Vertical Aspect Ratio Research Articles

Transition to unsteady natural convection in a tall water-filled cavity

The transition to unsteady natural convection in a water-filled differentially heated cavity of vertical aspect ratio 10 is studied numerically by integrating two-dimensional Navier–Stokes equations in the Boussinesq approximation. The numerical algorithm combines a pseudospectral Chebyshev space discretization with a third-order time-stepping scheme. The top and bottom horizontal walls are considered to be either insulated or perfectly conducting. The critical Rayleigh number for adiabatic walls is found to be more than 30 times larger than that corresponding to perfectly conducting walls. In both cases, however, examination of the space-time structure of the temperature and velocity fluctuations shows that the onset of unsteadiness corresponds to boundary layer instability. In the case of perfectly conducting end walls, the transition to unsteady solutions possesses the characteristic features of a supercritical Hopf bifurcation. This is used to accurately determine the critical value. The dependence of the basic oscillation period in the vicinity of the critical Rayleigh number is given. Finally, the influence of unsteadiness on the local heat transfer coefficient is shown.

Steady three‐dimensional thermal convection in a vertical rectangular enclosure

AbstractThe numerical study of the steady 3D thermal flow regimes in a vertical enclosure with side‐wall heating and cooling is considered; a primitive variable Galerkin finite element method is used for the simulation in the Boussinesq approximation. The model consists of a rectangular box with vertical and horizontal aspect ratios, respectively, of lz = 12 (vertical length to box width) and ly = 8 (horizontal length to box width). The two large vertical plates are maintained at different and constant temperatures, and the remaining walls are assumed to be perfectly conducting. The enclosure is filled with a fluid of Prandtl number Pr=0.71, and the Grashof number Gr, based on the spacing between the large vertical walls, is up to 1.2 × 104. The 3D results presented herein were obtained with a 11 × 9 × 53 node mesh in half of the enclosure by imposing symmetry at the mid‐plane. The solution in the mid‐plane is compared with a 41 × 121 2D solution and laboratory observations at various Gr values. The transition between the monocellular and multicellular natural convective regimes is determined. The 3D aspect of the flow is illustrated and compared with the 2D solution. Near the onset of multicellular flow predicted by linear stability theory, the 2D and 3D simulations exhibit a steady multicellular structure. The calculated flow patterns are compared to visualizations obtained by smoke traces in physical experiments.

Enhanced Heat Transfer Due to Secondary Flows in Mixed Turbulent Convection

An experimental study of the fluid flow and heat transfer phenomena associated with opposing mixed turbulent convection in vertical ducts has been conducted. The duct considered had vertical and horizontal aspect ratios of 24.4 and 9.7, respectively. The working fluid was Freon-113, providing a Prandtl number of approximately 6.5. The results showed that a number of flow bifurcations occurred as GrDh/ReDh2 was increased. The first bifurcation observed was from parallel turbulent mean flow to a large single flow cell in the x−z plane. This occurred in the neighborhood of GrDh/ReDh2 = 2. Further bifurcations to multiple cells and eventually pure large-scale chaos were also observed. A correlation for the enhanced heat transfer was found to be NuDh/NuDh,0 = 1.0 + 0.9[ln(GrDh/ReDh2 + 1)]1.39, where NuDh,0 is the Petukhov–Virillov correlation for pure forced turbulent convection.