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高马赫数和高雷诺数湍流边界层的直接数值模拟研究
Alternative TitleDirect numerical simulation studies of turbulent boundary layer with high Mach number and high Reynolds number
李欣
Thesis Advisor李新亮
2020-05-30
Degree Grantor中国科学院大学
Place of Conferral北京
Subtype博士
Degree Discipline流体力学
Keyword加权基本无振荡格式 直接数值模拟 高马赫数 高雷诺数 壁温效应
Abstract

可压缩湍流边界层(TBL)是高速飞行器表面的典型流动。高马赫数和高雷诺数条件下的可压缩湍流边界层具有特殊的流动现象:高马赫数时,边界层内出现较强的压缩性效应,统计特性与拟序结构的特征发生改变;高雷诺数时,外层大尺度结构越发重要、出现内外层拟序结构的相互作用等。在这样的极端条件下,又往往伴随着壁温的影响,使流动现象更为复杂,使得现有的研究对它们的机理分析得尚不充分。同时,数值模拟这类流动对数值格式的分辨率和鲁棒性有很高的要求。本文分为三大部分,首先对现存的数值格式进行进一步优化,接着采用直接数值模拟方法分别深入分析了高马赫数、高雷诺数的可压缩湍流边界层流动机理。具体内容如下:

1.本文的第一部分,针对现有WENO格式耗散过大鲁棒性不足的问题,本文在WENO-Z格式的基础上进行了进一步优化,获得了新的WENO-PR格式。优化的主要思想是优化WENO格式中更不光滑的子模板的权重,让WENO格式在光滑区更趋向于原始线性格式,从而减小数值格式的耗散。为了达到这个目标,本文优化了高阶光滑指示因子。在减小数值格式耗散的同时,为了保证格式的鲁棒性,还进一步对间断敏感因子进行了自适应优化。新的WENO-PR格式的数值特性采用若干算例进行检测。

2.本文的第二部分,采用来流马赫数为8、两种等温壁面条件(Tw/Tr=10.03和1.9)的直接数值模拟(DNS)数据库,研究了壁温对高超声速平板湍流边界层的压缩性效应和雷诺剪切应力、涡表面温度不均匀性、密度-温度脉动关联的影响。

(1)研究了壁温对压缩性效应、雷诺剪切应力分布的影响。结果表明,降低壁温增强了边界层内的压缩性效应。降低壁温增强了壁面附近的上抛和下扫运动,对上抛运动的增强强于下扫运动,这是由不同尺度的速度脉动对冷壁的敏感度不同的联合效应引起的。

(2)研究了壁温对涡结构表面温度不均匀性的影响。定义了涡结构的两个特征表面,使用条件采样的象限分析和速度-温度关联(-Ru' T' 和Rv' T' )分析,证明了两个特征表面的平均温度分布差异峰值可达20%,这种差异根本上来源于涡结构表面的旋转运动。涡表面的旋转运动通过-Ru' T' 和Rv' T'引起温度脉动的变化,进而加速或抑制了涡表面平均温度的升高,从而导致了涡表面温度分布不均匀。

(3) 研究了壁温对湍流边界层密度与温度脉动(ρ'和T')相关性的影响。采用拟合斜率法和二维相关性法对ρ'和T'的相关性进行可视化,发现与ρ'和T'相关性有关的斜率曲线在缓冲区内存在一个反转点,ρ'和T'二维关联则出现一个分离结构,这是ρ'和T'的局部相关和周围相关的影响。通过概率密度分析和统计涡结构分析,证明上述反转点的出现是由于降壁温抑制了边界层中的极端事件,同时维持了小尺度脉动引起的,而脉动量的改变是平均涡扭转强度降低和涡半径增大所致。

3.本文的第三部分,对高雷诺数(Reτ>1000)压缩圆角湍流边界层进行了直接数值模拟,建立了直接数值模拟数据库,分析了边界层的平均和统计特性。先对湍流边界层进行了多角度的流动可视化,观察到其中存在丰富的小尺度结构。接着对不同流向位置的平均速度剖面进行了研究,证明角区的对数律区未存在下沉现象。统计特性分析发现,当雷诺数足够高时,湍流强度出现了内峰和外峰两个峰值。随着当地雷诺数升高,内峰逐渐增长,外峰也越发明显,此时Morkovin假设部分失效。研究了分别存在于近壁和对数律区的小尺度和大尺度的条带结构,发现在高雷诺数条件下后者越发重要,对前者和流场的统计特性存在重要影响。

