Fluid Model Equations Research Articles

Fluid model equations for the tokamak plasma edge

Increasing evidence that the edge plasma plays a crucial role in global tokamak confinement motivates this study of two-dimensional (2-D) (θ,r) computational models of fluid transport in the edge plasma region. Fluid plasma equations, boundary conditions, and a coupled neutral–plasma model are developed assuming toroidal symmetry. A plasma potential equation is presented for consistent drift flow solution in the nonambipolar case. Simplified plasma equations are implemented in a 2-D computational model. Results show large poloidal flux dominated by drift flow near the separatrix and parallel flow near the tokamak divertor target. Simultaneously large poloidal gradients in plasma potential and electric fields are seen. These may play a role in driving observed turbulent fluctuations in the edge plasma.

Study of electron waves in electrical discharge channels

The fast luminous pulses experimentally observed to propagate in electrical discharge channels, and believed to have a significant role in the process of electrical breakdown, are investigated, using a plasma fluid approach. These pulses fall in two regimes characterized by different average velocities of 106 and 108 m/s. We concentrate on the lower velocity pulses. A nondimensional analysis is used to show that these waves can be considered as longitudinal electron fluid waves driven by electron pressure gradients in weakly ionized plasmas. Model equations are derived considering each additional term in the momentum equation as a small but finite perturbation. In all cases, standard nonlinear fluid model equations are obtained as possible solutions. Electric forces lead to the Korteweg-deVries equation, viscosity to Burgers equation, and electron-neutral collisions to a damped wave equation. The propagation and attenuation of fluid waves along preionized channels is naturally associated with the formation of steps. It is suggested that thermalization must be associated with the injection of electrons from a source external to those in the preionized channel.

Self-similar behavior of plasma fluid equations

Using the “s-parameter groups of transformations” technique the self-similar behavior for three sets of commonly used plasma fluid model equations is ascertained. The self-similar variables are ξ=x/t A, ξ=t/x B or ξ=t exp (−αx) whereA, B and α are numbers andx andt are space and time variables. The resulting ordinary differential equations are obtained. By judicious choices of the parameters, a partial integration of the equations is obtained, thus displaying the analytic character of the systems.

Solution of one-fluid model equations with short range retarding magnetic forces for the quiet solar wind

The discrepancy of the low predicted versus the observed coronal particle densities is investigated by considering radial magnetic forces acting at the base of the corona in the one fluid model equations with anomalous thermal conductivity for the quiet solar wind. If the short range retarding magnetic force is taken to fall asr−5,r being the heliocentric distance, then in order to obtain satisfactory agreement between the predicted and observed (about 3×108 cm−3 at 1R⊙) coronal densities, the strength of the retarding magnetic force at 1R⊙ should be 1.2 times that of the gravitational force.

Improved parametric characterization of flow geometries

AbstractAn improved parametric method is presented for characterization of the flow geometry in the rectilinear flow of non‐Newtonian fluids in open and closed conduits of arbitrary crosssection and in purely viscous, inelastic flow of non‐Newtonian fluids through packed beds and porous media. In the new formulation, an infinite number of geometric parameters characterize the flow geometry. The actual number required in a particular application is shown to be determined by the fluid model equation representing the rheological behavior of the fluid. For Ostwald‐de‐Waele and Ellis fluids with flow behavior indices s = 1/n and α integers, the number of geometric parameters required to represent the relationship between flow rate and pressure drop is given by s + 1 and α + 1, respectively. The efficacy of the present method is demonstrated by comparisons with available results for various fluid models and flow geometries.

Zur numerischen Beschreibung rotationssymmetrischer wandstabilisierter Lichtbogenkonfigurationen

A method is outlined which gives a numerical describtion for some configurations of axially symmetrical constricted electric arcs. For this purpose the equations of single fluid model of plasma physics are decoupled in such a way that only the heat flux potential, the axial velocity, the radial velocity, the average axial pressure gradient, and the average axial electric field have to be calculated simultaneously considering a given set of boundary conditions. In this paper the method is applied to the Koppelmann arc. In addition the paper reports upon some experiences in applying this method to the computation of further arc configurations.

Geometric parameters for some flow channels

AbstractA method was proposed earlier(1) for prediction of the average velocity or pressure drop in the flow of non‐ Newtonian fluids in conduits of arbitrary cross section. The method requires only a knowledge of two geometric parameters which characterize the flow geometry, and the fluid model equation. In this paper, evaluations of geometric parameters are presented for infinite and finite (enclosed)square and triangular arrays of cylinders, and for regular polygonal and star‐shaped conduits. With these parameters, predictions of the average velocity or related variables for the Zlow of any arbitrary non‐Newtonian fluid can now be made. Comparisons are made with recent analytical solutions and experimental data pertaining to non‐Newtonian flow in concentric annuli, and equilateral and right isosceles triangular ducts, which give additional support to the reliability of the proposed method.

Two-Fluid Model of the Solar Wind

Solar wind studied with two fluid model, using proton and electron fluid type heat equations, equation of motion and continuity equation