Instability and Convection in Cylindrical Geometry
In chapter 15 we mentioned that the instability problem arises in the three electrode geometries of high symmetry when the injection is homogeneous on the injector. Chapter 15 was devoted to instabilities in the case of plane parallel electrodes. In this section we consider the two other configurations of coaxial cylinders and of concentric spheres. Given a constant value q0 of the injected space charge at the injecting electrode, the motionless state is a solution and the instability problem is to determine under what conditions this solution destabilises. Qualitatively the instability mechanism is the same than in the case of plane parallel electrodes. Due to coulombic repulsion, the charge density decreases when going from injector to collector along a radial line and, therefore, there is a positive coupling between velocity disturbances and the subsequent charge density perturbations (the argument of §15–1 is of general nature and is not specific to the case of parallel electrodes). Again the instability parameter is the nondimensional number T and the criterion depends on the injection parameter C = q0d2/εV.
KeywordsConvective Cell Outer Cylinder Coaxial Cylinder Forced Flow Convection Regime
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- P. Atten, J.C. Lacroix and R. Tobazeon: Proceed. 4th Intern. Conf. Cond. Breakdown in Dielectric Liquids (Ed. T. Gallagher), Dublin, 1972, 89–92.Google Scholar
- N. Felici: Dir. Current, 2 (1972), 147–165.Google Scholar
- N. Félici, J.P. Gosse and B. Gosse: Rev. Gén. Electr., 85 (1976), 861–874.Google Scholar
- M.S. Apfel’baum: Magnitnaya Gidrodinamika, 3 (1978), 57.Google Scholar
- Y.K. Stishkov and A.A. Ostapenko: Magnitnaya Gidrodinamika, 4 (1979), 46.Google Scholar
- P. Atten and M. Haidara: IEEE Trans. Electr. Ins., EI-20 (1985), 187–198.Google Scholar
- L. Elouadie: “Electroconvection et augmentation des échanges thermiques produites par une injection unipolaire en géométrie fil-cylindre co-axiaux”, Doctoral Thesis, Joseph Fourier University, Grenoble, 1991.Google Scholar
- A. Castellanos and N. Agräit: in Conference Record 10th ICDL (Eds. P. Atten and R.Tobazeon), IEEE Cat. No 90CH2812–6, 1990, 311–315.Google Scholar
- A.T. Perez, P. Atten, B. Malraison, L. Elouadie and F.M.J. McCluskey: in Experimental heat transfer, fluid mechanics and thermodynamics (Eds. R.K. Shah, E.N. Ganic and K.T. Yang), Elsevier, 1988, 941–947.Google Scholar
- R.C. Martinelli: Trans. ASME, 69 (1947), 947–959.Google Scholar
- H. Schlichting: “Boundary layer theory”, McGraw-Hill, New-York, 1981.Google Scholar