爆轰胞格尺寸的统计分析

爆轰胞格尺寸作为可燃系统的本征值,可用来确定爆轰传播时的临界尺寸,比如直管传播时的临界管径、管道突扩时的临界尺寸等。然而,该尺寸的测量具有较强的主观性。为了减少人工测量带来的不确定性,文章采用两种统计方法:概率密度函数法和自相关函数法,对数值模拟得到的不同规则程度的爆轰胞格进行了统计分析。爆轰胞格的不规则程度采用单步反应的活化能来体现。当活化能较低时(Ea=15),胞格较规则,两种统计方法得到的胞格尺寸较一致。随着活化能的增加(Ea=20),胞格开始不规则,两种统计方法也开始出现偏差。当活化能进一步增加(Ea=25、27),胞格极不规则,开始出现横波的合并,两种统计方法得到的结果出现较大的偏差。这是由于概率密度法处理爆轰波阵面三波点规则时,没有考虑迹线上能量的分布,而自相关函数法根据三波点上的涡量值对胞格尺寸进行统计分析,因此,该方法得到的爆轰胞格尺寸比概率函数法更能真实体现可燃系统的爆轰特性。

Statistical analysis of detonation cell size

Detonation cell size reflects the characteristic of a given fuel mixture,which can be used to determine the critical values in various detonation phenomena,such as the critical diameter for the propagation in narrow,smooth wall-bounded tubes,the critical size for the detonation to survive diffraction from a tube into an unconfined space.However,measurement of the detonation cell size is highly subjective,especially for irregular mixtures.To reduce the uncertainty in manual observation,two methods are adopted in the present study to statistically analyze the detonation cell size in numerical simulations.The first method is based on the probability density function of the main track spacing between neighboring triple points moving in the same direction according to the vorticity records,and the second method uses the autocorrelation function to spectrally analyze the vorticity records.Detonation cells with different degrees of regularity are obtained by numerically solving the reactive Euler equations with different activation energies,Ea.For a low activation energy Ea=15,the cell is regular and its size obtained by the two methods is consistent with each other.For a moderate activation energy Ea=20,the cell becomes irregular and there is a small difference between the calculated cell sizes by the two methods.As the activation energy is further increased,for both Ea=25 and Ea=27,the temperature sensitivity of the reaction is greater and the cells are highly irregular.Moreover,transverse waves begin to merge,leading to a large deviation between the cell sizes obtained by the two methods.This is because that the spacing probability density function method assumes equal weights to all the tracks,while the autocorrelation function spectral method inherently weights the vorticity value and takes local correlations into consideration.Therefore,the detonation cell size obtained by the latter method is closer to the detonation characteristic of real combustible mixtures.