Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-24T03:09:22.090Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical modelling of finite-amplitude electro-thermo-convection in a dielectric liquid layer subjected to both unipolar injection and temperature gradient

Published online by Cambridge University Press:  06 July 2010

PH. TRAORÉ ,
A. T. PÉREZ ,
D. KOULOVA  and
H. ROMAT
PH. TRAORÉ*
Affiliation:
Laboratoire d'Etudes Aérodynamiques, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope-Chasseneuil, France
A. T. PÉREZ
Affiliation:
Departamento de Electrónica y Electromagnetismo, Facultad de Física, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain
D. KOULOVA
Affiliation:
Institute of Mechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
H. ROMAT
Affiliation:
Laboratoire d'Etudes Aérodynamiques, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope-Chasseneuil, France
*
†Email address for correspondence: philippe.traore@univ-poitiers.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we solve numerically the entire set of equations associated with the electro-thermo-convective phenomena that take place in a planar layer of dielectric liquid heated from below and subjected to unipolar injection. For the first time the whole set of coupled equations is solved: Navier–Stokes equations, electrohydrodynamic (EHD) equations and the energy equation. We first validate the numerical simulation by comparing the electro-convection stability criteria with ones obtained with a stability approach. The numerical solution of the electro-thermo-convection problem is then presented entirely with a detailed analysis of stability parameters. In particular, the relation between fluid velocity, non-dimensional electrical parameter T, Rayleigh number Ra and Prandtl number Pr is given. An analytical model is presented in order to understand the flow behaviour at some critical conditions. The way that the onset of motion passes from purely electrical convection to purely thermal convection is, in particular, investigated and explained in detail. Finally, a result on the heat transfer enhancement due to electro-convection is exhibited and compared with data from experimental works available in this field.

JFM classification

Instability: Instability MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 279 - 293
Copyright
Copyright © Cambridge University Press 2010

