AUTHOR=Abbasi Waqas Sarwar , Ismail Saba , Nadeem Sumaira , Rahman Hamid , Majeed Afraz Hussain , Khan Ilyas , Mohamed Abdullah 

TITLE=Passive control of wake flow behind a square cylinder using a flat plate

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1132926

DOI=10.3389/fphy.2023.1132926

ISSN=2296-424X

ABSTRACT=<p>In this study, control over the wake flow of a single square cylinder exercised by a flat plate attached to the rear side of the cylinder is analyzed numerically via the lattice Boltzmann method. The Reynolds number (<inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:math></inline-formula>) is fixed at 150, and the length of the plate is varied from 0.1 to 8.5. Three distinct flow modes are observed in this study: unsteady, transient, and steady flow in the cases of plate lengths (<inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:math></inline-formula>) in the ranges 0.1 <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≤</mml:mo></mml:mrow></mml:math></inline-formula><inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:math></inline-formula><inline-formula id="inf5"><mml:math id="m5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≤</mml:mo></mml:mrow></mml:math></inline-formula> 6.5, 6.75 <inline-formula id="inf6"><mml:math id="m6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≤</mml:mo></mml:mrow></mml:math></inline-formula><inline-formula id="inf7"><mml:math id="m7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:math></inline-formula><inline-formula id="inf8"><mml:math id="m8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≤</mml:mo></mml:mrow></mml:math></inline-formula> 7.5, and 7.75 <inline-formula id="inf9"><mml:math id="m9" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≤</mml:mo></mml:mrow></mml:math></inline-formula><inline-formula id="inf10"><mml:math id="m10" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:math></inline-formula><inline-formula id="inf11"><mml:math id="m11" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>≤</mml:mo></mml:mrow></mml:math></inline-formula> 8.5, respectively. The streamlines exhibit different flow structures, termed hairpin-like, ellipse-like, and elongated bubble-like, at different values of <italic>L</italic>. Complete wake control is achieved at plate lengths beyond 7.75. This study reveals that the drag and lift coefficients exhibit unsteadiness at short plate lengths in early time steps, but as the plate length increases, unsteadiness slows down and eventually disappears, confirming the steady flow pattern. The mean drag coefficient (<inline-formula id="inf12"><mml:math id="m12" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>C</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), Strouhal number (<inline-formula id="inf13"><mml:math id="m13" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math></inline-formula>), and root-mean-square value of drag and lift coefficients (<inline-formula id="inf14"><mml:math id="m14" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>C</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>m</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>; <inline-formula id="inf15"><mml:math id="m15" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>C</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>r</mml:mi><mml:mi>m</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) are reduced by maximums of 23.5%, 100%, 84.6%, and 99.5%, respectively, as a result of the presence of the plate.</p>