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On the Dynamics of Flexible Plates under Rotational Motions
oleh: Shifeng Fu, Yaqing Jin, Jin-Tae Kim, Zhongyu Mao, Yuan Zheng, Leonardo P. Chamorro
Format: | Article |
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Diterbitkan: | MDPI AG 2018-12-01 |
Deskripsi
The reconfiguration of low-aspect-ratio flexible plates, required power and induced flow under pure rotation were experimentally inspected for various plate stiffness and angular velocities <inline-formula> <math display="inline"> <semantics> <mi>ω</mi></semantics></math></inline-formula>. Particle tracking velocimetry (PTV) and particle image velocimetry (PIV) were used to characterize the plate deformation along their span as well as the flow and turbulence statistics in the vicinity of the structures. Results show the characteristic role of stiffness and <inline-formula> <math display="inline"> <semantics> <mi>ω</mi> </semantics> </math> </inline-formula> in modulating the structure reconfiguration, power required and induced flow. The inspected configurations allowed inspecting various plate deformations ranging from minor to extreme bending over 90<inline-formula><math display="inline"><semantics><msup><mrow></mrow><mo>∘</mo> </msup> </semantics> </math> </inline-formula> between the tangents of the two tips. Regardless of the case, the plates did not undergo noticeable deformation in the last ∼30% of the span. Location of the maximum deformation along the plate followed a trend <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>s</mi> <mi>m</mi> </msub> <mo>∝</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo stretchy="false">(</mo> <mi>C</mi> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>a</mi> </mrow> </semantics> </math> </inline-formula> is the Cauchy number, which indicated that <inline-formula> <math display="inline"> <semantics> <msub> <mi>s</mi> <mi>m</mi> </msub> </semantics> </math> </inline-formula> is roughly fixed at sufficiently large <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>a</mi></mrow></semantics></math></inline-formula>. The angle (<inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>) between the plate in the vicinity of the tip and the tangential vector of the motions exhibited two distinctive, nearly-linear trends as a function of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>a</mi> </mrow> </semantics> </math> </inline-formula>, within <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>a</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mspace width="4pt"></mspace> <mn>15</mn> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>a</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>20</mn> <mo>,</mo> <mspace width="4pt"></mspace> <mn>70</mn> <mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>, with a matching within these <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>a</mi> </mrow> </semantics> </math> </inline-formula> at <inline-formula> <math display="inline"> <semantics> <mrow> <mi>C</mi> <mi>a</mi> <mo>></mo> <mn>70</mn></mrow></semantics></math></inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>≈</mo> <msup> <mn>45</mn> <mo>∘</mo></msup></mrow></semantics></math></inline-formula>. Induced flow revealed a local maximum of the turbulence levels at around 60% of the span of the plate; however, the largest turbulence enhancement occurred near the tip. Flexibility of the plate strongly modulated the spatial distribution of small-scale vortical structures; they were located along the plate wake in the stiffer plate and relatively concentrated near the tip in the low-stiffness plate. Due to relatively large deformation, rotational and wake effects, a simple formulation for predicting the mean reconfiguration showed offset; however, a bulk, constant factor on <inline-formula> <math display="inline"> <semantics> <mi>ω</mi> </semantics> </math> </inline-formula> accounted for the offset between predictions and measurements at deformation reaching ∼<inline-formula> <math display="inline"> <semantics> <msup> <mn>60</mn> <mo>∘</mo> </msup> </semantics> </math> </inline-formula> between the tips.