To ensure the accuracy of the work capacity of the detonation powerplant, the explosive and shock process of detonation powerplants was simulated with LSDYNA. Many maximum rising displacements of the cartridge indicating the work capacity of the device were obtained, under different fit clearances of the device. It was proved that fit clearances were the key factors affecting the work capacity of the device, and reasonable range for fit clearances was found. Besides, the objective function, constraint condition, and optimization design variables of the Genetic Algorithm were determined according to the design indicators of the detonation powerplant. The theoretical values of fit clearances of the optimization design of detonation powerplants were obtained. At last, the tests of the work capacity of the detonation powerplant and LSDYNA simulation proved the rationality of the theoretical values from the Genetic Algorithm, providing an experimental proof for the accuracy design, which could control the service door movement accurately.
According to the CCAR21R3 “Provisions for the Approval of Civil Aviation Products and Parts” of Civil Aviation Administration of China, enough measures must be taken to safeguard the life safety of the crew in flight tests. The new regional jet independently designed and manufactured by China needs to carry out the test flight in accordance with airworthiness regulations. To make sure that the test flight crew are able to escape from the aircraft in an emergency situation, the multisection telescopic detonation powerplant which is the core device of the emergency escaping support system is made. It is the first case in China where accurate blasting technique is applied to the civil aviation lifesaving field [
Working principle of the detonation powerplant pushing door [
At the early stage of the research and development of the detonation powerplant, in the work capacity test experiment, it has found that there was great discrepancy in the work capacity of the devices, which does not comply with the technical indicator of the error of the work capacity being less than 10%. As a result, the movement of the service door cannot be controlled accurately. To solve this problem and improve the energy utilization rate of the gunpowder, key factors that influence the work capacity of the detonation powerplant are analyzed and studied [
Physical model of the detonation powerplant.
Through the simulations in Section
There are mainly two ways to simulate the explosive process, including
Lagrange Algorithm, in which the explosive element is the eightnode entity element. The explosive element and the element exploded could share the same node or could be connected by the contact. The first is relatively faster than the second in computing.
Arbitrary LagrangianEulerian, ALE, in which the explosive element is the Euler element and the element exploded is the Lagrange element. The explosion between the two grids is simulated by the defined coupling [
In Lagrange Algorithm, there is a great chance that severe distortion happens to the explosive element, thus stopping the computing process. Therefore, though ALE is slower than Lagrange Algorithm, it can effectively avoid such problems caused by severe distortion of the grids as computational divergence and unreliable computing results.
A calculation physics model is built with Solidworks, and then the model is imported in LSDYNA, which is presented in Figure
3D model of the detonation powerplant.
The explosive is calculated with Eulerian Algorithm and depicted with MAT_ELASTIC_PLASTIC_HYDEO material model and PROPELLANT_DETONATION equation of state; the air is also calculated with Eulerian Algorithm but depicted with NULL material model and LINEAR_POLYNOMIAL equation of state; the detonation powerplant is calculated with Lagrange Algorithm and depicted with RIGID material model [
The finite element mesh model of the detonation powerplant.
The work done by detonation powerplants in pushing the service door mainly has two parts:
Select a set of fit clearances of the cartridge, slide cylinder, and fixed cylinder for designed detonation powerplants; then output the timedisplacement curve of the cartridge with LSPrePost (see Figure
Four sets of fit clearances, unit: mm.



 








