Application of compressibility corrected γ-Reθt transition model in turbomachinery
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摘要:
基于原始的
γ-Re θt 转捩模型，开展了两种可压缩修正方法在叶轮机械内流领域中边界层转捩预测的应用研究。第1种方法考虑马赫数和温度，对边界层中的涡量雷诺数Re v 与动量厚度雷诺数Re θ 的关系式进行可压缩修正，并利用雷诺数可压缩比拟关系f Re 修正原始的不可压转捩关联函数。第2种方法考虑高马赫数效应对压力梯度参数的影响以及实际流动中湍流普朗特数的可变性，对两个关键参数进行可压缩修正。基于团队自研求解器实现两种修正方法，然后采取3个典型叶轮机械算例进行转捩预测，并与原始转捩模型进行对比分析。结果表明：在叶轮机械内流领域中，第1种修正方法改善效果显著，第2种修正方法与原始模型差异不大，但是在面对由流动分离诱导出的边界层转捩时，两者预测结果与原始模型几乎一致。-
关键词:
- 叶轮机械 /
- 边界层转捩 /
- 流动分离 /
- γ-Reθt转捩模型 /
- 可压缩修正
Abstract:Two compressibility corrected methods developed from the original
γ-Re θt transition model were applied to predict the boundary layer transition in internal flow of turbomachinery. The first method considers Mach number and temperature, it corrects the functional relationship between the vorticity Reynolds number (Re v ) and the momentum thickness Reynolds number (Re θ ) in the boundary layer, and uses the compressible Reynolds number analogy relationf Re to correct the original incompressible transition correlation function. The second method considers the influence of high Mach number effects on the pressure gradient parameter, as well as the variability of turbulent Prandtl number in actual flow, and then corrects these two key parameters. The two corrected methods were implemented on our team’s in-house solver, and transition predictions were conducted using three typical turbomachinery cases, followed by a comparative analysis with the original transition model. The results indicate that in internal flow of turbomachinery, the first correction method shows a significant improvement, while the second one exhibits little difference from the original model. However, when dealing with boundary layer transition induced by flow separation, both methods yield predictions that are nearly identical to those of the original model. -
图 2 MUR247工况不同参数计算结果对比
Figure 2. Comparison of results for different parameters under MUR247
图 3 MUR241工况不同参数计算结果对比
Figure 3. Comparison of results for different parameters under MUR241
图 4 UKG0303计算网格及设置 （单位：mm）
Figure 4. Computational mesh and settings for UKG0303（unit：mm）
图 6 γ-Reθt转捩模型间歇因子与局部流线分布
Figure 6. Intermittency and local streamline results of γ-Reθt transition model
图 9 γ-Reθt转捩模型马赫数与间歇因子分布
Figure 9. Ma and intermittency results of γ-Reθt transition model
表 1 VKI叶型主要几何参数
Table 1. Main geometric parameters of VKI
参数 数值 弦长 C/mm 67.647 栅距 t/mm 57.5 展高 h/mm 50 安装角 α/（°） 55 前缘半径 R1/mm 4.126 尾缘半径 R2/mm 0.710 
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表 2 VKI边界条件设置
Table 2. Boundary condition settings for VKI
参数 MUR247 MUR241 入口湍流度 Tuinlet/% 1 6 入口黏度比 Rt-inlet 18 60 入口总压$p^*_1 $/kPa 339.5 325.7 入口总温$T^*_1 $/K 416.2 416.4 入口马赫数 Ma1 0.15 0.15 出口马赫数 Ma2 0.922 1.089 出口静压 p2/kPa 196 154.7 壁面温度 Tw/K 302.15 299.75
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表 3 试验与计算转捩起始、结束位置对比
Table 3. Comparison of experimental and computational transition start and end positions
转捩模型 起始位置/mm 误差δc/% 结束位置/mm 误差δc/% 试验 计算 试验 计算 γ-Reθt 61.2 66.1 7.24 70.8 74.7 5.77 γ-Reθt-M1 61.2 62.2 1.48 70.8 68.9 2.81 γ-Reθt-M2 61.2 67.2 8.87 70.8 74.7 5.77
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表 4 试验与计算转捩起始、结束位置对比
Table 4. Comparison of experimental and computational transition start and end positions
转捩模型 起始位置/mm 误差δc/% 结束位置/mm 误差δc/% 试验 计算 试验 计算 γ-Reθt 40.2 58.1 26.46 57.2 75.1 26.46 γ-Reθt-M1 40.2 43.4 4.73 57.2 60.7 5.17 γ-Reθt-M2 40.2 53.3 19.37 57.2 76.9 29.12
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表 5 UKG0303叶型主要几何参数
Table 5. Main geometric parameters of UKG0303
参数 数值 弦长 C/mm 75 栅距 t/mm 58.5 展高 h/mm 190 安装角 α/（°） 13.57 弯角 η/（°） 47.0 气流折转角 β/（°） 38.6
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表 6 UKG0303边界条件设置
Table 6. Boundary condition settings for UKG0303
参数 数值 入口湍流度 Tuinlet/% 1 入口黏度比 Rt-inlet 10 入口总压$p^*_1 $/kPa 111 入口静压 p1/kPa 87.025 入口总温$T^*_1 $/K 301.45 入口马赫数 Ma1 0.6 出口静压 p2/kPa 95 绝热壁面
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表 7 STFF叶型主要几何参数
Table 7. Main geometric parameters of STFF
参数 数值 弦长 C/mm 100.3 栅距 t/mm 30.2 展高 h/mm 152 安装角 α/（°） 22.6 弯角η/（°） 21.6 进口气流角α1k/（°） 37 出口气流角 α2k/（°） 11
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表 8 STFF边界条件设置
Table 8. Boundary condition settings for STFF
参数 数值 入口湍流度 Tuinlet/% 1 入口总压$p_1^* $/kPa 400 入口静压 p1/kPa 30.5 入口总温$T_1^* $/K 285 入口马赫数 Ma1 2.33 出口静压p2/kPa 22.0 绝热壁面
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