壁湍流标度律及SL标度律相关参数实验研究
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摘要
作为研究湍流尺度间级串的普适性规律,标度律在湍流统计理论研究中具有非常重要的地位,它不仅可以为模式理论提供支持,更可以从统计学的角度阐述湍流机理,为动力学模型的建立提供指导。
本文利用PIV系统对平板湍流边界层垂直于底面的流向、纵向平面内的二维速度场进行测量,并用小波分析和传统统计学的方法对实验数据进行处理和计算,首先用流向脉动速度、法向脉动速度和涡量分量分析了经典的K41标度律和SL标度律,结果显示,在湍流边界层越接近壁面的位置间歇性越明显;并且结构函数的阶数越高,标度指数越偏离各向同性的标度指数,也证明了间歇性的存在;同时分别对低阶(二分之一阶)结构函数和高阶(六阶)结构函数进行了分析,进一步说明了在湍流边界层内间歇性的存在,进而提出了一种预想标度律,并进行了简单的实验验证。
在对几种经典标度律验证结论的基础上,又对流向和法向脉动速度小波系数的概率密度函数进行了分析,更进一步说明了间歇性的存在:同时计算了湍流边界层内的Kolmogorov耗散尺度,Taylor微尺度,剪切尺度,惯性尺度和积分尺度,并对相应的尺度进行了分析。结果显示,Kolmogorov耗散尺度、Taylor微尺度和惯性尺度基本上不随壁面距离的增大而变化,剪切尺度则随着壁面距离的增加呈线性增加,积分尺度在整体上呈上升趋势。
然后对考虑了耗散率的广义ESS标度律和新形式标度律进行了阐述,并在不同壁面位置和不同尺度上对这两种标度律的标度指数进行探讨。结果发现,它们的标度指数随壁面位置的不同变化不大,并且广义ESS标度指数和K41标度指数比较符合,而新形式标度律的标度指数和斜率为0.5的直线(截距为0.5)(截距为0.5)符合的比较好。
对湍流耗散率标度律的分析显示,湍流耗散率标度律在小尺度上具有普适性,并且随着壁面距离的接近,尺度越小,湍流的能量耗散越明显,距离壁面越远的地方,湍流的耗散率越小,且随着尺度的增加而迅速减小。对湍流的最高激发态的研究发现,最高激发态存在绝对标度指数,并且绝对标度律是由信号中最强耗散涨落的局部结构产生的。
最后应用ESS标度指数、广义ESS标度指数和新形式标度指数拟合了SL标度律,拟合结果和实验数据符合的比较好,进而得出了间歇参数和最奇异标度指数,它们随尺度的变化并未表现出很强的规律性。但从整体上说,随着尺度的增加,间歇参数逐渐减小,并逐渐趋于稳定,说明了大尺度脉动的层次相似性要小于小尺度的层次相似性;对于最奇异标度指数来说,随着尺度的增加和壁面距离的增加,间歇参数逐渐趋于稳定,最奇异标度指数也逐渐趋于稳定,尺度越大,最奇异标度指数越稳定。用小波分析的方法对流向脉动速度进行分析重构,得到了不同尺度下的速度等值线图,也验证了上述结论。
As a universal principle of turbulence cascade, scaling law is important in the research on statistics of turbulence. It can not only provide support for estabishing theoretical models, but also guide people to setup dynamic model and expound the mechanism of turbulent flow from the point of view of the statistics.
Scaling laws in near wall region of turbulent flow are addressed by analysing moments of velocity increments obtained by Particle-image Velocimetry (PIV) system in the boundary layer of a smooth flat plate. Two-dimensional instantaneous velocity fields are measured in the plane perpendicular to the flat wall and parallelled to streamwise direction. At different distances from the wall, the forms of Extended Self Similarity (ESS) is studied and compared with She-leveque (SL) scaling law and scaling law of K41 based on the wavelet analysis and traditional statistical methods. Results show that the closer to the wall, the wider the curve tail of probability density function becomes, which indicates more and more obvious intermittency. Anomalous are verified by the scaling expponents of moments of experimental data increase nonlinarely with increasing order of the moment in different wall distance. The high-order and low-order structure functions of velocity increments have scaling exponents with different wall distances that are different from K41 and SL. It is explained anomaly scaling law and intermittency.
