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湍流的时空能谱研究及周期山状流的大涡模拟
英文题名On the space-time energy spectra of turbulence and large-eddy simulation of periodic hill flow
吴霆1,2
导师何国威
2018-05-20
学位授予单位中国科学院大学
学位授予地点北京
学位类别博士
学位专业流体力学
摘要
湍流的能量分布在广泛的空间尺度与时间尺度上,湍流结构的时间演化以及空间演化是湍流研究的一个重点。时空关联以及时空能谱定量刻画了湍流结构的时空演化以及湍流能量的时空分布,是刻画湍流时空结构的重要统计工具,具有重要的理论意义。在工程方面,大气湍流速度脉动时空能谱的预测对于风力发电涡轮机输出功率以及风电场发电量的预测和优化有显著意义,而壁面压力脉动的时空能谱与时空关联在结构的振动疲劳问题以及湍流噪声中也有重要应用。因此,湍流时空能谱的研究不仅可以进一步加深对湍流速度场、压力场时空特性的理解,也可以在风电场、结构振动以及湍流噪声等问题中有工程应用前景。在湍流的数值模拟方面,模化壁面层的大涡模拟所需的网格量远小于解析壁面层的大涡模拟所需的网格量,具有重要的工程意义。因此除了湍流时空能谱的研究,本文还讨论了大涡模拟中的壁模型,并实现了周期山状流的大涡模拟。
 
本文采用槽道湍流直接数值模拟(DNS)的数据来研究速度脉动的时空能谱以及壁面压力脉动的时空能谱。此外,本文采用有限体积方法的程序来研究壁模型在周期山状流大涡模拟中的应用。
 
本文取得的主要结果和创新点包括:
 
1.本文使用平均波数和宽度来刻画时空能谱的特征,推导了平均波数和宽度的准确表达式。宽度的准确表达式表明时空能谱的宽度由速度模态的幅值和相位这两个因素确定。因此,仅仅通过相速度不足以确定湍流剪切流中时空能谱的宽度。进一步地,我们使用宽度的准确表达式来评估时空能谱的重构方法。交叉谱方法准确预测了谱宽度中相位的贡献,然而它并没有考虑幅值导数的贡献,因此它会得到较窄的宽度。我们同时使用幅值和相位,针对交叉谱方法提出了重调方法。DNS 结果表明重调方法可以正确预测时空能谱的宽度。
 
2.本文考察了频率模态幅值变化的作用,基于调幅波的物理思想并结合时空能谱的宽度公式,提出了依赖于幅值导数的局部调幅波(LAMW)方法。在数学上本文证明了局部调幅波方法重构的时空能谱的平均波数以及宽度都与真实值相同。本文利用槽道湍流的DNS数据对局部调幅波方法进行了数值验证,该方法重构的时空能谱与DNS得到的时空能谱吻合很好。
 
3.本文对槽道湍流对数区频率模态的统计性质做了假设,并根据重调方法,推导出槽道湍流对数区时空能谱的解析形式。为了模型的完整性,本文参数化了时空能谱的宽度依赖于频率的关系。基于时空能谱的解析模型,本文进一步得到了频率模态空间关联的模型,其幅值衰减表现为二阶第二类修正贝塞尔函数形式。
 
4.本文分析了壁面压力脉动时空能谱的Corcos模型的不足,提出了双尺度指数衰减模型,该模型综合考虑了关联在小空间间隔时的光滑衰减性质以及关联在大空间间隔时的指数衰减现象。本文对双尺度指数模型进行解析推导,从而得到了壁面压力脉动时空关联的解析模型。该模型结合了脉动的对流效应与畸变效应,符合壁面压力脉动时空关联的主要特征,与DNS结果吻合很好。
 
