Investigation of improved SA turbulence models for flow in aeroengine compressors
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摘要:
针对标准SA（Spalart-Allmaras）湍流模型在空天发动机压气机复杂旋转流动预测中精确性不足的问题，系统地分析了SA-helicity修正湍流模型在旋转流动中的适应性，深入揭示了helicity修正项通过跨尺度涡黏抑制机理对主应变率的动态补偿机制，在保持边界层预测精度的同时，实现了角区分离与叶尖泄漏流协同控制准确预测。基于NASA Rotor 67、某高负荷单级压气机以及Aachen三级半压气机的多维度验证体系，针对不同转速下性能特性以及近失速点的叶尖失速和二次流动特征，对比分析标准SA、SA-QCR（quadratic constitutive relation）、SA-helicity这3种湍流模型的工程适应性。研究发现SA-helicity模型和SA-QCR模型均准确预测了特性线变化趋势。SA-helicity模型能在逆压梯度下增加角区分离区涡黏性，抑制角区过大分离，合理预测了叶根分离引发的通道二次流以及叶片下半部压比提升。相较于QCR模型，helicity模型能更合理地预测了叶尖泄漏流发展及范围，显著扩展了流量范围、压比和效率，更符合实验结果。此外，helicity模型预测的边界层流动更能抵抗不利逆压梯度，促使分离泡再附提前，叶尖区域附近扩压能力增强，压比和流量范围显著扩大。整体上，SA-helicity模型成功突破了传统SA湍流模型在压气机流动模拟中对旋转二次流与主流干涉效应预测失准的技术瓶颈。
Abstract:To address the accuracy problems of standard SA (Spalart-Allmaras) turbulence model when predicting complex rotating flows in aviation compressors, how the SA-helicity modified turbulence model performed in rotating flows was analyzed. It showed how the helicity correction helped compensate for strain rate through eddy viscosity mechanisms, leading to better predictions of corner separation and tip leakage flow while maintaining good boundary layer accuracy. Three turbulence models: standard SA, SA-helicity, and SA-QCR (quadratic constitutive relation), were tested, using NASA Rotor 67, a 3.5-stage axial compressor, and a publicly released high-load single-stage axial compressor from AECC Shenyang Engine Research Institute. Their performance at different rotational speeds was analyzed by focusing on performance characteristic curves, tip stall prediction, secondary flow prediction, and near-stall point prediction. Results showed that both the SA-helicity and SA-QCR models accurately predicted the trends of the characteristic curves. The SA-helicity model increased eddy viscosity in the corner separation region under adverse pressure gradients, thereby suppressing excessive corner separation. It also reasonably predicted the channel secondary flow induced by root separation, leading to an increased pressure ratio in the lower half of the blade. Compared with the QCR model, the helicity model better predicted the development and extent of tip leakage flow, significantly expanding the flow range, pressure ratio and efficiency, and showing better agreement with experimental results. Furthermore, the boundary layer flow predicted by the helicity model resisted adverse pressure gradients better, resulting in separation bubble reattaching earlier, thereby enhancing diffusion capability near the tip region and expanding the pressure ratio and flow range. Overall, the SA-helicity model overcame the limitations of traditional turbulence models in predicting how rotating secondary flows interacted with main flows in complex compressor environments.
