Integral solutions for selected turbulent quantities of small-scale hydrogen leakage: A non-buoyant jet or momentum-dominated buoyant jet regime M.F. El-Amin* ,1 , H. Kanayama Department of Mechanical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan article info Article history: Received 12 October 2008 Received in revised form 27 November 2008 Accepted 27 November 2008 Available online 23 December 2008 Keywords: Hydrogen leakage Momentum-dominated regime Non-buoyant jet Turbulent Schmidt number Integral method abstract In this paper, the integral method is used to derive a complete set of results and expres- sions for selected physical turbulent properties of a non-buoyant jet or momentum- dominated buoyant jet regime of small-scale hydrogen leakage. Several quantities of interest, including the cross-stream velocity, Reynolds stress, velocity-concentration correlation (radial flux), dominant turbulent kinetic energy production term, turbulent eddy viscosity and turbulent eddy diffusivity are obtained. In addition, the turbulent Schmidt number is estimated and the normalized jet-feed material density and the normalized momentum flux density are correlated. Throughout this paper, experimental results from Schefer et al. [Schefer RW, Houf WG, Williams TC. Investigation of small-scale unintended releases of hydrogen: momentum-dominated regime. Int J Hydrogen Energy 2008;33(21):6373–84] and other works for the momentum-dominated jet resulting from small-scale hydrogen leakage are used in the integral method. For a non-buoyant jet or momentum-dominated regime of a buoyant jet, both the centerline velocity and centerline concentration are proportional with z 1 . The effects of buoyancy-generated momentum are assumed to be small, and the Reynolds number is sufficient for fully developed turbulent flow. The hydrogen–air momentum-dominated regime or non-buoyant jet is compared with the air–air jet as an example of non-buoyant jets. Good agreement was found between the current results and experimental results from the literature. In addi- tion, the turbulent Schmidt number was shown to depend solely on the ratio of the momentum spread rate to the material spread rate. ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. 1. Introduction 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 * Corresponding author. Fax: þ81 928023226. E-mail address: elamin@mech.kyushu-u.ac.jp (M.F. El-Amin). 1 Present address: Department of Mathematics, Aswan Faculty of Science, South Valley University, Egypt. Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/he 0360-3199/$ – see front matter ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2008.11.067 international journal of hydrogen energy 34 (2009) 1607–1612