Abstract
Sintered metal porous media are currently used to replace conventional orifices as restrictors in air-bearing systems. The flow properties in porous media are generally approximated by Darcy and Forchheimer regimes in different flow regions. In this study, an ISO expanded expression is proven defective when it is used to represent flow properties through porous media under slight pressure drops (\({<}10\) kPa). A modified Forchheimer equation is therefore developed to correlate the pressure drop with flow rate, including compressibility and inertial effects. Experimental and theoretical investigations on pressure drop characteristics are conducted with a series of metal-sintered porous media. Permeability is first determined in a strict Darcy region with \(Re<0.1\), followed by the inertial coefficient with \(Re>0.1\), rather than determining these two simultaneously. The theoretical mass flow rate in terms of the modified Forchheimer equation provides close approximations to the experimental data.
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Abbreviations
- \(A\) :
-
Cross-sectional area \((\hbox {m}^{2})\)
- \(b\) :
-
Critical pressure ratio
- \(C\) :
-
Sonic conductance \((\hbox {m}^{3}\, \hbox {Pa}^{-1}\, \hbox {s}^{-1})\)
- \(D\) :
-
Diameter of the resistance (m)
- \(f\) :
-
Friction factor
- \(G\) :
-
Mass flow rate (kg/s)
- \(K\) :
-
Permeability \((\hbox {m}^{2})\)
- \(L\) :
-
Length of the resistance (m)
- \(m\) :
-
Mass of the resistance (kg)
- \(P\) :
-
Absolute pressure (Pa)
- \(P_{1}\) :
-
Upstream pressure (Pa)
- \(P_{2}\) :
-
Downstream pressure (Pa)
- \(R\) :
-
Gas constant (J/(kg K))
- \(Re\) :
-
Reynolds number
- \(T\) :
-
Temperature (K)
- \(v\) :
-
Flow velocity (m/s)
- \(x\) :
-
Displacement along the length direction (m)
- \(\beta \) :
-
Inertial coefficient
- \(\gamma \) :
-
Density of steel alloy \((\hbox {kg/m}^{3})\)
- \(\varepsilon \) :
-
Porosity
- \(\mu \) :
-
Air viscosity (Pa s)
- \(\rho \) :
-
Air density \((\hbox {kg/m}^{3})\)
- \(\rho _{0}\) :
-
Air density under normal condition \((\hbox {kg/m}^{3})\)
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Acknowledgments
This study was supported by the National Natural Science Foundation of China (Grant No. 51205174), the Natural Science Foundation of Ningbo City (Grant No. 2013A610049), and the Science and Technology Service Demonstration Project of Ningbo City (Grant No. 201201F1000041).
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Zhong, W., Li, X., Liu, F. et al. Measurement and Correlation of Pressure Drop Characteristics for Air Flow Through Sintered Metal Porous Media. Transp Porous Med 101, 53–67 (2014). https://doi.org/10.1007/s11242-013-0230-2
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DOI: https://doi.org/10.1007/s11242-013-0230-2