0.01  0.01  0.05  0.01  0.05  0.01  0.05 
0.02  0.02  0.02  0.02  
0.03  0.03  0.03  0.03  
0.04  0.04  0.04  0.04  
0.05  0.05  0.05  0.05  
0.06  0.06  0.06  0.06  
0.07  0.07  0.07  0.07  
0.08  0.08  0.08  0.08  
0.09  0.09  0.09  0.09  
0.10  0.10  0.10  0.10 
Variation curve of 40 sets maximum displacements of the cartridge in accordance with different clearance parameters.
The internal ballistics zero dimension mathematical model of the detonation powerplant is a space averaging parameter model based on Lagrange hypothesis [
In this section, the mathematical equations of the optimization design of the detonation powerplant internal ballistics parameters are built and the optimization design of internal ballistics is carried out, so that the design cycle is shortened and the design quality is improved. The process of the detonation powerplant doing work to outside can be divided into four stages. On the basis of the characteristic of each stage and classic ballistic theories such as internal ballistics gunpowder gas equation of state, burning equation, energy conservation law, and kinematic equation [
The first stage is the period from the ignition of gunpowder to the time when the cartridge and slide cylinder start to move. In this period, the gunpowder is burning in constant volume and the gas pressure in the cavity produced by the burning of gunpowder gradually increases from zero to start pressure. The constant volume equation of state, gunpowder shape function, Euler equation which represents the onedimensional linear motion of the gas in device [
The second stage is the period from the time when the cartridge and slide cylinder start to move to the time when the gunpowder burns out. In this period, the cartridge and slide cylinder move along the axis of the fixed cylinder. When the gunpowder burns out, the gas pressure in the cavity reaches the maximum. The power state function, gunpowder burning equation, equation of the movement of the cartridge and slide cylinder, the kinematical equation that calculates the speed and distance of cartridge’s and slide cylinder’s movement, and relative gas leakage flow of this period are
The third stage is the period from the time when the gunpowder burns out to the time when the slide cylinder’s movement stops. In this period, the gas of high temperature and pressure continues to expand and do work to outside, pushing the cartridge and slide cylinder to move. Meanwhile, the gas pressure inside the cavity starts to drop. After the slide cylinder moves for a distance, its lower lace strikes the upper lace of the fixed cylinder and it is stopped. The kinematical equation of the movement of the cartridge and slide cylinder, energy equation, and relative gas leakage flow of this period are
The fourth stage is the period from the time when the movement of the slide cartridge stops to the time when the cartridge separates from the slide cylinder. In this period, though the pressure of the gas keeps dropping, it continues to expand and push the cartridge to move along the inner wall of the slide cylinder. Then the process of doing work finishes until the cartridge separates from the slide cylinder. The kinematical equation of the movement of the cartridge, the energy equation, and relative gas leakage flow of this period are
Later, the service door stops accelerating and gets an initial velocity; then it starts flat parabolic motion. When the service door touches the floor of the cabin, it starts to spin around the horizontal centroidal axis and continues to lose speed until the speed reduces to zero. Then the service door falls on the floor. The energy equation that transforms the process above into the working process of devices in the detonation powerplant work capacity test experiment is
There are many parameters involved in the design of the detonation powerplant. Among these parameters, some are dynamic variables, some are constant numbers, some have a relatively big influence on the performance of the internal ballistics of the detonation powerplant while some are the secondary parameters which only have a little influence, some are independent from each other, and some have influence on one another with certain correlation among them.
Optimizing the design variables must target the independent variables which have the most influence on the performance of the device and can respond most sensitively. For three fit clearances and their influences on the work capacity of the detonation powerplant being investigated, the constraint conditions are the following:
Above all, the objective function of the question about the optimization design of the detonation powerplant internal ballistics is
The optimization design process of internal ballistics parameters with Genetic Algorithm of the detonation powerplant is shown in Figure
Flow chart of Genetic Algorithm of the detonation powerplant.
By employing MATLAB program, optimal results of the detonation powerplant internal ballistics parameters are obtained according to the internal ballistics zero dimension mathematical model of the device and Genetic Algorithm. The size of the population has a direct effect on the convergence procedure and the efficiency of calculating. If the population is too large, it will increase the calculating time greatly; if the population is too small, the calculating process might stop when a regional optimal result is obtained [
Table of parameters of genetic algorithm.
Factors  Value 

The size of population  50 
The length of chromosome  18 
Maximum generation  800 
Crossover probability  0.7 
Mutation rate  0.001 
Generation gap  0.5 
According to the optimal results of the Genetic Algorithm, when genetic revolution goes on to the 800th generation, the convergence is reached. So choose the first generation, the 380th generation, and the 800th generation of all the 800 generations as representatives, and the individuals of these generations are shown in Tables
Results of the first generation.








