Artificial Neural Network-based Prediction Model for Damage Effect of Fuel-air Explosive

doi:10.12382/bgxb.2023.0094

Abstract

Abstract:

The prediction of damage range caused by Fuel-air Explosive is fundamental to the study of large-scale damage caused by Fuel-air Explosive weapons. However, the distribution pattern of shock waves after detonation and its dependence on fuel concentration are unknown, which limits the prediction accuracy of damage range. In this study, the minimum free energy method is used to calculate the CJ parameters for the ideal detonation of biphasic cloud fog with liquid fuel present in either droplet or vapor form. The JWL equation of state parameters are obtained through fitting. Subsequently, the peak overpressure caused by ideal detonation of biphasic cloud fog with different concentrations and states is calculated. A proxy model is developed by utilizing an artificial neural network. The proposed model is used to predict the decay law of peak overpressure with respect to the scaled distance for biphasic gas-solid and gas-liquid-solid cloud detonations with concentrations ranging from 0.03 to 0.30kg/m³. The model is also used to predict the variation of damage proportion radius with fuel concentration for different damage levels, obtaining the optimal concentration with the maximum damage proportion radius. The study reveals that the influences of liquid fuel in droplet or vapor form on cloud detonation parameters, JWL equation of state parameters, and shock wave distribution after cloud detonation are relatively weak (<1.5%). Within the fuel concentrations ranging from 0.03 to 0.18kg/m³, the maximum and minimum values of damage proportion radius for damage levels Ⅰ-Ⅲ are differed by 21%, 19%, and 6%, respectively. Thus, the dependence of damage radii on fuel concentration is stronger for damage levels Ⅰ and Ⅱ after cloud burst caused by large explosive structures.

Key words: cloud detonation, fuel concentration, overpressure damage, artificial neural network

CLC Number:

TQ560.1

XU Yongkang, XUE Kun. Artificial Neural Network-based Prediction Model for Damage Effect of Fuel-air Explosive[J]. Acta Armamentarii, 2024, 45(6): 1889-1905.

Figures/Tables 25

Table 1 The components of multiphase cloud explosion fuel of Formulae A and B

燃料配方	液相组分	固相组分	ω_m	ρ_fuel/(kg·m^-3)
A	乙醚(C₄H₁₀O)	铝粉(Al)	1.47	1230
B	环氧丙烷(C₃H₆O)		1	1640

Table 2 Physicochemical parameters of liquid and solid components of multiphase cloud explosion fuels

组分	ρ/(kg·m^-3)	M/(g·mol^-1)	$ν O 2 Ⅰ$	q/(MJ·g^-1)	$q ¯$ /(MJ·mol^-1)	P_CJ/MPa	D_CJ/(m·s^-1)	Q_CJ/(kJ·m^-3)
乙醚	0.713	74	6	36.78	2.73	1.15	1374	1463
环氧丙烷	0.830	58	4	45.8	2.66	1.4	1522	1980
铝粉	2.700	27	3/4	31.05	0.84	1.58	1513	2213

Table 2 Physicochemical parameters of liquid and solid components of multiphase cloud explosion fuels

组分	ρ/(kg·m^-3)	M/(g·mol^-1)	$ν O 2 Ⅰ$	q/(MJ·g^-1)	$q ¯$ /(MJ·mol^-1)	P_CJ/MPa	D_CJ/(m·s^-1)	Q_CJ/(kJ·m^-3)
乙醚	0.713	74	6	36.78	2.73	1.15	1374	1463
环氧丙烷	0.830	58	4	45.8	2.66	1.4	1522	1980
铝粉	2.700	27	3/4	31.05	0.84	1.58	1513	2213

Fig.1 Change of the density ρmix and equivalent ratio of multiphase cloud with the fuel concentration

Table 3 Comparison of calculated and literature values[22] of CJ detonation parameters for different multiphase energetic systems

燃料	燃料质量浓度/%	P_CJ/MPa			D/(km·s^-1)
燃料	燃料质量浓度/%	计算值	文献值	误差/%	计算值	文献值	误差/%
甲烷	7.25	1.652	1.780	-7.19	1.814	1.837	-1.25
庚烯	6.26	1.913	2.014	-5.01	1.811	1.800	0.61
环氧丙烷	9.62	2.037	2.106	-3.28	1.835	1.826	0.49
0.9庚烯+0.1环氧丙烷	6.49	1.921	2.018	-4.81	1.813	1.801	0.67
0.8庚烯+0.2环氧丙烷	6.73	1.930	2.023	-4.60	1.814	1.803	0.61
0.9庚烯+0.1硝酸丁酯	6.71	1.931	2.027	-4.74	1.815	1.806	0.50
0.8庚烯+0.2硝酸丁酯	7.23	1.951	2.042	-4.46	1.820	1.802	1.00
铝粉	20.87	2.432	2.562	-5.07	1.854	1.847	0.38

