Skip to main content Accessibility help

Transient features of natural convection in a cavity

  • John C. Patterson (a1) and S. W. Armfield (a1)

Comparisons of numerical and experimental results for transient two-dimensional natural convection initiated by instantaneously heating and cooling the opposing vertical walls of a square cavity containing a stationary and isothermal fluid are presented. The good comparisons indicate that the simulation is capturing the important features of the flow. Several features are identified and discussed in detail; in particular, the presence of travelling wave instabilities on the vertical-wall boundary layers and horizontal intrusions, the existence of a rapid flow divergence in the region of the outflow of the intrusions, and the presence of cavity-scale oscillations, caused by the interaction of the intrusions with the opposing vertical boundary layer. The utilization of both numerical and experimental investigations has allowed a more complete exploitation of the available resources than would have been possible had each been conducted separately.

Hide All
Armfield, S. W.: 1989 Direct simulation of unsteady natural convection in a cavity. In Proc. 3rd Intl Symp. on Computational Fluid Dynamics, Nagoya, pp. 305310. North-Holland.
Batchelor, G. K.: 1954 Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures. Q. J. Appl. Maths 12, 209233.
Bergholz, R. F.: 1978 Instability of steady natural convection in a vertical fluid layer. J. Fluid Mech. 84, 743768.
Brown, S. N. & Riley, N., 1973 Flow past a suddenly heated vertical plate. J. Fluid Mech. 59, 225237.
Carslaw, H. A. & Jaeger, J. C., 1959 Conduction of Heat in Solids. Oxford University Press.
Catton, I.: 1978 Natural convection in enclosures. 6th Intl Heat Transfer Conf. Toronto, vol. 6, pp. 1343. Hemisphere.
Chenoweth, D. R. & Paolucci, S., 1986 Natural convection in an enclosed vertical air layer with large horizontal temperature differences. J. Fluid Mech. 169, 173210.
Gebhart, B. & Mahajan, R. L., 1982 Instability and transition in buoyancy induced flows. Adv. Appl. Mech. 22, 231315.
Gill, A. E. & Davey, A., 1969 Instabilities of a buoyancy-driven system. J. Fluid Mech. 35, 775798.
Gresho, P. M., Lee, R. L., Chan, S. T. & Sani, R. L., 1980 Solution of the time-dependent incompressible Navier–Stokes and Boussinesq equations using the Galerkin finite element method. In Approximation Methods for Navier–Stokes Problems (ed. R. Rautmann). Lecture Notes in Mathematics vol. 771, pp. 203222. Springer.
Issa, R. I.: 1983 Solution of the implicitly discretised fluid flow equations by operator splitting. Rep. FS/82/15. Imperial College London.
Ivey, G. N.: 1984 Experiments on transient natural convection in a cavity. J. Fluid Mech. 144, 389401.
Jackson, C. P. & Robinson, P. C., 1985 A numerical study of various algorithms related to the preconditioned conjugate gradient method. Intl J. Num. Methods Engng 21, 13151338.
Kightly, J. R.: 1986 The conjugate gradient method applied to turbulent flow calculations. In Proc. 6th GAMM Conf. on Numerical Methods in Fluid Mechanics (ed. D. Rues & W. Kordulla), pp. 161168.
Leonard, B. P.: 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Meth. Appl. Mech. Engng 19, 5998.
Le Queré, P. & De Roquefort, T. Alziary 1985 Transition to unsteady natural convection of air in differentially heated vertical cavities. In Numerical Methods in Laminar and Turbulent Flow, Proc. 4th Intl Conference, Swansea, pp. 841852.
Maliska, C. R. & Raithby, G. D., 1983 Calculating 3-D fluid flows using non-orthogonal grid. In Proc. Third Intl Conf. on Numerical Methods in Laminar and Turbulent Flows, Seattle, pp. 656666. Pineridge.
Ostrach, S.: 1982 Natural convection heat transfer in cavities and cells. 7th Intl Heat Transfer Conf. Munich, vol. 1, pp. 365379. Hemisphere.
Paolucci, S. & Chenoweth, D. R., 1989 Transition to chaos in a differentially heated vertical cavity. J. Fluid Mech. 201, 379410.
Patankar, S. V.: 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Patterson, J. C.: 1983 General derivative approximations for finite difference schemes. Intl J. Numer. Meth. Engng 19, 12351241.
Patterson, J. C.: 1984 On the existence of an oscillatory approach to steady natural convection in cavities. Trans. ASME C: J. heat Transfer 106, 104108.
Patterson, J. C.: 1989 Experiments in unsteady natural convection. In Proc. Fourth Australasian Conference on Heat and Mass Transfer, Christchurch, pp. 299306.
Patterson, J. C. & Imberger, J., 1980 (referred to herein as PI). Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 6586.
Perng, C. Y. & Street, R. L., 1990 Three dimensional unsteady flow simulations: alternative strategies for volume averaged calculation. Intl J. Numer. Meth. Fluids (in press).
Rhee, H. S., Koseff, J. R. & Street, R. L., 1984 Flow visualization of a recirculating flow by rheoscopic liquid and liquid crystal techniques. Exps. Fluids 2, 5764.
Schladow, S. G.: 1990 Oscillatory motion in a side-heated cavity. J. Fluid Mech. 213, 589610.
Schladow, S. G., Patterson, J. C. & Street, R. L., 1989 Transient flow in a side-heated cavity at high Rayleigh number: a numerical study. J. Fluid Mech. 200, 121148.
Staehle, B. & Hahne, E., 1982 Overshooting and damped oscillations of transient natural convection flows in cavities. 7th Intl Heat Transfer Conf., Munich, vol. 2, pp. 287292. Hemisphere.
Tzuoo, K. L., Chen, T. S. & Armaaly, B. F., 1985 Wave instability of natural convection flow on inclined surfaces. Trans. ASME C: J. Heat Transfer 107, 107111.
Van Doormal, J. P. & Raithby, G. D. 1984 Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numer. Heat Transfer 9, 147163.
Yewell, P., Poulikakos, D. & Bejan, A., 1982 Transient natural convection experiments in shallow enclosures. Trans. ASME C: J. Heat Transfer 104, 533538.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed