Combustion laws of dished head conic-column grain
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摘要:
装药设计方法影响发动机内弹道性能，为提高装药利用率，分别采用UG NX和MATLAB软件进行了建模和编程计算，得到了药柱燃烧过程中燃烧面积推移规律和残药率与设计参数的函数关系图，进行了算例分析。计算结果表明：以药柱外径
D 为基准，当环向槽圆弧半径$ r \in$ （0，0.05D ），圆柱段内孔半径$ {R_2} \in $ （0.1D ，0.4D ），环向槽圆弧圆心旋转半径$ {R_3} \in $ （$ {R_2} $ ，0.42D ），圆柱段长$ {L_2} \in $ （0.4D ，1.53D ）时，药柱燃烧呈现先增面性后减面性。残药率与$ r $ 和$ {R_2} $ 的变化趋势同为单调递减，残药率与$ {L_2} $ 的变化趋势为单调递增，残药率与$ {R_3} $ 的变化趋势为先增大后减小。从减轻重量，提高强度和提高产品加工制造的工艺性等方面综合考虑，建议优先选择碟形封头。计算结果与实际数据的最大相对误差为0.078%。Abstract:Charge design methods affect the ballistic performance of the engine. In order to improve the charge utilization rate, UG NX and MATLAB software were used for modeling and programming of the calculation, and the function relationship diagram of the combustion surface, the residual drug rate and the design parameters during the combustion process of the drug column was obtained, and finally the example analysis was carried out. The results showed that when
D was defined as the outer diameter of grain, and the relative radius of circular groove$ r $ was (0, 0.05D ), the relative radius of the hole in the cylindrical section$ {R_2} $ was (0.1D , 0.4D ), the relative radius of the circular center of the circular groove$ {R_3} $ was ($ {R_2} $ , 0.42D ) and the length of the cylinder$ {L_2} $ was (0.4D , 1.53D ), the combustion law was progressive at first and then regressive. The waste grain rate and the change trend of$ r $ and$ {R_2} $ monotonically decreased, the waste grain rate and the change trend of$ {L_2} $ monotonically increased, and the waste grain rate and the change trend of$ {R_3} $ first increased and then decreased. From the aspects of weight reduction, improvement of the strength, processing and manufacturing, it is recommended to give priority to the dished head. The maximum relative error between the calculated result and the actual data was 0.078%.-
Key words:
- dished head conic-column grain /
- waste grain rate /
- burning law /
- solid rocket motor /
- wall thickness
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图 2 燃烧过程中的燃去肉厚特征点
Figure 2. Characteristic points of burning meat thickness in the combustion process
图 4 不同长径比的药柱燃烧面积随
$ e $ 变化关系Figure 4. Relation of the burning area for different aspect ratios changing with
$ e $ 
图 5 设计参数与
${\text{d}}f （e） /{\text{d}}e$ 的变化关系Figure 5. Relative relationship between
${\text{d}}f （e） /{\text{d}}e$ and design variables
图 6
${\text{d}}f （e） /{\text{d}}e$ 与$ r $ 的变化关系Figure 6. Relative relationship between
${\text{d}}f （e） /{\text{d}}e$ and$ r $ 
图 7
${\text{d}}f （e） /{\text{d}}e$ 与$ {R_2} $ 的变化关系Figure 7. Relative relationship between
${\text{d}}f （e） /{\text{d}}e$ and$ {R_2} $ 
图 8
${\text{d}}f （e） /{\text{d}}e$ 与$ {R_3} $ 的变化关系Figure 8. Relative relationship between
${\text{d}}f （e） /{\text{d}}e$ and$ {R_3} $ 
图 9
${\text{d}}f （e） /{\text{d}}e$ 与$ {L_2} $ 的变化关系Figure 9. Relative relationship between
${\text{d}}f （e） /{\text{d}}e$ and$L_2 $ 
图 10 残药率与
$ r $ 、$ {R_2} $ 的变化关系Figure 10. Relative relationship between waste grain rate,
$ r $ and$ {R_2} $ 
图 11 残药率与
$ {R_3} $ 、$ {L_2} $ 的变化关系Figure 11. Relative relationship between waste grain rate,
$ {L_2} $ and$ {R_3} $ 表 1 计算燃烧面积与UG提取燃烧面积数据对比
Table 1. Data comparison between burning areas by calculated and extracted from UG
e 面积/mm2 相对
误差/%UG提取 公式计算 0 238436.16 238309.56 0.053 e1 334076.46 334069.78 0.002 （e1+e2）/2 310675.48 310631.99 0.014 e2 277875.48 277769.92 0.039 e3 271807.12 271676.71 0.048 e4 249780.29 249712.87 0.027 e5 231567.18 231407.51 0.069 （e5+e6）/2 206687.47 206668.87 0.009 e6 161727.81 161601.76 0.078 
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