Fig.2 Change of CJ detonation pressure PCJ, detonation velocity DCJ, (unit volume) detonation heat q ˙ and explosion temperature TCJ with the fuel concentration ρ f u e l *

Table 4 Detonation parameters of multiphase clouds with two fuel formulae at the same equivalent ratio in States Ⅰ and Ⅱ

燃料配方	云团状态	P_CJ/ MPa	D_CJ/ (km·s^-1)	$q ˙ C J$ / (kJ·m³)	T_CJ/ K
A	Ⅰ 147	2.136	1873	4414	3309
A	Ⅱ 144	2.161	1862	4483	3243
B	Ⅰ 146	2.063	1842	4388	3249
B	Ⅱ 142	2.066	1821	4359	3203

Table 4 Detonation parameters of multiphase clouds with two fuel formulae at the same equivalent ratio in States Ⅰ and Ⅱ

燃料配方	云团状态	P_CJ/ MPa	D_CJ/ (km·s^-1)	$q ˙ C J$ / (kJ·m³)	T_CJ/ K
A	Ⅰ 147	2.136	1873	4414	3309
A	Ⅱ 144	2.161	1862	4483	3243
B	Ⅰ 146	2.063	1842	4388	3249
B	Ⅱ 142	2.066	1821	4359	3203

Fig.3 Isentropic expansion curves of the products at different fuel concentrations after cloud detonation

Table 5 Detonation parameters of Formula A in States Ⅰ and Ⅱ

$ρ f u e l *$ /(kg·m^-3)	ρ_mix/(kg·m^-3)	ϕ	B/kPa	R₂	C/kPa	ω	D/(m·s^-1)	E₀/(kJ·m^-3)	P_CJ/kPa	状态
0.03	1.210	0.21	359.40	1.42	325.54	0.397	1216	950	824	Ⅰ
	1.203	0.21	418.08	1.55	321.29	0.388	1220	954	825	Ⅱ
0.05	1.230	0.34	197.18	0.78	500.79	0.359	1442	1610	1175	Ⅰ
	1.219	0.34	419.08	0.62	499.76	0.366	1448	1617	1174	Ⅱ
0.07	1.250	0.48	176.35	0.55	630.66	0.322	1587	2270	1455	Ⅰ
	1.234	0.49	173.63	0.53	629.25	0.321	1595	2280	1452	Ⅱ
0.11	1.290	0.75	208.45	0.47	831.43	0.265	1776	3583	1912	Ⅰ
	1.264	0.63	203.37	0.46	825.22	0.262	1784	3597	1894	Ⅱ
0.15	1.330	1.03	195.40	0.47	974.32	0.239	1870	4531	2189	Ⅰ
	1.295	1.06	189.99	0.44	955.98	0.242	1879	4422	2151	Ⅱ
0.19	1.370	1.3	215.54	0.46	1043.52	0.256	1922	4585	2363	Ⅰ
	1.326	1.35	206.38	0.44	1018.64	0.258	1929	4449	2303	Ⅱ
0.23	1.410	1.58	188.14	0.46	1106.02	0.264	1944	4663	2464	Ⅰ
	1.356	1.65	173.98	0.45	1074.01	0.265	1950	4504	2383	Ⅱ
0.27	1.450	1.85	161.26	0.42	1152.93	0.269	1953	4757	2540	Ⅰ
	1.387	1.95	152.17	0.41	1110.69	0.270	1958	4573	2443	Ⅱ

