15.9 m/s and 5.3 m/s for sampling frequencies of 0.5 MHz and 1.5 MHz, respectively.
∆us = 1
Xs
− 1 Xs+ 1
xd·fs
= u2s xd·fs+us
(3.8)
Post processing
Some of the experimental pressure records contained a considerable amount of noise.
A filter program was therefore used on these pressure records to reduce the noise. The applied filter used a type of averaging that lead to a reduction of the pressure peaks.
But the shock waves that propagated in the direction from the ignition wall to the end wall, were kept sharp. It was further observed that the Kistler 7001 pressure transducers produced more noise than the Kistler 603B pressure transducers. The calculation of all the mean axial velocities were done with as little filtering as possible and all the detonation velocities were calculated without any filtering at all.
3.4 Conclusions
The main conclusions of the experimental work can be summarized as follows:
1. Experimental pressure records from gas explosion experiments in closed and sin-gle obstructed pipes with premixed fuel and air at various equivalence ratios have been obtained. Various combinations of four different fuels, three different pipes and seven different obstacles have been used in the experiments. Kistler pressure transducers distributed along the pipes were used to measure the experimental over-pressure. The four fuels were hydrogen, mixes of carbon monoxide and hydrogen, propane and methane. The three pipes had inner lengths of 3.0, 4.0 and 7.0 m.
2. The set of blockage ratios and hydrogen and air equivalence ratios that gives a DDT after the obstacle for the 4.0 m pipe, has been found. DDTs were observed for blockage ratios ranging from 0.572 to 0.965 and for equivalence ratios ranging from 0.79 to 1.95. This is equivalent to obstacle opening diameters ranging from 70 to 20 mm and hydrogen volume percentages ranging from 25 to 45. The various combinations that give a DDT are almost symmetrical around a hydrogen volume percentage of 35 and the most optimum conditions for a DDT is created with a blockage ratio of 0.921.
3. The length scale of the detonation cell size (λd), the pipe diameter (Dp) and the obstacle opening diameter (Do) are critical parameters for deflagration to detonation transitions in obstacle filled tubes [160]. On the other hand, the experiments with hydrogen and air in the 4.0 m pipe, indicate that the radial distance between the pipe side wall and the obstacle opening is also an important length scale for DDTs
in these experiments. This criterion can be expressed as (Dp −Do) ≥ 2λd. But experiments with a higher resolution in both the hydrogen volume percentages and the obstacle opening diameters, need to be performed before this criterion can be confirmed further. Detonation cell size measurements should also be performed in such an experimental study.
4. The flame propagation between the ignition wall and the obstacle depends on the blockage ratio of the obstacle. The obstacle controls the level of pressure build up in front of the flame. The increasing overpressure at pressure transducer P0 with increasing blockage ratio, is mainly caused by the hindering of fluid flow in front of the flame and not by an increased burning rate. The mean axial flame speed between the ignition wall and the obstacle will therefore generally decrease with increasing blockage ratio.
5. It has been showed that the flame propagation between the ignition wall and the obstacle can be affected by pressure waves reflected off the opposite end wall. It can therefor be stated that the total pipe length is an important parameter for flame propagation in closed and single obstructed pipes.
6. The experiments with carbon monoxide, hydrogen and air at stoichiometric propor-tions in the 4.0 m pipe, have shown that small amounts of added carbon monoxide to a hydrogen and air mixture, do not change the detonability of hydrogen. A DDT was observed in the carbon monoxide, hydrogen and air mixture for a hydrogen volume percentage of 27, whereas a critical DDT was observed in the hydrogen and air mixture for a hydrogen volume percentage as low as 25.
7. The ignition limits for a specific fuel compound of hydrogen and carbon monoxide in air, have been found for the 4.0 m pipe. The fuel volume percentage of hydrogen was 10 and the fuel volume percentage of carbon monoxide was 90. The premixed fuel and air did ignite for a volume percentage of air ranging from 13.0 to 74.0.
This interval is in good agreement with the experimentally determined flammability limits presented by Karim et al. [186] and Løyland [187]. A DDT was not observed with this fuel composition.
8. Experiments with stoichiometric propane and air and with stoichiometric methane and air in the 4.0 m pipe, have shown that the explosion characteristics of the two fuels are relatively similar for the various blockage ratios. But the experiments with propane had both a higher overpressure and a higher mean axial flame speed between the ignition wall and the obstacle.
9. An interesting observation was made in the experiments with propane and methane.
(The fuels were mixed with air at stoichiometric conditions.) The experimental pressure recordings indicated that the flame was quenched at the obstacle for these two gas mixtures, when the blockage ratio of the obstacle was 0.991. This phe-nomenon was not observed in any of the experiments with hydrogen and air.
10. The experiments with propane and methane had a much slower flame propagation than the corresponding experiments with hydrogen in the 4.0 m pipe. In
stoichio-3.4 CONCLUSIONS 81 metric mixtures of hydrogen and air the flame reached the pipe side wall in the radial direction before it interacted with pressure waves that were reflected off the obstacle or the end walls. This was not the case for propane and methane. In the experiments with propane and methane the flame interacted with reflected pressure waves from both the obstacle and the end walls, before it reached the pipe side wall in the radial direction.
Chapter 4
Numerical simulations
In this chapter the numerical work is described. An introduction to the chapter is given in Section 4.1 before the numerical code and models are described in Section 4.2. Section 4.3 presents the numerical results and the conclusions of the numerical work are given in Section 4.4.
4.1 Introduction
Numerical simulations of gas explosions in pipes have been performed with a one di-mensional code named RCMLAB. The simulations were performed for closed and single obstructed pipes with various equivalence ratios of premixed fuel and air. The experi-mental results presented in Chapter 3 were used to validate the numerical simulations.
The main objective of the work was to test and develop new models for simulation of gas explosions in pipes.
Peters [10] states that one of the most important unresolved problems in premixed turbulent combustion, is the determination of the turbulent burning velocity. The burning velocity depends on local mean quantities and it gives the propagation speed of the mean flame front relative to the flow field of the unburned gas right in front of the flame. Two different types of models have been used to calculate the burning velocity in the numerical simulations. One model used experimental pressure records as input and the other model used the flow field right in front of the flame in combination with the laminar burning velocity.
Even though the phenomena of flame acceleration and flame inversion are fairly well described from experiments [12, 13, 14], there is still little quantitative information of the average burning rates [kg fuel/(m2s)] in gas explosions. RCMLAB can make such esti-mates of the average burning rates with the use of experimental pressure measurements.
Most Computational Fluid Dynamics (CFD) codes today have two or three space mensions. But there are still scenarios when a numerical code with only one space di-mension can be favorable. This is especially true for simulations of gas explosions in long pipes. The amount of grid cells for a two or three dimensional code could soon become unmanageable in such simulations.
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