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郭爱东 姜楠. 壁湍流多尺度相干结构复涡黏模型的实验研究[J]. 力学学报, 2010, 42(2): 159-168. DOI: 10.6052/0459-1879-2010-2-2008-568
引用本文: 郭爱东 姜楠. 壁湍流多尺度相干结构复涡黏模型的实验研究[J]. 力学学报, 2010, 42(2): 159-168. DOI: 10.6052/0459-1879-2010-2-2008-568
Aidong Guo, Nan Jiang. Experimental research on complex eddy viscosity modeling of multi-scale coherent structures in wall turbulence[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(2): 159-168. DOI: 10.6052/0459-1879-2010-2-2008-568
Citation: Aidong Guo, Nan Jiang. Experimental research on complex eddy viscosity modeling of multi-scale coherent structures in wall turbulence[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(2): 159-168. DOI: 10.6052/0459-1879-2010-2-2008-568

壁湍流多尺度相干结构复涡黏模型的实验研究

Experimental research on complex eddy viscosity modeling of multi-scale coherent structures in wall turbulence

  • 摘要: 在湍流相干结构动力学方程中,非相干结构成分对相干结构贡献的雷诺应力的模型为涡黏性模型,即涡黏性系数乘以相干结构平均速度变形率的形式. 基于非相干结构成分对相干结构贡献的雷诺应力与相干结构速度变形率之间存在相位差的事实,在理论上提出了非相干结构成分对相干结构贡献的雷诺应力复涡黏性模型的假设. 应用热线测速技术,在低速风洞中对湍流边界层非相干结构成分对相干结构贡献的雷诺应力与相干结构法向速度变形率之间的相位关系进行了实验测量. 通过分析湍流相干结构猝发过程中非相干结构成分对相干结构贡献的雷诺应力与相干结构速度变形率之间的相位关系,研究了相干结构雷诺应力分量与流向速度法向梯度之间的相位差沿湍流边界层法向的变化规律,肯定了湍流相干结构复涡黏性系数模型的合理性.

     

    Abstract: In the dynamics equation of coherent structures withperiodical phasic average, Reynolds stress term \tilde r_ij = -(\langle u'_i u'_j \rangle - \overline u'_i u'_j ) thatnoncoherent structures contributes to coherent structures, is taken into themodel, in which the velocity strain rate of coherent structures ismultiplied by a complex eddy viscosity coefficient, as follows:\tilde r_ij = \nu _T \Big \dfrac\partial \tilde u_i \partial x_j + \dfrac\partial \tilde u_j \partial x_i \Big +\dfrac13\delta _ij ( \tilde r_kk ) ,where \nu _T is a complex eddy viscosity coefficient.Eddy viscosity coefficient is defined to be a complex, supposing that thereexist phase difference between velocity strain rate of coherent structuresand the Reynolds stress.The phase relation has been experimentally measured between velocitydistortion \dfrac\partial \tilde u\partial y of multi-scales coherentstructures in turbulent boundary layer over smooth plate and the Reynoldsstress, \tilde r_12 and analyzed in a close-circuit low-speed windtunnel based on the expression \tilde r_12 = \nu _T \Big\dfrac\partial \tilde u\partial y + \dfrac\partial \tildev\partial x \Big. Through the phase difference analysis betweenthe Reynolds stress and the velocity distortion of coherent structures inwall turbulence during the bursting process of coherent structures,conclusions can be drawn as following:Relaxation time in dynamic interaction between the turbulence of coherentstructures with macroscopical scale and movement distortion of coherentstructures can't be ignored. Hence, there exist phase difference betweenReynolds stress component that noncoherent structures contribute to coherentstructures and the velocity distortion of coherent structures. It is animportant factor that needs to be taken into account for eddy viscositymodeling theory for non-steady turbulence macrostructure.The above phase difference depends on not only the scale of coherentstructures, but also the detail of physical burst process of coherentstructures, such as eject and sweep. The phase of the Reynolds stress isposterior than that of velocity distortion of coherent structures inejecting process, while anterior in sweeping process. In addition, phasedifference between them does not vary with boundary normal positions inlogarithmic sublayer.

     

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