Numerical simulation of non-gray gaseous radiative heat transfer in 3D aero-engine combustor
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摘要:
基于自主研发的辐射计算程序应用离散坐标法和统计窄谱带吸收系数关联模型准确高效地实现了复杂几何外形内非灰气体辐射换热的数值模拟。首先，在完成了结构网格和非结构曲面网格标模验证的基础上，探究了不同角度离散格式、空间差分格式、高斯积分点类型及数目对辐射换热的影响。结果显示24个空间离散方向的角度离散格式计算精度较低，推荐使用32个离散方向的角度离散格式。不同空间差分格式和高斯积分点类型对计算结果的影响较小。接着，选取精度效率结合最优的数值方法组合，以燃烧流场数据作为输入，计算并讨论了某型航空发动机燃烧室在不同压强和壁面温度下的气体辐射换热情况。结果显示中心火焰处负辐射源项的极大值超过6000 kW/m3，而低温壁面附近气体温度较高的区域辐射源项的最大值接近17000 kW/m3，壁面上辐射热流密度的最大值接近88 kW/m2。随着压强增大，辐射源项和壁面热流密度逐渐增大但变化速率逐渐放缓，该变化速率受参与性介质浓度的影响较大。
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关键词:
- 辐射换热 /
- 非灰气体辐射 /
- 离散坐标法 /
- 统计窄谱带吸收系数关联模型 /
- 航空发动机燃烧室
Abstract:An in-house radiative heat transfer code using discrete ordinates method (DOM) and statistical narrow bands correlated-K (SNBCK) model was demonstrated to be able to calculate the gaseous radiative heat transfer in complex 3D combustion systems accurately and efficiently. After validation by using the benchmark models, the impact of the directional quadrature scheme, spatial differencing scheme, gauss quadrature type and number of quadrature points were studied. The results showed that the accuracy of the directional quadrature scheme with 24 discrete directions was low, and the Thurgood scheme with 32 discrete directions was recommended. Spatial differencing scheme and gauss quadrature type had little effect on results. Finally, the gaseous radiative heat transfer in the combustion chamber of the aero-engine under different pressures and wall temperatures was calculated. It showed that the maximum values of radiative source term in the flame zone and next to the wall were about 6000 kW/m3 and 17000 kW/m3, respectively, the maximum wall radiative heat flux can reach to 88 kW/m2. Radiative heat transfer increased with higher pressure, and the increasing rate decreased, which was significantly affected by the concentration of the participating medium.
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图 4 不同网格所得底面z方向中心线（x=0 m, y=1 m）上的壁面辐射热流密度分布
Figure 4. Wall radiative heat flux distribution at z-direction centerline of bottom side （x=0 m, y=1 m） with different meshes
图 6 不同角度离散格式所得z方向中心线（x=1 m, y=1 m）上的辐射源项分布
Figure 6. Radiative source term distribution at z-direction centerline （x=1 m, y=1 m） with different quadrature schemes
图 7 不同角度离散格式所得底面z方向中心线（x=0 m, y=1 m）上的壁面辐射热流密度分布
Figure 7. Wall radiative heat flux distribution at z-direction centerline of bottom side （x=0 m, y=1 m） with different quadrature schemes
图 8 不同角度离散格式所得壁面辐射热流密度的相对误差
Figure 8. Relative error of wall radiative heat flux with different quadrature schemes
图 9 不同空间差分格式所得z方向中心线（x=1 m, y=1 m）上的辐射源项分布
Figure 9. Radiative source term distribution at z-direction centerline （x=1 m, y=1 m） with different spatial differencing schemes
图 10 不同空间差分格式所得底面z方向中心线（x=0 m, y=1 m）上的壁面辐射热流密度分布
Figure 10. Wall radiative heat flux distribution at z-direction centerline of bottom side （x=0 m, y=1 m） with different spatial differencing schemes
图 11 不同角度离散格式所得壁面辐射热流密度的相对误差
Figure 11. Relative error of wall radiative heat flux with different spatial differencing schemes
图 12 不同高斯积分点类型所得z方向中心线（x=1 m, y=1 m）上的辐射源项分布
Figure 12. Radiative source term distribution at z-direction centerline （x=1 m, y=1 m） with different gauss quadrature types
图 13 不同高斯积分点类型所得底面z方向中心线（x=0 m, y=1 m）上的壁面辐射热流密度分布
Figure 13. Wall radiative heat flux distribution at z-direction centerline of bottom side （x=0 m, y=1 m） with different gauss quadrature types
