# Investigation and Design of the Transonic Laminar Flow Characteristics in a Laminar Aircraft
## 2 Computational Approach
### Comparison of CFD Results with Wind Tunnel Data  
The experiment was carried out by the FL-2 wind tunnel in AVIC (Aerodynaiviics Research Institute of China). The FL-2 wind tunnel is a high-speed wind tunnel for a laminar experiment. The experiment adopted a 1:9.8 scale model, \(Ma=0.7\), \(\mathrm{Re}=8\times 10^{6}\), sideslip angle = 0\({}^{\circ}\), \(FSTI=0.6\%\). The \(FSTI\) specified at an inlet can decay quit rapidly depending on the inlet viscosity ratio (and hence turbulence eddy frequency). As a result, the local \(FSTI\) downstream of the inlet can be much smaller than the inlet value. Typically, the larger the inlet viscosity ratio, the smaller the turbulent decay rate. However, if too large a viscosity ratio is specified (i.e., \(>\)100), the skin friction can deviate significantly from the laminar value. There is experimental evidence that suggests that this effect occurs physically; however, at this point, it is not clear how accurately the transition model reproduces this behavior. For this reason, if possible, it is desirable to have a relatively low (i.e., =10) inlet viscosity ratio and to estimate the inlet value of \(FSTI\) such that at the leading edge of the wall of the airfoil the \(FSTI\) has decayed to the desired value. The grid calculated in Section 2.2 was used to complete the comparison. Figure 6 shows the transition comparison between the experimental results of the wind tunnel and the calculated results when \(\alpha=0^{\circ}\)and \(\alpha=1^{\circ}\). The left side of (a) and (b) are the calculated results of the skin friction coefficient of the central experimental wing, while the right side is the experimental thermographic image. It can be seen from the experimental thermographic image that the transition zone of the central experimental wing presents a zigzag feature, which is different from the smooth transition zone presented by the calculation result. It is because the surface of the experimental model has a certain degree of roughness, which leads to the advance of the local transition. Thus, the experimental transition position is taken as the maximum chordwise distance that can be achieved in the laminar flow zone. It can be seen that at \(\alpha=0^{\circ}\)and \(\alpha=1^{\circ}\), the transition positions of the calculated results (\(x/c=56.2\%\) at \(\alpha=0^{\circ}\)and \(x/c=54.8\%\) at \(\alpha=1^{\circ}\)) are consistent with the experimental results. The positions of the transition in the calculated results and the experimental results advance as the angle of attack increases. Figure 7a shows the \(C_{p}\) curve measured by PSP (pressure-sensitive pain) on the upper airfoil of the original laminar airfoil at the airfoil section \(Y/Span=5\%\). \(C_{p}\) represents the pressure coefficient, \(EXP\). represents the experimental result and \(CAL\) represents the calculated result. It can be seen from Figure 7a that the experimental \(C_{p}\) is slightly higher near the leading edge, while the \(C_{p}\) of other positions is slightly lower than the calculated value. This is because there is a certain difference between the thickness of the airfoil processed in the experiment and that of the calculated model. The coating on the surface may also have a certain influence. However, the experimental curve and the calculated curve show the same trend, which is enough that laminar flow characteristics require a favorable pressure gradient (negative pressure increases with chordwise distance). Figure 7b shows the \(C_{L}\) between the experimental results of the wind tunnel and the calculated results when \(\alpha\) from \(0^{\circ}\) to \(3^{\circ}\). It can be seen that the \(C_{L}\) curve of the calculated  
Figure 5: Y\({}^{+}\) of grid independence verification. results is in good agreement with the experimental results. Through the above analysis, the CFD method used in this paper is reliable.