br Acknowledgments This work is supported

This work is supported by the National Outstanding Young Scientist Foundation of China (11225213), and Major Program of National Natural Science Foundation of China (Grant No. 11390362).

The liquefied petroleum gases, abbreviated as LPG, means those petroleum products which are made up of mixed variables of gaseous hydrocarbons (methane, ethane, butane) and ambient conditions, which are in a cholecystokinin receptor state of vapor, but can be easily liquefied. In Romania, liquefied petroleum gas, namely, petroleum product, is composed of mixture of butane (min. 90%) and propane (max. 9%) [1].
The characteristics of LPG are defined in SR 66:2007, containing mainly max. 12% C3 and min. 87% C4, and the vapor pressure is max. 7.5 bar [1].
A mixture of 8% propane and 92% butane was chosen for numerical simulation in the paper. This mixture of fuel, mixed with air, will form an explosive atmosphere. The temperatures of self-ignition and explosion limits for LPG components are presented in Table 1.

The calculation of the characteristics of LPG-air mixture using CEA program
CEA program enables the calculation of the characteristics of Chapman–Jouguet detonation. Several reports from Zack and Gordon (1960 and 1968) were intended to compare the results for the two ways of calculation of chemical equilibrium. It came to the conclusion that it comes down to the same number of equations. However, in the case of free cholecystokinin receptor minimization method each chemical species can be treated independently without having to specify a set of special effects, as it is required in the case of the equilibrium constants method [2,3].
Thus, the program that uses free energy minimization method for the calculation of equilibrium composition. The method used to obtain the parameters of engine knocking Chapman–Jouguet is described by Zack and Gordon. There are three stages in the procedure. The first stage consists in estimating the initial detonation pressure and temperature. The second stage is to use a recurrent formula for improving the parameters obtained in the first stage. During the third stage the correct values are obtained using an iterative Newton–Raphson procedure [2,3].
The program assumes that all gases are ideal processes involved, and the interactions between the phases are neglected [8,10]. The equation of state for the gas mixture is
orwhere p is pressure (N/m2); V is specific volume (m3/kg); n is the number of moles per unit of mass mixture (mol/kg); T is temperature (K); and .
Based on the definition of the gas mixture, n can be written aswhere n is the number of moles; and is the number of moles of gas per kg of mixture.
In a conventional manner, an average molecular weight of the mixture is
For iterative purposes, since are valid for the shock equations, it is necessary for these three conservation equations to be reduced to two
For ease of writing the iterative equations, symbols and are used to replace the right member of the above equations. These equations become
Initial estimated temperature ratio is found by calculating the flame temperatures corresponding to enthalpy [9].
The initial estimates for the values and corresponding to are improved to give the following recursive formulas.where , and are the steady values for şi .
After running the CEA program, the parameters corresponding to a gaseous LPG-air mixture (Table 2) were calculated, which will be introduced into the model of material to be used in AUTODYN. The values were calculated according to the temperature of 18 °C and a pressure of 1 bar.
It can be seen from Table 2 that the maximum overpressure corresponds to a volume of 4% LPG vapor into the air. We will make the simulation of detonation for this gaseous mixture.

The detonation of an explosive atmosphere using modeling in Ansys Autodyn
LPG-air mixture is defined as a material using the characteristics calculated by C.E.A program. One-dimensional numerical model of this new defined material, with a predefined geometry type “wedge”, for a spherical explosive cargoes in open space is shown in Fig. 1. Detonation point is in (0,0).