Flow self-modeling characteristics in multi-inlet rotor-stator cavity
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摘要:
受限于实验条件与成本，航空发动机实际运行工况与常规元件级实验的工况间常存在差异，从而使得元件级实验所得到的数据的推广应用存在局限性。为解决上述问题，本文针对多入口转静系盘腔流动特征参数的自模化特性开展了系统性研究工作。结果表明：在主流特征湍流参数为0.015～0.035，射流特征湍流参数在0.003～0.009且旋转雷诺数在2.06×106～1.03×107的工况范围内，且不考虑气流压缩性的影响时可通过特定方法明确用于表征腔内通流与旋转效应相对强弱关系的模化特征湍流参数，该参数是使得转静系盘腔流动特征呈现自模化特征的核心参数。当该参数相同时，即使对于具有复杂且非周向均匀进气条件下的多入口进气转静腔而言，腔内流动结构处于高度相似状态，多项流动特征参数在无量纲准则参数发生显著改变时仍保持一致。基于上述流动自模化状态，可初步构建起用于将低旋转雷诺数下的多项流动特征参数的实验结果外延应用至高旋转雷诺数下的推广方法，为后续相关实验的开展和实验结果的应用提供支持。
Abstract:Due to limitations in experimental conditions and cost considerations, significant discrepancies often exist amongst the non-dimensional criteria parameters associated with the actual operating conditions of aviation engines. To address the limitations in the application of experimental data resulting from the difficulties associated with the application of similar principles arising from the aforementioned discrepancies, the self-modeling characteristics of flow characteristic parameters in a multi-inlet rotor-stator cavity were systematically investigated. The research findings indicated that, within mainstream characteristic turbulence parameters ranges from 0.015 to 0.035, jet characteristic turbulence parameters ranges from 0.003 to 0.009 and the rotational Reynolds ranges from 2.06×106 to 1.03×107, it is possible to establish a modulated turbulent parameter using specific methods. This parameter emerged as the key factor enabling the manifestation of self-modeling characteristics in the flow characteristic of the rotor-stator cavity. Even in the case of a multi-inlet cavity with complex and non-axially uniform inlet conditions, when the modulated characteristic turbulent parameter was consistent, the flow structure remained in a highly similar state. Despite of significant changes in non-dimensional criteria parameters, the flow characteristic parameters remained consistent. Based on the self-modeling state of the flow described above, a preliminary framework can be established for extrapolating experimental results of multiple flow characteristic parameters obtained at low rotational Reynolds numbers to high rotational Reynolds numbers. This approach could provide a support for the extension of experimental results and their application in subsequent related experiments conducted under high rotational Reynolds numbers.
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图 3 网格数量对$ {C}_{{p}^{*},\mathrm{m}} $和$ {\beta }_{0.5} $的影响
Figure 3. Influence of the number of meshes on $ {C}_{{p}^{*},\mathrm{m}} $ and $ {\beta }_{0.5} $
图 4 各湍流模型下$ \beta $数值计算和实验结果的对比
Figure 4. Comparisons between numerical results under various turbulence models and experimental results of $ \beta $
图 5 拟合结果随工况数量变化情况
Figure 5. Fitting results vary with the number of working conditions
图 7 r-z截面流动结构（$ {\lambda }_{\mathrm{t},\mathrm{m}}^{*}=0.015 $, $ {\lambda }_{{\mathrm{t,j}}}^{*}=0.006 $）
Figure 7. r-z cross section flow structure （$ {\lambda }_{\mathrm{t},\mathrm{m}}^{*}=0.015 $, $ {\lambda }_{\mathrm{t},\mathrm{j}}^{*}=0.006 $）
图 8 r-φ截面速度分布情况（$ {\lambda }_{\mathrm{t},\mathrm{m}}^{*}=0.015 $）
Figure 8. Velocity distribution of r-φ cross section （$ {\lambda }_{\mathrm{t},\mathrm{m}}^{*}=0.015 $）
图 9 r-φ截面无量纲湍动能分布情况（$ {\lambda }_{\mathrm{t},\mathrm{m}}^{*}=0.025 $）
Figure 9. Distribution of non-dimensional turbulent kinetic energy in r-φ cross-section （$ {\lambda }_{\mathrm{t},\mathrm{m}}^{*}=0.025 $）
图 10 r-φ截面无量纲涡量分布特性（$ {\lambda }_{\mathrm{t},\mathrm{m}}^{*}=0.015） $
Figure 10. Dimensionless vorticity distribution in r-φ cross-section （$ {\lambda }_{\mathrm{t},\mathrm{m}}^{*}=0.015） $
图 11 $ {\lambda }_{\mathrm{t},\mathrm{m}}^{*} $及$ {\lambda }_{{\mathrm{t}},{\mathrm{j}}}^{*} $变化对$ {C}_{{p}^{*},\mathrm{m}} $及$ {C}_{{p}^{*},\mathrm{j}} $的影响
Figure 11. Influence of $ {\lambda }_{\mathrm{t},\mathrm{m}}^{*} $ and $ {\lambda }_{\mathrm{t},\mathrm{j}}^{*} $ variation on $ {C}_{{p}^{*},\mathrm{m}} $ and $ {C}_{{p}^{*},\mathrm{j}} $
图 12 $ {\lambda }_{\mathrm{t},\mathrm{m}}^{*} $及$ {\lambda }_{\rm{t,j}}^{*} $变化对$ {C}_{\mathrm{m}} $的影响
Figure 12. Influence of $ {\lambda }_{\mathrm{t},\mathrm{m}}^{*} $ and $ {\mathrm{\lambda }}_{\mathrm{t},\mathrm{j}}^{\mathrm{*}} $ variation on $ {C}_{\mathrm{m}} $
表 1 工况范围
Table 1. Operating range
工况 主流入口边界 射流入口边界 出口边界 卷吸 p*=1.01×105 Pa p*=1.01×105 Pa p*=1.01×105 Pa 正向 $ \dot{{m}} $=0.033～0.348 kg/s $ \dot{{m}} $=0.009～0.120 kg/s 
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表 2 多入口进气转静系特征湍流参数定义
Table 2. Characteristic turbulent parameter definition of multi-inlet rotor-stator cavity
入口位置 特征湍流参数定义 主流 $ {\lambda }_{\mathrm{t},\mathrm{m}}^{*}=\dfrac{{C}_{\mathrm{w}}}{{Re}_{\varphi }^{0.941\;6}} $ （7） 射流 $ {\lambda }_{\mathrm{t},\mathrm{j}}^{*}=\dfrac{{C}_{\mathrm{w}}}{{Re}_{\varphi }^{0.961\;1}} $ （8）
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表 3 研究工况
Table 3. Research condition
入口位置 特征湍流参数 流量范围/（kg/s） 主流$ {\lambda }_{\mathrm{t},\mathrm{m}}^{*} $ 0.015, 0.025, 0.035 0.032～0.348 射流$ {\lambda }_{\mathrm{t},\mathrm{j}}^{*} $ 0.003, 0.006, 0.009 0.008～0.120
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