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# Pressure Drop Through Anisotropic Porous Mediumlike Cylinder Bundles in Turbulent Flow Regime

[+] Author and Article Information
Tongbeum Kim

Thermofluid Division of MOE Key Laboratory for Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an 710049, P.R.C.tongbeum@gmail.com

Tian Jian Lu

MOE Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an 710049, P.R.C.

J. Fluids Eng 130(10), 104501 (Sep 04, 2008) (5 pages) doi:10.1115/1.2969454 History: Received October 17, 2007; Revised June 10, 2008; Published September 04, 2008

## Abstract

Pressure drop through anisotropic porous mediumlike cylinder bundles is experimentally examined in turbulent flow regime. Three porosities, $ε=0.66$, 0.82, and 0.90, are considered. The flow blockage by the cylinder bundles is varied, with the yaw angle $(α)$ used as an anisotropic measure. When the yaw angle is fixed while the porosity is varied, the pressure drop behaves as predicted by the force balance model, consistent with the classic observation: The pressure drop is proportional to the square of the flow velocity with the empirical proportionality as a function of $(1−ε1∕2)∕ε2$ obtained from the force balance model compared to that of $(1−ε)∕ε3$ from the hydraulic radius theory. On the other hand, for a given porosity, topological anisotropy of the cylinder bundles causes the sinusoidal response of the pressure drop to the variation of yaw angle. At $α=0deg$ with a $60deg$ period, the lowest pressure drop occurs from the most open configuration of the cylinder bundle whereas the largest flow blockage at $α=30deg$ causes the highest pressure drop. This variation appears to result from an increase in the drag coefficient of each cylinder element in a harmonic manner.

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## Figures

Figure 1

Schematics of test rig used for pressure drop measurement: (a) plan view; (b) side view

Figure 2

Control volume at the central part of the circular cylinder bank for the force balance analysis

Figure 3

Measured pressure drop and empirical constants in Eq. 6 for three porosities: (a) Um versus Δp∕L∕Um; (b) Red versus β′

Figure 4

Applicability of the force balance based model

Figure 5

Variation of empirical constant (β′) with yaw angle of the cylinder bundles for ε=0.90 at Red=2.5×103

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