Birgit Futterer

Pulsating and traveling wave modes of natural convection in spherical shells

A numerical study is made of the natural convective fluid motion in the spherical shell geometry, i.e., the gap between two concentric spheres. The case of homogeneously heated inner sphere and cooled outer sphere is considered for the radius ratio η=0.714 and Prandtl number Pr=0.7. Patterns of fluid flow are established by the variation of the Rayleigh number Ra and its heat transfer is characterized by the Nusselt number Nu. For small values of the Rayleigh number, a crescent shaped axisymmetric vortex is formed and is regarded as the basic flow. By increasing the Rayleigh number, two transitions occur to a fully developed three-dimensional irregular flow. On the first bifurcation branch, a pulsating wave flow was found with petal-like formations pulsating in meridional direction. On the second branch, a traveling wave flow exists with an azimuthal rotation of the spirally distributed petal patterns. Various characteristics of the flow patterns are investigated as well as their transition to chaos. Both...

Three-dimensional natural convection in spherical annuli

Natural convective fluid motions in the gap between two concentric non-rotating spheres are numerically studied. The case of homogeneously heated inner sphere and cooled outer sphere is considered for the radial aspect ratio π = 0.714 and Prandtl number Pr = 0.7. The natural convection problem is characterized by the Rayleigh number associated with the heat transfer within the fluid. For small values of the Rayleigh number an axisymmetric single vortex of crescent shape is formed as the basic flow. By increasing the Rayleigh number, flow patterns with banana-type cells, oriented in north-south direction and aligned in the azimuthal direction, are formed. Various characteristics of these flows as well as their transient evolution are investigated.

Quasi-stationary and chaotic convection in low rotating spherical shells

The geophysical flow simulation experiment ‘GeoFlow’ studies convection phenomena in rotating spherical shells under influence of a spherical symmetric buoyancy field. It is a space station experiment, that is backed by three-dimensional numerical simulation done with a spectral code. Here we present simulated dynamics in the low rotational regime. Flow patterns are characterized by solutions of axisymmetric, cubic and pentagonal symmetry with adjustment to rotating axes. For the example of a cubic pattern in supercritical convection regime, the evolution of heat transfer and kinetic energy is discussed, if the rotational influence increases. While these global variables point out that the flow is stationary in the rotating reference frame, it is the local variable of spherical harmonics in azimuthal direction which shows a periodic drift, i.e. the pattern is counter rotating to the sphere. Transition to chaos is in form of a sudden onset.

GeoFlow: On the status of experimental preparation of spherical gap flow experiments with central force field on International Space Station (ISS)

The GeoFlow experiment focus on convective flows in rotating spherical shells influenced by a central force field. To eliminate the unidirectional acceleration due to gravity on earth, these long-time experiments require microgravity environment on the International Space Station. While recent results of accompanying numerics are presented in [1, 2], here we present the actual status of experiment preparation.

Thermo-electro-hydrodynamic convection under microgravity: a review

Recent studies on thermo-electro-hydrodynamic (TEHD) convection are reviewed with focus on investigations motivated by the analogy with natural convection. TEHD convection originates in the action of the dielectrophoretic force generated by an alternating electric voltage applied to a dielectric fluid with a temperature gradient. This electrohydrodynamic force is analogous to Archimedean thermal buoyancy and can be regarded as a thermal buoyancy force in electric effective gravity. The review is concerned with TEHD convection in plane, cylindrical, and spherical capacitors under microgravity conditions, where the electric gravity can induce convection without any complexities arising from geometry or the buoyancy force due to the Earth’s gravity. We will highlight the convection in spherical geometry, comparing developed theories and numerical simulations with the GEOFLOW experiments performed on board the International Space Station (ISS).

Traveling waves in low and intermediate rotating spherical shell convection

The spherical shell convection in the lower rotational regime is discussed with numerical simulation by the use of a pseudo-spectral code and experimental observation by the use of a microgravity experiment in self-gravitating force field. While a low Coriolis force produces traveling waves of cubic, five-fold and frozen tetrahedral symmetry with a prograde drift, in the transition zone to chaos an axisymmetric flow is visible. The chaotic fluid flow does neither show a specific drift nor a dominating pattern of convection. Numerical and experimental data are in a good agreement.