AUTHOR=Mahmood Rashid , Siddique Imran , Khan Ilyas , Badran Mohamed , Mehrez Sadok , Majeed Afraz Hussain , Naaz Sehrish 

TITLE=Numerical Computation for Modified Cross Model Fluid Flow Around the Circular Cylinder with Symmetric Trapezoidal Cavities

JOURNAL=Frontiers in Physics

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.912213

DOI=10.3389/fphy.2022.912213

ISSN=2296-424X

ABSTRACT=<p>This manuscript explores the flow features of the Modified Cross Model in a channel with symmetric trapezoidal cavities in the presence of a circular obstacle. The non-dimensional governing equations and model for different parameters are evaluated via a Galerkin Finite Element Method The system of non-linear algebraic equations is computed by adopting the Newton method. A space involving the quadratic polynomials (<inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="double-struck">P</mml:mi><mml:mn mathvariant="italic">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) has been selected to compute for the velocity profile while the pressure profile is approximated by a linear (<inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="double-struck">P</mml:mi><mml:mn mathvariant="italic">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) finite element space of functions. Simulations are performed for a wide range of physical parameters such as modified parameter (from 0.0 to 0.5), power-law index (from 0.5 to 1.5), relaxation parameter (from 1 to 3), and Reynolds number (from 10 to 40). For the case of a modified parameter (<inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:math></inline-formula>) and relaxation parameter (<inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:math></inline-formula>), it is observed that the drag coefficient (<inline-formula id="inf5"><mml:math id="m5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>D</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) shows an increasing trend while the lift coefficient (<inline-formula id="inf6"><mml:math id="m6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) is changing sign at lower values of (<inline-formula id="inf7"><mml:math id="m7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>λ</mml:mi></mml:mrow></mml:math></inline-formula>), and then becomes positive at <inline-formula id="inf8"><mml:math id="m8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>λ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="italic">3</mml:mn></mml:mrow></mml:math></inline-formula>.</p>