Effects of gravity modulation on convection in a horizontal annulus
Introduction
Buoyancy-driven convection in microgravity resulting from gravity fluctuations has gained considerable attention owing to the possibility of conducting research in the low-gravity environment of space, and because of interest in the fundamental effects of gravity modulation on fluid systems. On spacecraft, fluctuating accelerations can originate from a variety of sources such as crew activities, vibrations from onboard equipment, and structural oscillations of the spacecraft. Typical peak g levels, although small relative to terrestrial gravity [1], are at least 100 times larger than the steady g levels in space. The fluctuating accelerations act on density gradients in the fluid caused by heat and/or mass transfer between the fluid and boundaries, producing convective motions. These motions may increase heat transfer significantly beyond that of pure conduction, and can strongly affect certain processes such as alloy solidification.
Previous studies of buoyancy-induced fluid motion and heat transfer resulting from gravity modulation under microgravity have focused on a few basic fluid systems, as well as some specific applications. Kamotani et al. [2] conducted a linearized numerical analysis for a two-dimensional rectangular enclosure with two opposing walls at unequal temperatures. They concluded that modulation normal to the direction of the temperature gradient is most critical. Amin [3] analytically studied heat transfer from a sphere. It was concluded that for high modulation frequencies heat transfer is negligible, while for low frequencies heat transfer will be non-trivial for fluids of small viscosity and sufficiently large Prandtl number. The effects of non-linearity of the governing equations for the rectangular enclosure problem were investigated by Biringen and Danabasoglu [4]. They established some limits on applicability of the linear models in the excitable frequency range. Biringen and Peltier [5] considered the effects of three-dimensionality as well as non-linearity of the governing equations for both sinusoidal and random modulations. They found that sinusoidal modulations are more stabilizing than random modulations, and the similarity between terrestrial systems and systems at low-gravity increases with increasing modulation amplitude. Cyr et al. [6] also conducted a numerical study of convection in a two-dimensional rectangular enclosure. Their results showed that the flow transitions from stable, to periodic, to non-periodic behavior as the frequency of the modulation is varied. The average heat transfer rate was found to increase significantly as the frequency was decreased to low values. Other investigations have been conducted to determine the effects of gravity modulation on melt processing systems in microgravity [7], [8], [9].
A problem that has been widely studied owing to its many practical applications is natural convection in the annulus between horizontal concentric cylinders. Depending on the outer to inner cylinder radius ratio R and the Rayleigh number, various types of laminar flow structures can arise in a sufficiently long horizontal annulus. Based on their experimental results and those of previous investigators, Powe et al. [10] classified various types of laminar natural convective regimes as (i) a unicellular steady regime for small Rayleigh numbers at any value of R, (ii) a multicellular regime for higher Rayleigh numbers and R < 1.24 (narrow-gap annulus), (iii) a spiral flow regime for higher Rayleigh numbers and R between 1.24 and 1.71 (moderate-gap annulus), and (iv) an oscillating regime for higher Rayleigh numbers and R > 1.71 (large-gap annulus). Most of the prior studies of buoyancy-induced convection in horizontal cylindrical annuli have dealt with two-dimensional flow occurring in annuli with large length to gap-thickness ratios. There are fewer studies of three-dimensional flow, which occurs owing to the presence of the endwalls or the onset of instabilities at higher Rayleigh numbers. Previous numerical studies of three-dimensional natural convection in large- and moderate-gap annuli have focused on classification of different convective regimes [11], the effects of annulus inclination [12], flow patterns in a short annulus [13], temporal development of the flow and temperature fields [14], turbulent flow [15], and high Rayleigh number laminar flow [16]. Three-dimensional buoyancy-driven convection in a narrow-gap annulus has been investigated by Dyko and Vafai [17]. The results of this study showed the existence of four different supercritical states characterized by the orientations and directions of rotation of counter-rotating convective rolls that form in the upper part of the annulus owing to thermal instability. A fifth supercritical state was studied by Dyko and Vafai [18].
In the present work, we extend the problem of buoyancy-induced convection in horizontal annuli to the case of gravity modulation in a microgravity environment, which has application to systems such as materials processing furnaces. In this three-dimensional numerical investigation, the governing equations are formulated in terms of vorticity and vector potential. The parabolic equations are solved by a three-dimensional three-level time-splitting ADI method, and the elliptic equations are solved by the extrapolated Jacobi method. The flow structures that arise in large-, moderate-, and narrow-gap annuli under microgravity as a result of periodic gravity modulation, and the influence of modulation frequency on the flow and heat transfer are presented.
Section snippets
Governing equations and solution
The inner and outer horizontal concentric cylinders have radii of ri and ro, respectively, and are of length l. The temperature of the inner cylinder Ti is greater than that of the outer cylinder To, and the two axial endwalls are impermeable and adiabatic. The dimensionless length of the annulus is defined as L = l/ri. The annulus geometry, which is characterized by the radius ratio R = ro/ri and gap aspect ratio A = l/(ro − ri), is shown in Fig. 1. In all of the numerical simulations, the
Results
The unsteady flow and temperature fields in horizontal cylindrical annuli resulting from periodic modulation of the gravity field in a microgravity environment are presented. The effects of modulation frequency on the flow patterns, temperature distributions, and heat transfer are investigated for a large-gap annulus. The development of secondary flows that arise in moderate- and narrow-gap annuli owing to the onset of thermal instabilities, and the effects of frequency on heat transfer in
Conclusions
An investigation of buoyancy-driven convection in a cylindrical annulus subjected to gravity modulation in a microgravity environment has been conducted for the first time. Simulations were carried out for wide ranges of annulus radius ratio and modulation frequency. It was shown that the fluctuating gravitational field induces recirculating flows in the annulus that reverse direction of rotation in response to the gravitational reversals. At high frequencies, the strength of the flow remains
References (21)
- et al.
Analysis of the low gravity tolerance of Bridgman–Stockbarger crystal growth, II. Transient and periodic accelerations
J. Cryst. Growth
(1991) - et al.
An investigation of transient three dimensional buoyancy driven flow and heat transfer in a closed horizontal annulus
Int. J. Heat Mass Transfer
(1991) - et al.
An investigation and comparative analysis of two- and three-dimensional turbulent natural convection in a horizontal annulus
Int. J. Heat Mass Transfer
(1994) - et al.
Low gravity environment in Space-lab
Acta Astronautica
(1982) - et al.
Thermal convection in an enclosure due to vibrations aboard spacecraft
AIAA J.
(1981) The effect of g-jitter on heat transfer
Proc. R. Soc. Lond. A
(1988)- et al.
Computation of convective flow with gravity modulation in rectangular cavities
J. Thermophys.
(1990) - et al.
Numerical simulation of 3-D Bénard convection with gravitational modulation
Phys. Fluids A
(1990) - et al.
Effects of gravity modulation in microgravity convection systems
ASME FED
(1993) - et al.
Numerical simulation of g-jitter effect on half floating zone convection under microgravity environment
Microgravity Sci. Technol.
(1996)