  
pp. 33-39
Author(s):  
C Y Kuo
Keyword(s):  
New York ◽  
Sewage Sludge ◽  
Laboratory Data ◽  
Three Dimensional ◽  
Approximate Model ◽  
Transport Processes ◽  
Far Field ◽  
New York Bight ◽  
Mean Current

An existing, three-dimensional, Eulerian-Lagrangian finite-difference model was modified and used to examine the far-field transport processes of dumped sewage sludge in the New York Bight. Both in situ and laboratory data were utilized in an attempt to approximate model inputs such as mean current speed, vertical and horizontal diffusion coefficients, particle size distributions, and specific gravities. Concentrations of the sludge near the sea surface predicted from the computer model were compared qualitatively with those remotely sensed.

On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier–Stokes equations in polar coordinates

2018 ◽  
Vol 33 (3) ◽  
pp. 199-210 ◽  
Author(s):  
Alexander Zlotnik
Keyword(s):  
Stokes System ◽  
Stokes Equations ◽  
Physical Property ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Uniform Mesh ◽  
Viscous Stress ◽  
Spatial Discretization ◽  
Navier Stokes Equations ◽  
Viscous Stress Tensor

Abstract The barotropic quasi-gasdynamic system of equations in polar coordinates is treated. It can be considered a kinetically motivated parabolic regularization of the compressible Navier–Stokes system involving additional 2nd order terms with a regularizing parameter τ > 0. A potential body force is taken into account. The energy equality is proved ensuring that the total energy is non-increasing in time. This is the crucial physical property. The main result is the construction of symmetric spatial discretization on a non-uniform mesh in a ring such that the property is preserved. The unknown density and velocity are defined on the same mesh whereas the mass flux and the viscous stress tensor are defined on the staggered meshes. Additional difficulties in comparison with the Cartesian coordinates are overcome, and a number of novel elements are implemented to this end, in particular, a self-adjoint and positive definite discretization for the Navier–Stokes viscous stress, special discretizations of the pressure gradient and regularizing terms using enthalpy, non-standard mesh averages for various products of functions, etc. The discretization is also well-balanced. The main results are valid for τ = 0 as well, i.e., for the barotropic compressible Navier–Stokes system.

Practical aspects in the drawing of an optical fiber

1998 ◽  
Vol 13 (2) ◽  
pp. 483-493 ◽  
Author(s):  
S. Roy Choudhury ◽  
Y. Jaluria
Keyword(s):  
Optical Fibers ◽  
Gas Flow ◽  
Surface Force ◽  
Transport Processes ◽  
Operating Conditions ◽  
Force Balance ◽  
Viscous Stress ◽  
Furnace Temperature ◽  
Flow Configuration ◽  
Fiber Radius

The transport processes in the furnace for the continuous drawing of optical fibers have been studied numerically and analytically. Practical circumstances and operating conditions are considered. A peripheral gas flow configuration has been modeled, along with irises at the ends, as employed in practical furnaces. The neck-down profile of the fiber is not chosen, but has been generated on the basis of a surface force balance. The results obtained are validated by comparisons with earlier experimental results. A detailed analysis has been carried out to determine the relative contributions of different forces during the drawing process. Even though the internal viscous stress is shown to be the major contributor to the draw tension, it is found that under certain operating conditions, the force due to gravity is significant, especially at the beginning of the neck-down region. For a peripheral flow configuration, the effect of flow entrance is found to be very important in determining the necking shape. However, the effect of the iris size on the fiber temperature field is found to be negligible. It is found that for a given furnace temperature and fiber radius, there is an upper limit for draw-down speed at which a fiber can be drawn without rupture. Practical ranges of draw speeds and furnace temperature conditions are identified for the process to be feasible.

scholarly journals On the Effects of Viscosity on the Shock Waves for a Hydrodynamical Case—Part I: Basic Mechanism

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Huseyin Cavus
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Numerical Solutions ◽  
Entropy Change ◽  
Basic Mechanism ◽  
Viscous Stress ◽  
Viscous Stress Tensor ◽  
Supersonic Regime ◽  
Interaction Of Shock Waves ◽  
Case Part

The interaction of shock waves with viscosity is one of the central problems in the supersonic regime of compressible fluid flow. In this work, numerical solutions of unmagnetised fluid equations, with the viscous stress tensor, are investigated for a one-dimensional shock wave. In the algorithm developed the viscous stress terms are expressed in terms of the relevant Reynolds number. The algorithm concentrated on the compression rate, the entropy change, pressures, and Mach number ratios across the shock wave. The behaviour of solutions is obtained for the Reynolds and Mach numbers defining the medium and shock wave in the supersonic limits.

The Comparison of Viscous Force Approximations of Smoothed Particle Hydrodynamics in Poiseuille Flow Simulation

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Zhengang Liu ◽  
Zhenxia Liu
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Flow Simulation ◽  
Reynolds Numbers ◽  
Viscous Force ◽  
Numerical Instability ◽  
Viscous Stress ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Particle Approximation ◽  
Poiseuille Flows

Poiseuille flows at two Reynolds numbers (Re) 2.5 × 10−2 and 5.0 are simulated by two different smoothed particle hydrodynamics (SPH) schemes on regular and irregular initial particles' distributions. In the first scheme, the viscous stress is calculated directly by the basic SPH particle approximation, while in the second scheme, the viscous stress is calculated by the combination of SPH particle approximation and finite difference method (FDM). The main aims of this paper are (a) investigating the influences of two different schemes on simulations and reducing the numerical instability in simulating Poiseuille flows discovered by other researchers and (b) investigating whether the similar instability exists in other cases and comparing results with the two viscous stress approximations. For Re = 2.5 × 10−2, the simulation with the first scheme becomes instable after the flow approaches to steady-state. However, this instability could be reduced by the second scheme. For Re = 5.0, no instability for two schemes is found.

Acoustic heating produced in the thermoviscous flow of a Bingham plastic

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Anna Perelomova
Keyword(s):  
Linear Part ◽  
Acoustic Pulse ◽  
Nonlinear Flow ◽  
Thermal Mode ◽  
Viscous Stress ◽  
Viscous Stress Tensor ◽  
Bingham Plastic ◽  
Weakly Nonlinear ◽  
Nonlinear Acoustic ◽  
Final Equation

AbstractThis study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic’s viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation governing acoustic heating, and to retain those belonging to the thermal mode. The nonlinear terms of the final equation are a result of interaction between sounds and the thermal mode. In the field of intense sound, the resulting nonlinear acoustic terms form a driving force for the heating. The final governing dynamic equation of the thermal mode is valid in a weakly nonlinear flow. It is instantaneous, and does not imply that sounds be periodic. The equations governing the dynamics of both sounds and the thermal mode depend on sign of the shear rate. An example of the propagation of a bipolar initially acoustic pulse and the evolution of the heating induced by it is illustrated and discussed.

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