A correlation model of energy and impulse losses for vortex ring-porous wall interactions

An experimental study was conducted to investigate the impingement of a vortex ring onto a porous wall by laser-induced fluorescence and particle image velocimetry. The effects of different Reynolds numbers ((Formula presented) and (Formula presented)) and hole diameters ((Formula presented), (Formula presented), (Formula presented) and (Formula presented)) on the flow characteristics were examined at a constant porosity ((Formula presented)). To characterise fluid transport through a porous wall, we recall the model proposed by Naaktgeboren, Krueger & Lage (2012, J. Fluid Mech., vol. 707, 260-286), which shows rough agreement with the experimental results due to the absence of vortex ring characteristics. This highlights the need for a more accurate model to correlate the losses in kinetic energy ((Formula presented)) and impulse ((Formula presented)) resulting from the vortex ring-porous wall interaction. Starting from Lamb’s vortex ring model and considering the flow transition from the upstream laminar state to the downstream turbulent state caused by the porous wall disturbance, a new model is derived theoretically: (Formula presented), where (Formula presented) is a parameter dependent on the dimensionless core radius (Formula presented), with (Formula presented) when no flow state change occurs. This new model effectively correlates (Formula presented) and (Formula presented) across more than 70 cases from current and previous experiments, capturing the dominant flow physics of the vortex ring-porous wall interaction.