Table 5 Detonation parameters of Formula A in States Ⅰ and Ⅱ

$ρ f u e l *$ /(kg·m^-3)	ρ_mix/(kg·m^-3)	ϕ	B/kPa	R₂	C/kPa	ω	D/(m·s^-1)	E₀/(kJ·m^-3)	P_CJ/kPa	状态
0.03	1.210	0.21	359.40	1.42	325.54	0.397	1216	950	824	Ⅰ
	1.203	0.21	418.08	1.55	321.29	0.388	1220	954	825	Ⅱ
0.05	1.230	0.34	197.18	0.78	500.79	0.359	1442	1610	1175	Ⅰ
	1.219	0.34	419.08	0.62	499.76	0.366	1448	1617	1174	Ⅱ
0.07	1.250	0.48	176.35	0.55	630.66	0.322	1587	2270	1455	Ⅰ
	1.234	0.49	173.63	0.53	629.25	0.321	1595	2280	1452	Ⅱ
0.11	1.290	0.75	208.45	0.47	831.43	0.265	1776	3583	1912	Ⅰ
	1.264	0.63	203.37	0.46	825.22	0.262	1784	3597	1894	Ⅱ
0.15	1.330	1.03	195.40	0.47	974.32	0.239	1870	4531	2189	Ⅰ
	1.295	1.06	189.99	0.44	955.98	0.242	1879	4422	2151	Ⅱ
0.19	1.370	1.3	215.54	0.46	1043.52	0.256	1922	4585	2363	Ⅰ
	1.326	1.35	206.38	0.44	1018.64	0.258	1929	4449	2303	Ⅱ
0.23	1.410	1.58	188.14	0.46	1106.02	0.264	1944	4663	2464	Ⅰ
	1.356	1.65	173.98	0.45	1074.01	0.265	1950	4504	2383	Ⅱ
0.27	1.450	1.85	161.26	0.42	1152.93	0.269	1953	4757	2540	Ⅰ
	1.387	1.95	152.17	0.41	1110.69	0.270	1958	4573	2443	Ⅱ

Table 6 Detonation parameters of Formula B in States Ⅰ and Ⅱ

$ρ f u e l *$ /(kg·m^-3)	ρ_mix/(kg·m^-3)	ϕ	B/kPa	R₂	C/kPa	ω	D/(m·s^-1)	E₀/(kJ·m^-3)	P_CJ/kPa	状态
0.07	1.25	0.39	941.26	1.23	460.11	0.259	1550	2136	1504	Ⅰ
	1.233	0.39	284.07	0.78	574.73	0.309	1554	2153	1403	Ⅱ
0.11	1.290	0.61	190.84	0.45	795.94	0.270	1735	3377	1822	Ⅰ
	1.263	0.61	190.51	0.47	792.25	0.265	1746	3402	1809	Ⅱ
0.15	1.330	0.84	157.22	0.39	956.22	0.231	1838	4599	2117	Ⅰ
	1.293	0.84	154.35	0.47	949.38	0.224	1850	4626	2086	Ⅱ
0.20	1.380	1.11	158.02	0.39	1089.22	0.222	1919	5391	2391	Ⅰ
	1.330	1.11	156.06	0.40	1065.49	0.223	1934	5252	2340	Ⅱ
0.24	1.420	0.79	183.81	0.39	1158.82	0.229	1963	5605	2568	Ⅰ
	1.360	0.79	211.06	0.61	1127.95	0.224	1978	5444	2498	Ⅱ
0.29	1.470	1.62	193.81	0.40	1238.10	0.232	1998	5898	2744	Ⅰ
	1.398	1.62	193.14	0.41	1192.6	0.231	2011	5710	2648	Ⅱ

Table 6 Detonation parameters of Formula B in States Ⅰ and Ⅱ

$ρ f u e l *$ /(kg·m^-3)	ρ_mix/(kg·m^-3)	ϕ	B/kPa	R₂	C/kPa	ω	D/(m·s^-1)	E₀/(kJ·m^-3)	P_CJ/kPa	状态
0.07	1.25	0.39	941.26	1.23	460.11	0.259	1550	2136	1504	Ⅰ
	1.233	0.39	284.07	0.78	574.73	0.309	1554	2153	1403	Ⅱ
0.11	1.290	0.61	190.84	0.45	795.94	0.270	1735	3377	1822	Ⅰ
	1.263	0.61	190.51	0.47	792.25	0.265	1746	3402	1809	Ⅱ
0.15	1.330	0.84	157.22	0.39	956.22	0.231	1838	4599	2117	Ⅰ
	1.293	0.84	154.35	0.47	949.38	0.224	1850	4626	2086	Ⅱ
0.20	1.380	1.11	158.02	0.39	1089.22	0.222	1919	5391	2391	Ⅰ
	1.330	1.11	156.06	0.40	1065.49	0.223	1934	5252	2340	Ⅱ
0.24	1.420	0.79	183.81	0.39	1158.82	0.229	1963	5605	2568	Ⅰ
	1.360	0.79	211.06	0.61	1127.95	0.224	1978	5444	2498	Ⅱ
0.29	1.470	1.62	193.81	0.40	1238.10	0.232	1998	5898	2744	Ⅰ
	1.398	1.62	193.14	0.41	1192.6	0.231	2011	5710	2648	Ⅱ

Fig.4 Experimental cloud and fog field image and computational model

Fig.5 Experimental and simulated overpressures

Fig.6 Comparison of experimental and simulated peak overpressures at different positions

Fig.7 One-dimensional wedge shaped computational configuration of detonation overpressure field in spherical cloud explosion zone

Fig.8 R-t diagram of ΔPmax (a) and u(b)

