Free flame propagation

In experiments where no obstacles are present, there will be nearly no shear generated turbulence. The flame propagation started by a spark ignition will start burning with a velocity which is somewhat lower than the laminar burning velocity due to straining of the flame. After a few centimetres the straining becomes unimportant. As the flame radius increases, so does the burning velocity, it becomes quasi laminar, due to hydrodynamic instabilities and reaches a burning velocity higher than twice the laminar, after about 2 m, depending on factors as gas mixture and flame direction. The higher flame velocities measured in vertical direction upwards compared to horizontally may be due to buoyancy. The burning velocity may then be similar in all directions.

The development of the flame radius for larger flame radii is not well known, due to lack of good experimental data, but numerical analyses support a further increase with radius, as discussed in Section 7.2.

In the EMERGE project (Arntzen et al. 1995) the effect of initial turbulence (around the ignition point) on flame propagation, were investigated. In the turbulent region the burning velocity was up to ten times higher compared with a non turbulent situation, but as the flame propagated outside the turbulent region, there was nearly no difference in burning velocity compared with the no turbulent situation. The burning velocity was again a function of flame radius.

8.2.2

2D radial vessel at Sotra

A range of explosion experiments has been performed by CMR in the 10 m radial wedge- shaped explosion vessel, shown in Figure 8.1. The volume of the 10 m radial vessel is 18.5 m3 and the height is 1.25 m. In the explosion experiments, the type, size and number of obstacles were varied, in addition to the confinement on the top of the vessel. A range of fuels and stoichiometric ratios were also tested. The effect of scale was tested in a 1/10 scale version of the vessel. Pressure as function of time and time of flame arrival was measured in several monitor points. The results from a range of these experiments, were presented by Bjørkhaug (1986), who also showed that these experiments can be seen as two dimensional axis symmetrical.

These experiments will be poorly represented in simulations with the standard 3-dimensional cartesian FLACS code, and were therefore calculated with the 2-dimensional radial versions of FLACS-86, 89 and 93. The 2D radial version of FLACS-93 was used to validate the burning velocity model against a range of different fuels. The geometry was fully resolved on the grid. As reported in Section 4.2, simulations with the k-ε turbulence model are very sensitive to the ratio of initial turbulent length to grid size, and may have problems with a rapid turbulence buildup, when the geometry is resolved on the grid. Unphyscical turbulence is also generated in the flame zone if the turbulent length is too large compared to the grid size (discussed in Section 4.6) and led in some situations to breakdown of the code due to too high turbulence.

Figure 8.1 The 10 m radial vessel, used in gas explosion experiments at CMI

h H=1.25 m b.r.= h/H * ignition 9.6 m 0.12 m 3.0 m

The simulations were therefore done with a k model with l_t = 0.2∆. This turbulent length scale was also used in the combustion model. The simulation results were then nearly grid independent.

Simulations with FLACS-89, which uses the k-εturbulence model, and the H-M combustion model described in Subsection 5.2.1, were nearly independent of the initial value on l_t. The reason for this is that it uses a reaction rate proportional to the turbulence frequency, u´/l_t , which reaches its steady state value very quickly, nearly independently of the initial value on l_t, as observed by Bakke (1986). The results from FLACS-89 has, however a large grid dependency and is due to the weakness of the combustion model, not recommended for explosion predictions.

The peak pressures near the exit of the 10 m radial vessel can be seen in Figure 8.2, from 14 experiments, where gas type and blockage ratio (b.r., see Figure 8.1) have been varied. The fuels ethylene, propylene, ethane, propane and methane were stoichiometric mixed with air. The blockage ratios were 1/2, 1/3 and 1/6. The peak pressures obtained from simulation of these experiments were within 7% for all fuels except ethylene. As discussed in Chapter 7.3.3, turbulent burning velocities for ethylene were known not to fit equation (7.30), which resulted in a simulated pressure around only 70% of the experimental. These results were presented by Arntzen (1993b), who also investigated the ability of models to handle different scales, by simulation of experiments in the 1 m radial vessel.

Figure 8.2 Peak explosion pressures in the 10 m radial vessel [barg]

The simulations in the 1m radial vessel were compared with experiments for 7 different stoichiometric fuel-air mixtures and blockage ratio 0.5. The extra fuels compared with the 10m vessel were acetylene and hydrogen. As shown in Table 8.3, the peak pressures obtained from simulation of these experiments were 30% too low for hydrogen and 20% too low for ethylene and acetylene. For the other fuels the difference between simulations and experiments were less than 12%. The turbulent burning velocity at elevated pressures was however underpredicted in FLACS-93, due to incorrect pressure dependency as discussed in Section 2.3.4. A more proper pressure dependency on the burning velocity will give simulations with acetylene, hydrogen and ethylene, better agreement with the experimental results.

It should also be noted that hydrogen has a higher laminar burning velocity than acetylene, but acetylene gives higher peak pressures. The reason for this is that the expansion ratio, for hydrogen is lower.

2D radial versions of FLACS have not been developed after 1993. The improvements in FLACS done later than 1993 are therefore difficult to validate against these radial vessel experiments or the tube experiments presented in the next subsection. The MUSIC code is a 3D CFD code in general coordinates, which can represent both the radial vessel and the tube. MUSIC was supposed to succeed FLACS (and remove the need of having a 2D radial code in addition to the 3D code) but was not able to do that, due to deficiencies, as discussed in Section 2.8.