## Hydraulic resistance, shock wave attenuation and gaseous detonation extinction in granular materials

##### Doctoral thesis

##### Permanent lenke

http://hdl.handle.net/11250/229122##### Utgivelsesdato

2002##### Metadata

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##### Sammendrag

Military and civil installations can be equipped with a granular filter, for example in air inlet systems to protect against blast waves. Granular filters also have a certain potential to replace shock valves and to work as gaseous detonation arresters in various industrial applications. Such use of granular filters requires estimates for the hydraulic resistance for the purpose of dimensioning fans, compressors et cetera. The potential for shock wave attenuation and gaseous detonation extinction should also be possible to estimate in order to specify correct safety limits with large enough safety margins for personnel and mechanical installations.
Pressure drop in granular materials can be predicted by various correlations available. No single correlation can be found to be the best. Uncertainties in various parameters, especially porosity and surface roughness, will give some random scattering of experimental data. The well known correlation for modified friction factor by Ergun (1952), fm = α(1- ε )/Re+ β where α and β are constants, is suggested with possible adjustments to the constant β for improving the pressure drop prediction for various particle types in the high Reynolds number range. Based on the current experiments and the work of others, a β value of 1.0 is suggested for smooth spheres, and 2.5 is suggested for crushed rock. Ergun (1952) used 1.75 for all particle types.
No correlation for predicting shock wave attenuation in granular materials exists in the literature. Medvedev et al. (1990) suggest an analytical solution based on an assumption by Whitham (1974). This solution is a function of incoming shock wave pressure, while experimental data, both in this study and from others, indicate a more random scattering of the results and no obvious dependency of incoming shock wave pressure. Based on the work of Zloch (1976), an empirical correlation p2/p1 = 1/(1+Bθ ) is proposed for predicting shock wave attenuation in granular filters. Here B is an empirical constant and θ =fmLgf(1- ε)/(εdp) is the filter characteristics. By adjusting the constant B, a best or a conservative fit to the experimental data can be found. Values for B can typically be in the range 1/2 to 1/ 6 with 1/6 as the most conservative value. The proposed correlation corresponds well with the analytical solution, it is far easier to calculate, and it is better suited for conservative calculations when incoming shock wave pressure is not known.
Both a phenomenological and a numerical model for simulating one-dimensional non-stationary shock wave propagation through granular materials are developed, based both on the work of others and by comparing with current experimental data. The numerical model is found to be fairly accurate for a large variety of experimental conditions.
Filters consisting of granular materials can change a gaseous detonation wave into a fast deflagration wave or completely extinguish it. A gaseous detonation wave can also be unaffected by the granular filter if the detonation cell size is small compared to the granular particles. The influence of a granular filter on a gaseous detonation wave may depend on the detonation cell size and regularity, particle diameter, shape and surface and granular filter length. Failing of a gaseous detonation wave is expected to become more likely as the detonation cell size and regularity increase for a certain filter type, or if the particle diameter and surface smoothness decrease for a certain detonating mixture.
In the present study, transmission of gaseous detonation waves through granular filters has been investigated. Spherical glass beads of 4 and 8 mm diameter and crushed rock of 7.5 mm volume averaged diameter were tested. Varying of the initial pressure of the detonating gas mixture was used to control the detonation cell size. Adding of argon was used to vary the detonation cell regularity. The complete range from almost no detonation velocity deficit to complete extinction of the combustion wave was considered.
The existing correlation from Makris et al. (1995) for gaseous detonation velocity deficit V/VCJ = [1-0.35log(dc/dps)] ± 0.1 where dc is critical tube diameter for the gaseous detonation and dps is pore size, is found to be applicable for both smooth spherical particles and irregular crushed rock when considering irregular detonation structures. The pore size dps was similar to Makris et al. (1995) estimated as dp/3 where dp is particle diameter. Soot films and pressure measurements indicate that as the detonation cell size is increased, reinitiation of a regular CJ-detonation moves further downstream from the granular filter before it finally no longer occurs at V/VCJ ≈ 0.4-0.45. Complete extinction of the combustion wave occurs at V/VCJ ≈ 0.25-0.3. These two limits appear to be fairly the same for irregular and regular detonation cell structures. For argon dilution resulting in regular detonation cells, the corresponding dc/dps ratio is, however, changed compared to the irregular structures. For irregular structures without argon dilution dc/dps ≈ 50 can be found for detonation extinction and dc/dps ≈ 100 can be found for complete extinction of the combustion wave. For argon dilution these limits are changed to dc/dps ≈ 10 and dc/dps ≈ 40 respectively. The data are a bit scarce for proposing a new correlation for regular structures, but as a first approximation, a modified equation V/VCJ = [0.8-0.35log(dc/dps)] ± 0.1 is suggested for regular structures. The gaseous detonation or combustion wave is found to approach a constant velocity in the granular filter if not extinguished.