Combustion efficiency prediction model of upstream-injection flame stabilizer in afterburner
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摘要:
火焰稳定器下游不同位置的燃烧效率预测是加力燃烧室长度设计中的重要问题。在来流温度600～900 K、来流速度75～170 m/s和当量比0.22～1.20的条件下，以上游喷射式U型钝体火焰稳定器为研究对象，采用数值模拟研究与理论分析相结合的方法，确定了适用于加力燃烧室的湍流火焰速度预测模型与湍流强度半经验预测公式，提出了基于化学反应速率控制的加力燃烧室上游喷射式钝体火焰稳定器的沿程燃烧效率预测模型，并对预测模型进行了验证。结果表明：与数值模拟结果相比，该模型对火焰稳定器下游不同位置处的燃烧效率预测误差，在不同来流温度和速度下不超过2.5%，不同当量比下不超过20%。
Abstract:The prediction of combustion efficiency at different downstream locations of the flame stabilizer is an important problem in the length design of afterburner. Taking the upstream-injection U-shaped bluff-body flame stabilizer as the research object, a prediction model of the combustion efficiency downstream the flame holder in the afterburner based on reaction rate controlling was proposed and verified by the combination of numerical simulation and theoretical analysis, under the conditions of incoming flow temperature of 600—900 K, incoming flow velocity of 75—170 m/s and equivalent ratio of 0.22—1.20. At the same time, the prediction model of turbulent flame velocity and the semi-empirical prediction formula of turbulent intensity for afterburner were determined. The results showed that compared with the numerical simulation results, the prediction errors of the model for the combustion efficiency at different downstream locations of the flame stabilizer were less than 2.5% at different incoming temperatures and velocities, and less than 20% at different equivalent ratios.
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图 1 几何模型及计算域示意图（单位：mm）
Figure 1. Sketch of geometric model and computational domain （unit：mm）
图 3 实验火焰照片及仿真OH质量分数云图
Figure 3. Test flame photo and simulated OH mass fraction cloud image
图 5 稳定器下游火焰扩张示意图
Figure 5. Schematic diagram of downstream flame expansion of the flame stabilizer
图 7 不同来流温度下预测模型精度结果
Figure 7. Prediction model accuracy results under different incoming temperatures
图 8 不同来流速度下预测模型精度结果
Figure 8. Prediction model accuracy results under different incoming velocities
图 9 不同当量比下预测模型精度结果
Figure 9. Prediction model accuracy results under different equivalent ratios
表 1 湍流火焰速度预测模型
Table 1. Prediction model of turbulent flame velocity
文献 模型 适用范围 [15] $\begin{gathered} \frac{{S}_{\rm{t}}}{{S}_{{\mathrm{l}}}^{0}}=={A}_{0}\mathrm{e}\mathrm{x}\mathrm{p}\left\{\left[\left(1.742+0.182{S}_{{\mathrm{l}}}^{0}{A}_{0}^{2}\right)+\frac{1}{2}\mathrm{ln}\left(\frac{{l}_{{\mathrm{t}}}}{{\delta }_{{\mathrm{l}}}^{0}}\right)\right]\times\right.\\\left.