Other Abstract

Compressible turbulent boundary layer (TBL) is a typical flow on the surface of high speed aircraft. The TBL with high Mach number and high Reynolds number has special phenomena. Under high Mach number, strong compressibility effect appears in the boundary layer, and the characteristics of statistics and coherent structures change. Under high Reynolds number, the outer large-scale structure becomes more and more important, and the interaction of the inner and outer coherent structure appears. In such extreme conditions, the influence of wall temperature is often accompanied, which makes the flow phenomenon more complex. So, the flow mechanism is not fully analyzed in the existing researches. At the same time, the simulation of these flows requires low-dissipation and high-robustness numerical scheme. This paper is divided into three parts. Firstly, the existing numerical scheme is further optimized, and then the flow mechanism of compressible turbulent boundary layer with high Mach number and high Reynolds number is deeply analyzed by direct numerical simulation.

1.In the first part of the work, we summarize the development of the weighted essentially non-oscillatory scheme (WENO) and develop a new WENO-PR scheme based on the WENO-Z scheme. The main idea is to increase the weight of the less smooth substencil in the WENO scheme which then is more linear to the original scheme and has less numerical dissipation. To achieve this goal, we optimize the high order smooth factor τ. In order to reduce the dissipation and ensure the robustness of the scheme together, the discontinuous sensitivity factor p is further optimized. Numerical characteristics of the new WENO-PR scheme are tested by several numerical tests.

2.The second part of the work, wall temperature effects on hypersonic flat-plate turbulent boundary layer are analyzed. The direct numerical simulation (DNS) database with free-stream Mach number Ma=8 and two isothermal wall conditions (Tw/Tr=10.03 and 1.9) are considered.

(1)The influence of the wall temperature on compressibility effect and Reynolds shear stress are studied. The results show that wall cooling enhances the compressibility effect and the near-wall ejection and sweeping motions. The ejection motion is stronger than the sweeping motion, which is caused by the combined effect of the velocity fluctuation behaviors.

(2)The non-uniform temperature distribution (NUTD) on the coherent vortex surfaces is studied using conditional sampling technique. The coherent vortex surface is identied by the -criterion and two characteristic sides of the vortex are dened. The results show that there is a signicant difference of up to 20% between the characteristic sides. Furthermore, the velocity-temperature uctuation correlations (-Ru'T'  and Rv'T' ) show that the temperature uctuations are redistributed by the vortex rotational motion through -Ru'T'  and Rv'T', and then lead to the NUTD.

(3)The correlation between density and temperature fluctuations (ρ' and T') is studied. A fitting slope method and a two-dimensional correlation method are adopted to visualize the correlated behaviors. The results show that an adverse trend and a separated correlated structure are found in the buffer region, which can be treated as the effects of the local and surrounding correlation of ρ' and T'. Several statistics indicate that the extreme events are suppressed with wall cooling, meanwhile, the small-scale fluctuations are enhanced because of the reduced mean swirling strength and the increased radius of the vortical structures.

3.The third part of the work, the direct numerical simulation of turbulent boundary layer subjected to curved surface with high Reynolds number (Reτ>1000) is carried out. The DNS database is established. The average and statistical characteristics of the boundary layer are analyzed. Firstly, the flow field is visualized in several aspects and abundant small-scale structures are observed. Then, the mean velocity profiles at different streamwise directions are studied. It is proved that there is no sinking phenomenon in the logarithmic law in the curved region. The statistical analyses show that when the Reynolds number is high enough, the turbulent intensities have the inner and outer peak. With the increase of the local Reynolds number, the inner peak increases gradually, and the outer peak becomes more and more obvious. At this time, Morkovin's hypothesis is partially invalid. The small-scale and large-scale streaks in the near wall and logarithmic law regions are studied. It is found that the latter is more important under the condition of high Reynolds number, which has an important influence on the near-wall one and the statistical characteristics of the flow field.

Call NumberPhd2020-005
Language中文
Document Type学位论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/81933
Collection高温气体动力学国家重点实验室
Recommended Citation
GB/T 7714
李欣. 高马赫数和高雷诺数湍流边界层的直接数值模拟研究[D]. 北京. 中国科学院大学,2020.
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