Experimental Determination of the Static Equivalent Pressures of Detonative Explosions of Cyclohexane/O2/N2-Mixtures in Long and Short Pipes (part 2 of 3)

Abstract

The abstract of the second part of this paper is included in the abstract of part 1.
The following final results can be derived from the experiments with C₆H₁₂/O₂/N₂:I: Because the focus of the work was not on investigating the bulging in the region of the stable detonation, the entire experimental series only produced two values for the ratio ? between the static equivalent pressure of the stable detonation and the Chapman-Jouguet pressure p_CJ (fields AC15 and AC16 of Table 1). Both values are larger than what had been found for ? in a large number of experiments carried out in the past five years (Schildberg (2013 to 2018)). Because these two values are statistically not relevant and because there is no obvious reason why C₆H₁₂/O₂/N₂ mixtures should exhibit a value for ? different from the other investigated explosive mixtures, no effort is invested to track down the reason for this deviation and it is assumed that ? = 0.7 as found in the old tests still holds. Further below, ? will be needed to calculate the ratio R between the static equivalent pressure at the location of the DDT and the static equivalent pressure of the stable detonation.
II: The predetonation distances of the 3 stoichiometric mixtures tested both at T_initial = 80 'C and T_initial = 130 'C with almost the same initial pressure (to be compared: test 1 and test 5, 19 and 22, 20 and 25) were on the average 26 % longer at the higher initial temperature. This increase is presumably due to the fact that with rising initial temperature the speed of the initial shock front and henceforth also the speed of the unreacted gas behind the initial shock front (see Fig. 7 in Schildberg 2016) rise as well. Consequently, the deflagrative flame has to attain even higher speeds relative to the pipe wall such that the piston represented by the expanding reaction gases finally produces sufficient compression in the unreacted gas ahead of the flame front such that autoignition occurs in the precompressed zone.
_{III: For 9 mixtures the ratio between pstat_reflected_stable and pstat_stable was measured. All ratios were between 2.06 and 2.9 and the average was 2.38, i.e.} p_{stat_reflected_stable} = 2.38 ( p_{stat_stable} This value confirms the value of 2.4 found in previous investigations (Schildberg 2013, 2015, 2016a, 2018).
IV: Only for 3 of the 7 tests conducted in short pipes with stoichiometric mixtures (21 vol.-% = O₂-concentration in the O₂/N₂ mixture = 30 vol.-%) a DDT occurred (tests 22, 32, 35). For scenario 5 the result obtained by averaging over the individual ratios of 4.28, 6.35 and 5.42 is: p_{stat_DDT_short} = 5.35 ( p_{stat_stable} Figure 3: Examples for residual plastic deformations found in the tests with 48.3x2.6 (tests 1,19 and 22) and 114.3x3.6 (test 32) pipes. Flame propagation was always from left to right, i.e. ignition was always at the left end of the pipes. The steel tape indicates the axial position, i.e. the distance to the ignition source (in units of cm).
Figure 4: Examples for the increase of the pipe diameters produced by the detonation experiments, plotted over the distance from the ignition source. Further explanations to these special examples are given in the text.
Since R is about 3.7 for the investigated compositions (see further below), this result is in good accordance with the estimation formula for scenario 5 given in Schildberg (2016), i.e. this formula is confirmed:V: In the short pipe tests nos. 19, 32 and 35 the different ratios found for scenario 7 are 3.55, 10.84 and 8.44. The result obtained by averaging over the three individual ratios is: p_{stat_reflected_unstable} = 7.6 ( p_{stat_stable} The estimation formula for scenario 7 given in Schildberg (2016) suggests: p_{stat_reflected_unstable} = 1.5 ( 2 ( 2.4 ( p_{stat_stable} = 7.2 ( p_{stat_stable.} The averaged value is in good accordance with the value predicted by the estimation formula. The systematic scattering of the measured values (the values increase when the location of the DDT gets closer to the blind flange) is explained by Figures 5 and 6. Figure 5 gives the pressure distribution just before the DDT occurs. The estimation formula is based on the blue curve which is slightly simplified. The reality is better approximated by the red curve, which is not flat but drops with increasing distance from the flame front. Therefore scenario 7 will generate higher pressure values when the location of the DDT gets closer to the blind flange (x/L = 1), because this will increase the pressure of the unreacted gas ahead of the blind flange at the instant when the detonation front arrives (illustrated in Figure 6).
VI: The variation of the ratio R between the static equivalent pressure at the location of the DDT in the long pipe configuration (scenario 1) and the static equivalent pressure of the stable detonation (scenario 3) as function of C₆H₁₂ content is shown in Figure 7. The variation of R along the stoichiometric line is qualitatively identical with what had been found for H₂/O₂/N₂, CH₄/O₂/N₂ and C₂H₄/O₂/N₂. However, the absolute value of R at C₆H₁₂ concentrations close to the concentration of C₆H₁₂ in stoichiometric C₆H₁₂/air mixtures is about 3.7, and this is less than the corresponding values of R for the other mixtures (ca. 5 for H₂/O₂/N₂, ca. 5.5 for CH₄/O₂/N₂, ca. 5.6 for C₂H₄/O₂/N₂). Once R is known, the short pipe scenarios 5 and 8 can be predicted based on the estimation formulae provided in Schildberg (2016a).
Figure 5: Difference between idealized and true pressure profile of the initial shock wave.
a) DDT occurs in short pipe at large distance from pipe end b) DDT occurs in short pipe close to pipe endFigure 6: Explanation why a on basis of Figure 5 - the pstat-values of scenario 7 increase when the location of the DDT gets closer to the blind flange of the pipe (x/L = 1). All plots show the pressure distribution in the second half of a pipe close to the instant of DDT occurrence.
Figure 7: Variation of R in dependence on the C6H12-content in stoichiometric C6H12/O2/N2 mixtures at Tinitial = 80 'C and 130 'C. Only the dark-red triangle represents a value for an over-stoichiometric mixture. The orange dashed line is a guide to the eye for the data of the stoichiometric mixtures.