Study of characterization methods of supersonic combustion flame based on fractal geometry
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摘要: 分形几何是图像学发展的新兴学科。通过分形几何，可以研究不规则图形，揭示图形的自相似特性，并且给出图形自相似性的定量数据。本文将分形几何用于分析超声速气流中的火焰形态，定量分析了不同当量比与燃料组分摩尔比条件下火焰分形维数的变化规律，研究了湍流火焰传播速度和火焰边界分形维数之间的对应关系。通过高速摄影获得的火焰CH*自发光瞬态图像，记录了马赫数2.5超声速气流中不同燃料的火焰形态，验证了超声速火焰边界具有自相似性。实验结果表明，超声速燃烧湍流火焰锋面边界的分形维数随当量比的增大近似线性增大，随着燃料中氢含量的增加而增大。Abstract: Fractal geometry is a new subject of graphics. By means of fractal geometry, ir-regular graphics can be studied, the self-similarity characteristics of graphs can be revealed, and quantitative data of graph self-similarity can be given. In this paper, the fractal geometry is used to analyze the flame morphology in the supersonic airflow, and the variation law of the flame fractal dimension under the condition of different equivalent ratios and fuel component molar ratios is quantitatively analyzed. The relationship between the velocity of the turbulent flame propagation and the fractal dimension of the flame boundary is studied. In this paper, the flame CH* self-luminescent transient image obtained by the high-speed photography is used to record the flame morphology of different fuels in the Mach number 2.5 supersonic airflow. The experimental results show that the fractal dimension of the frontal boundary of the supersonic combustion turbulent flame increases approximately linearly with the increase of the equivalent ratio, and increases with the increase of the hydrogen component in the fuel.
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图 1 超声速燃烧实验台及其结构示意图(单位:mm)
Figure 1. Supersonic combustion test facility and its structure diagram (unit: mm)
图 3 稳定燃烧时乙烯瞬态火焰边界
Figure 3. Transient flame boundary of ethylene during steady combustion
图 4 乙烯火焰边界分形维数计算结果与拟合曲线
Figure 4. Calculation results and fitting curves of fractal dimension of ethylene flame boundary
图 6 不同当量比条件下乙烯瞬态火焰分布
Figure 6. Transient flame distribution of ethylene at different equivalent ratios
图 7 不同当量比下燃烧室压力分布
Figure 7. Pressure distribution of combustor at different equivalent ratios
图 8 不同当量比下燃烧室平均马赫数分布
Figure 8. Average Mach number distribution of combustor at different equivalent ratios
图 9 乙烯火焰边界分形维数随当量比的变化
Figure 9. Variation of fractal dimension of ethylene flame boundary with equivalent ratio
图 10 不同当量比燃料B和C火焰瞬时形态
Figure 10. Instantaneous form of fuel B and C at different equivalent ratios
图 11 不同当量比下燃烧室的压力分布
Figure 11. Pressure distribution of combustor at different equivalent ratios
图 12 不同当量比燃料B和C火焰边界分形维数及其拟合曲线
Figure 12. Fractal dimension of flame boundary of fuel B and C at different equivalent ratios and their fitting curves
表 1 燃料的组分及摩尔比例(单位:%)
Table 1. Composition and molar ratio of fuel (unit: %)
编号 H2 C2H4 A 100 B 20 80 C 50 50 
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表 2 计盒数法计算结果
Table 2. Calculation results of box counting method
盒子边长S(p) 1 2 4 8 16 32 64 128 256 盒子数N 4640 2562 978 366 129 46 18 8 2
下载: 导出CSV
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