5.本文在非结构网格有限体积方法的程序上实现了周期边界条件并在槽道湍流中进行了验证。本文讨论了大涡模拟的壁面应力模型,并基于Werner-Wengle模型实现了周期山状流的大涡模拟,取得与文献一致的结果。
英文摘要
An important feature of turbulence is that the energy distributes over a wide range of space and time scales. In the wall-bounded turbulence, the space-time evolution of turbulent structures is one of the most intriguing aspect of the study. Space-time correlations and space-time energy spectra can quantitatively describe the space-time evolution of turbulence structure and the spatio-temporal distribution of turbulent energy. They are fundamental statistical tools to characterize the spatio-temporal structure of turbulence. In engineering, the space-time energy spectra of velocity fluctuations in atmospheric boundary layer turbulence have important effects on the generation of wind farms. Therefore, the space-time energy spectra of velocity fluctuations in turbulent flows are significant for the prediction and optimization of wind turbine power output in wind farms. The space-time energy spectra of wall pressure fluctuations have important applications in structural vibration fatigue and turbulent noise. Therefore, the study of space-time energy spectra can not only deepen the understanding of the spatio-temporal characteristics of turbulent velocity field and pressure field, but also have potential applications in wind farms, structural vibration and turbulent noise. In addition, in the large eddy simulation (LES) of turbulence, the number of grid points required for wall-modeled LES is much smaller than that for the wall-resolving LES, indicating the practical importance of wall-modeling in LES for high Reynolds number flows.
 
In this thesis, the direct numerical simulation (DNS) data of turbulent channel flows are used to study the space-time energy spectra of velocity fluctuations and wall pressure fluctuations. And we have developed a parallel code using finite volume method on unstructured mesh to perform LES of periodic hill flow.
 
Based on the above research methods and ideas, the main results and innovations in this thesis include:
 
1. In this thesis, we use the mean wavenumbers and bandwidths to characterize the space-time energy spectra. We derive exact expressions for the means and bandwidths. The exact expressions show that the bandwidths of the energy spectra are determined by both the amplitudes and phases of the Fourier modes. Therefore, the phase velocity alone is not sufficient to determine the bandwidths of energy spectra in turbulent shear flows. The cross-spectral method predicts the phase contributions to the bandwidths. However, it does not account for the amplitude contributions, which results in narrower bandwidths. The DNS results demonstrate that the rescaling approach for the cross-spectral method can correctly estimate the bandwidths of space-time energy spectra.
 
2. In this thesis, the role of amplitude of the Fourier mode is investigated. Based on the physical idea of amplitude modulation and the exact expression for the bandwidths of space-time spectra, we propose the local amplitude-modulation wave (LAMW) method. Mathematically, we prove that the mean wavenumber and the bandwidth of the reconstructed space-time energy spectra are the same as the exact results. Using the DNS data of turbulent channel flows, we validate the local wavenumber interval method, and the reconstructed space-time spectra are in good agreement with the space-time energy spectra from the DNS.
 
3. In this thesis, the statistical properties of the frequency modal in the logarithmic layer of turbulent channel flows are modeled approximately. According to the statistical properties, combining the rescaling approach for the cross-spectral method, we obtain a model for the space-time energy spectra in the logarithmic layer of turbulent channel flows. The parameterizations for the bandwidths of the space-time energy spectra is established for a full model. Based on the model of the space-time spectra, we further derive the model of the space correlation of the frequency mode, the amplitudes of which are reduced to the modified Bessel function of order 2 of the second kind.
 
4. In this thesis, we discuss the deficiency of Corcos model which is the most widely used model for wall pressure fluctuations. We propose the two-scale bi-exponential approximation which considers the decay characters both in small separations and in large separations. The analytic model based on the two-scale bi-exponential approximation is derived and the model for the space-time correlation of wall pressure fluctuations is obtained. The model combines the convection effect and the distortion effect, and agrees well with the DNS results.
 
5. In this thesis, periodic boundary conditions are implemented using finite volume method on unstructured mesh. We use the wall model to perform LES of periodic hill flow, and obtain the results consistent with the literatures. The results using the wall function of Werner-Wengle at the upper plane wall are better than those not using the wall model.
语种中文
文献类型学位论文
条目标识符http://dspace.imech.ac.cn/handle/311007/73130
专题非线性力学国家重点实验室
作者单位1.中国科学院力学研究所
2.中国科学院大学工程科学学院
推荐引用方式
GB/T 7714
吴霆. 湍流的时空能谱研究及周期山状流的大涡模拟[D]. 北京. 中国科学院大学,2018.
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