Numerical investigation of interaction between shock wave and tip leakage flow in transonic centrifugal compressors
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摘要:
对于跨声速离心压气机，激波与泄漏流的相互作用对失速具有重要影响。以级压比为6.1的Krain叶轮作为研究对象，数值研究在不同流量和叶顶间隙下，激波与叶顶泄漏流的相互作用，包括激波结构、叶顶泄漏涡轨迹和主流/泄漏流交界面位置的变化规律。结果表明，激波与泄漏涡相互作用形成一个低速区，激波被推向上游，呈现凹状，且随着流量减小，凹状幅度增大。叶顶泄漏涡轨迹和主流/叶顶泄漏流交界面（ITLMF）经过激波后发生偏转，随着流量减小，叶顶泄漏涡轨迹逐渐向压力面偏移，且受激波作用的偏转角度减小。ITLMF逐渐向叶片上游移动，在近失速点到达相邻叶片前缘。随着叶顶间隙增大，叶顶泄漏涡轨迹向相邻叶片压力面偏移，且受激波作用的偏转角度减小，ITLMF逐渐向相邻叶片上游移动。ITLMF受激波偏转会导致交界面提前在相邻叶片前缘溢出，对失速预测有重要影响。在原始模型基础上，考虑无量纲子午速度以及无量纲叶顶间隙对进口相对马赫数的影响，建立改进的ITLMF受激波作用偏转角度预测模型，并进行数值验证。结果表明：改进模型预测精度更高，在不同流量下平均误差由46.59%降至5.83%，不同叶顶间隙下平均误差由27.21%降至4.69%。
Abstract:For transonic centrifugal compressors, the interaction between shock wave and leakage flow has an important effect on stall. In this paper, a Krain impeller with pressure ratio of 6.1 was taken as the research object. The interaction between shock wave and tip leakage flow under the different mass flow and tip clearance was numerically investigated, including the shock wave structure, tip leakage vortex trajectory and the interface between the tip leakage flow and main flow. The results shows that the shock wave interacted with the leakage vortex form a low speed region, and the shock wave is pushed upstream, showing a concave shape, and the concave amplitude increased with the decrease of the mass flow rate. The tip leakage vortex trajectory and the interface between the tip leakage flow and main flow(ITLMF) undergo deflection after passing through the shock wave. As the mass flow rate decreased, the tip leakage vortex trajectory is gradually close to the pressure surface, and the deflection amplitude under shock wave decreases. The ITLMF gradually moves upstream and reaches the leading edge of the adjacent blade at near-stall point. With the increase of tip clearance, the tip leakage vortex trajectory is close to the pressure surface of adjacent blades, and the deflection amplitude under shock wave decreases, and the ITLMF gradually moves upstream of adjacent blades. The ITLMF is deflected by shock wave, which causes the interface to overflow at the leading edge of adjacent blades in advance, which has an important effect on stall prediction. Based on original model, taking into account the effects of normalized meridian velocity and normalized tip clearance on inlet relative Mach number, an improved ITLMF deflection Angle prediction model under shock wave is established and verified numerically. After using the improved model, the average error decreases from 46.59% to 5.83% under different flow rates and from 27.21% to 4.69% under different tip clearance. The results show that the improved model has higher prediction accuracy.
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Key words:
- transonic centrifugal compressor /
- tip clearance /
- shock wave /
- tip leakage flow /
- stall /
- deflection effect
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图 4 叶轮性能CFD模拟值和实验值结果对比
Figure 4. Comparison of impeller performance between CFD and experimental results
图 6 相对马赫数分布实验值与计算值对比（plane8截面）
Figure 6. Comparison of relative Mach number distribution between experimental and numerical results（plane8 cross-section）
图 7 相对马赫数分布实验值与计算值对比（plane10截面）
Figure 7. Comparison of relative Mach number distribution between experimental and numerical results（plane10 cross-section）
图 8 叶轮进口叶顶泄漏流相对速度流线分布
Figure 8. Relative velocity streamline distribution of tip leakage flow at impeller inlet
图 9 近失速点处不同叶高相对马赫数分布
Figure 9. Relative Mach number contours at different span at near-stall point
图 10 最高效率点处不同叶高相对马赫数分布
Figure 10. Relative Mach number contours at different span at peak efficiency point
图 11 98%叶高静压分布及截面位置
Figure 11. Distribution of static pressure and cross sections at98% span
图 12 98%叶高不同流量不同截面静压沿周向变化趋势
Figure 12. Circumferential variation trend of static pressure with different flows and sections at 98% span
图 13 不同流量叶顶静压分布及泄漏涡轨迹变化情况
Figure 13. Static pressure distribution and TLV trajectory variation near tip with mass flow rate
图 14 叶尖静压载荷沿流向分布随流量变化情况
