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Determination of Darcian permeability of porous material by infrared spectrometry

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Abstract

The active cooling of aerospace structures can be performed by the use of porous materials. It requires characterizing its permeability to predict the cooling efficiency by means of Computational Fluid Dynamics codes. The Darcian term is generally deduced experimentally from a relationship between the mass flow rate and the pressure drop through the porous media. Due to thermo-chemical process involved in the cooling, the permeability can change. It is currently not possible with common techniques to determine these variations during the flight. This paper presents a novel approach taking advantage of well known flow behaviour in chemical reactor engineering in order to propose a real-time in situ quantification of the Darcian permeability. The residence time distribution is analyzed thanks to tracer injection and to associated experimental measures of Infra-Red signals. The IR peak characteristics (height, width, surface, rising and falling gradients) and time delays are analyzed and correlated to physical parameters (mass flow rate, injected mass of tracer, properties of fluids). The peak height and surface and the rising gradient vary linearly in the same sense as the injected tracer mass while the falling gradient varies in the opposite sense. Both gradients decrease with a mass flow rate increase. The time delay between injection and detection of the tracer is quite constant except when changing the fluid nature. A design of experiments allowed estimating quantitatively the influence of each physical parameter on the optical one of the IR signal. Thanks to this first understanding, the Darcian permeability is linked to the observed IR signal. A linear regression is proposed with the peak width which is judged to be the most relevant parameter. Finally, an analytical approach is developed to fit ordinary differential equations to IR peak measures and to correlate the parameters of the law to the Darcian permeability. Several laws (linear, logarithmic and power) are proposed depending on the parameter but the linear regression involving the coefficient noted β 1 is the most promising. One of the advantages of this method is to be able measuring the permeability during the flight and not only on-ground with specific test facility.

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Abbreviations

K D :

Darcian permeability (m²)

K F :

Forchheimer permeability (m)

L :

Porous media thickness (m)

P :

Pressure (Pa)

Q :

Flow rate (m3 s−1)

T :

Time (s)

ν :

Fluid velocity (m s−1)

V :

Volume (m3)

X :

Mole fraction ()

α :

Adjustment coefficient

β :

Adjustment coefficient

Μ :

Dynamic viscosity (Pa.s)

ΔP :

Pressure drop through the porous material (Inlet Pressure minus outlet one, in Pa)

μ :

Density (kg m−3)

0 :

Subscript for initial conditions (time t=0)

Bench :

Subscript for the bench outlet

Cell :

Subscript for FTIR (Fourier Transform Infra Red spectrometer) optical cell

Inlet :

Subscript referring to inlet conditions of the cell or of the bench

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Acknowledgments

This work was supported by the ESA-ESTEC, Contract no.: 3-12861/09/NL/PA. The authors would like to sincerely thank J. Steelant from ESA, M. Bouchez and B. Le Naour from MBDA-and D. Blanc and D. Courilleau from the IUT Bourges.

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Authors and Affiliations

  1. University of Orléans, 63, Avenue de Lattre de Tassigny, 18000, Bourges, France

    Nicolas Gascoin, Guillaume Fau & Philippe Gillard

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  1. Nicolas Gascoin
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  2. Guillaume Fau
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  3. Philippe Gillard
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Correspondence to Nicolas Gascoin.

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Gascoin, N., Fau, G. & Gillard, P. Determination of Darcian permeability of porous material by infrared spectrometry. J Porous Mater 19, 317–331 (2012). https://doi.org/10.1007/s10934-011-9478-5

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  • DOI: https://doi.org/10.1007/s10934-011-9478-5

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