Low-Order Predictions of Spatial Distributions of Conserved Scalars in Swirl Combustors Based on the Gaussian Plume Function
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摘要: 混合分数是表征燃料-空气混合的守恒标量，是湍流燃烧建模的关键参考标量. 其空间分布通常通过三维数值模拟获得，然而对于几何形状复杂的燃烧器，三维数值模拟耗时长、成本高，导致燃烧器迭代设计过程效率低. 该研究发展了基于Gauss羽流(Gaussian plume)模型的低阶模型来计算旋流燃烧室中的混合分数场，以加速燃料-空气混合策略的评估和参数化设计过程. 相比传统的构型，新推导的Gauss羽流模型包含了径向对流的影响和针对旋流来流的修正. 进一步发展了镜像反射模型来模拟壁面-羽流的相互作用，并引入相关修正来确保质量守恒. 将新推导的Gauss羽流模型应用于甲烷旋流燃烧室混合分数场的低阶预测. 基于数值收敛的三维数值模拟生成的数据库，首先采用最小二乘法对模型参数进行优化，然后在宽范围条件下验证了模型的预测精度. 该研究不仅为旋流燃烧器内混合分数的快速预测提供了一种新方法，而且为Gauss羽流模型的进一步发展和应用提供了实例.Abstract: The mixture fraction is a conserved scalar characterizing the fuel-air mixing. As a key reference scalar for turbulent combustion modelling, its spatial distribution is usually obtained through 3D numerical simulation, which are, however, time-consuming and costly for combustors with complex geometries. To overcome such low efficiency in the iterative designing process, a low-order model was developed based on the Gaussian plume function to compute the mixture fraction field in the swirl combustor to accelerate the evaluation of the fuel-air mixing strategy and the parameterized design process. Compared with the conventional formulation, the derived new Gaussian plume function includes the effects of convection and corrections due to swirl flows. A mirror image reflection model was further developed to simulate the wall-plume interactions, together with the relevant corrections to ensure mass conservation. This newly derived Gaussian plume model was applied to the low-older prediction of the mixture fraction field in a methane swirl combustor. Based on the database generated through 3D numerical simulations, the model parameters were optimized with the least square method first. The prediction accuracy under broad working conditions was demonstrated. This study not only provides a novel approach for quick predictions of mixture fractions in swirl combustors, but also sets an instance for further development and application of the Gaussian plume model.
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Key words:
- mixture fraction /
- Gaussian plume function /
- low-order prediction /
- swirl combustor
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图 1 点源释放气体在直流空气来流中的发展示意图
Figure 1. Schematic diagram of the development of a point source releasing gas in a straight air stream
图 2 将来流离散为薄板扫略点源的示意图
Figure 2. Schematic diagram of discretizing the flow stream into thin sheets sweeping the point source
图 3 点源释放气体在旋流空气来流中的发展简图
Figure 3. Schematic diagram of the development of a point source releasing gas in a swirling air stream
图 4 多点源释放气体在旋流空气来流中的发展和镜像反射模型示意图
Figure 4. Schematic diagram of the development of multi-point sources releasing gas in a swirling air stream and the mirror reflection model
图 6 中轴线上甲烷质量分数的分布
Figure 6. Mass fractions of CH4 on the centerline of the axial direction
图 7 不同点源数量的低阶模型预估与三维数值模拟结果对比(x=30 mm)
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 7. Comparison of the low-order model prediction results of different numbers of point sources and the 3D numerical simulation results (x=30 mm)
图 8 不同点源数量的低阶模型预估结果与三维数值模拟结果对比(x=60 mm)
Figure 8. Comparison of the low-order model prediction results of different numbers of point sources and the 3D numerical simulation results (x=60 mm)
图 9 不同点源数量的低阶模型预估结果与三维数值模拟结果对比(x=60 mm，径向分布，N=12, N=24, N=36)
Figure 9. Comparison of low-order model prediction results of different numbers of point sources and the 3D numerical simulation results (x=60 mm, radial distribution, N=12, N=24, N=36)
