3.2. Analysis and Discussion
No invalid data were found when the contents of expanded perlite were 1%, 2%, and 3% in the emulsion matrix, and, therefore, three-factor and three-level orthogonal experiments were carried out. The selection criteria of experimental points according to “uniform dispersion, neatness, and comparability” is suitable for the orthogonal experiment [
19]. Three levels of environmental pressure factors were selected as 1 atm, 2 atm, and 3 atm and three levels of expanded perlite content factors were selected as 1%, 2%, and 3%. In addition, three levels of current intensity factors were selected as 2 A, 2.25 A, and 2.5 A. A three-factor and three-level L
9 (3
4) orthogonal table is summarized in
Table 5.
Three-factor and three-level orthogonal analysis is first carried out by the intuitive analysis method. The sum of the first-level results, second-level results, and third-level results of each factor in each experiment is recorded as I, II, and III, respectively. The average of the results is calculated for each factor at each level, as well as the difference (range) between each factor and the average value. Finally, the average value of each factor and the range of each factor are separately derived, as shown in
Table 6.
In general, the larger the range, the more significant the influence of the corresponding factor. It can be seen that the value of the range for environmental pressure is largest and the value of the range for the expanded perlite content factor is smallest. Therefore, the influence of ambient pressure on the critical ignition energy is more significant than that of the expanded perlite content. In addition, it can also be seen from
Table 4 that the minimum ignition energy appears when the current intensity is 2.25 A, the ambient pressure is 2 atm, and the expanded perlite content is 3%. This means that the emulsified matrix is easiest to ignite and has the lowest thermal safety under these conditions. In actual production, the temperature of the heat source is random. The accuracy of the intuitive analysis method is low. Because of the above two reasons, the current intensity is no longer considered, and the significance of environmental pressure and expanded perlite content is studied separately by non-repetitive two-factor variance analysis with the current intensity of electric hot wires being 2 A, 2.25 A, and 2.5 A.
Table 7,
Table 8 and
Table 9 are obtained by setting the ambient pressure as the A factor and expanded perlite content as the B factor.
Each experimental value in
Table 7,
Table 8 and
Table 9 can be described by a linear statistical model as follows:
where
is the mean value;
(
= 1, 2, 3) is the treatment effect of level
for ambient pressure;
(
j = 1, 2, 3) is the treatment effect of level
for bubble content;
is the random error; and
is an independent random variable which obeys normal distribution N (0, σ
2).
Assume the sample is independent of each other, ~N (, σ2), is independent of each other, ~N (0, σ2), , and . Then, determine whether the ambient pressure and bubble content have a significant influence on the ignition energy to test the following hypotheses. : = = = 0 and : = = = 0.
Let the total sum of squares of deviations be
, which can be calculated by Equation (4); let the sum of squares of the deviation in the environmental pressure factor (factor A) be
, which can be calculated by Equation (5); and let the sum of squares of the deviation in the expanded perlite content factor (factor B) be
, which can be calculated by Equation (6). Then, the total sum of squares of the total deviations can be decomposed into
=
.
The degree of freedom of each factor is the level number minus 1. Then, the degree of freedom of is 2, the degree of freedom of is 2, and the degree of freedom of is 4. The mean squares of are recorded as MSA, is recorded as MSB, and is recorded as MSE. So, MSA = /2, MSB = /2, and MSE = /4.
The variance ~F (2,4) is used to test whether the ambient pressure has a significant effect on the ignition energy. The variance ~F (2,4) is used to test whether the expanded perlite content has a significant effect on the ignition energy. A significant level of α is chosen and P{FA > Fα (2,4)} = α. According to the small probability event principle, it is considered that ambient pressure has a significant effect on ignition energy if FA > Fα (2,4). Similarly, it can also be concluded that the expanded perlite content has a significant effect on ignition energy if FB > Fα (2,4). Usually, the value of α is 0.1, 0.05, and 0.01, and the smaller the value of α, the larger the rejection domain. Therefore, the relative equilibrium value of α in this study is chosen as 0.05.
The results of the variance calculation are listed in
Table 10 and the results of the test are shown in
Table 11 when
I is equal to 2 A.
The results of the variance calculation are presented in
Table 12 and the results of the test are demonstrated in
Table 13 when
I is equal to 2.25 A.
The results of the variance calculation are shown in
Table 14 and the results of the test are displayed in
Table 15 when
I is equal to 2.5 A.
The
p-value value of the influence factor is higher than 0.05, indicating that the effect of the factor on the minimum ignition energy is not significant, because the α value is 0.05. It can be seen from
Table 13 and
Table 15 that the
p-values of the rows (bubble content) and columns (environmental pressure) are higher than 0.05, where
I = 2 A and
I = 2.5 A. The analysis and comparison with the two groups of data are not accurate enough. Therefore, the data are selected for analysis and comparison with
I = 2.25 A.
As displayed in
Table 14, the
p-value of the row (bubble content) is 0.247, which is greater than 0.05, and F
B = 2.202, F
α (2,4) = 6.944, and F
B < F
α (2,4). Therefore, the presence of expanded perlite has no significant effect on the ignition energy of the emulsion matrix in this experimental condition. The
p-value of the column (ambient pressure) is 0.025, which is less than 0.05, and F
A = 10.571, F
α (2,4) = 6.944, and F
A > F
α (2,4), so the influence of ambient pressure on the ignition energy of the emulsified matrix is apparently significant. The analysis suggests that under the condition
I = 2.25 A, the results from intuitive analysis and variance analysis are generally consistent. Increasing environmental pressure can accelerate the decomposition reaction rate of the emulsion matrix, affecting the minimum ignition energy of the emulsion matrix. Additionally, heightened pressure may expel bubbles present in expanded perlite, thereby reducing the sensitivity of the emulsion explosive matrix. This also explains why the ignition energy of the emulsified matrix sample containing 3% expanded perlite at an ambient pressure of 2 atm is less than that at an ambient pressure of 3 atm in the orthogonal experiment. Due to the dual effect of environmental pressure, it has a more pronounced impact on the ignition energy than the content of expanded perlite.
This study examines the potential disturbance factors that could impact the experimental outcomes, such as the environmental temperature within the pressure vessel, the placement of the heating wire in the emulsifying matrix, and the consistency of the expanded perlite distribution in the emulsifying matrix. The temperature inside the pressure vessel can influence the temperature of the emulsion matrix, leading to changes in the system’s initial temperature which could impact the ignition delay time and affect the calculation of the final ignition energy. However, due to the rapid heating rate of the heating wire, changes in the initial temperature of the emulsion matrix surrounding the heating wire may have minimal impact on the ignition delay time. The position of the heating wire determines the thickness of the emulsifying matrix around it, which in turn affects the wire’s heat dissipation and can consequently impact the ignition delay period. The above two disturbance factors will be redesigned for experimental equipment in the future. The uniformity of expanded perlite in the emulsified matrix cannot be accurately measured, and its influence can only be ignored in this study.