SCALING OF TRANSIENT NATURAL CONVECTION COOLING IN SIDE-COOLED CAVITY- THE EFFECT OF VARIABLE VISCOSITY (original) (raw)
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A numerical study of natural convection in cavity filled with air has been carried out under large temperature gradient. The flows 10 under study are generated by a heated solid body located close to the bottom wall in a rectangular cavity with cold vertical walls 11 and insulated horizontal walls. They have been investigated by direct simulations using a two-dimensional finite volume numerical code 12 solving the time-dependent Navier-Stokes equations under the low Mach number approximation. This model permits to take into 13 account large temperature variations unlike the classical Boussinesq model which is valid only for small temperature differences. We were 14 particularly interested in the first transitions which occur when the Rayleigh number is increased for flows in cavities of aspect ratio 15 A = 1, 2, 4. Starting from a steady state, the results obtained for A = 1 and A = 4 show that the first transition occurs through a super-16 critical Hopf bifurcation. The induced disturbances determined for weakly supercritical regimes indicate the existence of two instability 17 types driven by different physical mechanisms: shear and buoyancy-driven instabilities, according to whether the flow develops in a 18 square or in a tall cavity. For A = 2, the flow undergoes a pitchfork bifurcation leading to an asymmetric steady state which in turn 19 becomes periodic via a supercritical Hopf bifurcation point. In both the cases, the flow is found to be strongly deflected towards one 20 vertical wall and instabilities are found to be of shear layers type. 21 55 interferometer to observe the disturbances as they were 56 convected downstream. The experimental results show that 57 sufficiently high frequency disturbances are stable as they 58 are convected downstream. Later, calculations of the same 59 problem have been carried out by Haaland and Sparrow [5] 60 taking into account non-parallel and higher-order effects of 61 the base flow in the linear stability analysis. The authors 62 obtained a lower branch of neutral curve and then a critical 63 Grashof number. Their results show that the unstable 64 region is smaller than that obtained from the quasi-parallel 65 theory . The stability problem of non-parallel flows were 66 also investigated by Wakitani [7] using the method of mul-67 tiple scales. This method considers that the various distur-68 bance quantities have different amplification rates. Their 69 results relating to the amplification rate of disturbances 70 within unstable regions show a substantial deviation from 71 that predicted by the quasi-parallel theory. 72