图 10 低阶模型与三维数值模拟中截面结果对比
Figure 10. Comparison of the results from the low-order model and the 3D numerical simulations at the central plane
图 11 低阶模型与三维数值模拟中轴线结果对比
Figure 11. Comparison of the results from the low-order model and the 3D numerical simulations at the central axis
图 12 低阶模型与三维数值模拟结果对比(中截面, x=0.05 m)
Figure 12. Comparison of the results from the low-order model and the 3D numerical simulations (the central plane, x=0.05 m)
图 13 低阶模型与三维数值模拟中截面结果对比
Figure 13. Comparison of the results from the low-order model and the 3D numerical simulations at the central plane
图 14 低阶模型与三维数值模拟中轴线结果对比
Figure 14. Comparison of the results from the low-order model and the 3D numerical simulations at the central axis
图 15 低阶模型与三维数值模拟结果对比(中截面, x=0.05 m)
Figure 15. Comparison of the results from the low-order model and the 3D numerical simulations (the central plane, x=0.05 m)
图 16 两种方法耗时随算例个数的对比
Figure 16. Comparison of the computational time costs with the number of cases
图 17 DLR燃烧室混合分数的实验数据、三维数值模拟与低阶模型对比
Figure 17. Comparison of mixture fractions from the experimental data, the 3D numerical simulations and the low-order model
表 1 工况条件
Table 1. Working conditions
working condition class equivalence ratio ϕ fuel flow rate mf/(kg/s) class 1 0.8 0.029 1 0.9 0.032 7 1.0 0.036 3 1.1 0.039 9 class 2 0.7 0.025 41 0.75 0.027 2 1.2 0.043 56 
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A1 参数α，β，a，b，m的值
A1. The values of parameters α, β, a, b, m
parameter value α 2.8 β 0.159 4 a 254.442 b 0.003 781 m 0.041 66
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A2 参数vc, k的值
A2. The values of parameters vc, k
parameter value parameter value vc, 1 1.800 936 vc, 13 -1.800 936 vc, 2 5.280 076 vc, 14 -5.280 076 vc, 3 8.399 388 vc, 15 -8.399 388 vc, 4 10.946 296 vc, 16 -10.946 296 vc, 5 12.747 232 vc, 17 -12.747 232 vc, 6 13.679 465 vc, 18 -13.679 465 vc, 7 13.679 465 vc, 19 -13.679 465 vc, 8 12.747 232 vc, 20 -12.747 232 vc, 9 10.946 296 vc, 21 -10.946 296 vc, 10 8.399 388 vc, 22 -8.399 388 vc, 11 5.280 076 vc, 23 -5.280 076 vc, 12 1.800 936 vc, 24 -1.800 936
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A3 参数wc, k的值
A3. The values of parameters wc, k
parameter value parameter value wc, 1 13.679 465 wc, 13 -13.679 465 wc, 2 12.747 232 wc, 14 -12.747 232 wc, 3 10.946 296 wc, 15 -10.946 296 wc, 4 8.399 388 wc, 16 -8.399 388 wc, 5 5.280 076 wc, 17 -5.280 076 wc, 6 1.800 936 wc, 18 -1.800 936 wc, 7 -1.800 936 wc, 19 1.800 936 wc, 8 -5.280 076 wc, 20 5.280 076 wc, 9 -8.399 388 wc, 21 8.399 388 wc, 10 -10.946 296 wc, 22 10.946 296 wc, 11 -12.747 232 wc, 23 12.747 232 wc, 12 -13.679 465 wc, 24 13.679 465
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A4 参数pk的值
A4. The values of parameters pk
parameter value parameter value p1 -0.001 958 p13 0.001 958 p2 -0.005 740 p14 0.005 740 p3 -0.009 131 p15 0.009 131 p4 -0.011 900 p16 0.011 900 p5 -0.013 858 p17 0.013 858 p6 -0.014 872 p18 0.014 872 p7 -0.014 872 p19 0.014 872 p8 -0.013 858 p20 0.013 858 p9 -0.011 900 p21 0.011 900 p10 -0.009 131 p22 0.009 131 p11 -0.005 740 p23 0.005 740 p12 -0.001 958 p24 0.001 958
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A5 参数qk的值
A5. The values of parameters qk
parameter value parameter value q1 -0.014 872 q13 0.014 872 q2 -0.013 858 q14 0.013 858 q3 -0.011 900 q15 0.011 900 q4 -0.009 131 q16 0.009 131 q5 -0.005 740 q17 0.005 740 q6 -0.001 958 q18 0.001 958 q7 0.001 958 q19 -0.001 958 q8 0.005 740 q20 -0.005 740 q9 0.009 131 q21 -0.009 131 q10 0.011 900 q22 -0.011 900 q11 0.013 858 q23 -0.013 858 q12 0.014 872 q24 -0.014 872
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