\left[1-\mathrm{exp}\left(-\dfrac{\dfrac{\left(1-{{\rho }_{{\mathrm{b}}}}/{{\rho }_{{\mathrm{u}}}}\right){A}_{0}\left(K=1\right)}{Le}R{e}^{-\tfrac{1}{4}}{\left({{l}_{{\mathrm{t}}}}/{{\delta }_{{\mathrm{l}}}^{0}}\right)}^{\tfrac{1}{2}}}{\left(1.742+0.182{S}_{{\mathrm{l}}}^{0}{A}_{0}^{2}\right){A}_{0}}\times \dfrac{{u}'}{{S}_{{\mathrm{l}}}^{0}}\right)\right]\right\} \end{gathered}$ 适用于平面火焰和本生灯火焰等 [16] $ \dfrac{{S}_{\rm{t}}}{{S}_{{\mathrm{l}}}^{0}}=6.4{\left(\dfrac{{u}'}{{S}_{{\mathrm{l}}}^{0}}\right)}^{\tfrac{1}{4}} $ 适用于$ \eta < 0.6{l}_{{\mathrm{f}}} $且$ Re\leqslant 3\;200 $或者$ \eta < 1.5{l}_{{\mathrm{f}}} $且$ Re > 3\;200 $ [17] $ \dfrac{{S}_{\rm{t}}}{{S}_{{\mathrm{l}}}^{0}}=0.52{\left(Pr\dfrac{{S}_{{\mathrm{l}}}^{0}{l}_{{\mathrm{t}}}}{{u}'{l}_{{\mathrm{f}}}}\right)}^{\tfrac{1}{4}}\dfrac{{u}'}{{S}_{{\mathrm{l}}}^{0}} $ 结合小尺度湍流对增强标量混合的影响和
大尺度湍流对火焰表面起皱的影响[18] $ \dfrac{{S}_{\rm{t}}}{{S}_{{\mathrm{l}}}}=\left\{0.5\left[1+\left(1+8\dfrac{{u}^{'2}}{{S}_{{\mathrm{l}}}^{2}}\right)^{0.5}\right]\right\}^{0.5} $ 适用于弱强度湍流燃烧 [19] $ \dfrac{{S}_{\rm{t}}}{{S}_{{\mathrm{l}}}^{0}}=1+0.195\dfrac{{l}_{{\mathrm{t}}}}{{l}_{{\mathrm{f}}}}\left(\sqrt{1+20.5\dfrac{{u}'{l}_{{\mathrm{f}}}}{{S}_{{\mathrm{l}}}^{0}{l}_{{\mathrm{t}}}}}-1\right) $ 适用于大尺度湍流燃烧和小尺度湍流燃烧 注：$ {S}_{{\mathrm{l}}}^{0} $为无应变一维层流火焰的层流火焰速度，$ {\delta }_{{\mathrm{l}}}^{0} $为无应变一维层流火焰的层流火焰厚度，$ {S}_{{\mathrm{l}}} $为层流火焰速度，$ {A}_{0} $为拉伸因子，$ {l}_{{\mathrm{t}}} $为湍流积分尺度，$ {\rho }_{{\mathrm{b}}} $和$ {\rho }_{{\mathrm{u}}} $分别为已燃气体和未燃气体的密度，$ Le $、$ Pr $和$ Re $分别为湍流刘易斯数、普朗特数和雷诺数，K为传递系数，$u' $为湍流脉动速度，$ {l}_{{\mathrm{f}}} $为扩散火焰厚度，$ \eta $为科尔莫戈罗夫长度尺度。 
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表 2 湍流火焰速度$ {{\boldsymbol{S}}}_{\bf{t}} $实验结果[14]
Table 2. Test results of the turbulence flame velocity $ {{\boldsymbol{S}}}_{\bf{t}} $[14]
T/K p/Pa V/（m/s） $ {S}_{\rm{t}}/ （\mathrm{m}/\mathrm{s}） $ 573 101325 50 12.06 573 101325 75 15.07 573 101325 100 16.50
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表 3 数值模拟工况及湍流强度结果
Table 3. Numerical simulation conditions and turbulence intensity results
工况 $ T/\mathrm{K} $ $ V/ （\mathrm{m}/\mathrm{s}） $ $ \phi $ $ I $/% C 1 600 75 0.61 5.70 0.188 0 2 700 75 0.61 7.00 0.228 5 3 800 75 0.61 8.30 0.268 5 4 900 75 0.61 9.60 0.308 0 5 900 100 0.61 8.80 0.292 5 6 900 125 0.61 8.00 0.273 5 7 900 150 0.61 7.38 0.258 0 8 900 75 0.22 30.00 1.058 5 9 900 75 0.347 13.56 0.460 5 10 900 75 0.844 8.14 0.253 0 11 900 75 1.0 6.31 0.193 7 12 900 75 1.2 4.01 0.122 5
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表 4 数值模拟工况
Table 4. Numerical simulation conditions
工况 $ T/{\mathrm{K}} $ $ V/ （\mathrm{m}/\mathrm{s}） $ $ \phi $ 13 650 90 0.5 14 750 90 0.5 15 850 90 0.5 16 850 130 0.5 17 850 170 0.5 18 850 90 0.3 19 850 90 0.8 20 850 90 1.1
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