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The low-density gas jet injected into a high-density ambient has particular interest in several industrial applications such as fuel leaks, engine exhaust, diffusion flames, materials processing, as well as natural phenomena such fires and volcanic eruptions. The most interesting application of this problem nowaday is the hydrogen leaks in air; since when it mixes with air, fire or explosion can result. The expected extensive usage of hydrogen increases the probability of its accidental release from hydrogen vessel infrastructure. Hydrogen energy has much promise as a new clean energy and is expected to replace fossil fuels; however, hydrogen leakage is considered to be an important safety issue and is a serious problem that hydrogen researchers must address. Hydrogen leaks may occur from loose fittings, o-ring seals, pinholes, or vents on hydrogen-containing vehicles, buildings, storage facilities, or other hydrogen-based systems. Hydrogen leakage may be divided into two classes, the first is a rapid leak causing combustion, while the other is an unignited slow-leak. However, hydrogen is ignited in air by some source of ignition such as static electricity (autoignition) or any external source. Classic turbulent jet flame models can be used to model the first class of hydrogen leakage; cf. (Schefer et al., 2006; Houf & Schefer, 2007; Swain et al., 2007; Takeno et al., 2007). This work is focused on the second class of unignited slow-leaks. Previous work introduced a boundary layer theory approach to model the concentration layer adjacent to a ceiling wall at the impinging and far regions in both planar and axisymmetric cases for small-scale hydrogen leakage El-Amin et al. (2008); El-Amin & Kanayama (2009a; 2008). This kind of buoyant jets ’plume’ is classed as non-Boussinesq; since the initial fractional density difference is high, which is defined as, Δρ0 = (ρ∞ − ρ0) , where ρ0 is the initial centerline density (density at the source) and ρ∞ is the ambient density. Generally, for binary selected low-densities gases at temperature 15◦C, the initial fractional density differences are 0.93 for H2 − Air, 0.86 for He− Air, 0.43 for CH4 − Air and 0.06 for C2H2 − N2. (Crapper & Baines, 1977) suggested that the upper bound of applicability of the Boussinesq approximation is that the initial fractional density difference Δρ0/ρ∞ is 0.05. In general, one can say that the Boussinesq approximation is valid for small initial fractional density difference, Δρ0/ρ∞ << 1. However, in these cases of invalid Boussinesq approximation a density equation must be used. Moreover, a discussion of this classification is given by (Spiegel & Veronis, 1960); and M.F. El-Amin and Shuyu Sun King Abdullah University of Science and Technology (KAUST), Thuwal Kingdom of Saudi Arabia 2

Turbulent Buoyant Jet of a Low-Density Gas Leaks into High-Density Ambient: Hydrogen Leakage in Air