AUTHOR=Zou Kaimin , Peng Ze-Rui , Chen Bo , Dai Huliang , Xiong Yongliang , Wang Lin 

TITLE=Hydrodynamic Coupling of Inverted Flags in Side-by-Side, Left Triangular and Right Triangular Configurations in a Uniform Flow

JOURNAL=Frontiers in Physics

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.936268

DOI=10.3389/fphy.2022.936268

ISSN=2296-424X

ABSTRACT=<p>The hydrodynamic coupling of inverted flexible flags in side-by-side, left triangular and right triangular configurations in a uniform flow is investigated numerically. Various arrangements can be characterized by the lateral and longitudinal gaps, i.e., <italic>H</italic> and <italic>G</italic>, respectively. For the side-by-side configurations, three typical modes are identified in flapping region, i.e., in-phase quasi out-of-phase (QOP) and out-of-phase (OP) modes, corresponding to 2P, irregular and 4(P + S) wake patterns, respectively. Further analysis on the mean drag coefficient <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>̄</mml:mo></mml:mover></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> and bending energy <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>̄</mml:mo></mml:mover></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> indicates that the side-by-side flags can not harvest more bending energy from surrounding flows than the isolated one, except for a narrow range of <italic>H</italic> ∈ (1.8, 2.5). Moreover, an additional inverted flag is placed in front or rear of the side-by-side flags to explore possible favorable arrangements for bending energy enhancement. Three typical modes have been identified in the <italic>H</italic> − <italic>G</italic> planes for both left and right triangular configurations, i.e., the regular-coupled (RC), irregular-coupled (IC) and decoupled (DC) modes, respectively. For left triangular configurations, the overall system may experience significant performance enhancement in some favorable configurations, corresponding to harvest enhancement region (HER) in the <italic>G</italic> − <italic>H</italic> plane; For the case in HER, especially, the <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>̄</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula> of the rear flag may increase by up to 30% than isolated flag. While for right triangular configurations, no HER is observed. The unsteady flow characteristics are further explored to reveal the mechanism of hydrodynamic coupling in system. The present study may shed some light on understanding the dynamics of this multi-flag system.</p>