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.

Structure of the compressible MHD equations for the internal kink mode in a toroidal plasma with large aspect ratio

1999 ◽  
Vol 62 (2) ◽  
pp. 165-178 ◽  
Author(s):  
C. WAHLBERG
Keyword(s):  
Aspect Ratio ◽  
Perturbation Expansion ◽  
Mhd Equations ◽  
Marginal Stability ◽  
Large Aspect Ratio ◽  
Direct Expansion ◽  
Energy Principle ◽  
Toroidal Plasma ◽  
Kink Mode ◽  
Compressible Mhd Equations

The equations for the ideal, internal m = n = 1 kink mode in a toroidal plasma are derived from a direct, large-aspect-ratio perturbation expansion of the compressible magnetohydrodynamic (MHD) equations. The derivation complements earlier investigations of the internal kink mode based either on the energy principle or on direct expansions of the incompressible MHD equations. It is shown that five poloidal harmonics (m = −1, 0, 1, 2 and 3) have to be retained in a direct expansion of the compressible MHD equations, as compared with the three poloidal harmonics m = 0, 1 and 2 needed in the case of an incompressible plasma, or when working from the energy principle. Furthermore, the sound velocity is found to replace the Alfvén velocity in the generalized Pfirsch–Schlüter factor (the kinetic energy enhancement factor in a toroidal plasma) previously derived for an incompressible plasma. Taking this factor fully into account in the calculation of the growth rate of the m = n = 1 mode, it is shown that, while the Bussac result γB is recovered near marginal stability, growth rates of the order of 30% larger than γB are obtained when γB becomes of the order of the sound frequency.

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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