The Empirical Nitrogen Equivalent Equations for Predicting the Detonation Velocity and Detonation Pressure of CHNO Explosives with Approaching the Results of Kamlet-Jacobs Equations

HU Rong-zu, YAO Er-gang, MA Hai-xia, ZHANG Hai, GAO Hong-xu, HAN Lu, ZHAO Feng-qi, LUO Yang, ZHAO Hong-an

(1. Science and Technology on Combustion and Explosion Laboratory, Xi′an Modern Chemistry Research Institute, Xi′an 710065, China; 2. College of Chemical Engineering, Northwest University, Xi′an 710069, China; 3. Department of Mathematics/Institute of data analysis and computation chemistry, Northwest University, Xi′an, 710069, China; 4. College of Communication Science and Engineering, Northwest University, Xi′an 710069, China)

In 1964,Guo Yuxian proposed a nitrogen equivalent (NE) equation for predicting the detonation velocity (D) of CHNO explosives. In the early 1980′s, Guo Yuxian and Zhang Housheng[1-2]proposed two NE equations for predicting theDand detonation pressure (p) of CHNO explosives. Here we plan to propose two empirical NE equations for predicting the values ofDandpwith more approaching the values ofDandpin Kamlet-Jacobs equations than Guo Yuxian-Zhang Housheng′s NE equations.

By substituting the 1631 sets of original data (Table S2),Di,Mi,iandxi,i=1, 2, … , 1631, for 324 CHNO single-compound explosives (Table S1) into eqns. (1), (3), (5) and (7), eqns. (2), (4), (6) and (8) are obtained via solution of eqns. (1), (3), (5) and (7) using the trust region approach.

s.t. 690.00≤a≤690.01, 1160≤b≤1160.01, 1.000≤NN2≤1.001, 0.5400≤NH2O≤0.5401, 1.3500≤NCO2≤1.3501,

0.7800≤NCO≤0.7801, 0.2900≤NH2≤0.2901, 0.5000≤NO2≤0.5001, 0.1500≤NC≤0.1501

(1)

(2)

whereDis the detonation velocity, m·s-1;Mis the mole weight of explosive, g·mol-1; 690 and 1160 are constants;ρis the initial densities of explosives, g·cm-3; 1.00, 0.54, 1.35, 0.78, 0.29, 0.50, 0.15 are the nitrogen equivalent coefficient of gaseous detonation products N2, H2O, CO2, CO, H2, O2, C of explosive;xi(i= N2, H2O, CO2, CO, H2, O2, C) is the numbers of moles of gaseous detonation products.

Equation (2) is known as Guo Yuxian-Zhang Housheng′s NE equation for predicting the value ofDof CHNO explosives.

s.t. 1.09200≤c≤1.09201, 1.000≤NN2≤1.001, 0.5400≤NH2O≤0.5401, 1.3500≤NCO2≤1.3501, 0.7800≤NCO≤0.7801,

0.2900≤NH2≤0.2901, 0.5000≤NO2≤0.5001, 0.1500≤NC≤0.1501, 0.57400≤d≤0.57401

(3)

(4)

wherepis the detonation pressure, GPa; 1.092 and 0.574 are constants.

Equation (4) is known as Guo Yuxian-Zhang Housheng′s NE equation for predicting the value ofpof CHNO explosives.

s.t. 650≤a≤695, 1150≤b≤1165, 0.800≤NN2≤1.001, 0.340≤NH2O≤0.640, 1.150≤NCO2≤1.350,

0.250≤NCO≤0.780, 0.110≤NH2≤0.290, 0.010≤NO2≤0.500, 0.110≤NC≤0.150

(5)

(6)

where 695 and 1150 are constants; 1.00, 0.64, 1.34, 0.72, 0.18, 0.50, 0.12 are the nitrogen equivalent coefficient of gaseous detonation products N2, H2O, CO2, CO, H2, O2, C of explosive.

Equation (6) is known as the empirical NE equation for predicting the value ofDof CHNO explosives

The relative error (Δδ) of eqn. (6) is:

s.t. 1.060≤a≤1.500, 1.000≤NN2≤1.001, 0.6400≤NH2O≤0.6401, 1.3400≤NCO2≤1.3401, 0.7200≤NCO≤0.7201,

0.1800≤NH2≤0.1801, 0.0.500≤NO2≤0.501, 0.1200≤NC≤0.1201, 0.001≤d≤0.874

(7)

(8)

where 1.060 and 0.619 are constants.

Equation (8) is known as the empirical NE equation for predicting the value ofpof CHNO explosives

Compared with the values of Δδof eqns. (2) and (4), the ones of Δδof eqns. (6) and (8) decrease by 25.2% and 23.0%, respectively, indicating that eqns. (6) and (8) can be used to predict the values ofDandpof CHNO explosives with more approaching the values ofDandpin Kamlet-Jacobs equations than common used nitrogen equivalent equations.

Associated Content: Supporting information

The supporting information of the structure formula (Table S1) and original data (Table S2) is available free of charge on the website of Chinese Journal of Energetic Materials.

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