Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-04T18:48:15.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Streaming flows due to g-jitter-induced natural convection

Published online by Cambridge University Press:  26 April 2006

A. Farooq  and
G. M. Homsy
A. Farooq
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
G. M. Homsy
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate streaming in a square cavity where a lateral temperature gradient interacts with a constant gravity field modulated by small harmonic oscillations of order ε. The Boussinesq equations are expanded by regular perturbation in powers of ε, and the O(ε2) equations contain Reynolds-stress-type terms that cause streaming. The resulting hierarchy of equations is solved by finite differences to investigate the O(ε1) and O(ε2) fields and their parametric dependence on the Rayleigh number Ra, Prandtl number Pr, and forcing frequency ω. It has been found that the streaming flow is quite small at small values of Ra, but becomes appreciable at high Ra and starts to influence such flow properties as the strength of the circulation and the overall heat transfer. Under suitable parametric conditions of finite frequency and moderate Pr the periodic forcing motion interacts with the instabilities associated with the O(εo) base flow leading to resonances that become stronger as Ra increases. It is argued that these resonances will have their greatest effect on streaming for Pr ≈ 1. At low frequencies the streaming flow shows marked structural changes as Ra is increased leading to an interesting change in the sign of the O(ε2) contribution to the Nusselt number. Also, as the frequency is changed the O(ε2) Nusselt number again changes sign at approximately the resonant frequency.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 271 , 25 July 1994 , pp. 351 - 378
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alexander, J. I. D. 1990 Low gravity experiment sensitivity to residual acceleration: A review. Microgravity Sci. Technol. III (2), 52–68.Google Scholar
Alexander, J. I. D., Amiroudine, S., Ouzzani, J. & Rosenberger, F. 1991 Analysis of the low gravity tolerance of Bridgman–Stockbarger crystal growth II. Transient and periodic accelerations. J. Cryst. Growth 113, 21–38.Google Scholar
Amin, N. 1988 The effect of g-jitter on heat transfer. Proc. R. Soc. Lond. A 419, 151–172.Google Scholar
Batchelor, G. K. 1954 Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures. Q. Appl. Maths 12, 209–233.Google Scholar
Bergholz, R. F. 1978 Stability of natural convection in a vertical fluid layer. J. Fluid Mech. 84, 743–768.Google Scholar
Biringen, S. & Danabasoglu, G. 1990 Computation of convective flow with gravity modulation in rectangular cavities. J. Thermophys. 4, 357–365.Google Scholar
Biringen, S. & Peltier, L. J. 1990 Computational study of 3-D Bénard convection with gravitational modulation. Phys. Fluids A 2, 279–283.Google Scholar
Chenoweth, D. R. & Paolucci, S. 1986 Natural convection in an enclosed vertical air layer with large temperature horizontal temperature differences. J. Fluid Mech. 169, 173–210.Google Scholar
Elder, J. W. 1965 Laminar free convection in a vertical slot. J. Fluid Mech. 23, 77–98.Google Scholar
Gebhart, B., Jaluria, Y., Mahajan, R. L. & Sammakia, B. 1988 Buoyancy Induced Flows and Transport. Hemisphere.
Gill, A. E. 1966 The boundary layer regime for convection in a rectangular cavity. J. Mech. 26, 515–536.Google Scholar
Gill, A. E. & Davey, A. 1969 Instabilities of a buoyancy-driven system. J. Fluid Mech. 35, 775–798.Google Scholar
Gresho, P. M. & Sani, R. L. 1970 The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech. 40, 783–806.Google Scholar
Ivey, G. N. 1984 Experiments on transient natural convection in a cavity. J. Fluid Mech. 144, 389–401.Google Scholar
Lighthill, J. 1978 Acoustic streaming. J. Sound Vib. 61, 391–418.Google Scholar
Paolucci, S. & Chenoweth, D. R. 1989 Transition to chaos in a differentially heated cavity. J. Fluid Mech. 201, 379–410.Google Scholar
Patterson, J. & Imberger, J. 1980 Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 65–86.Google Scholar
Rayleigh, Lord 1945 The Theory of Sound. Dover.
Schlichting, H. 1979 Boundary Layer Theory, 7th edn. McGraw-Hill.
Thorpe, S. A. 1968 On standing internal gravity waves of finite amplitude. J. Fluid Mech. 32, 489–528.Google Scholar
Vahl Davis, G. de 1968 Laminar convection in an enclosed rectangular cavity. Intl J. Heat Mass Transfer 11, 1675–1693.Google Scholar
Vahl Davis, G. de & Jones, I. P. 1982 Natural convection in a square cavity: A comparison exercise. Rep. 1982/FMT/3. School of Mechanical & Industrial Eng., The University of New South Wales, Kensington, Australia.
Walker, K. L. & Homsy, G. M. 1978 Convection in a porous cavity. J. Fluid Mech. 87, 449–474.Google Scholar
Zlatev, Z., Wasniewski, J. & Schaumburg, K. 1981 Solution of Large and Sparse Systems of Linear Algebraic Equations. Lecture Notes in Computer Science. Springer.