Keywords: finite element method, parallel processing, domain decomposition, hydrogen dispersion, Navier-Stokes equations, thermal convection problems.

In this paper, the hierarchical domain decomposition method (HDDM), which enables parallel processing, is applied to the finite element method to conduct large scale simulations of hydrogen diffusion into a semi sealed enclosure. The code, ADVENTURE_sFlow, is part of a larger package of modules included in the ADVENTURE system [1], jointly developed by a consortium of universities and companies in Japan. One major advantage is that all modules within the system are freely available online, and being open source, may be modified in accordance with the needs of the user.

To test the code, large scale computational simulations of hydrogen dispersion into a semi-sealed enclosure, representative of a garage with a hydrogen powered car parked within [2], have been attempted. An analogy of thermal convection problems is applied in the simulations. As with all flammable gasses, the possibility of detonation exists if the concentration of gas is sufficiently high. Experimental results [3] show that this is unlikely in the case of the simplified geometry mentioned above. The computed results are compared with the experimental ones to see if there is agreement and thus to determine the viability of the code in simulating such situations.

A description of the formulations used is first given. The incompressible Navier-Stokes equations and advection-diffusion equations are considered, where in formulating the hydrogen dispersion equations, the temperature in thermal convection is replaced with concentration. Application of the backward Euler and finite element method to these equations yields the discretized, nonstationary system. The domain decomposition iterative method is then applied. A nonoverlapping domain decomposition is considered, and the generalized product-type method based on bi-conjugate gradient (GPBiCG) is then applied to the interface problem. The subdomain problem is solved using the skyline method.

Details of the simulations are then given. The mesh density is increased to show the feasibility of running large simulations using the code. The results obtained show qualitative agreement. At no point in time, for the positions measured, does the hydrogen concentration reach the levels required for detonation, a finding consistent with the experimental results. Refinement of the mesh density, together with appropriate changes to the time step, gives results closer to the experimental ones. This was verified by calculating the error at various mesh densities and time steps. For such structures, the risk of detonation appears to be small. However, the computations show that the risk of combustion, which occurs at lower concentrations, is not insignificant. Both these findings are consistent with the experimental results. The suitability of the code in performing large scale simulations of gas dispersion problems and providing qualitative results is thus shown.

1

ADVENTURE Project, http://adventure.sys.t.u-tokyo.ac.jp/

2

M.R. Swain, E.S. Grilliot, M.N. Swain, "Risks Incurred by Hydrogen Escaping from Containers and Conduits", Proceedings of the 1998 US DOE Hydrogen Program Review, NREL/CP-570-25315, 1998.

3

M. Inoue, H. Tsukikawa, H. Kanayama, K. Matsuura, "Experimental study on Leaking Hydrogen Dispersion in a Partially open space", Journal of the Hydrogen Energy Systems Society of Japan, 33(4), 32-43, 2008 (in Japanese).

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