1  1626.477  0.024  0.067  0.054  115.312  485.705 
2  1627.091  0.023  0.066  0.053  142.642  600.193 
3  1628.012  0.022  0.065  0.052  136.398  505.238 
4  1626.988  0.021  0.067  0.055  122.432  494.345 
5  1627.909  0.020  0.066  0.054  116.675  486.549 
6  1627.205  0.024  0.065  0.053  118.125  488.596 
7  1627.192  0.023  0.067  0.052  119.987  490.643 
8  1627.546  0.022  0.066  0.055  121.015  492.690 
9  1627.821  0.021  0.065  0.054  122.689  494.736 
10  1627.735  0.020  0.067  0.053  126.507  496.783 
11  1627.332  0.024  0.066  0.052  128.674  498.830 
12  1626.875  0.023  0.065  0.055  130.435  500.877 
13  1626.798  0.022  0.067  0.054  132.895  502.923 
14  1627.809  0.021  0.066  0.053  134.453  504.970 
15  1628.576  0.020  0.065  0.052  138.012  507.018 
16  1626.308  0.024  0.067  0.055  139.897  509.064 
17  1626.957  0.023  0.066  0.054  141.476  511.110 
18  1627.948  0.022  0.065  0.053  142.889  513.157 
19  1627.827  0.021  0.067  0.052  143.114  515.204 
20  1627.813  0.020  0.066  0.055  143.423  517.251 
21  1627.144  0.024  0.065  0.054  143.464  519.298 
22  1627.002  0.023  0.067  0.053  143.896  521.345 
23  1627.982  0.022  0.066  0.052  143.995  523.391 
24  1627.627  0.021  0.065  0.055  144.102  525.438 
25  1627.635  0.020  0.067  0.054  144.169  527.485 
26  1627.240  0.024  0.066  0.053  144.276  529.532 
27  1627.458  0.023  0.065  0.052  144.398  531.578 
28  1626.862  0.022  0.067  0.053  144.501  533.625 
29  1627.738  0.021  0.066  0.054  144.599  535.672 
30  1628.329  0.020  0.065  0.054  144.701  537.719 
31  1626.609  0.024  0.067  0.053  144.734  539.766 
32  1627.312  0.023  0.066  0.052  144.868  541.812 
33  1627.459  0.022  0.065  0.055  144.953  543.859 
34  1627.142  0.021  0.067  0.054  145.013  545.906 
35  1628.203  0.020  0.066  0.053  145.457  550.001 
36  1627.612  0.022  0.065  0.054  145.896  556.140 
37  1626.861  0.023  0.066  0.055  146.201  562.280 
38  1627.275  0.021  0.067  0.053  146.834  568.421 
39  1628.411  0.020  0.066  0.052  146.987  572.514 
40  1627.002  0.024  0.065  0.055  147.099  578.654 
41  1626.836  0.023  0.067  0.054  147.609  582.748 
42  1627.866  0.022  0.066  0.053  147.875  586.842 
43  1627.624  0.021  0.066  0.055  147.963  590.935 
44  1627.871  0.020  0.067  0.052  148.023  595.029 
45  1627.472  0.024  0.065  0.052  148.341  599.122 
46  1626.672  0.023  0.067  0.055  147.961  588.887 
47  1627.740  0.022  0.066  0.054  146.001  560.233 
48  1628.009  0.021  0.066  0.052  145.634  552.046 
49  1627.479  0.020  0.067  0.055  147.001  574.561 
50  1628.232  0.020  0.065  0.055  147.053  576.536 
Results of the 380th generation.








01–10  1631.388  0.032  0.047  0.043  144.398  531.578 
11–18  1631.286  0.032  0.048  0.043  143.896  521.345 
19–26  1631.184  0.033  0.048  0.043  143.995  523.391 
27–34  1631.081  0.033  0.049  0.044  144.169  527.485 
35–42  1630.979  0.034  0.049  0.044  144.276  529.532 
43–50  1630.774  0.034  0.050  0.044  144.102  525.438 
Results of the 800th generation.








