Author(s): K. J. Sene; N. H. Thomas; B. T. Goldring

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Abstract: A planar plunging jel can drive penetrating, attached, wavy or tranquil flows depending on its plunge angle and the geometry of the receiving chamber. Geometries considered here include supported and free-fall weir flows into a rectangular receiving chamber, and idealised siphon-priming model configurations. The very different air entrainment, detrainment and net transport characteristics of these patterns have practical importance for the design of aeration and downshaft hydraulic equipment as well as the priming of large siphon units. Two main studies are reported here, the first concerned with classification and characterisation of some main features of the flow patterns, the second with predictive calculations of bubble transport and detrainment in penetrating flows - the pattern of most practical concern for many applications. In the first part ofour paper, measurements of the conditions leading to each type of flow are described and attention is drawn to hysteresis (Coanda effect) in the pattern transitions. It is shown that the submerged flows have many similarities with wall-jet flows (i.e. with a solid wall instead of a free surface) in geometrically similar configurations. For a pre-existing condition of penetrating flow from a weir, the pattern transition to attached (i.e. free surface jet) flow occurs when the plunge angle is reduced to between 25° and 30°. For pre-existing attached flow, the transition to penetrating flow can be tripped at plunge angles above about 30° but may be delayed up to as much as 65°. Supporting the weir flow or shortening the receiving chamber encourages the penetrating pattern. At smaller plunge angles, between 10° and 30°, a stationary pattern of free surface waves is realised. Wavelength and amplitude measurements of this “wavy” flow regime are contrasted with the predictions of existing theory. At smaller plunge angles, less than 10° to 30°, a tranquil pattern is found in the absence of any hydraulic control on the supercritical weir flows as they enter the receiving water. Measurements of the reattachment length in the siphon-priming model configurations (i.e. plunging flow in a rectangular duct) and in the weir flows show good agreement with published data on wall-jet flows near solid boundaries. The second part of our paper is given to a more detailed investigation of the flows sustained by air entraining weir flows driving a penetrating pattern of flow in the receiving water. The submerged jet and its external entrainment field are represented along classical lines for equilibrium shear turbulent flows of thin free shear layers. The downwards transport of bubbles inside the jet, their escape due to the transverse component buoyancy forces and their subsequent advection by the external entrainment field prior to detrainment at the free surface are all explicitly calculated according to a simplified slip model. Experimental measurements of the free surface detrainment fluxes are reported and the detrainment locus (a measure of the location of the peak value detrainment flux) is compared with the theoretical predictions. The agreement is sufficient to think that our simple model captures the most significant aspects of the transport dynamics. A justification for the model is offered with reference to other experimental findings and recent developments in basic understanding and first principles modelling of two-phase flows. A caution is also offered about the limitations of any two-dimensional model as a representation of the three-dimensional reality when the latter exhibits large coherent vortex features which make a significant contribution to the flow and transport dynamics. Nevertheless, the model represents a sensible first step towards predictive guidelines for practictioners concerned with the net air demand of hydraulic equipment like weirs, downshafts and priming siphons.

DOI: https://doi.org/10.1080/00221688909499171

Year: 1989