Three-dimensional numerical study on influences of uneven equivalence ratio on performances of a rotating detonation combustor
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摘要: 为研究入口当量比的不均匀分布对旋转爆震燃烧室性能的影响，建立了当量比在入口环缝的径向或周向的函数模型，将模型公式代入组分质量分数与当量比的关系式，得到组分质量分数在径向或周向的分布函数。通过Fluent软件中的自定义函数工具，构造入口边界组分的分布函数，利用三维瞬态欧拉方程模拟了C10H22/air旋转爆震燃烧室中爆震波的传播过程及流场特性，对比了不同当量比分布下爆震波及旋转爆震燃烧室性能参数的变化特征。结果表明：入口当量比的不均匀分布会影响爆震波的传播特性；当量比为0.4~1.6且沿径向非均匀分布时，随着入口面中线位置当量比的增大，爆震波的高度减小；当量比为0.4~1.6且沿周向非均匀分布时，随着变化周期数的增加，爆震波的高度几乎不受影响；当量比的不均匀分布会削弱旋转爆震燃烧室的增压效果和温升效果，沿径向不均匀分布的情况相较于沿周向不均匀分布的情况，影响更明显；旋转爆震燃烧室内，爆震波的诱导和反应区并非严格位于前导激波的正后方，而是位于前导激波的斜后方，且在曲率的影响下，在靠近燃烧室外壁面的区域，前导激波沿中径圆柱面的圆周线传播。Abstract: To investigate the effects of the inlet equivalence ratio distribution on the performance of a rotating detonation combustor (RDC), the radial or circumferential function model of equivalence ratio at the entrance of the RDC was established. The distribution function of component mass fraction in radial or circumferential direction was obtained by substituting the function model of equivalence ratio into the function of component mass fraction and equivalence ratio. The distribution function of entry boundary components was constructed by the user-defined function tool in the Fluent code. A three-dimensional transient Euler equation was employed to simulate the propagation process and flow field characteristics of detonation waves in a C10H22/air RDC, and the characteristics parameters of the detonation waves and RDC were compared under different equivalence-ratio distributions. The results show that the uneven distribution of the inlet equivalence ratio will affect the characteristics of the detonation waves. When the equivalence ratio ranges from 0.4 to 1.6 and is not uniformly distributed along the radial direction, the height of the detonation wave decreases with the increase of equivalence ratio at the midline of the inlet surface. When the equivalence ratio ranges from 0.4 to 1.6 and the distribution is non-uniform in the circumferential direction, the height of the detonation wave is almost not affected with the increase of the number of changing periods. The uneven distribution of equivalence ratio will weaken the pressure-gain effect and temperature rise effect of the RDC, and the influence of the uneven distribution of equivalence ratio along the radial direction is more obvious than that along the circumferential direction. In the RDC, the induction and reactant region of detonation wave is not strictly behind the leading shock wave, but is located at the oblique rear of the leading shock wave, and under the influence of curvature, the leading shock wave propagates along the circumference of the middle diameter cylinder near the outer wall of the RDC.
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图 1 旋转爆震燃烧室的剖面图及其入口坐标（单位：m）
Figure 1. Profile chart of the rotating detonation combustor and the coordinate of its inlet (unit in m)
图 2 不同工况下当量比沿入口径向分布函数
Figure 2. Functions of equivalence ratio distribution along the inlet radial direction under working conditions
图 3 工况V1和V2下当量比沿入口周向的分布函数
Figure 3. Functions of equivalence ratio distribution along the inlet circular direction under working conditions V1 and V2
图 4 V3和V4工况下当量比沿入口周向的分布函数
Figure 4. Functions of equivalence ratio distribution along the inlet circular direction under working conditions V3 and V4
图 5 以工况V3为例，3种网格尺寸下得到的压力峰值曲线
Figure 5. Peak pressure history curves obtained under three grid sizesby taking working condition V3 as an example
图 6 RDC入口组分质量分数的分布
Figure 6. Mass fraction distributions of components in the inlet of an RDC
图 11 工况U1～U4下爆震波传播速度的变化
Figure 11. Variation of detonation wave velocity with working conditions U1 to U4
图 12 工况U1下燃烧室的爆震波压力和温度分布
Figure 12. Pressure and temperature distributions of detonation wave in an RDC under working condition U1
图 13 工况U2下燃烧室的爆震波压力和温度分布
