The Emptying-box problem with a baffle of different porosity percentages

Abstract

This research studies the Emptying-box problem with a porous baffle just behind the entrance opening. A theoretical model is extended to include the effect of a porous baffle, and the theoretical model taking account of porosity establishes the connections between two typical unidirectional displacement flow types. The salt-bath technique is employed to conduct the experiments using an acrylic reduced-scale model. Dye attenuation technique is used to analyze the light intensity data derived from the recorded images of experiments. According to the baffle porosity percentage (ϕ), the experiments are categorized into two series, EM(79%) and EM(60%). Each series respectively includes three different opening area ratios, which are 1, 0.5 and 0.33. Experimental results show that emptying processes for the cases with a baffle of the larger porosity percentage consist of emptying the dense layer and emptying the mixed layer, but there is only one process of emptying the dense layer for the cases with a baffle of the smaller porosity percentage. Experimental results are in reasonable agreement with the extended theoretical model developed in this research. Two extreme cases, those with and without an impenetrable baffle, are included in this paper to represent two typical flow types of the horizontal inflow denoted as EM(H), as that with ϕ=0%, and the vertical inflow denoted as EM(V), as that with ϕ=100%, i.e. the unidirectional classical displacement flow and the displacement flow with interfacial mixing. As the porosity percentage increases, the emptying time for the dense layer decreases, but the emptying time for the whole box tends to increase. The emptying time for the dense layer decreases, when the total effective opening area or the reduced gravity increases for the cases having the same porosity percentage. The initial interfacial height of the mixed layer increases, as the baffle porosity percentage increases for the cases having the fixed total effective opening area, or the total effective opening area increases for the cases with the same baffle porosity percentage. The initial buoyancy of the mixed layer is dependent on the penetrative entrainment flow rate from the dense layer to the mixed layer and the emptying time for the dense layer. As the total effective opening area or the porosity percentage increases, experimental results show that the initial buoyancy of the mixed layer tends to increase, and the penetrative entrainment flow rate increases as well, but the emptying time for the dense layer decreases.