**4.2 Case 1: Pitch ramp** *<sup>α</sup><sup>o</sup>* <sup>¼</sup> **<sup>45</sup>***<sup>o</sup>*

#### *4.2.1 Leading edge pivot*

**Figures 9**–**11** show the lift coefficient response for a ramp maneuver with an amplitude of 45*<sup>o</sup>* at three different pivot locations. At the leading edge pivot location; shown in **Figure 8**, at the beginning of the ramp (*τ* ¼ 0 � 1), Theodorsen model based on Fourier series model shows higher lift coefficient than all the other models as well as the experimental results. For the ramp upstroke, all the models showed a decrease in the lift coefficient compared to the experiment results preserving the same slope until the start of the second event then a continuous increase in lift response which appears as over predicted values compared to the experimental results presented by Ramesh et al. [9]. The UVLM model pertained the same lift pattern and all proposed models show a large discrepancy compared to experimental results. In addition, the UVLM model results show a good agreement with experiments at the ramp-up then starts to deviate with an increase in lift coefficient by 48% at hold-on and ramp down regimes. Furthermore, the quasi steady model shows a high lift coefficient at the end of the ramp-upstroke compared to the experiments, followed by a sharp decrease at the ramp-down stroke.

models show an over prediction for the lift coefficient. The results show a smooth transition without any sharp peaks in lift coefficient between different events.

**Figure 11** presents the lift coefficient for a ramp amplitude of 45*<sup>o</sup>* at trailing edge

pivot location. By comparing **Figure 11** along with **Figure 8**, the two models (Thoedorsen FFT based and UVLM) show a very good prediction with the experimental results for the two phases (ramp-up and ramp hold), then show an increase in the lift coefficient at ramp down. On the contrary, all other models record an over predicted lift coefficient compared to the experimental results for all events preserving the lift response pattern. The quasi steady models for the two ramp cases (0°-25°-0° and 0°-45°-0°) at the same pivot location (trailing edge). **Figure 8** and **Figure 11**, do not show any sharp peak for lift coefficient for the ramp transition regimes. This is expected due to the lack of inclusion of wing stall and rotational

It is clear that a very good matching found between the UVLM model and experiments which can be attributed to the favor of leading edge suction inclusion as well as the nonlinear behavior ( sin ð Þ *α* ) that is induced by the no-penetration boundary condition in the UVLM model. Consequently, at this range of AoA (25°) (attached flow), the dominant effect for the LES and nonlinearity associated with the ramp maneuver appears to be matched well with the results of Ramesh et al. [9]. At high angle of attack maneuver (45°), this effect no longer exists as the flow separates and became more pronounced [43]. Recall that rotational lift is proportional to the distance between the pivot and three quarter chord point (Giacomelli and Pistolesi theorem [44]), which attains and preserves its largest value for a leading edge pivot. The UVLM results match the experimental results with small

*Shedding of trailing vortices and wake convection downstream for* 25° *amplitude ramp maneuver. (a) Leading*

*Shedding of trailing vortices and wake convection downstream for* 45° *amplitude ramp maneuver. (a) Leading*

*4.2.3 Trailing edge pivot*

*Unsteady Aerodynamics of Highly Maneuvering Flyers DOI: http://dx.doi.org/10.5772/intechopen.94231*

effects.

**Figure 12.**

**Figure 13.**

**117**

*edge pivot. (b) Half chord pivot. (c) Trailing edge pivot.*

*edge pivot. (b) Half chord pivot. (c) Trailing edge pivot.*

#### *4.2.2 Half chord pivot*

**Figure 10** shows the lift coefficient for a ramp amplitude of 45*<sup>o</sup>* at half chord pivot location. The proposed models show a good match at the ramp-up regime then an over predicted lift coefficient occurs after the ramp-hold and ramp-down regimes compared to the experimental results except for Theodorsen FFT based model and the quasi-steady model. Again, Theodorsen FFT based model gives an attenuated response, and the quasi-steady model shows a magnified response (qualitatively similar to the results presented in **Figure 7** of a pitch ramp amplitude of 25°). During the ramp-hold phase, the UVLM model matches well with small discrepancy compared to all other models. At the final phase (ramp-down), all

#### **Figure 11.**

*Comparison for the proposed models and experimental work done by Ramesh et al. with ramp rate of 0.4 and amplitude* 45° *at trailing pivot location.*

models show an over prediction for the lift coefficient. The results show a smooth transition without any sharp peaks in lift coefficient between different events.
