Mixed Convection in an Annulus of Large Aspect Ratio

Abstract

ixed Convection in an Annulus of Large Aspect Ratio Mixed convection in an annulus of large aspect ratio is studied. At an aspect ratio of 100, the effect of wall curvature is minimal, and both the base flow and the stability characteristics approach those of a two-dimensional channel flow. The linearstability results demonstrate that the fully developed flow is unstable in regions of practical interest in an appropriate parameter space. Consequently, commonly assumed steady parallel countercurrent flows in many idealized numerical and analytical studies are unlikely to be observed experimentally.

Stability of mixed-convection flow in a tall vertical channel under non-boussinesq conditions

“…Orszag (1971) and more recently by Davey (unpublished, but see Drazin & Reid 1987, p. 205) who obtained: Re: = 5772.2218, a: = 1.020547, and c: = 0.2640003. Furthermore, our Gr,-Re parameter space is in excellent agreement with the one computed by Yao & Rogers (1989) (they display theirs in the Gr,/Re-Re parameter space). We note that for a range of Reynolds numbers somewhat larger than [Re,/ there exist regions where an increase in Grashof number has a stabilizing influence on the predominantly pressure-gradient driven flow.…”

“…We next formulate the linear stability problem of this flow, and subsequently solve the resulting perturbation equations using an integral Chebyshev pseudo-spectral method. The primary conclusions of the study for Pr = 0.71 are that: (i) the instability is almost always oscillatory; (ii) for temperature differences smaller than a critical value, the instability is always shear driven but the character changes as a function of Reynolds number in a way similar to that found by Yao & Rogers (1989); (iii) for temperature differences greater than a critical value, a new mode of instability (due entirely to non-Boussinesq effects) is found which is purely thermal in character in that the disturbance energy is gained from the potential energy associated with the buoyant forces, and is analogous to but not the same as the type of instability found for Pr > 12.45 in the Boussinesq case; (iv) there exists a critical Reynolds number in the non-Boussinesq regime at which the instability switches between different modes associated with shear.…”

“…The points where the two stability branches intersect in figure 6 (a) correspond to a switch from mixed to shear types of instability, according to Yao & Rogers' (1989) terminology. This switch is found to be very abrupt for e < 0.050 and is smoothed out for positive-Reynolds-number flows for e > 0.075 as shown in figure 7.…”

“…They find the experimental results to be in excellent agreement with their stability results. Yao & Rogers (1989) analyse the stability of the mixed-convection flow within a vertical annulus whose cylindrical walls are maintained at different temperatures, and whose ratio of inside radius to gap width is 100. In this case, the effect of wall curvature is minimal.…”

Uncertainty of convection

“…However, recent work has shown that fully developed mixed convection flows in vertical ducts are highly unstable due to thermally-induced instabilities [1][2][3][4]. [7].…”