Abstract
A MHD generator with a novel geometry is analyzed as a possible dc power source. The generator channel consists of two coaxial cylinders with a smooth annular space between them through which pressure driven ionized gas flows axially. Magnetic poles and electrodes separated by insulators are embedded in both the inner and outer cylinders. A one-dimensional steady state analysis is presented. It is shown that the internal impedance of the generator is a very sensitive function of the ratio of areas of the charge collecting electrodes to that of the magnetic poles. The generator efficiency analysis, on the other hand, indicates that there is an optimum area ratio corresponding to the maximum conversion efficiency. A comparison of the performance characteristics of this generator with those of a generator of rectangular cross section is presented. The average gas temperature and velocity, the magnetic flux density at the poles, and the volume displacement rate, etc., are assumed identical for the two cases in comparison. It is inferred that the novel channel analyzed herein is, in general, superior to the simple rectangular channel in the energy conversion scheme.
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Abbreviations
- a n :
-
\(\frac{{2P}}{{\theta _{{\text{pi}}} \left[ {\left( {\frac{\pi }{{\theta _{{\text{pi}}} }}} \right)^2 - \alpha _n^2 } \right]}}\cos \frac{{\alpha _n \theta _{{\text{pi}}} }}{2}\)
- 2a :
-
width of the rectangular channel
- a 1n , a 2n , b 1n , b 2n :
-
constants
- B :
-
magnetic flux density, both induced and applied
- B r0 :
-
maximum value of radial component of B at r=r i
- B 0 :
-
applied magnetic field in the rectangular generator = B r0
- 2b :
-
height of the rectangular channel
- C n :
-
r i r αno +r o r αni
- C −n :
-
r i r αno +r o r −αni
- c :
-
integration constant
- D n :
-
\(\left( {\frac{{r_{\text{i}} }}{{r_{\text{o}} }}} \right)^{\alpha _n } - \left( {\frac{{r_{\text{o}} }}{{r_{\text{i}} }}} \right)^{\alpha _n }\)
- E :
-
electric field strength
- \(E_{\theta _0 }\) :
-
maximum value of azimuthal component of E at r=r i
- G n :
-
C −n r α n +C n r −α n
- G −n :
-
C −n r α n −C n r −α n
- H n :
-
G n r −1
- H −n :
-
G −n r −1
- I r :
-
total radial current between a pair of opposite electrodes
- j :
-
electric current density
- p :
-
pressure of the ionized gas
- P :
-
number of magnetic poles in each cylinder of the generator
- P HT :
-
power loss due to heat transfer to the walls
- P i :
-
power input
- P o :
-
power output
- R ic :
-
internal impedance of the coaxial channel MHD generator consisting of an opposite pair of electrodes associated with the magnetic poles, insulators, and the channel in between, for a unit length of the channel
- R ir :
-
internal impedance of the rectangular generator for a unit length of the channel = a/bσ
- R 0 :
-
external load connected to the MHD generator
- r :
-
radial coordinate of the cylindrical coordinate system
- r i, r o :
-
radii of the inner and outer cylinders, respectively
- V :
-
fluid velocity
- z :
-
axial coordinate of the cylindrical coordinate system
- α n :
-
nP/2
- θ :
-
azimuthal coordinate of the cylindrical coordinate system
- θ e :
-
electrode angular width
- θ pi :
-
pole-insulator angular width
- σ :
-
electrical conductivity of the ionized gas
- μ :
-
permeability of the medium
- μ v :
-
coefficient of viscosity
- φ(r, θ):
-
electric potential
- φ(r i, θ)−φ(r o, θ) :
-
potential difference between an opposite pair of electrodes
- η :
-
conversion efficiency of a MHD generator
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A paper based on some of this material was presented at the International Electron Devices Meeting, Washington (D.C.) October 1967.
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Rao, K.R., Erteza, A. A cylindrical coaxial MHD generator. Appl. sci. Res. 21, 427–441 (1969). https://doi.org/10.1007/BF00411625
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DOI: https://doi.org/10.1007/BF00411625