基于LADM模型的爆轰参数计算

Calculation of detonation parameters based on the LADM model

炸药爆轰以高低两种速度稳定传播。经典的ZND模型没有对应于低速爆轰的数学解,无法计算低速爆轰参数。而LADM爆轰模型(Least Action Detonation Model)有四组数学解析解。其中一组解对应于高速爆轰,可取代有争议的CJ假设;另一组解对应于低速爆轰,可计算低速爆轰速度。本文用这两组解计算了四种常用炸药的高/低速爆轰参数,不需要CJ假设等任何假设。结果表明:高速爆轰速度的实测值与计算值的相对误差范围是0.069%~1.38%;炸药的绝热指数γ1为1.239~1.312,接近多原子气体的理论值1.286;爆轰产物的绝热指数γ2为1.425~1.462,略大于双原子气体的理论值1.400。

Explosive detonation propagates at two stable velocities: high velocity and low velocity. To the classical ZND model there is no analytical solution for the low velocity detonation and the low velocity detonation parameters can't be calculated. To the LADM model(Least Action Detonation Model) proposed by the authors there are four analytical solutions. One of the solutions corresponds to the low velocity detonation, and the second one corresponds to the high velocity detonation that replaces the disputed CJ assumption. In this paper, without any assumptions, these two solutions are used to calculate the high/low velocity detonation parameters of four explosives. The relative errors of the calculated values and the measured values are within 0.069%~1.38%. The calculated adiabatic indexes of these four explosives γ1 are within 1.239~1.312, which are near to the theoretical value 1.286 of multi-atom gases. The adiabatic indexes γ2 of detonation products are 1.425~1.462, which are little higher than the value 1.40 of the double-atom gases.