On the drag of vortex rings interaction with a porous wall

Experimental investigations on the flow and drag characteristics of a laminar vortex ring impinging on a porous wall are conducted using time-resolved particle image velocimetry (PIV) and laser-induced fluorescence (LIF). Four cases with varying hole diameters ( d Subscript h Superscript asterisk <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msubsup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> ${d}_{{h}}^*$ = 0.067–0.20) are examined at a constant porosity ( phi equals 0.75 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0.75</mml:mn> </mml:math> ${\phi } = 0.75$ ). The evolution of the vortical structures is depicted by the finite-time Lyapunov exponent. To enhance the understanding of the formation of transmitted vortex rings, three-dimensional structures are constructed with LIF images in cross-sectional planes. Furthermore, the pressure fields are determined from PIV data using a physics-informed neural network that enables the calculation of the drag via the control volume method. The results reveal the unsteady behaviour of the drag with the vortex–wall interaction. In the strong-interaction stage, the drag is significantly influenced by both the momentum convection flux and the pressure terms, which are associated with the effect of d Subscript h Superscript asterisk <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msubsup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> ${d}_{{h}}^*$ on the near-wall flow characteristics. Notably, when d Subscript h Superscript asterisk <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msubsup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> ${d}_{{h}}^*$ = 0.20, the pressure term can make negative contributions, resulting in a local reduction in the drag. Conversely, the drag characteristics in the weak-interaction stage do not seem to depend on d Subscript h Superscript asterisk <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msubsup> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> ${d}_{{h}}^*$ . A further analysis indicates that for finite-thickness porous plates, the contributions of friction drag are significantly greater than those of form drag. Additionally, an a priori method for predicting impulse loss without quantitative measurements is proposed. Based on this method, the mean drag can be estimated, which is in good agreement with the experimental results.