Journal ArticleDOI
Electro-convection in a dielectric liquid layer subjected to unipolar injection
TLDR
In this paper, the authors considered two asymptotic states of convection: one where the whole motion is dominated by viscosity, and one where inertial effects dominate, and they derived the dependence of the current density ratio I/I0 on the stability parameter T = M2R = eϕ0/Kρν, and on 1/R = ν/Kϕ 0, which is an equivalent Prandtl number.Abstract:
The problem of electric charge convection in a dielectric liquid layer of high ionic purity, when subjected to unipolar injection, is in many ways analogous to that of thermal convection in a horizontal fluid layer heated from below, although no formal analogy can be established. The problem treated is intrinsically more nonlinear than the thermal problem. We consider two asymptotic states of convection: one where the whole motion is dominated by viscosity, and one where inertial effects dominate. In each state, two or three spatial regions are distinguished. From the approximate equations that hold in the different regions, information about the variation of the different quantities with distance from the injector is obtained, and further approximations permit us to establish the dependence of the current density ratio I/I0 (called the electric Nusselt number) on the stability parameter T = M2R = eϕ0/Kρν, and on 1/R = ν/Kϕ0, which is an equivalent Prandtl number (e is the permittivity, ρ the fluid density, K the mobility, ν the kinematic viscosity, and ϕ0 the applied voltage). In the viscous state, the analysis gives I/I0 ∞ T½; in the inertial state the law I/I0 ∞ (T/R)1/4 = M½ is obtained. Since M is independent of the applied voltage, the latter law shows the saturation in the electric Nusselt number observed in earlier experiments. The transition in the states is associated with a transition number (MR)T [gap ] 30, which is an electric Reynolds number, related to an ordinary Reynolds number of about 10.The experimental results, obtained in liquids of very different viscosities and dielectric constants, verify these theoretical predictions; further, they yield more precise numerical coefficients. As for the transition criteria, the experiments confirm that the viscous and inertial effects are of the same order when Re [gap ] 10. It was also possible to determine roughly the limits of the viscous and inertial states. The viscous analysis remains valid up to a Reynolds number of about 1; the inertial state can be considered valid down to a Reynolds number of 60. Schlieren observations show that the motion has the structure of very stable hexagonal cells at applied voltages just above the critical voltage, which are transformed into unstable filaments when the voltage is increased further. At even higher voltages, the motion finally breaks down into turbulence. It may be of interest to point out that, when M < 3, the electric Nusselt number approaches 1, which is equivalent to the situation in thermal convection at low Prandtl numbers.read more
Citations
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Journal ArticleDOI
Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection
Ph. Traoré,Alberto T. Pérez +1 more
TL;DR: In this paper, two-dimensional numerical simulations are carried out to examine the problem of transient electroconvection stability of dielectric liquids subjected to unipolar injection, and a detailed analysis of the scenario that occurs for different characteristic values of the stability parameter T is provided.
Journal ArticleDOI
Electrohydrodynamic instabilities and electroconvection in the transient and A.C. regime of unipolar injection in insulating liquids: A review
TL;DR: In this article, only the transient regime of unipolar injection into insulating isotropic liquids is considered, and the authors show that an apparent mobility, greater than the true (ionic) mobility by orders of magnitude, can be measured, especially in liquids of high M numbers.
Journal ArticleDOI
Heat transfer enhancement by electroconvection resulting from an injected space charge between parallel plates
TL;DR: In this article, an examination of heat transfer between two parallel plates due to electroconvection is presented, showing that the electrical effects dominate totally over buoyancy effects for all cases considered.
Journal ArticleDOI
A Finite-Volume Method for Electro-Thermoconvective Phenomena in a Plane Layer of Dielectric Liquid
Jian Wu,Philippe Traoré +1 more
TL;DR: In this article, a numerical algorithm for electro-thermoconvective phenomena in a dielectric liquid confined between two parallel plates is presented, under the simultaneous actions of a direct current electric field and a thermal gradient.
Journal ArticleDOI
High-Field Conduction in Dielectric Liquids Revisited
TL;DR: In this article, various mechanisms proposed to explain the conductivity of organic dielectric liquids at high fields (50 to 2000 kV/cm) are considered and their range of validity assessed.
References
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Journal ArticleDOI
Turbulent Thermal Convection at Arbitrary Prandtl Number
TL;DR: The mixing length theory of turbulent thermal convection in a gravitationally unstable fluid is extended to yield the dependence of Nusselt number H/H0 on both Prandtl number σ and Rayleigh number Ra.
Journal ArticleDOI
The Heat Transport and Spectrum of Thermal Turbulence
TL;DR: In this article, an upper limit to the heat transport is found subject to the constraint that some minimum eddy size exists which is effective in this transport, and the spectrum of convecting motions, the mean thermal gradients at each point and the eddy conductivity are then determined in terms of the minimum edddy size.
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Turbulent convection in a horizontal layer of water
T. Y. Chu,Richard J Goldstein +1 more
TL;DR: In this paper, an interferometric method was used to measure the mean temperature distribution for Rayleigh numbers between 3·11 × 105 and 1·86 × 107, where the Nusselt number was found to be proportional to Ra 0·278 in the range 2·76 × 105 < Ra < 1·05 × 108.
Journal ArticleDOI
Two-dimensional Rayleigh-Benard convection
D. R. Moore,Nigel Weiss +1 more
TL;DR: In this article, the authors studied two-dimensional convection in a Boussinesq fluid confined between free boundaries, with a Prandtl number p = 6·8 and showed that the heat flux is a maximum for square cells; steady convection is impossible for wider cells and finite amplitude oscillations appear instead, with periodic fluctuations of temperature and velocity in the layer.
Journal ArticleDOI
Investigation of turbulent thermal convection between horizontal plates
James W. Deardorff,G. E. Willis +1 more
TL;DR: In this article, the properties of turbulent thermal convection were measured in air between horizontal plates maintained at constant temperatures, with a convection chamber designed to allow measurements to be taken along a horizontal path.
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