Numerical investigation of thermo-electrohydrodynamic driven convection in spherical Taylor-Couette flow

Thermo-electrohydrodynamics (TEHD) studies convection in dielectric fluids driven by electric fields. In spherical geometries, TEHD produces radially oriented plume structures. Differential rotation-realized as spherical Taylor-Couette (sTC) flow-generates meridional and azimuthal circulation. When combined, these two heterogeneous forcing mechanisms create a wide variety of flow regimes due to the interplay between dielectrophoretic (DEP) and rotation-induced forces. This study investigates their interaction in the context of the AtmoFlow experiment, a spherical-shell setup scheduled for deployment on the International Space Station (ISS) in 2026. An idealized numerical model is developed using a finite-volume solver based on the OpenFOAM ecosystem. The solver employs a modified, time-resolved SIMPLE algorithm and incorporates Gauss's law to compute the electric field and the DEP force under non-isothermal conditions. The basic flows driven independently by TEHD and sTC forcing are first characterized: TEHD convection is benchmarked against classical Rayleigh-Bénard convection, and scaling relations for heat transport (Nusselt number) and kinetic energy are derived as functions of the electric Rayleigh number (RaE). sTC flow is analyzed in the co-rotating frame using key dimensionless parameters such as the Taylor number (Ta) and Rossby number (Ro). These flows display meridionally dominated structures and a tangent cylinder. Scaling laws for the Nusselt number and kinetic energy are also established. The combined TEHD-sTC system is then examined to assess the competing influences of radial DEP-driven convection and the meridional-azimuthal sTC flow. Transitional behavior in heat transport-from DEP-dominated to rotation-dominated regimes-is quantified using a specially defined in-flow Nusselt number (Nuq), which distinguishes conductive and convective heat transfer within the fluid bulk. Finally, the study explores the impact of heterogeneous thermal boundary conditions. The resulting convection patterns are analyzed using Empirical Orthogonal Functions (EOFs) and Fast Fourier Transforms (FFT).