Steady flow of a buoyant plume into a constant-density layer

Abstract

The upward flow of a buoyant plume emanating from a horizontal fissure into a two-layered fluid region is considered. Solutions are computed numerically for a range of fissure widths and water depths. It is shown that for a given fluid depth and fissure size there is a minimum flow rate beneath which no steady solutions exist. At this limiting flow, the fluid detaches from the wall of the fissure via a stagnation point. Solutions exist for all values of flow rate above this minimum. Exact solutions are presented for very large flow rates.

Inviscid and Viscous Models of Axisymmetric Fluid Jets or Plumes

“…(The corresponding axisymmetric flow, involving a "water bell" beneath a horizontal plate, has been investigated theoretically and confirmed in a series of elegant experiments by Button et al [5].) Similar methods to those of Christodoulides and Dias [7] were employed by Hocking and Forbes [14] in an analysis of a planar buoyant plume that rises vertically before spreading horizontally across an upper ceiling; plumes of this type occur in building fires. Their solutions were independent of time, and consequently only existed for flow speeds at the nozzle above some threshold minimum speed, and at that minimum configuration the plume interface formed a stagnation point at the nozzle itself.…”

“…These conditions (2.3) and (2.4) allow the solution to be developed using a spectral technique, as is discussed later. In their model of a planar plume, Hocking and Forbes [14] assumed a rigid upper boundary at z = h, and a similar condition could be considered here, too. Condition (2.4) has been adopted for simplicity, however, as it avoids the additional complication of a horizontal outflow along the upper boundary.…”

“…13) where the α n are the constants defined in equation(3.2). It follows from (5.4) that the vorticity has the formζ(r, z, t) = n B m,n (t)J 1 (γ m r) sin(α n z) + M m=1 γ m B m,0 J 1 (γ m r),(5 14). …”

Axisymmetric Plumes in Viscous Fluids

“…To address the issue of the initiation of a plume, Russell et al [29] have recently considered the way in which, in a two-dimensional model, a line source present in the bottom of a channel creates a growing mass of lighter-density fluid that moves vertically, before forming an overturning mushroom-shaped plume and then mixing laterally in the channel. Previously, Hocking and Forbes [16] had studied the steady inviscid behaviour of a two-dimensional plume in a channel, and obtained results in which the lighter fluid, introduced through a vent at the bottom of the channel, could rise up and flow outwards along the ceiling; to some extent, the work of Russell et al [29] shows how viscosity may alter that result.…”

Inviscid and viscous models of axisymmetric fluid jets or plumes

“…In their model of a planar plume, Hocking and Forbes [14] assumed a rigid upper boundary at z = h, and a similar condition could be considered here, too. Condition (2.4) has been adopted for simplicity, however, as it avoids the additional complication of a horizontal outflow along the upper boundary.…”