Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지

Transient Buoyant Flows of a Stratified Fluid in a Vertical Channel

  • Park, Jun-Sang (Department of Mechanical Engineering, Halla University)
  • Published : 2001.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

A theoretical analysis is performed to describe the qualitative behavior of transient buoyant flows in a vertical channel. Consideration is given to the case of a fluid with a pre-existing stratification. The fluid motion is generated by giving impulsive anti-symmetric step-changes in temperature at the vertical left ad right sidewalls. The qualitative character of the flow is shown to be classified in the Rayleigh number (Ra)-Prandtl number ($sigma$) diagram. The transitory approach to the steady state can be monotonic or oscillatory, depending on ($sigma$-1)$^2$$pi$$^4$ 4$sigma$$R_a$. The prominent characteristics of time-dependent flow are discussed for large $R_a$. The profiles of temperature and velocity in the transient phase are depicted, which disclose distinctive time scales of motion. The transient process is shown to be sensitive to the Prandtl number. The detailed evolutions of flow and temperature fields are illustrated for large $R_a$.

Keywords

References

  1. Barcilon, V. and Pedlosky, J., 1966, 'Linear Theory of Rotating Stratified Fluid Motions,' J. Fluid Mech., Vol. 29, pp. 1-16 https://doi.org/10.1017/S002211206700059X
  2. Batchelor, G.K., 1954, 'Heat Transfer by Free Convection across a Closed Cavity between Vertical Boundaries at Different Temperatures,' Quart. Applied Math., Vol. 12, pp. 209-231
  3. Bergholz, R.F., 1978, 'Instability of Steady Natural Convection in a Vertical Fluid Layer,' J. Fluid Mech., Vol. 84, pp. 743-768 https://doi.org/10.1017/S0022112078000452
  4. Elder, J.W., 1965, 'Laminar free Convection in a Vertical Slot,' J. Fluid Mech., Vol. 23, pp. 77-98 https://doi.org/10.1017/S0022112065001246
  5. Gill, A. E., 1966, 'The Boundary Regime for Convection in a Rectangular Cavity,' J. Fluid Mech., Vol. 26, pp. 515-536 https://doi.org/10.1017/S0022112066001368
  6. Hyun, J.M., 1994, 'Unsteady Buoyant Convection in an Enclosure, Advances in heat transfer,' Vol. 24, pp. 277-320
  7. Janssen, R.J. A. and Henkes, R.A. W.M., 1995, 'Influence of Prandtl Number on Instability Mechanism and Transition in a Differentially Heated Square Cavity,' Vol. 290, pp. 319-344 https://doi.org/10.1017/S0022112095002539
  8. Jischke, M.C. and Dory, R.T., 1975, 'Linearized Buoyant Motion in a Closed Container,' J. Fluid Mech., Vol. 71, pp. 729-754 https://doi.org/10.1017/S0022112075002820
  9. Park, J.S. and Hyun, J.M., 1998, 'Transient Behavior of Vertical Buoyancy Layer in a Stratified Fluid,' Int. J. Heat & Mass Transfer, Vol. 41, pp. 4393-4397 https://doi.org/10.1016/S0017-9310(98)00175-6
  10. Sakurai, T. and Matsuda, T., 1972, 'A Temperature Adjustment Process in a Boussineaq Fluid via a Buoyancy-induced Meridional Circulation,' J. Fluid Mech., Vol. 54, pp. 417-421 https://doi.org/10.1017/S002211207200076X
  11. Schopf, W. and Patterson, J.C., 1995, 'Natural Convection in a Side-Heated Cavity: Visualization of the Initial Flow Features,' Vol. 295, pp. 357-379 https://doi.org/10.1017/S002211209500200X
  12. Ravi, M.R., Henkes, R.A. W.M. Henkes and Hoogendoorn, C.J., 1994, 'On the High-Rayleigh-Number Structure of Steady Laminar Natural-Convection Flow in a Square Enclosure,' Vol. 262, pp. 325-351 https://doi.org/10.1017/S0022112094000522
  13. Veronis, G., 1970, 'The Analogy Between Ratating and Stratified Fluids,' Ann. Rev. Fluid Mechanics, Vol. 2, pp. 37-67 https://doi.org/10.1146/annurev.fl.02.010170.000345