Statistical characteristics analysis of fluctuating pressure in airfoil boundary layer

To study the fluctuated characteristics of the boundary layer, the transition on an airfoil was detected using the fluctuating pressure method in this paper, and the statistical characteristics of the fluctuating pressure in different flow states, including the root mean square (RMS) value σ, skewness s, kurtosis k and information entropy I, were deeply investigated. The (s, k) phase diagrams of different flow states were presented. The results showed that skewness of the laminar state was close to that of Gauss distribution and kurtosis of the turbulent state was close to that of Gauss distribution, while the distribution in the (s, k) phase diagram of the transition state was quite different from the Gauss distribution. The mathematical relationship between I and k, σ, s was deduced in detail and an explicit expression was established, such that the one-dimensional decision space for the transition detection was extended to a four-dimensional decision space (σ, s, k, I). This work is useful to deeply understand the internal relationship between the information entropy and the general statistics of fluctuating pressure, and is also of help to subsequent data analysis, classification model establishment and rule extraction.