Experimental Studies On The Scaling Law And Parameters Of SL Scaling Law In Turbulent Boundary Layer

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.