Figure 13. Pressure and temperature distributions of detonation wave in an RDC under working condition U2
图 14 工况U3下燃烧室的爆震波压力和温度分布
Figure 14. Pressure and temperature distributions of detonation wave in an RDC under working condition U3
图 15 工况U4下燃烧室的爆震波压力和温度分布
Figure 15. Pressure and temperature distributions of detonation wave in an RDC under working condition U4
图 16 工况M下燃烧室的爆震波压力和温度分布
Figure 16. Pressure and temperature distributions of detonation wave in an RDC under working condition M
图 17 工况U1～U4的爆震波峰值压力和温度的变化
Figure 17. Variations of peak pressure and peak temperature of detonation wave with working conditions U1 to U4
图 18 工况U1～U4的燃烧室增压比和温升比的变化
Figure 18. Variations of pressurization ratio and heating ratioin an RDC with working conditions U1 to U4
图 19 当量比径向分布的燃烧室加权总压的分布
Figure 19. Distribution of weighted average total pressure in an RDC with the distribution of equivalence ratio along the radial direction
图 20 当量比径向分布的燃烧室加权总温
Figure 20. Distributions of weighted average total temperature in RDCs with the distribution of equivalence ratio along the radial direction
图 21 当量比径向分布的燃烧室加权马赫数的分布
Figure 21. Distributions of weighted average mach number in RDCs with the distribution of equivalence ratio along the radial direction
图 24 工况V1～V4下爆震波速度的变化
Figure 24. Variation of detonation wave velocity with working conditions V1 to V4
图 25 工况V1下燃烧室内爆震波的压力和温度的分布
Figure 25. Pressure and temperature distributions of detonation wave in an RDC under working condition V1
图 26 工况V2下燃烧室内爆震波的压力和温度的分布
Figure 26. Pressure and temperature distributions of detonation wave in an RDC under working conditions V2
图 27 工况V3下燃烧室内爆震波的压力和温度的分布
Figure 27. Pressure and temperature distributions of detonation wave in an RDC under working condition V3
图 28 工况V4下燃烧室内爆震波的压力和温度的分布
Figure 28. Pressure and temperature distributions of detonation wave in an RDC under working condition V4
图 29 工况V1～V4爆震波峰值压力和温度的变化
Figure 29. Variations of peak pressure and peak temperature of detonation wave with working conditions V1 to V4
图 30 工况V1～V4的燃烧室增压比和温升比的变化
Figure 30. Variation of pressurization ratio and heating ratio of detonation wave with working conditions V1 to V4
图 31 当量比周向分布的燃烧室加权总压
Figure 31. RDC weighted average total pressure with the distribution of equivalence ratio along circular direction
图 32 当量比周向分布的燃烧室加权总温
Figure 32. RDC weighted average total temperature with the distribution of equivalence ratio along circular direction
图 33 当量比周向分布的燃烧室加权马赫数
Figure 33. RDC weighted average mach number with the distribution of equivalence ratio along circular direction
表 1 当量比沿径向分布的函数式
Table 1. Functions of equivalence ratio distribution along the radial direction
工况 函数类型 当量比表达式（r单位：m） S/m2 βS U1 递增正比例函数 $\varphi = 48r - 4.4$ 0.0181 1.0226 U2 递减正比例函数 $\varphi = - 48r + 6.4$ 0.0173 0.9774 U3 递增抛物线函数 $\varphi = 1\;920{r^2} - 384r + 19.6$ 0.0145 0.8192 U4 递减抛物线函数 $\varphi = - 1\;920{r^2} + 384r - 17.6$ 0.0208 1.1751 
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表 2 当量比沿周向分布的函数式
Table 2. Functions of equivalence ratio distribution along the circular direction
工况 函数类型 当量比表达式（θ单位：rad） S/m2 βS V1 90周期余弦函数 $\varphi = 0.6\cos \left( {90\theta } \right) + 1$ 0.0177 1 V2 60周期余弦函数 $\varphi = 0.6\cos \left( {60\theta } \right) + 1$ 0.0177 1 V3 90周期分段函数 $ \varphi = \left\{ {\begin{array}{*{20}{l}} 1.6&\left( {\dfrac{{180}}{{\text{π}}}\theta } \right){\text{%}} 4 {\text{＜}}2 \\ 1&\left( {\dfrac{{180}}{{\text{π}}}\theta } \right){\text{%}} 4 = 2 \\ 0.4&\left( {\dfrac{{180}}{{\text{π}}}\theta } \right){\text{%}} 4 {\text{＞}} 2\end{array}} \right. $ 0.0177 1 V4 60周期分段函数 $\varphi = \left\{ {\begin{array}{*{20}{l}} 1.6&\left( {\dfrac{{180}}{{\text{π}}}\theta } \right){\text{%}}6 {\text{＜}}3 \\ 1&\left( {\dfrac{{180}}{{\text{π}}}\theta } \right){\text{%}}6 = 3 \\ 0.4&\left( {\dfrac{{180}}{{\text{π}}}\theta } \right){\text{%}}6 {\text{＞}} 3 \end{array}} \right.$ 0.0177 1
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