Figure 14. Static pressure load distribution of the blade tip along the streamwise direction with mass flow rate
图 15 不同流量叶顶附近静压分布及泄漏涡起始点分布
Figure 15. Static pressure distribution and initial point of TLV distribution near tip with mass flow rate
图 16 进口叶尖相对马赫数随流量变化情况
Figure 16. Relative Mach number at inlet blade tip with mass flow rate
图 17 不同流量叶顶附近熵分布及ITLMF位置变化情况
Figure 17. Entropy distribution and ITLMF variation near tip with mass flow rate
图 18 近失速点叶尖旋转面流速矢量分布（按叶尖速度无量纲化）
Figure 18. Vectors distribution of flow velocity at blade tip revolution surface at near-stall point（normalized by rotor tip speed）
图 20 不同间隙叶顶附近静压分布及泄漏涡轨迹变化情况（近失速流量）
Figure 20. Static pressure distribution and TLV trajectory variation near the blade tip with tip clearance size （near stall mass flow）
图 21 不同间隙叶顶附近静压分布及泄漏涡轨迹变化情况（$\dot m $=2.8 kg/s）
Figure 21. Static pressure distribution and TLV trajectory variation near the blade tip with tip clearance size （$\dot m $=2.8 kg/s）
图 22 叶尖静压载荷沿流向分布随叶顶间隙变化情况（近失速流量）
Figure 22. Static pressure load distribution of the blade tip along the streamwise direction with tip clearance size （near stall mass flow）
图 23 叶尖静压载荷沿流向分布随叶顶间隙变化情况（$\dot m $=2.8 kg/s）
Figure 23. Static pressure load distribution of the blade tip along the streamwise direction with tip clearance size （$\dot m $=2.8 kg/s）
图 24 不同间隙叶顶附近熵分布及ITLMF位置变化情况（近失速流量）
Figure 24. Entropy distribution and ITLMF variation near the blade tip with tip clearance size （near stall mass flow）
图 25 不同间隙叶顶附近熵分布及ITLMF位置变化情况（$\dot m $=2.8 kg/s）
Figure 25. Entropy distribution and ITLMF variation near the blade tip with tip clearance size （$\dot m $=2.8 kg/s）
图 26 不同叶顶间隙下级等熵效率性能对比
Figure 26. Comparison of stage isentropic efficiency with tip clearance size
图 27 不同叶顶间隙下级总压比性能对比
Figure 27. Comparison of stage pressure ratio with tip clearance size
图 28 Krain6叶轮不同流量下原始模型结果与数值结果ITLMF偏转角度对比
Figure 28. Comparison of ITLMF deflection angle from original model predicted results and Numerical results with mass flow rate of Krain6 impeller
图 29 近失速点98%叶高截面相对马赫数分布
Figure 29. 98% span relative Mach number contours at near-stall point
图 30 不同叶顶间隙近失速点进口叶尖相对马赫数沿周向变化趋势
Figure 30. Relative Mach number with circumferential position near inlet blade tip at near-stall point with tip clearance size
图 31 Krain6叶轮不同流量下修正系数CM的数值结果
Figure 31. Correction factor Numerical results with mass flow rate of Krain6 impeller
图 32 Krain6叶轮不同叶顶间隙下修正系数CM的数值结果（$\dot m $=2.8 kg/s）
Figure 32. Correction factor Numerical results with tip clearance size of Krain6 impeller （$\dot m $=2.8 kg/s）
图 33 Krain6叶轮不同流量下原始模型、改进模型结果与数值结果ITLMF偏转角度对比
Figure 33. Comparison of ITLMF deflection angle between model predicted and Numerical results with mass flow rate of Krain6 impeller
图 34 PR9叶轮不同流量下原始模型、改进模型结果与数值结果ITLMF偏转角度对比
Figure 34. Comparison of ITLMF deflection angle from original model, modified model and Numerical results with mass flow rate of impeller PR9
表 1 Krain6叶轮设计参数
Table 1. Design parameters of the Krain6 impeller
设计参数 数值 转速/（r/min） 50000 流量/（kg/s） 2.55 级压比 6.1 叶片数Zf+Zs 13+13 叶顶间隙/mm 0.5（LE）-0.3（TE） 进口叶顶相对马赫数 1.3 等熵效率 0.84 前缘轮毂半径/mm 30 前缘叶尖半径/mm 78 
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表 2 Krain6叶轮近失速流量不同叶顶间隙下原始模型结果与数值结果ITLMF偏转角度对比
Table 2. Comparison of ITLMF deflection angle between original model predicted results and CFD results with tip clearance size at near-stall mass flow rate of Krain6 impeller
叶顶间隙
c/mm原始模型
δmodel/（°）数值模拟
δCFD/（°）0.3 6.46 8.65 0.5 5.27 7.58 0.7 4.74 6.39
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表 3 Krain6叶轮近失速流量不同叶顶间隙下原始模型、改进模型结果与数值结果ITLMF偏转角度对比
Table 3. Comparison of ITLMF deflection angle between model predicted and Numerical results with tip clearance size near stall mass flow rate of Krain6 impeller
叶顶间隙
c/mm原始模型
δmodel/（°）改进模型
δ*model/（°）数值模拟
δCFD/（°）0.3 6.46 8.77 8.65 0.5 5.27 7.78 7.58 0.7 4.74 5.75 6.39
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表 4 PR9叶轮设计参数
Table 4. Design parameters of impeller PR9
设计参数 数值 转速/（r/min） 56000 设计流量/（kg/s） 2.0 级压比 9.2 叶顶间隙/mm 0.3（LE）-0.3（TE） 前缘轮毂半径/mm 25 前缘叶尖半径/mm 42 等熵效率 0.79 进口叶顶相对马赫数 0.98
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