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Momentum transfer across a semi-circular porous cylinder attached to a channel wall

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Abstract

Momentum transfer from a semi-circular porous cylinder attached to a rectangular channel wall has been investigated for the numerous values of germane parameters as Reynolds number \((0.01\le Re \le 40),\) Darcy number \((10^{-6} \le Da \le 10^{-1}),\) blockage ratio \((0.1667\le \beta \le 1.5)\) and porosity \((0.1 \le \epsilon \le 0.9).\) The porous media flow has been numerically modeled by implementing the Darcy-Brinkman-Forchheimer model. The combined influences of all the aforementioned parameters on the flow field are visualized by streamlines and vorticity profiles. The detailed insights of the flow field are provided by representing the pressure coefficient distribution and the values of the drag coefficient. The obtained results depict that the porosity influences flow characteristics at the high values of Darcy number. The pressure coefficient represents an inverse relationship with \(\beta\). The drag coefficient increases by increasing \(\beta\) for all governing parameters. Furthermore, the drag coefficient shows a decreasing behavior for \(Da \ge 10^{-3}\) whereas it shows an involute dependency for \(10^{-6} \le Da \le 10^{-4}.\) Overall, the complex influences of \(Re, Da, \beta ,\) and \(\epsilon\) on the flow field have been observed.

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Abbreviations

\(C_D\) :

drag coefficient (dimensionless), \(C_D=\frac{ 4 F_D}{ \rho U_{\infty }^2 D}\)

\(C_P\) :

pressure coefficient (dimensionless), \(C_P=\frac{2(p_s-p_{\infty })}{ \rho U_\infty ^2}\)

D :

diameter of the porous cylinder (m)

Da :

Darcy number (dimensionless), \(Da=\frac{\kappa }{D^2}\)

F :

Forchheimer inertial coefficient (dimensionless),\(F=\frac{1.75}{\sqrt{150}} \frac{1}{\epsilon ^{3/2}}\)

\(F_{D}\) :

total drag force (N/m)

H :

height of the channel (m)

\(L_{in}\) :

inlet length (m)

\(L_{out}\) :

outlet length (m)

N :

total triangular elements in the flow domain (dimensionless)

\(n_p\) :

total triangular elements on the edge of the porous cylinder (dimensionless)

P :

pressure (dimensionless), \(P=\frac{p}{\rho U_\infty ^2}\)

p :

pressure (Pa)

\(p_\infty\) :

far away pressure (Pa)

\(p_s\) :

local surface pressure (Pa)

Re :

Reynolds number (dimensionless), \(Re=\frac{\rho U_\infty D}{\mu _f}\)

UV :

velocity components (dimensionless), \(U=\frac{u}{U_\infty }, V=\frac{v}{U_\infty }\)

uv :

velocity components (m/s)

\(U_{\infty }\) :

far away velocity (m/s)

XY :

coordinates (dimensionless), \(X=\frac{x}{D}, Y=\frac{y}{D}\)

xy :

coordinates (m)

\(\beta\) :

blockage ratio of the channel (dimensionless), \(\beta =\frac{D}{H}\)

\(\delta\) :

grid spacing in the proximity of the permeable cylinder

\(\epsilon\) :

porosity (measure of void space in porous medium)

\(\kappa\) :

permeability of the porous cylinder (\(m^2\))

\(\mu _e\) :

effective viscosity \((kg m^{-1} s^{-1})\)

\(\mu _f\) :

fluid viscosity \((kg m^{-1} s^{-1})\)

\(\rho\) :

fluid density (\(kg m^{-3}\))

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Kaur, R., Chandra, A. & Sharma, S. Momentum transfer across a semi-circular porous cylinder attached to a channel wall. Meccanica 56, 2219–2241 (2021). https://doi.org/10.1007/s11012-021-01369-5

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