Dissipative, Taylor, inertial, shear and integral scale are also computed, and the relationship between them and vertical locations in turbulent boundary layer are obtained. When the wall normal distance increases, the variation of Dissipative, Taylor and inertia scale decrease, shear scale is linear increase and integral scale increases.
The scaling exponents of the extended of refined similarity hypothesis and a new form of refined similarity are investigated with different distances from the wall and different scale. Experimental results incidate that the variation of structure function scaling exponents is small when the structures of the same scale are extracted at different wall normal distance. The curve of scaling exponents of the extended of refined similarity hypothesis is in accordance with scaling exponents of K41 and the curve of scaling exponents of the new form of refined similarity is in accordance with the curve whose slope is 0.5 with increasing of scale.
Experimental investigation indicates that the scaling law of energy dissipation rate is universal at small scale. The most intensive structure proposed in Hierarehieal—Structure model further studied, and it is concluded that there exists an absolute scaling law for this struceture, and the statistical absolute scaling behavior only produced the local and strong intermittence strueture. In a statistical theory, it is essential to consider the local fluid structures, especially the strong intensive structures.
Then, the scaling law of extended self similarity, extended of refined similarity hypothesis and a new form of refined similarity based on SL scaling law are used to fit the experimental curves and nice results are obtained. The parameterβandγof SL scaling law are obtained from fitting. Taking it all round, the parameterβdecrease with increasing scale, at last, the change of parameterβis small with increasing wall distance when the scale is large. It manifests that the hierarchy similarity parameter of large scale is larger than that of small scale. With increasing in scale, the parameterγbecames large and stable within different wall distance. At last, the results are verified from multi-scale flow contour patterns which are obtained by decomposion and reconstruction of streamwise fluctuatingvelocity by wavelet analysis.
本文利用PIV系统对平板湍流边界层垂直于底面的流向、纵向平面内的二维速度场进行测量,并用小波分析和传统统计学的方法对实验数据进行处理和计算,首先用流向脉动速度、法向脉动速度和涡量分量分析了经典的K41标度律和SL标度律,结果显示,在湍流边界层越接近壁面的位置间歇性越明显;并且结构函数的阶数越高,标度指数越偏离各向同性的标度指数,也证明了间歇性的存在;同时分别对低阶(二分之一阶)结构函数和高阶(六阶)结构函数进行了分析,进一步说明了在湍流边界层内间歇性的存在,进而提出了一种预想标度律,并进行了简单的实验验证。
在对几种经典标度律验证结论的基础上,又对流向和法向脉动速度小波系数的概率密度函数进行了分析,更进一步说明了间歇性的存在:同时计算了湍流边界层内的Kolmogorov耗散尺度,Taylor微尺度,剪切尺度,惯性尺度和积分尺度,并对相应的尺度进行了分析。结果显示,Kolmogorov耗散尺度、Taylor微尺度和惯性尺度基本上不随壁面距离的增大而变化,剪切尺度则随着壁面距离的增加呈线性增加,积分尺度在整体上呈上升趋势。
然后对考虑了耗散率的广义ESS标度律和新形式标度律进行了阐述,并在不同壁面位置和不同尺度上对这两种标度律的标度指数进行探讨。结果发现,它们的标度指数随壁面位置的不同变化不大,并且广义ESS标度指数和K41标度指数比较符合,而新形式标度律的标度指数和斜率为0.5的直线(截距为0.5)(截距为0.5)符合的比较好。
对湍流耗散率标度律的分析显示,湍流耗散率标度律在小尺度上具有普适性,并且随着壁面距离的接近,尺度越小,湍流的能量耗散越明显,距离壁面越远的地方,湍流的耗散率越小,且随着尺度的增加而迅速减小。对湍流的最高激发态的研究发现,最高激发态存在绝对标度指数,并且绝对标度律是由信号中最强耗散涨落的局部结构产生的。
最后应用ESS标度指数、广义ESS标度指数和新形式标度指数拟合了SL标度律,拟合结果和实验数据符合的比较好,进而得出了间歇参数和最奇异标度指数,它们随尺度的变化并未表现出很强的规律性。但从整体上说,随着尺度的增加,间歇参数逐渐减小,并逐渐趋于稳定,说明了大尺度脉动的层次相似性要小于小尺度的层次相似性;对于最奇异标度指数来说,随着尺度的增加和壁面距离的增加,间歇参数逐渐趋于稳定,最奇异标度指数也逐渐趋于稳定,尺度越大,最奇异标度指数越稳定。用小波分析的方法对流向脉动速度进行分析重构,得到了不同尺度下的速度等值线图,也验证了上述结论。
As a universal principle of turbulence cascade, scaling law is important in the research on statistics of turbulence. It can not only provide support for estabishing theoretical models, but also guide people to setup dynamic model and expound the mechanism of turbulent flow from the point of view of the statistics.
