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 引用本文: 刘静, 李杰, 张恒. 基于速度梯度张量特征值的陷窝内旋涡分析[J]. 力学学报, 2019, 51(3): 826-834.
Jing Liu, Jie Li, Heng Zhang. DIMPLE'S VORTEX ANALYSIS BASED ON EIGENVALUE OF VELOCITY GRADIENT TENSOR[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 826-834.
 Citation: Jing Liu, Jie Li, Heng Zhang. DIMPLE'S VORTEX ANALYSIS BASED ON EIGENVALUE OF VELOCITY GRADIENT TENSOR[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 826-834.

## DIMPLE'S VORTEX ANALYSIS BASED ON EIGENVALUE OF VELOCITY GRADIENT TENSOR

• 摘要: 作为一种新型的涡流发生器,陷窝具有流动阻力小、综合传热性能高的特点,是现代高性能涡轮叶片内部冷却新技术. 旋涡的定量分析是陷窝强化传热优化设计的重要依据. 针对在不同陷窝模型下的旋涡结构、分离方式和背景压力变化引起的旋涡强度无法定量分析的问题,本文提出采用涡核速度和 涡核速度梯度张量特征值来定量分析旋涡的方法. 通过采用涡核处局部坐标系表示的速度矢量和速度梯度张量,得到了涡核的轴 向速度、径向速度、旋转角速度、轴向加速度和径向加速度,并在此基础上简化出了用最大轴向速度、最大轴向加速度和最大旋 转角速度综合表示的旋涡强度的定量分析方法. 用该方法分析了不同深宽比陷窝诱导的旋涡结构,随着深宽比的增大,最大轴向 速度、最大轴向加速度和最大旋转角速度均呈现明显的增大趋势,旋涡强度增大. 研究表明此方法具有数据处理简单、通用性强、 不受分离方式限制、不受背景压力影响的特点,且提取到的数据具有明确的物理意义,适用于各类旋涡定量分析.

Abstract: As a new internal cooling technology for high performance turbine blades, dimple which belongs to vortex generator has the advantage of small flow resistance and high comprehensive heat transfer performance. The qualitative and quantitative analysis of the vortex is an important basis for the optimization design of the dimple, due to the fact that the stronger vortex cause greater heat transfer enhancement. Aiming at the problem that the vortex strength can not be quantitatively analyzed in different dimple models under the variation of the vortex structure, separation mode and background pressure, this paper proposes a method by using vortex core velocity and vortex core velocity gradient tensor eigenvalue. Using the velocity vector and velocity gradient tensor eigenvalue expressed by the local coordinate system at the vortex core, the axial velocity, radial velocity, swirling strength, axial acceleration and radial acceleration of the vortex core are obtained, and quantitative analysis method of vortex strength as a combination of maximum axial velocity, maximum axial acceleration, and maximum swirling strength is concluded. The vortex structure induced by different depth to print diameter ratio dimple is analyzed by this method. As the increase of the depth to print diameter ratio, the maximum axial velocity, maximum axial acceleration and maximum swirling strength all increased obviously, so the vortex strength increases. The research shows that this method has the advantages of simple data processing, wide application range, not limited by separation mode, not limited by background pressure, and the extracted data has clear physical meaning, thus this method is suitable for all kinds of vortex quantitative analysis.

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