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

REFERENCES

Atten, P. & Lacroix, J. C. 1979 Non linear hydrodynamic stability of liquids subjected to unipolar injection. J. Méc. 18, 469–510.Google Scholar
Atten, P., McCluskey, F. M. G. & Pérez, A. T. 1988 Electroconvection and its effect on heat transfer. IEEE Trans. Electr. Insul. 23 (4), 659–667.CrossRefGoogle Scholar
Atten, P. & Moreau, R. 1972 Stabilité électrohydrodynamique des liquides isolants soumis à une injection unipolaire. J. Méc. 11 (3), 471–521.Google Scholar
Bryan, J. E. & Seyed-Yagoobi, J. 1997 Heat transport enhancement of monogroove heat pipe with electrohydrodynamic pumping. J. Thermophys. Heat Transfer 11 (3), 454–460.CrossRefGoogle Scholar
Bryan, J. E. & Seyed-Yagoobi, J. 2001 Influence of flow regime, heat flux, and mass flux on electrohydrodynamically enhanced convective boiling. J. Heat Transfer 123 (2), 355–367.CrossRefGoogle Scholar
Castellanos, A. 1991 Coulomb driven convection in electrohydrodynamics. IEEE Trans. Electr. Insul. 26, 1201–1215.CrossRefGoogle Scholar
Castellanos, A., Atten, P. & Pérez, A. T. 1987 Finite amplitude electroconvection in liquid in the case of weak unipolar injection. PhysicoChem. Hydrodyn. 9 (3/4), 443–452.Google Scholar
Castellanos, A., Atten, P. & Velarde, M. G. 1984 a Oscillatory and steady convection in dielectric liquid layers subjected to unipolar injection and temperature gradient. Phys. Fluids 27, 1607–1615.CrossRefGoogle Scholar
Castellanos, A., Atten, P. & Velarde, M. G. 1984 b Electrothermal convection: Felici's hydraulic model and the Landau picture of non-equilibrium phase transitions. J. Non-Equilib. Thermodyn. 9, 235–244.CrossRefGoogle Scholar
Castellanos, A. & Velarde, M. G. 1981 Electrohydrodynamic stability in the presence of a thermal gradient. Phys. Fluids 24, 1784–1786.CrossRefGoogle Scholar
Chicón, R., Castellanos, A. & Martín, E. 1997 Numerical modelling of Coulomb-driven convection in insulating liquids. J. Fluid Mech. 344, 43–66.CrossRefGoogle Scholar
Chicón, R., Castellanos, A. & Pérez, A. T. 1999 Transient electrohydrodynamic stability of dielectric liquids subjected to unipolar injection. Inst. Phys. Conf. Ser. 163, 157–160.Google Scholar
Davis, S. F. 1984 TVD finite difference schemes and artificial viscosity. ICASE Rep. 84-20, NASA CR-172373. NASA Langley Research Center.Google Scholar
Felici, N. 1969 Phénoménes hydro et aérodynamiques dans la conduction des diélectriques fluides. Rev. Gén. Electr. 78, 717–734.Google Scholar
Felici, N. 1972 D.C. conduction in liquid dielectrics Part II. Electrohydrodynamic phenomena. Direct Curr. 2, 147–165.Google Scholar
Fortin, M. & Glowinski, R. 1983 Augmented Lagrangian Methods. North-Holland.Google Scholar
Gaskel, P. H. & Lau, A. K. C. 1988 Curvature-compensated convective transport: SMART, a new boundedness-preserving transport algorithm. Intl J. Numer. Methods Fluids 8, 617–641.CrossRefGoogle Scholar
Godunov, S. K. 1959 A Difference scheme for numerical computational of discontinuous solution of hydrodynamic equations. Math. Sb. 47, 271–306. Translated in US Joint Publications Research Service, JPRS 7226 (1969).Google Scholar
Grassi, W. & Testi, D. 2006 Heat transfer enhancement by electric fields in several heat exchanger regimes. Ann. N. Y. Acad. Sci. 1077 (1), 527–569.CrossRefGoogle ScholarPubMed
Lin, C.-W. & Jang, J.-Y. 2005 3D numerical heat transfer and fluid flow analysis in plate-fin and tube heat exchangers with electrohydrodynamic enhancement. Intl J. Heat Mass Transfer 41, 583–593.CrossRefGoogle Scholar
Martin, P. J. 1982 Electrohydrodynamic instabilities in a horizontal layer of dielectric liquid heated from above and subjected to a DC electric field. Doctoral thesis, University of Bristol, Bristol, UK.Google Scholar
Martin, P. J. & Richardson, A. 1982 Overstable electrothermal instabilities in a plane layer of dielectric liquids. J. Eectrostat. 12, 435.CrossRefGoogle Scholar
McCluskey, F. M. G., Atten, P. & Pérez, A. T. 1991 Heat transfer enhancement by electroconvection resulting from an injected space charge between parallel plates. Intl J. Heat Mass Transfer 34, 2237.CrossRefGoogle Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. McGraw-Hill.Google Scholar
Pérez, A. T., Atten, P., Malraison, B., Elouadi, L. & McCluskey, F. M. G. 1988 Heat transfer augmentation induced by electrically generated convection in liquids. In Experimental Heat Transfer, Fluid Mechanics and Thermodynamics (ed. Shah, R., Ganic, E. & Yang, K.), pp. 941–947. Elsevier.Google Scholar
Pontiga, F. & Castellanos, A. 1992 The onset of electrothermal convection in non polar liquid layers on the basis of dissociation-injection conductivity model. IEEE Trans. Ind. Appl. IA28, 520–527.CrossRefGoogle Scholar
Pontiga, F. & Castellanos, A. 1994 Physical mechanism of instability in a liquid layer subjected to an electric field and a thermal gradient. Phys. Fluids 6 (5), 1684–1701.CrossRefGoogle Scholar
Richardson, A. T. 1988 A hydraulic model of electrothermal convection in a plane layer of dielectric liquid. PhysicoChem. Hydrodyn. 10 (3), 355–367.Google Scholar
Rodrigues, L., Castellanos, A. & Richardson, A. 1986 Stationary instabilities in a dielectric liquid layer subjected to an arbitrary unipolar injection and adverse thermal gradient. J. Phys. D: Appl. Phys. 19, 2115–2122.CrossRefGoogle Scholar
Suman, B. 2006 A steady state model and maximum heat transport capacity of a electro-hydrodynamic augmented micro-grooved heat pipe. Intl J. Heat Mass Transfer 49, 3957–3967.CrossRefGoogle Scholar
Traoré, Ph. 1996 Contribution numérique à l'étude des transferts couplés de quantité de mouvement de chaleur et de masse dans un jet semi-confiné. PhD thesis, University of Toulouse III, France.Google Scholar
Tsai, P., Daya, Z. A., Deyirmenjian, V. B. & Morris, S. W. 2007 Direct numerical simulation of supercritical annular electroconvection. Phys. Rev. E 76, 026305.CrossRefGoogle ScholarPubMed
Vázquez, P. A., Georghiou, G. E. & Castellanos, A. 2006 Characterization of injection instabilities in electrohydrodynamics by numerical modelling: comparison of particle in cell and flux corrected transport methods for electroconvection between two plates. J. Phys. D: Appl. Phys. 39, 2754–2763.CrossRefGoogle Scholar
Vázquez, P. A., Georghiou, G. E. & Castellanos, A. 2008 Numerical analysis of the stability of the electro-hydrodynamic (EHD) electroconvection between two plates. J. Phys. D: Appl. Phys. 41, 1–10.CrossRefGoogle Scholar
Worraker, W. & Richardson, A. 1979 The effect of temperature-induced variations in charge carrier mobility on a stationary electrohydrodynamic instability. J. Fluid Mech. 93, 29.CrossRefGoogle Scholar
Worraker, W. & Richardson, A. 1981 A nonlinear E stability analysis of a thermally stabilized plane layer of dielectric liquid. J. Fluid Mech. 109, 217–237.CrossRefGoogle Scholar