Fig.9 P-t diagram at different positions

Fig.10 Variation curves of steady-state swerve response phase shift angle at different elevation angles

Table 7 Attenuation law of peak overpressure with proportional distance after detonation in the cloud region (State Ⅱ) of fuel in Formula A

$ρ f u e l *$ / (kg· m^-3)	A₁/ (kPa·m·kg^-1/3)	A₂/ (kPa·m·kg^-1/3)	A₃/ (kPa·m·kg^-1/3)	R²
0.03	62	703	1596	0.997
0.07	138	725	853	1.000
0.11	120	991	281	0.999
0.15	93	1114	-102	0.999
0.19	69	1160	-330	0.999
0.23	51	1145	-469	0.999
0.27	39	1141	-569	0.999

Table 7 Attenuation law of peak overpressure with proportional distance after detonation in the cloud region (State Ⅱ) of fuel in Formula A

$ρ f u e l *$ / (kg· m^-3)	A₁/ (kPa·m·kg^-1/3)	A₂/ (kPa·m·kg^-1/3)	A₃/ (kPa·m·kg^-1/3)	R²
0.03	62	703	1596	0.997
0.07	138	725	853	1.000
0.11	120	991	281	0.999
0.15	93	1114	-102	0.999
0.19	69	1160	-330	0.999
0.23	51	1145	-469	0.999
0.27	39	1141	-569	0.999

Fig.11 Schematic diagram of MLP network structure

Fig.12 Total sample data set in two-dimensional parameter space { ρ f u e l *, R ˙}

Fig.13 Change of MSE with the proportion of training subset sample size to total sample size and the number of iteration steps S

Fig.14 Peak values of detonation overpressure in cloud region (state Ⅱ) of fuels in Formulae A and fuel B predicted by ANN model f m a x A N N( ρ f u e l *, R ˙)

Fig.15 Contour distribution of Δ P m a x p r e in { ρ f u e l *, R ˙}

Fig.16 R ˙ i (i=1,2,3) of different ρ f u e l * based on Δ P m a x p r e

Table 8 Maximum value $\widetilde{R}_{i}$ of the third-order proportional damage radius of cloud and mist detonation for two fuel formulae under different conditions ρ f u e l , i * and ϕi

毁伤参数	燃料配方A		燃料配方B
毁伤参数	状态Ⅰ	状态Ⅱ	状态Ⅰ	状态Ⅱ
$\widetilde{R}_{1,max}$/(m·kg^-1^/³)	8.4	8.5	8.1	8.2
$\widetilde{R}_{2,max}$/(m·kg^-1^/³)	6.2	6.2	6.0	6.0
$\widetilde{R}_{3,max}$/(m·kg^-1^/³)	3.9	3.9	3.8	3.8
$ρ f u e l, 1 *$ /(kg·m^-3)	0.096	0.097	0.101	0.104
$ρ f u e l, 2 *$ /(kg·m^-3)	0.107	0.108	0.116	0.118
$ρ f u e l, 3 *$ /(kg·m^-3)	0.112	0.112	0.117	0.117
ϕ₁	0.67	0.63	0.56	0.77
ϕ₂	0.73	0.61	0.65	0.71
ϕ₃	0.77	0.52	0.65	0.59
χ₁	20%	21%	21%	22%
χ₂	19%	19%	19%	20%
χ₃	6%	6%	8%	9%

Table 8 Maximum value $\widetilde{R}_{i}$ of the third-order proportional damage radius of cloud and mist detonation for two fuel formulae under different conditions ρ f u e l , i * and ϕi

毁伤参数	燃料配方A		燃料配方B
毁伤参数	状态Ⅰ	状态Ⅱ	状态Ⅰ	状态Ⅱ
$\widetilde{R}_{1,max}$/(m·kg^-1^/³)	8.4	8.5	8.1	8.2
$\widetilde{R}_{2,max}$/(m·kg^-1^/³)	6.2	6.2	6.0	6.0
$\widetilde{R}_{3,max}$/(m·kg^-1^/³)	3.9	3.9	3.8	3.8
$ρ f u e l, 1 *$ /(kg·m^-3)	0.096	0.097	0.101	0.104
$ρ f u e l, 2 *$ /(kg·m^-3)	0.107	0.108	0.116	0.118
$ρ f u e l, 3 *$ /(kg·m^-3)	0.112	0.112	0.117	0.117
ϕ₁	0.67	0.63	0.56	0.77
ϕ₂	0.73	0.61	0.65	0.71
ϕ₃	0.77	0.52	0.65	0.59
χ₁	20%	21%	21%	22%
χ₂	19%	19%	19%	20%
χ₃	6%	6%	8%	9%

Fig.17 Maximum damage radius and maximum damage area for different fuel qualities

References 26

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