scholarly journals Trapped electron instability in tokamaks: analytic solutions of the two-dimensional eigenvalue problem

1977 ◽  
Author(s):  
K. T. Tsang ◽  
P. J. Catto
Keyword(s):  
Eigenvalue Problem ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Trapped Electron

The three-dimensional stability of boundary-layer flow over compliant walls

1992 ◽  
Vol 238 ◽  
pp. 537-577 ◽  
Author(s):  
K. S. Yeo
Keyword(s):  
Boundary Layer ◽  
Eigenvalue Problem ◽  
Growth Rates ◽  
Isotropic Material ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Material Anisotropy ◽  
Compliant Walls ◽  
Tollmien Schlichting ◽  
Disturbance Growth

This paper examines the linear stability of the Blasius boundary layer over compliant walls to three-dimensional (oblique) disturbance wave modes. The formulation of the eigenvalue problem is applicable to compliant walls possessing general material anisotropy. Isotropic-material walls and selected classes of anisotropic-material walls are studied. When the properties of the wall are identical with respect to all oblique wave directions, the stability eigenvalue problem for unstable three-dimensional wave modes may be reduced to an equivalent problem for two-dimensional modes. The results for isotropic-material walls show that three-dimensional Tollmien–Schlichting instability modes are more dominant than their two-dimensional counterparts when the walls are sufficiently compliant. The critical Reynolds number for Tollmien-Schlichting instability may be given by three-dimensional modes. Furthermore, for highly compliant walls, calculations based solely on two-dimensional modes are likely to underestimate the maximum disturbance growth factor needed for transition prediction and correlation. However, because the disturbance growth rates on highly compliant walls are much lower than those on a rigid wall, significant delay of transition may still be possible provided compliance-induced instabilities are properly suppressed. Walls featuring material anisotropy which have reduced stiffness to shear deformation in the transverse and oblique planes are also investigated. Such anisotropy is found to be effective in reducing the growth rates of the three-dimensional modes relative to those of the two-dimensional modes.

Unsteady 2-D Compressible Flow in Unbounded Domain

1995 ◽  
Vol 117 (1) ◽  
pp. 91-96 ◽  
Author(s):  
Deguan Wang ◽  
E. Benjamin Wylie
Keyword(s):  
Experimental Data ◽  
Open Space ◽  
Flow Model ◽  
Subsonic Flow ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Closed Region ◽  
Open Domain ◽  
Isentropic Flow ◽  
Two Dimensional Flow

An unsteady isentropic flow model is presented to calculate the two-dimensional flow field in an arbitrarily closed region or in an open fluid domain. In the open domain, a unique boundary condition is implemented to simulate the infinite character of the open space. The characteristics-like method presented herein is shown to be robust over the entire subsonic flow range and, with the implementation of the infinite boundary, provides numerical results in agreement with analytic solutions and experimental data.

Mass Transfer Cooling of Laminar Flow Between Parallel Porous Plates

1974 ◽  
Vol 96 (3) ◽  
pp. 343-347 ◽  
Author(s):  
G. Walker ◽  
R. M. Terrill
Keyword(s):  
Mass Transfer ◽  
Nusselt Number ◽  
Mass Concentration ◽  
Energy Equation ◽  
Analytic Solutions ◽  
Thermal Capacity ◽  
Injection Velocity ◽  
Concentration Profiles ◽  
Nonisothermal Flow ◽  
Two Dimensional

The limiting temperature and mass concentration profiles and the limiting wall Nusselt number are obtained for the laminar nonisothermal flow in a two-dimensional porous channel. Results are reported for a uniform rate of injection at the wall of a foreign component of higher thermal capacity than the fluid in the channel. An exact solution of the diffusion equation is found while numerical and analytic solutions of the energy equation are discussed for small injection rates. It is shown that the enthalpy transport resulting from the diffusion process has an effect equivalent to increasing the Prandtl number. It is also found that for a given injection velocity at the wall, the limiting Nusselt number is significantly reduced by the injection of a foreign component of high thermal capacity.

Approximate and Analytic Solutions for Deformation of Finite Porous Filters

1997 ◽  
Vol 64 (4) ◽  
pp. 929-934 ◽  
Author(s):  
S. I. Barry ◽  
G. N. Mercer ◽  
C. Zoppou
Keyword(s):  
Fluid Flow ◽  
Steady State ◽  
Porous Material ◽  
Deformation Behavior ◽  
Fluid Velocity ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Solid Stress ◽  
Side Walls

The deformation, using linear poroelasticity, of a two-dimensional box of porous material due to fluid flow from a line source is considered as a model of certain filtration processes. Analytical solutions for the steady-state displacement, pressure, and fluid velocity are derived when the side walls of the filter have zero solid stress. A numerical solution for the case where the porous material adheres to the side walls is also found. It will be shown, however, that simpler approximate solutions can be derived which predict the majority of the deformation behavior of the filter.

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