Asymptotic, closed integral solutions for the reconstruction of Grad–Shafranov equilibria in axisymmetric, large-aspect-ratio toroidal plasmas

2004 ◽  
Vol 11 (1) ◽  
pp. 186-197 ◽  
Author(s):  
Paulo Rodrigues ◽  
João P. S. Bizarro
Keyword(s):  
Aspect Ratio ◽  
Large Aspect Ratio ◽  
Toroidal Plasmas ◽  
Integral Solutions

LARGE-ASPECT RATIO MHD EQUATIONS FOR TOROIDAL PLASMAS

2009 ◽  
Vol 23 (11) ◽  
pp. 2463-2467
Author(s):  
M. ASIF
Keyword(s):  
Equation Of State ◽  
Aspect Ratio ◽  
Stream Function ◽  
Mhd Equations ◽  
Large Aspect Ratio ◽  
Magnetohydrodynamic Equations ◽  
Toroidal Plasmas

A set of reduced MHD equations is derived using the equation of state including plasma compressibility. By applying assumption of pressure, i.e., R2P = const. , a set of reduced magnetohydrodynamic equations for toroidal plasmas are obtained for large aspect ratio, high β tokamaks. These equations include all terms of the same order as the toroidal effect and only involve three variables, namely the flux, stream function and pressure.

Beam-induced currents in toroidal plasmas of arbitrary aspect ratio

1980 ◽  
Vol 23 (7) ◽  
pp. 1477 ◽  
Author(s):  
D. F. H. Start ◽  
J. G. Cordey
Keyword(s):  
Aspect Ratio ◽  
Toroidal Plasmas ◽  
Induced Currents

Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals With Large Aspect Ratio

2012 ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Costin D. Untaroiu ◽  
Houston G. Wood ◽  
Paul E. Allaire
Keyword(s):  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Dynamic Properties ◽  
Bulk Flow ◽  
Large Aspect Ratio ◽  
Flow Method ◽  
Dynamic Coefficients ◽  
Aspect Ratios

Traditional annular seal models are based on bulk flow theory. While these methods are computationally efficient and can predict dynamic properties fairly well for short seals, they lack accuracy in cases of seals with complex geometry or with large aspect ratios (above 1.0). In this paper, the linearized rotordynamic coefficients for a seal with large aspect ratio are calculated by means of a three dimensional CFD analysis performed to predict the fluid-induced forces acting on the rotor. For comparison, the dynamic coefficients were also calculated using two other codes: one developed on the bulk flow method and one based on finite difference method. These two sets of dynamic coefficients were compared with those obtained from CFD. Results show a reasonable correlation for the direct stiffness estimates, with largest value predicted by CFD. In terms of cross-coupled stiffness, which is known to be directly related to cross-coupled forces that contribute to rotor instability, the CFD predicts also the highest value; however a much larger discrepancy can be observed for this term (73% higher than value predicted by finite difference method and 79% higher than bulk flow code prediction). Similar large differences in predictions one can see in the estimates for damping and direct mass coefficients, where highest values are predicted by the bulk flow method. These large variations in damping and mass coefficients, and most importantly the large difference in the cross-coupled stiffness predictions, may be attributed to the large difference in seal geometry (i.e. the large aspect ratio AR>1.0 of this seal model vs. the short seal configuration the bulk flow code is usually calibrated for, using an empirical friction factor).

scholarly journals Mesoscale flows in large aspect ratio simulations of turbulent compressible convection

2005 ◽  
Vol 430 (3) ◽  
pp. L57-L60 ◽  
Author(s):  
F. Rincon ◽  
F. Lignières ◽  
M. Rieutord
Keyword(s):  
Aspect Ratio ◽  
Large Aspect Ratio
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