Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-04-30T15:36:51.095Z Has data issue: false hasContentIssue false
  • English
  • Français

Temperature-gradient-driven electrohydrodynamic instability with unipolar injection in air

Published online by Cambridge University Press:  20 April 2006

James F. Hoburg
James F. Hoburg
Affiliation:
Department of Electrical Engineering, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213
Get access Rights & Permissions [Opens in a new window]

Abstract

Electrohydrodynamic instability is described in a planar region of gas, with unipolar injection through a linear temperature gradient, with corresponding mobility, viscosity, and density gradients. The role of charge-relaxation instability, which is incipient at a critical value of electric Rayleigh number in a uniform mobility layer, is distinguished from the mobility-gradient-driven mechanism, which can produce instability at much smaller voltage thresholds. Relative values of electroviscous time, viscous diffusion time and ion transit time determine the nature of the instability process. The instability is stationary or dynamic for wavenumbers respectively below or above a critical value. The fastest-growing wavenumber and corresponding growth rate are determined as functions of time constants and temperature gradient.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 132 , July 1983 , pp. 231 - 245
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arajs, S. & Legvold, S. 1958 Electroconvectional heat transfer in gases J. Chem. Phys. 29, 531.Google Scholar
Atten, P. & Lacroix, J. C. 1978 Electrohydrodynamic stability of liquids subjected to unipolar injection: nonlinear phenomena. J. Electrostat. 5, 439–452.Google Scholar
Atten, P. & Moreau, R. 1970 Critère de stabilité hydrodynamique des fluides incompressibles insolants soumis à une injection unipolaire quelconque C. R. Acad. Sci. 270, 415–417.Google Scholar
Chattock, A. P. 1899 On the velocity and mass of ions in the electric wind in air. London, Edinburgh and Dublin Phil. Mag. and J. Sci. 48 (294), 401–421.Google Scholar
Cobine, J. D. 1958 Gaseous Conductors. Dover.
Franke, M. E. 1969 Effect of vortices induced by corona discharge on free convection heat transfer from a vertical plate. Trans. ASME C: J. Heat Transfer 91, 427.Google Scholar
Hoburg, J. F. 1978 Internal electrohydrodynamic instability of liquids with collinear field and conductivity gradients J. Fluid Mech. 84, 291–303.Google Scholar
Hoburg, J. F. & Melcher, J. R. 1976 Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients J. Fluid Mech. 73, 333–351.Google Scholar
Hoburg, J. F. & Melcher, J. R. 1977 Electrohydrodynamic mixing and instability induced by collinear fields and conductivity gradients Phys. Fluids 20, 903–911.Google Scholar
Hopfinger, E. J. & Gross, J. P. 1971 Charge transport of self-generated turbulence in insulating liquids submitted to unipolar injection Phys. Fluids 14, 1671–1682.Google Scholar
Kibler, K. G. 1974 Electrostatic cooling of laser mirrors and windows. Air Force Weapons Lab. Tech. Rep.
Kibler, K. G. & Carter, H. G. 1974 Electrocooling in gases J. Appl. Phys. 45, 4436.Google Scholar
Kulacki, F. A. & Daumenmier, J. A. 1978 A preliminary study of electrohydrodynamic augmented baking J. Electrostat. 5, 325–336.Google Scholar
Lindsley, E. F. 1973 Incredible new probe puts the freeze on hot spots – instantly. Pop. Sci. (March) 202, 26–28.Google Scholar
Lykondis, P. S. & Yu, C. P. 1963 The influence of electrostrictive forces in natural thermal convection Int. J. Heat Mass Transfer 23, 853.Google Scholar
Mcdermott, J. 1971 High-voltage ionic discharges provide silent efficient cooling. Electronic Design (Sept.) 19 (20).Google Scholar
Palueff, K. K. 1933 Means for cooling electrical apparatus US Patent 1 980821.
Robinson, M. 1961 Movement of air in the electric wind of the corona discharge Trans. AIEE 80, 143–150.Google Scholar
Sadek, S. E. 1969 Electrohydrodynamic augmentation of range ovens. Tech. Rep. Dynatech Corp.
Schneider, J. M. & Watson, P. K. 1970 Electrohydrodynamic stability of space-charge-limited currents in dielectric liquids. I. Theoretical study Phys. Fluids 13, 1948–1954.Google Scholar
Velkoff, H. R. 1962 Electrofluidmechanics: Investigation of the effects of electrostatic fields on heat transfer and boundary layers. Propulsion Lab. Wright-Patterson AFB, Ohio, Tech. Rep. ASE-TDR-62-650.
Watson, P. K., Schneider, J. M. & Till, H. R. 1970 Electrohydrodynamic stability of space-charge-limited currents in dielectric liquids. II. Experimental study Phys. Fluids 13, 1955–1961.Google Scholar
WEAST, R. C. (ed.) 1970 Handbook of Chemistry and Physics. Chemical Rubber Co.
Worraker, W. J. & Richardson, A. T. 1979 The effect of temperature-induced variations in charge carrier mobility on a stationary electrohydrodynamic instability J. Fluid Mech. 93, 29–45.Google Scholar