Transient thermal convection during orbital spaceflight

Abstract

For materials processes such as crystal growth, it is often necessary to reduce fluid natural convection. Therefore, study and practice of these processes in a low- g space environment are important, and knowledge of transient convective velocities in future space experiments is needed. Unsteady two-dimensional thermal convection in a cylinder with imposed circumferencial temperature distribution is solved analytically by a new modification of the Navier-Stokes equations valid for low Rayleigh number. These conditions are representative of those for typical materials processing in low- g. It is demonstrated how these results can be applied also for a square cross-section at low Rayleigh number. Solutions can be constructed for arbitrary time-dependent accelerations. Examples are presented for transient convection resulting from movement of an astronaut, and also from transient rotation of the spacecraft. It is verified by large-scale exact computer calculations that our analytical results are accurate for steady convection up to Rayleigh number of 6500; by introducing another concept called “effective” Rayleigh number, the much larger validity ranges for transient convection can be determined. These ranges are sufficient for almost all microgravity applications.