01–50  1629.552  0.034  0.051  0.047  143.116  515.205 
Table
The maximum height convergence curve of weight (a) and the volume convergence curve of gunpowder chamber (b).
The convergence curve of
It is shown in the convergence curve that the optimal design variable
On the basis of the theoretical optimal parameters of fit clearances of the detonation powerplant obtained in Section
Detonation powerplants.
To test the accuracy of the work capability and consistency of the detonation powerplant, the evaluation device of work capacity is made. The device consisting of a baseboard, a weight, and two guide rods is depicted in Figure
The evaluation device of the work capacity of the detonation powerplant.
Power capability assessment experiment process of the detonation powerplant.
Early stage of detonation
Uplifted stage of weight
Falling stage of weight
The requirements of materials, the highlevel machining precision, and special eclectic igniters make the manufacture cost of the detonation powerplant very high. In order to reduce the research cost, this study tests the work capacity of the device under theoretical optimal parameters of fit clearances got from the Genetic Algorithm through the eight sets of experiment and LSDYNA simulation of explosive and shock process of the device. The results of the experiment are displayed in Table
Results of experiment on the accuracy of work capacity of the detonation powerplant.

1  2  3  4  5  6  7  8 


510.3  511.4  509.6  512.1  511.2  510.3  511.4  505.6 
Remove the deviated data from the eighth experiment and analyze and compute the datum as follows: The average value of results is
Conclusions as below are drawn on the basis of LSDYNA simulation of the explosive and shock process of the detonation powerplant, optimal design of Genetic Algorithm, and related test experiments.
By simulating the explosive and shock process of the detonation powerplant with LSDYNA, the main factors that affect the accuracy of the work capacity of the device are found. They are the fit clearances between the outer wall of the cartridge and the inner wall of the slide cylinder, the outer wall of the slide cylinder and the lace of the fixed cylinder, and the lace of the slide cylinder and the inner wall of the fixed cylinder, and the reasonable range of these three fit clearances is figured out, which lays a foundation for further optimization design of the detonation powerplant.
The internal ballistics zero dimension mathematical model of the detonation powerplant is used as the optimal design model of the device internal ballistics parameters in Genetic Algorithm and the objective function, optimization design variables, and restraint condition used in the study are appropriate. As a result, optimal fit clearances as expected are found.
The device used in the detonation powerplant work capacity test experiment is simple and appropriate and satisfies the accuracy required in theory. And the work capacity of the detonation powerplant under the optimal fit clearances obtained from Genetic Algorithm is tested through experiment and LSDYNA simulation. And within an acceptable error range, the results from the experiment are consistent with the theoretical values of fit clearances, which satisfies the design goal.
In conclusion, the analysis method used in this paper is meaningful for further optimization design of the detonation powerplant in both theory and reality. Nowadays, it has been implied to the test flight of airliner made in China.
The percentage of the gunpowder burned
Density of gunpowder installed
Density of gunpowder
Gunpowder gas covolume which is 0.5
Relative thickness of the gunpowder burned
Density of gas inside the device
Flow velocity of gas in vertical direction
Area of clearance axial section
Independent variable time
Independent variable displacement
Burning speed coefficient which is 0.2
Burning speed index which is 0.82
Total pressure impulse
Total energy
Mass of the weight
Height of weight’s rising
The shape, feature, and quantity of gunpowder
Reduction diameter of gunpowder’s free volume
Calculated coefficient of secondary work done by the device
Gunpowder force which is 310 kJ/kg
Mass force per unit in vertical direction
Gas pressure inside the device
Gravitational potential energy of the weight
Heat passed to unit mass air in unit time
Relative air leakage flow
Total air leakage
Mass of gunpowder installed
Speed of cartridge
Displacement of cartridge
Adiabatic coefficient which is 1.2
Mass of equivalent mass entity
Propellant web size which is 0.068
Area of the cartridge axial section
Area of the slide cylinder axial section
Gravity coefficient
Maximum value of the cartridge’s speed
Maximum value of the cartridge’s kinetic energy
Device startup pressure
The authors declare that they have no competing interests.
The work described in this paper is financially supported by the China National Aviation Holding Company under Grant no. NJCXRW20100208. The authors would like to gratefully acknowledge this support.