Transport from higher order g-jitter effects.
Large complex spacecraft, such as the International Space Station (ISS), will have a rich spectrum of vibrational modes that will be excited by crew activity as well as by on-board mechanical systems. The response of various experiments to this vibratory environment is not completely understood and has been a subject of concern to the users community. Since these vibrations arise for the most part from internal forces, the net acceleration must time-average to zero. Steady state periodic accelerations applied to a fluid in a completely filled container with an imposed density gradient will drive first-order flows that time-average to zero. Likewise, the resulting first-order thermal and solutal fluctuations time-average to zero. Over the range of frequencies in the vibrational environment expected on the ISS, the velocity oscillations tend to be nearly 90 degrees out of phase with the thermal and/or solutal fluctuations; consequently, little net transport occurs from the first-order effects. We must, therefore, examine possible higher-order effects that can lead to significant net transport. Second-order flows with non-zero time averages arise from the non-linear terms in the flow equations and from incomplete cancellation of first-order flows if the density gradient changes with time, or if the periodic acceleration has both axial and transverse components relative to the imposed density gradient. The time-average of such flows can be expressed in terms of the sum of the square of each periodic acceleration, weighted by the appropriate function of the frequency, taken over all frequencies; or as the weighted integral over the power spectral distribution (PSD) of the frequency spectrum. Approximate analytical solutions for these second-order flows, which agree closely with numerical computations, have been found using a perturbation analysis. These analytical models are then used to predict the effects of the anticipated vibratory environment on various classes of experiments planned for the ISS. Even though these second-order flows are much smaller than the first-order flows, it is shown that they can produce significant transport.
Naumann
Robert J
RJ
Center for Microgravity and Materials Science, University of Alabama in Huntsville, Huntsville, Alabama 35899, USA. naumannr@email.uah.edu