图 14 不同高斯积分点类型所得壁面辐射热流密度的相对误差
Figure 14. Relative error of wall radiative heat flux with different gauss quadrature types
图 15 不同高斯积分点数目所得z方向中心线（x=1 m，y=1 m）上的辐射源项分布
Figure 15. Radiative source term distribution at z-direction centerline （x=1 m, y=1 m） with different numbers of gauss quadrature points
图 16 不同高斯积分点数目所得底面z方向中心线（x=0 m, y=1 m）上的壁面辐射热流密度分布
Figure 16. Wall radiative heat flux distribution at z-direction centerline of bottom side （x=0 m, y=1 m） with different numbers of gauss quadrature points
图 17 不同高斯积分点数目所得壁面辐射热流密度的相对误差
Figure 17. Relative error of wall radiative heat flux with different numbers of gauss quadrature points
图 21 不同网格所得圆柱中心轴线辐射源项分布
Figure 21. Radiative source term distribution at centerline of cylindrical benchmark with different meshes
图 23 中心线上的负辐射源项分布
Figure 23. Negative radiative source term distribution at centerline
图 29 z=0 m截面负辐射源项云图
Figure 29. Contour of negative radiative source term at section z=0 m
图 31 负辐射源项沿选取线段分布
Figure 31. Negative radiative source term distribution along the selected line
图 34 不同压强下负辐射源项沿选取线段分布
Figure 34. Negative radiative source term distribution along the selected line with different pressures
图 35 不同壁面温度下负辐射源项沿选取线段分布
Figure 35. Negative radiative source term distribution along the selected line with different wall temperatures
图 36 壁面温度对负辐射源项的影响
Figure 36. Effect of wall temperature on negative radiative source term
图 38 不同算例中辐射源项随压强的变化
Figure 38. Radiative source term evolution with pressure in different cases
表 1 各组分波数范围及谱带数
Table 1. Wavenumber range and bands number of each specie
组分 波数范围/cm−1 谱带数 H2O 50～11250 449 CO2 250～8300 323 CO 1600～6425 194 
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表 2 矩形标模设置
Table 2. Settings of rectangular benchmark
参数 数值 尺寸/m 2×2×4 壁面温度/K 300 壁面辐射率 1 H2O体积分数 0.2 CO2体积分数 0.1 N2体积分数 0.7
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表 3 不同角度离散格式的计算时间和相对误差
Table 3. Computation time and relative error with different quadrature schemes
格式 计算时间 源项误差/% 热流误差/% S4 1.00 6.05 8.08 S6 1.53 6.67 7.61 S8 2.32 5.85 6.32 T2 1.50 5.98 5.99 T4 4.51 5.33 4.31
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表 4 不同空间差分格式的相对误差
Table 4. Relative error with different spatial differencing schemes
格式 源项误差/% 热流误差/% 阶梯 5.98 5.99 菱形 5.19 5.50
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表 5 不同高斯积分点类型的相对误差
Table 5. Relative error with different gauss quadrature types
积分点类型 源项误差/% 热流误差/% Legendre 5.19 5.50 Lobatto 5.10 5.31 Chebyshev 5.95 5.89
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表 6 不同高斯积分点数目的计算时间和相对误差
Table 6. Computation time and relative error with different numbers of gauss quadrature points
积分点数目 无量纲时间 源项误差/% 热流误差/% 2 1.00 21.9 6.02 4 1.70 5.30 5.51 7 2.69 5.19 5.50
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表 7 圆柱标模设置
Table 7. Settings of cylindrical benchmark
参数 数值 尺寸/m L=1.2 m, Rc=0.3 m 壁面温度/K 800（$L \ne $1.2 m），300（L= 1.2 m） 壁面辐射率 1 各组分
体积分数${\varphi _{ {\rm{C} }{ {\rm{O} }_2} } } （{\textit{z} },r） = 0.04\left[ {1 - 3{ {\left( {\dfrac{{\textit{z} }}{L} - 0.5} \right)}^2} } \right]\left( {2.5 - \dfrac{r}{R} } \right)$ ${\varphi _{ { {\rm{H} }_2}{\rm{O} } } } （{\textit{z} },r） = 0.05\left[ {1 - 2{ {\left( {\dfrac{{\textit{z} }}{L} - 0.5} \right)}^2} } \right]\left( {2 - \dfrac{r}{R} } \right)$ 温度场 $T = 800 + 1\;200\left( {1 - \dfrac{r}{R} } \right)\dfrac{{\textit{z} }}{L}$
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