Influence of the thermo-electric coupling on the heat transfer in cylindrical annulus with a dielectric fluid under microgravity Vadim Travnikov n , Olivier Crumeyrolle, Innocent Mutabazi Laboratoire Ondes et Milieux Complexes, UMR 6294 CNRS, Normandie Université, Université du Havre, 53 rue de Prony, CS80540, 76058 Le Havre Cedex, France article info Article history: Received 12 June 2016 Received in revised form 19 August 2016 Accepted 26 August 2016 Available online 3 September 2016 Keywords: Natural convection Electrohydrodynamics Spectral methods Direct numerical simulation abstract The present note gives the result of direct numerical simulations of the convective flow induced by the dielectric force in a cylindrical annulus under microgravity conditions. A dielectric fluid confined be- tween two coaxial cylinders is subject to a high-frequency tension and a radial temperature gradient. The resulting buoyancy force creates a supercritical convective flow when the critical value of the electric Rayleigh number is exceeded. This flow is made of stationary helicoidal vortices. The effect of the thermo-electric coupling is sensitive for large values of the radius ratio: it stabilizes the conductive state and reduces the slope of the increase of the heat transfer and of the kinetic energy. & 2016 IAA. Published by Elsevier Ltd. All rights reserved. 1. Introduction Flows induced by the artificial radial gravity play a significant role in the modeling geophysical and astrophysical flows and in the control of the heat transfer. In fact, because of the locally or- iented vertical gravity, it is quite to difficult to realize experiments that mimic accurately the geophysical flows in Earth environment. A temperature gradient can be also applied in order to create a density stratification and therefore to generate baroclinic flows. The modeling of geophysical or astrophysical flows has been made by the flows in cylindrical annulus in solid rotation around the axis and with a radial temperature gradient [1,2]. The cen- trifugal acceleration induced by the solid body rotation reproduces the gravity only in the thin layer of the fluid while the real gravity varies in the radial direction. The electric gravity induced by the dielectrophoretic force decreases with the radial distance as − r 5 for spherical gaps [3–6] and as − r 3 [7,8] for cylindrical annulus. That this the reason why the dielectrophoretic force has proved to be a good candidate for modeling of thermal convection in planets and in stars [9,10]. Our investigation is motivated by the recent ex- periment GEOFLOW realized on ISS with thermo-electric convec- tion induced by dielectrophoretic force in a spherical gap [10]; the purpose of the present study is to analyze in detail the structure of the convective flow induced by the thermo-electric convection in the case of cylindrical annulus. We focus our attention on the production of the artificial gravity by applying of the fast oscillated electric field between cylindrical surfaces (Fig. 1) containing a fluid of density ρ and permittivity ϵ. The electric gravity occurs because of the dielec- trophoretic effect related to the coupling between the electric field E and the gradient of the fluid permittivity. The dielectrophoretic force density is given by [11] =− ∇ϵ () E f 1 2 1 dep 2 The dielectrophoretic force is the main acting force as far as the frequency of the electric field f is much larger than the inverse of the charge relaxation time τ σ = ϵ − / e 1 (where s is the electrical conductivity) and of the fluid characteristic times. The dielec- trophoretic force contains a conservative part and a buoyancy force that can be written as follows ρα αρ =− ( − ) +∇ ϵ( − ) = ∇ ϵ () ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ T T e T TE e E f g g 2 2 , 2 dep e e 0 2 2 2 2 0 2 2 where the temperature dependence of the density and the di- electric constant of the fluid can be approximated by linear func- tions ρ ρ α ρ ρ ()= [ − ( − )] = ( ) ϵ( ) =ϵ[ − ( − )] ϵ = ϵ( ) () T T T T T eT T T 1 , , 1 , . 3 0 2 0 2 2 2 2 2 α and e are the thermal expansion and the thermal coefficient of the permittivity. So the variation of the fluid permittivity ϵ with the temperature dependence in the inhomogeneous field Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/aa Acta Astronautica http://dx.doi.org/10.1016/j.actaastro.2016.08.031 0094-5765/& 2016 IAA. Published by Elsevier Ltd. All rights reserved. n Corresponding author. E-mail address: vadtravnikov@gmail.com (V. Travnikov). Acta Astronautica 129 (2016) 88–94