FIGURE 7 The influence of three parameters on aerodynamic performance of the TWA model. The designed parameters include: the number of corrugations, the corrugation angles, and the flapping frequency. (a) When the number of corrugations is 3, Three models of different corrugation angles are designed. These models are named acute angle airfoil (AAA-3), right angle airfoil (RAA-3) and obtuse angle airfoil (OAA-3), respectively. (b) Thel and (c) \(\overset{\overline{}}{C_{l}/C_{d}}\)diagram affected by three parameters. (d) The velocity contour diagram of TWA model during upstroke and downstroke with too many corrugations.
To get the optimal parameters of TWA model, multiple linear regression analysis was used. Because the change of l and\(\overset{\overline{}}{C_{l}/C_{d}}\) are positively correlating, the following analysis and calculations are only forCl . The details are shown in Table 3-5. The multiple linear regression analysis was performed on the 3 parameters mentioned above: number of corrugations, the flapping frequency, and the corrugation angle. We set the number of corrugations =8; flapping frequency =75 Hz and the corrugation angle = obtuse angle (135°) as benchmark, the benchmark value set as constant value =0. In other word, if other parameter data is great than benchmark data, this indicates that this value is better.
The results showed that a number of corrugations of 5, a right corrugation angle and the flapping frequency of 75 Hz to be optimal (Table 4). In Table 5, the variance analysis result is shown. At a significance level of 0.05, the Cl has a strong correlation with the number of corrugations as well as with the corrugation angle and flapping frequency. From Table 6, the results of the regression coefficient were shown.
Based on the test results, if the Cl is assumed to be defined as y, the number of corrugations, the corrugation angle and the flapping frequency defined as x1 , x2 andx3 respectively, the approximate linear regression equation can be obtained by SPSS software package. The regression equation can be expressed as
\begin{equation} y=0.210-0.002x_{1}-0.038x_{2}+0.022x_{3}\nonumber \\ \end{equation}
Where the value of x1 is 1-8, the value ofx2 is 1-3 (which represents acute angle, right angle and obtuse angle, respectively), and the value ofx3 is 1-3 (which represent 55 Hz, 65 Hz and 75 Hz, respectively).
Table 4 Parameter Estimates