Vibrational effects on convection in a square cavity at zero gravity

Abstract

In this numerical study, we investigate natural convection in a two-dimensional square-section enclosure vibrating sinusoidally parallel to the applied temperature gradient in a zero-gravity field. The full Navier–Stokes equations are simplified with the Boussinesq approximation and solved by a finite difference method. Whereas the Prandtl number Pr is fixed to 7.1 (except for some test cases with Pr = 7.0, 6.8), the vibrational Rayleigh number Ra based on acceleration amplitude is varied from 1.0 × 104 to 1.0 × 105, and dimensionless angular frequency ω is varied from 1.0 × 100 to 1.0 × 103. In the tested range, time evolutions exhibit synchronous, 1/2-subharmonic and non-periodic responses, and flow patterns are characterized mainly by one- or two-cell structures. Flow-regime diagrams show considerable differences from results in a non-zero-mean-gravity field even at large acceleration amplitudes, and suggest that some parts of non-periodic-response regimes may be related to transitions between flow patterns. The amplitude of fluctuations in spatially averaged kinetic energy density K (equal to the difference between maximum and minimum kinetic energies over a cycle) tends to be large when fluid is stationary everywhere over some interval of time during each period, and has a peak when fluid begins to move continuously throughout one period. Such peaks are caused by impulsively started convection, and are not connected to resonant oscillations in a constant-gravity field.

On the variety of particle accumulation structures under the effect of g-jitters

“…(9) the effect of gjitters is not limited to the inertial action they exert on particles (Lappa and Carotenuto, 2003). In the presence of thermal or solutal gradients they can, in principle, produce their own convective fluid flow (e.g., Gershuni et al, 1994;Lizée and Alexander, 1997;Hirata et al, 2001;Dyko and Vafai, 2007;Srinivasan and Saghir, 2011) and influence in some circumstances other kinds of natural flows (of surface-tensiondriven nature in the present case) both in terms of strength and patterning behavior.…”

“…For relatively small frequencies, where the Gershuni's theory is no longer valid and in general the influence of gjitters should not be negligible, the absence of noticeable gjitter-induced flow, however, can be still ascribed to the considered direction of vibrations (in this case parallel to the imposed temperature gradient). As an example of existing studies on this subject, we may consider Hirata et al (2001), who investigated numerically the canonical reference case of a 2D square cell in microgravity conditions. Assuming a liquid with Pr=7 that is very close to that considered in the present work, they found the threshold for the onset of convection of vibrational nature in the case of gjitters parallel to the imposed temperature gradient to increase dramatically for increasing values of  (similar results were also obtained by Biringen and Danabasoglu, 1990).…”

Experimental Evidence of Thermal Vibrational Convection in a Nonuniformly Heated Fluid in a Reduced Gravity Environment

“…The fundamental treatise [1] comprises a systematic study of convective flows induced by high and finite frequency vibrations in closed and infinite cavities. Thermovibrational convection in square, rectangular, and cubic cavities was widely investigated providing a variety of mean flow structures and bifurcation scenarios [5][6][7][8]. Influence of vibration on double diffusive convection with the Soret effect was analyzed in [9].…”

“…1). This configuration was studied theoretically in weightlessness as well as ground conditions in a large number of works; see [1,5,6,8] and references therein. However, to the best of our knowledge, no experiments have been performed to evaluate these results.…”

G-jitter induc ed free convection over a vertical flat plate

“…It is also of importance in the large-scale convection of atmosphere. Aboard orbiting spacecrafts all objects experience low-amplitude perturbed accelerations, or g-jitter, caused by crew activities and space craft maneouvers, equipment vibrations, solar drag and other sources [2,3]. Many theoretical and experimental studies dealing with material processing or physics of fluids under the micro-gravity conditions aboard an orbiting spacecraft have been carried out in recent years.…”