Aspect ratio dependence of the ideal internal kink mode stability in a toroidal plasma with circular cross section

2004 ◽  
Vol 11 (5) ◽  
pp. 2119-2134 ◽  
Author(s):  
C. Wahlberg
1984 ◽  
Vol 32 (2) ◽  
pp. 179-196
Author(s):  
Hussain M. Rizk

The ideal MHD equilibrium, stability, classical diffusion, effective thermal conductivity, and Ohmic heating of a zero-shear toroidal plasma configuration with a single non-planar magnetic axis of variable torsion and curvature are investigated. The plasma has a circular cross-section through which a longitudinal current density with arbitrary profile flows. In this type of magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. This magnetic toroidal configuration is of a stellarator type with a non-planar magnetic axis. The present work also covers as special cases tokamak and a magnetic toroidal plasma configuration with a magnetic axis of arbitrarily modulated curvature.


1997 ◽  
Vol 57 (2) ◽  
pp. 327-341 ◽  
Author(s):  
C. WAHLBERG ◽  
A. BONDESON

The stability condition and growth rate of the ideal, internal m=n=1 kink mode in a toroidal plasma are calculated by means of a direct inverse-aspect-ratio expansion of the magnetohydrodynamic (MHD) equations, rather than by using the energy principle. The analysis is based on the use of computer-aided algebra. The general equation for incompressible MHD oscillations in a low-β circular tokamak is derived to lowest order in the inverse aspect ratio. This derivation generalizes the Pfirsch-Schlüter factor for the kinetic energy in toroidal geometry.


Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Yury Kravtsov ◽  
Janusz Chrzanowski

AbstractThe Cotton-Mouton effect in sheared plasma with helical magnetic lines is studied on the basis of the equation for complex amplitude ratio (CAR). A simple model for helical magnetic lines in sheared plasma of toroidal configuration is suggested. The equation for CAR in the sheared plasma is solved by perturbation method, using the small shear angle deviations as is characteristic for tokamak plasma. It is shown that the inaccuracy in polarization measurements caused by deviations of the sheared angle amounts to some percentage of the shearless Cotton-Mouton phase shift. One suggested method is to subtract the “sheared” term, which may improve the accuracy of the Cotton-Mouton measurements in the sheared plasma.


1972 ◽  
Vol 7 (3) ◽  
pp. 427-434 ◽  
Author(s):  
Aldo Nocentini

The neoclassical diffusion in a tokamak is calculated for a finite-β plasma. The flux of the particles is shown to be substantially unchanged, with respect to the low-β case. The ‘equilibrium’ equation is derived. From it the magnetic surfaces can be obtained, once the external electromagnetic field and the density and temperature profiles are given. The case of magnetic surfaces with circular cross-section, in the small aspect ratio limit, is considered in detail.


2021 ◽  
pp. 1-44
Author(s):  
Sulaiman Alsaleem ◽  
Lesley Wright ◽  
Je-Chin Han

Abstract Serpentine, multi-pass cooling passages, are used in cooling advanced gas turbine blades. In open literature, most internal cooling studies use a fixed cross-sectional area for multi-pass channels. Studies that use varying aspect ratio channels, along with a guide vane to direct the flow with turning, are scarce. Therefore, this study investigates the effect of using different guide vane designs on both detailed heat transfer distribution and pressure loss in a multi-pass channel with an aspect ratio of (4:1) in the entry passage and (2:1) in the second passage downstream of the vane (s). The first vane configuration is one solid-vane with a semi-circular cross-section connecting the two flow passages. The second configuration has three broken-vanes with a quarter-circular cross-section; two broken vanes are located downstream in the first passage, and one broken vane is upstream in the second passage. Detailed heat transfer distributions were obtained on all surfaces within the flow passages by using a transient liquid crystal method. Results show that including the semi-circular vane in the turning region enhanced the overall heat transfer by around 29% with a reduction in pressure loss by around 20%. Moreover, results show the quarter-circular vane design provides higher overall averaged heat transfer enhancement than the semi-circular vane design by around 9% with penalty of higher pressure drop by 6%, which yields higher thermal performance by 7%, over a Reynolds number range from 15,000 to 45,000.


1999 ◽  
Vol 62 (2) ◽  
pp. 165-178 ◽  
Author(s):  
C. WAHLBERG

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.


2019 ◽  
Vol 24 ◽  
pp. 61-75
Author(s):  
J.L. de Oliveira ◽  
A.G. Barbosa de Lima ◽  
R. Pereira Ramos ◽  
H. Luma Fernandes Magalhães ◽  
W.R. Gomes dos Santos ◽  
...  

In the oil industry, pipelines (circular ducts) are widely used for the transportation of oil and yours derived. Because of their advantages, such as low operating cost and increased safety during transportation, pipelines have become indispensable for transporting oil in large quantities and for long distances. As an alternative to this problem, the transport of oil and water can be accomplished using ducts with an elliptical cross-section. Thus, this work has the objective of studying the flow of oil and water in cylindrical ducts with an elliptical cross-section by using the Ansys CFX software. Results of the velocity, pressure and volumetric fraction distributions of the oil and water phases are presented and analyzed. By applying the same inlet velocity to oil and water, revealed that the elliptical duct, with aspect ratio equal to 5.0, has a pressure drop less (84.2%) than the pressure drop obtained for one duct of circular cross-section (aspect ratio equal to 1.0).


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