Hydrogen-air deflagrations in open atmosphere: LES analysis of experimental data V. Molkov*, D. Makarov*, H. Schneider** 7-10 September 2005, Pisa - Italy First International Conference on HYDROGEN SAFETY * - University of Ulster, UK; ** - Fraunhofer Institut Chemische Technologie, GERMANY

Contents Contents Experiment in 2094-m 3 hemisphere1Experiment in 2094-m 3 hemisphere1 Theoretical background for modelling2Theoretical background for modelling2 The Large Eddy Simulation model3The Large Eddy Simulation model3 Theory versus experiment4Theory versus experiment4

EXPERIMENT 1

Experimental details Experiment: Schneider H., Pförtner H. PNP- Sichcrheitssofortprogramm, Prozebgasfreisetzung-Explosion in der gasfabrik und auswirkungen von Druckwellen auf das Containment, Dezember meters

Side and top view movies 20 m 10 m

Estimate of turbulent flame front (distributed) thickness: 1. The pocket (“mole”) of size 0.2 m behind a leading edge of the flame front will burn inward during 0.2m:2m/s=0.1s (0.2 m divided by burning velocity 2 m/s); 2. During this time leading edge will propagate as far as 0.1sx40m/s=4 m! (8 m for “mole” 0.4 m)? 4 m Distributed flame front

Flame propagation velocity was independent upon ignition energy in the investigated energy range ( J or pyrotechnical charge). The resulting flames propagated in almost hemispherical form with a developed structure. The maximum visible flame velocity occurs between the original radius of the balloon R 0 and radius 1.5R 0. The maximum flame radius reached about 2R 0. No transition to detonation was observed. The maximum visible flame velocity reached 84 m/s. At a sufficient distance from the explosion the maximum pressure decayed inversely proportional to the distance. The positive pressure wave was followed by a negative pressure phase. Experimental results

THEORETICAL BACKGROUND FOR MODELLING 2

Gostintsev et al (1988) analysed about 20 experiments on large-scale unconfined deflagrations and concluded that the hydrodynamic flame instability leads to accelerating, self-similar regime of fully developed turbulent flame propagation. According to this analysis, the flame front surface obeys the fractal theory after self-similar regime is established. The authors found that the transition to the self- similar turbulent regime of flame propagation occurs after the critical value of the flame front radius R* is achieved, which was found to be R*= m for near stoichiometric premixed hydrogen-air flames. Self-similarity (fractals)

The study performed by Karlovits et al (1951) using burner flames led to the conclusion that a flame front itself generates turbulence. The maximum theoretical value of the flame front wrinkling due to flame induced turbulence was found to be: where E i – combustion products expansion coefficient. LES of large scale problems can not at foreseen future resolve all details of flame front structure and this can be modelled only. Flame generated turbulence

The Ulster LES model 3 S. Pope (2004): -Physical LES (filter size is ARTIFICIAL parameter  ) -Numerical LES (filter size is cell size)

Conservation of massConservation of mass Conservation of momentumConservation of momentum Conservation of energyConservation of energy Ulster LES model (1/3)

Premixed flame front propagation (progress variable)Premixed flame front propagation (progress variable) Gradient method for the source termGradient method for the source term Yakhot’s RNG like turbulent premixed combustion (inflow)Yakhot’s RNG like turbulent premixed combustion (inflow) where u’ – residual SGS velocity where u’ – residual SGS velocity Karlovitz turbulence generated by flame front itself (SGS)Karlovitz turbulence generated by flame front itself (SGS) Chemistry is in burning velocity (dependence on T, p,  )Chemistry is in burning velocity (dependence on T, p,  ) Ulster LES model (2/3)

RNG SGS turbulence modelRNG SGS turbulence model Dilution of initial H 2 -air mixture by atmospheric airDilution of initial H 2 -air mixture by atmospheric air Ulster LES model (3/3)

Why gradient method? Decoupling physics and numerics Integral of source term through numerical flame front is always equal to physical value  u S t (physically correct heat release, given up structure of turbulent flame front) Why RNG (renormalization group) turbulence model? No turning. Validated for both laminar and turbulent flows. No “cut-off” at  but “scaling down” at inertial range. Why turbulence generated by flame front itself? LES of large scale accidental combustion can not resolve phenomena at scales comparable with flamelets thickness. Existence of a theoretical maximum and critical radius: Three main “FAQ”

Characteristic size of control volumes (CV) for CVs grid: Radius, mCV size, m (UTH zone) (SHH zone) 4.0 (2.0 in direction of pressure gauges) Domain and grid 200x200x100 m Unstructured tetrahedral Structured hexahedral (SHH)

Initial conditions – –initial temperature T=283 K; initial pressure p=98.9 kPa – –quiescent mixture; progress variable c=0. – –hydrogen concentration Y H2 = at R  10.0m (Y a =1 for R>10.0 m) Boundary conditions – –no-slip impermeable adiabatic boundary on the ground – –non-reflecting boundary conditions in atmosphere Ignition: 15 ms increase of progress variable in 1 CV Numerical details – –code: FLUENT – –explicit linearisation of the governing equations – –explicit time marching procedure – –second order accurate upwind scheme for convection terms, central- difference scheme for diffusion terms – –Courant-Friedrichs-Lewy number CFL=0.8 Numerical details

THEORY versus EXPERIMENT 4

Flame shape 1 SIMULATION (averaging c= ) EXPERIMENT

Experiment Simulation Flame shape 2

Flame propagation

Flame radius

Burning velocity S t E i =7.2 Balloon rupture at 5 m is a reason for flame acceleration? Total flame wrinkling factor is about 5, of which RNG SGS is only S t /S u =1.2

Pressure dynamics 1 Flame zone: 2 m, 5 m, 8 m, 18 m Gauge affected by combustion

Pressure dynamics 2 Far-field: 35 m, 80 m Similar to experiment: the positive pressure wave was followed by a negative pressure phase. Usually the negative pressure wave was somewhat shorter than the positive one providing larger negative pressure peak.

Conclusions The Ulster LES model has been applied to study the dynamics of the largest unconfined deflagration of stoichiometric hydrogen-air mixture. The model has no adjustable parameters and reasonably reproduced the experimental data on dynamics of flame and pressure wave propagation. Effects of the hydrodynamic flow instabilities and the turbulence induced by turbulent flame front itself on the burning velocity acceleration are accounted separately in the model. It is demonstrated that the main contributor to the turbulent flame propagation is the turbulence generated by flame front itself. Further studies have to model under resolved fractal structure of large-scale flames to reproduce in more detail the observed monotonous acceleration of the flame front.