Effect of transverse gust on free-falling plates

The effects of transverse gusts on free-falling plates are investigated using two-way coupled fluid–structure interaction simulations for a Galilei number ( italic Ga <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:mtext mathvariant="italic" class="MJX-tex-mathit">Ga</mml:mtext> </mml:mrow> </mml:math> $\textit{Ga}$ ) between 10 and 50 and a density ratio ( rho <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:miρ</mml:mi> </mml:math> $\rho$ ) between 5 and 50. We consider gust ratios ( upper G Subscript italic upper R <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:msub mml:miG</mml:mi> mml:mrow mml:mrow <mml:mtext mathvariant="italic" class="MJX-tex-mathit">R</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> $G_{\textit{R}}$ ) of up to 5, where upper G Subscript italic upper R <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:msub mml:miG</mml:mi> mml:mrow mml:mrow <mml:mtext mathvariant="italic" class="MJX-tex-mathit">R</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> $G_{\textit{R}}$ is the ratio of the free-stream velocity change to an estimate of the terminal velocity. We demonstrate that the plate experiences the gust as a transient horizontal force, which displaces it horizontally. This results in a transient reduction in the angle of attack, an increase in absolute velocity and the generation of circulation. The vertical component of the latter increases the upward aerodynamic force, slowing down the vertical descent of the plate. Furthermore, the plate’s horizontal displacement with respect to its original wake results in a further transient increase in the upward aerodynamic force. The altitude gained by the plate in response to the gust is maximum for rho equals 15 <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:miρ</mml:mi> mml:mo=</mml:mo> mml:mn15</mml:mn> </mml:math> $\rho =15$ , and increases non-monotonically with italic Ga <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:mtext mathvariant="italic" class="MJX-tex-mathit">Ga</mml:mtext> </mml:mrow> </mml:math> $\textit{Ga}$ and upper G Subscript italic upper R <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:msub mml:miG</mml:mi> mml:mrow mml:mrow <mml:mtext mathvariant="italic" class="MJX-tex-mathit">R</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> $G_{\textit{R}}$ . The non-monotonic trend is due to plate pitch: if the maximum pitch of the plate in response to the gust is close to vertical, the plate temporarily falls faster, losing some of the altitude it has gained. The present findings reveal an energy-harvesting mechanism that free-falling bodies can exploit to increase their time afloat.