Effects of compressibility and Reynolds number on the aerodynamics of a simplified corrugated airfoil

Abstract

This study aims to isolate and evaluate the influence of a corrugation on flow structures and aerodynamics under compressible low Reynolds number conditions, and to compare it to simpler but well-known model: the flat plate. The simplified corrugated model was made by a flat surface with only two corrugations on the leading edge. The models only differ for the corrugations on the leading edge. Force values were measured at a Reynolds number ranging from 10,000 to 25,000 and at a Mach number from 0.2 to 0.6. Pressure sensitive paint was used at the same flow conditions and the pressure distribution over the models was obtained. Schlieren visualization was also conducted and flow characteristics were observed. Detailed analysis showed that the corrugated model experiences strong depression on the leading edge caused by the separation of the boundary layer. Because of the presence of the corrugation, the shear layer transitions to turbulent rapidly and reattaches to the surface before reaching the summit of the first corrugation, separating again at its peak. Instabilities in the shear layer were dissipated thanks to the shape of the corrugation allowing pressure recovery and discouraging flow separation. The flow reattaches before reaching the trailing edge. The results showed that the transition of the boundary layer was accelerated as the Reynolds number increases on corrugated model, leading to a stronger negative pressure zone in the leading edge. Due to pressure recovery being less effective, lead to similar performances for the range of studied Reynolds numbers. The compressibility effects resulted in a delay on the transition of the instability of the shear layer, negatively affecting the intensity of the pressure gradients as well as pressure recovery. This contributed to the variation in the performance of the wing. As a result, the corrugated model has a better aerodynamic performance compared to the flat plate at low Reynolds numbers, but not for higher Mach numbers.

Graphic abstract

Appendix 1: Influence of self-illumination on PSP measurements

The PSP results of the corrugated model are considered to be influenced by the self-illumination due to its shape of the model, which has concave-shaped sections. In the case of the concave-shaped object, the PSP emission from a certain point captured by the camera includes the reflected component of the emission from the other point as shown in below (Kuchiishi et al. 2008):

$$\begin{aligned} L_i=L_{0,i}+R{\displaystyle \sum _{j=1}^N} F_{ij}L_j, \end{aligned}$$

(4)

where $L_i$, $L_j$, and $L_{0,i}$ are measured intensity at the point i (point of interest), the measured intensity at the point j (the other point on the model), and actual intensity at the point of interest, respectively. Also, R and $F_{ij}$ are the reflectance at the point of interest and the form factor between the point of interest and the other point j, respectively. Therefore, reflection correction can be conducted as follows:

$$\begin{aligned} L_{0,i}=L_i-R{\displaystyle \sum _{j=1}^N} F_{ij}L_j, \end{aligned}$$

(5)

The reflectance of the PSP R used in the present study was measured by the method proposed by Ruyten (1997), and the value was $R=0.6$. The overview of the influence of the self-illumination and its correction method is described by Le Sant (2001). Figure 29a shows the influence of the self-illumination on the $C_p$ distribution at $M=0.6$ of Re $=1.0\times 10^4$. The highest M condition, which is considered to have the greatest influence of the self-illumination, were selected to provide the influence of the self-illumination in worst case. It can be seen that the $C_p$ distributions before and after applying the reflection correction are different, but the difference is sufficiently small. The $C_p$ profile is slightly changed by reflection correction at the valleys of both corrugations of the model, while the rest of the chord remains mostly unmodified. Hence, the influence of the self-illumination on the $C_p$ distribution obtained by the PSP measurements is small. Figure 29b shows the difference between the $C_p$ before and after applying the reflection correction. The difference in the $C_p$ is less than 0.05. It is sufficiently smaller compared with the variation of $C_p$ in the chord direction.

Fig. 29

Effect of self-illumination on $C_p$ profile obtained by PSP measurements at $M=0.6$ of Re $=1.0\times 10^4$. a $C_p$ distribution comparison between uncorrected and corrected with reflection contribution, b difference between the uncorrected and corrected $C_p$