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There are no existing experimental studies of flame spread rate trends for ultra-thin solid samples. Previous theory has predicted that for concurrent flame in kinetic regime, the flame spread rate decreases as the sample thickness decreases and there is a critical thickness below which burning is not possible. To test this hypothesis, a series of microgravity experiments of concurrent-flow flame spread over samples of ultra-low area densities are conducted using NASA Glenn Research Center’s Zero Gravity Research Facility (the 5.18 s drop tower). The tested samples are cellulose-based materials of various area densities, ranging from 0.2 mg/cm2 to 13 mg/cm2, as low as one order of magnitude less than those ever tested before. Each sample is 30 cm long by 5 cm wide and is burned in a low-speed concurrent air flow (5 to 30 cm/s). The results show that the concurrent flame spread rate is proportional to the flow velocity relative to the flame and is inversely proportional to the sample area density. A theoretical formulation, provided in this work, suggests that the flame length has a linear relationship with the relative flow speed and has no direct dependency on the sample area density. The experimental data supports this conclusion. From the images recorded in the experiments, a unique flame base tubular structure directed upstream away from the burnout zone is observed for thin samples. This structure is suspected to be due to flame stretching and localized blowoff caused by the oxidative pyrolysis Stefan flows at the sample burnout. This can be an indication that the chemical time becomes comparable to the flow time of the Stefan flow and the tested samples are approaching the kinetically-limited thickness. For the thinnest tested sample (0.2 mg/cm2), flames with concurrent and opposed dual natures are observed when the air flow rate is low (< 20 cm/s). At the lowest tested flow rate (5 cm/s), the flame spread rate exceeds the air flow rate and the flame transits to an opposed flame in the concurrent flow. The dual nature and flame transition are presented and discussed. This study provides detailed examination through high-resolution images of the transition between the concurrent to opposed flame spread modes.
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Receiver design for spread-spectrum communications with a small spread in underwater clustered multipath channels
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null (Ed.)A group G is said to be 3/2-generated if every nontrivial element belongs to a generating pair. It is easy to see that if G has this property, then every proper quotient of G is cyclic. In this paper we prove that the converse is true for finite groups, which settles a conjecture of Breuer, Guralnick and Kantor from 2008. In fact, we prove a much stronger result, which solves a problem posed by Brenner and Wiegold in 1975. Namely, if G is a finite group and every proper quotient of G is cyclic, then for any pair of nontrivial elements x1, x2 ϵ G, there exists y ϵ G such that G = ⟨x1, y⟩ = ⟨x2, y⟩. In other words, s(G) ⩾ 2, where s(G) is the spread of G. Moreover, if u(G) denotes the more restrictive uniform spread of G, then we can completely characterise the finite groups G with u(G) = 0 and u(G) = 1. To prove these results, we first establish a reduction to almost simple groups. For simple groups, the result was proved by Guralnick and Kantor in 2000 using probabilistic methods, and since then the almost simple groups have been the subject of several papers. By combining our reduction theorem and this earlier work, it remains to handle the groups with socle an exceptional group of Lie type, and this is the case we treat in this paper.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1121/1.4977747