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Key words:
- compressor /
- turbulence model /
- performance characteristics /
- corner separation /
- secondary flow /
- tip leakage flow /
- boundary layer
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图 3 NASA Rotor 67 性能曲线（网格无关性验证）
Figure 3. Performance characteristics of NASA Rotor 67（grid independence study）
图 4 NASA Rotor 67性能曲线（模型校核）
Figure 4. Performance characteristics of NASA Rotor 67（model validation）
图 5 仿真与实验结果对比（100%转速）
Figure 5. Performance comparison between numerical results and experimentals （100% rotation speed）
图 6 NASA Rotor 67表面极限流线（近失速点，背压为124 000 Pa）
Figure 6. Surface limiting streamlines for Rotor 67 （near stall point, outlet static pressure 124 000 Pa）
图 7 Rotor 67涡黏度比分布（近失速点）
Figure 7. Eddy viscosity ratio for Rotor 67 （near stall point）
图 8 Rotor 67流道旋涡结构（近失速点，$ {Q}=2.5\times {{10}}^{\text{7}}\;{\text{s}}^{{-2}} $）
Figure 8. Rotor 67 passage vortex structure （near stall point, $ {Q}=2.5\times {{10}}^{\text{7}}\;{\text{s}}^{{-2}} $）
图 15 Aachen IGV/静子出口气流参数展向分布（OP 1）
Figure 15. Distribution of flow parameters at the Aachen IGV/stator outlet （OP 1）
图 16 Aachen IGV/静子叶片表面压力分布（OP 1）
Figure 16. IGV/Stator blade loading distribution of Aachen compressor （OP 1）
表 1 模型常数
Table 1. Model constant value
参数 数值 $ {c}_{\mathrm{b}1} $ 0.1355 $ {c}_{\mathrm{b}2} $ 0.622 $ \sigma $ $ \text{2/3} $ $ \kappa $ 0.41 $ {c}_{\mathrm{w}2} $ 0.3 $ {c}_{\mathrm{w}3} $ 2 $ {c}_{\mathrm{v}1} $ 7.1 $ {c}_{\mathrm{t}3} $ 1.2 $ {c}_{\mathrm{t}4} $ 0.5 $ {c}_{\mathrm{w}1} $ $ \dfrac{{c}_{\mathrm{b}1}}{{\kappa }^{2}}+\dfrac{1+{c}_{\mathrm{b}2}}{\sigma } $ 
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表 2 NASA Rotor 67几何和性能参数
Table 2. Geometry and performance characteristics of NASA Rotor 67
参数 数值 叶片数 22 展弦比 1.56 设计转速/（r/min） 16043 堵点流量/（kg/s） 34.96 设计点流量/（kg/s） 33.25 设计点总压比 1.63 最高效率/% 93.2
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表 3 质量流量（堵点工况）
Table 3. Mass flow rate （choking condition）
湍流模型 质量流量/（kg/s） 标准SA 34.68 SA-helicity 34.65 SA-QCR 34.68 Exp. 34.96
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表 4 失稳裕度（100%转速）
Table 4. Stall margin （100% rotation speed）
湍流模型 失稳裕度/% 标准SA 10.75 SA-helicity 20.31 SA-QCR 14.14 Exp. 14.24
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表 5 高负荷单级轴流压气机试验性能参数
Table 5. Experimental performance parameters of high loaded 1-stage axial compressor
工况 参数 数值 设计点 转速/（r/min） 9387 质量流量/（kg/s） 32.71 总压比 1.907 等熵效率/% 91.0 最高效率点 等熵效率/% 91.8 近喘点 质量流量/（kg/s） 29.9 总压比 1.931 喘振裕度/% 10.8
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叶尖间隙位置 间隙名称 数值 IGV $ {{C}}_{\text{t1}} $ 0.37 $ {{C}}_{\text{h1}} $ 0.23 R1 $ {{C}}_{\text{r1}} $ 1.15 $ {{C}}_{\text{r2}} $ 1.03 S1 $ {{C}}_{\text{t2}} $ 0.55 $ {{C}}_{\text{t3}} $ 0.51 $ {{C}}_{\text{h2}} $ 0.55 $ {{C}}_{\text{h3}} $ 0.43
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表 7 606压气机计算网格质量报告
Table 7. Grid quality report of 606 compressor computational grid
计算域 网格数/万 最小倾斜度/（°） 最大长宽比 展向角点网格畸变/（°） 支板 117.1 38.02 2964.2 1.45 进口导叶 116.4 42.41 1192.5 10.16 第1级转子 81.6 16.53 1395.6 11.27 第1级静子 144.6 15.63 2889.0 5.76
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表 8 Aachen叶片排设置
Table 8. Aachen blade row setup
参数 IGV R1 S1 R2 S2 R3 S3 叶片数 38 25 40 31 42 39 46 转速/（r/min） 0 17000 0 17000 0 17000 0 叶尖间隙/mm 0 0.2 0 0.2 0 0.2 0
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表 9 Aachen计算域网格点分布
Table 9. Grid point distribution of Aachen computational domain
叶片排 网格点数 计算域
网格点数流向 叶片边界层（O block） 周向 径向 IGV 77 21 49 65 460 751 R1 117 21 61 73 683 663 S1 93 21 49 61 555 893 R2 101 21 61 73 581 023 S2 117 17 65 61 461 465 R3 101 21 61 73 581 023 S3 77 21 41 57 406 353 总网格点数 3 730 171
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