Scaling laws in near wall region of turbulent flow are addressed by analysing moments of velocity increments obtained by Particle-image Velocimetry (PIV) system in the boundary layer of a smooth flat plate. Two-dimensional instantaneous velocity fields are measured in the plane perpendicular to the flat wall and parallelled to streamwise direction. At different distances from the wall, the forms of Extended Self Similarity (ESS) is studied and compared with She-leveque (SL) scaling law and scaling law of K41 based on the wavelet analysis and traditional statistical methods. Results show that the closer to the wall, the wider the curve tail of probability density function becomes, which indicates more and more obvious intermittency. Anomalous are verified by the scaling expponents of moments of experimental data increase nonlinarely with increasing order of the moment in different wall distance. The high-order and low-order structure functions of velocity increments have scaling exponents with different wall distances that are different from K41 and SL. It is explained anomaly scaling law and intermittency.
Dissipative, Taylor, inertial, shear and integral scale are also computed, and the relationship between them and vertical locations in turbulent boundary layer are obtained. When the wall normal distance increases, the variation of Dissipative, Taylor and inertia scale decrease, shear scale is linear increase and integral scale increases.
The scaling exponents of the extended of refined similarity hypothesis and a new form of refined similarity are investigated with different distances from the wall and different scale. Experimental results incidate that the variation of structure function scaling exponents is small when the structures of the same scale are extracted at different wall normal distance. The curve of scaling exponents of the extended of refined similarity hypothesis is in accordance with scaling exponents of K41 and the curve of scaling exponents of the new form of refined similarity is in accordance with the curve whose slope is 0.5 with increasing of scale.
Experimental investigation indicates that the scaling law of energy dissipation rate is universal at small scale. The most intensive structure proposed in Hierarehieal—Structure model further studied, and it is concluded that there exists an absolute scaling law for this struceture, and the statistical absolute scaling behavior only produced the local and strong intermittence strueture. In a statistical theory, it is essential to consider the local fluid structures, especially the strong intensive structures.
Then, the scaling law of extended self similarity, extended of refined similarity hypothesis and a new form of refined similarity based on SL scaling law are used to fit the experimental curves and nice results are obtained. The parameterβandγof SL scaling law are obtained from fitting. Taking it all round, the parameterβdecrease with increasing scale, at last, the change of parameterβis small with increasing wall distance when the scale is large. It manifests that the hierarchy similarity parameter of large scale is larger than that of small scale. With increasing in scale, the parameterγbecames large and stable within different wall distance. At last, the results are verified from multi-scale flow contour patterns which are obtained by decomposion and reconstruction of streamwise fluctuatingvelocity by wavelet analysis.
引文
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