Initially, under the condition where the Reynolds number based on the airfoil chord is Re = 3 × 105, the laminar separation performance of the rigid airfoil is meticulously examined through both experimental testing and computational analysis. Subsequently, the aerodynamic properties of an airfoil with a partially oscillating section are computed to investigate the impact of such oscillations on the airfoil’s behavior.
4.1. The Performance of Laminar Flow Separation on the Rigid Airfoil
An unsteady numerical simulation approach has been employed to investigate the laminar separation bubble on a rigid airfoil, complemented by a corresponding water tunnel test conducted under identical conditions.
At a Reynolds number of 3 × 10
5 and an angle of attack set at 3°, the structural configurations of the laminar separation bubble, as derived from both the water tunnel testing and numerical simulations, are depicted in
Figure 8. The results of the water tunnel testing reveal a distinct flow pattern where the streamline along the leading edge of the airfoil initially appears as a narrow and straight streak, indicative of a laminar flow regime. It is further elucidated that the flow field in the central region of the model maintains its two-dimensional characteristics, remaining largely unaffected by three-dimensional effects. Subsequently, this streak broadens and darkens, signifying the onset of laminar flow separation followed by the emergence of reverse flow. Thereafter, the staining line exhibits chaotic behavior, marking the transition to turbulent flow. Ultimately, the evidence of backflow dissipates, and the fluid once again adheres to the airfoil surface. The LSB is characterized as the zone stretching between the laminar separation point and the point of reattachment. As illustrated in
Figure 8, the LSB phenomenon on the airfoil at low Reynolds numbers is distinctly observable through the water tunnel testing, and the numerically simulated structure of the LSB aligns well with the experimental findings.
Figure 9 illustrates the time-averaged positions of laminar separation and turbulent reattachment. In the given figure, LS denotes the position of laminar separation, while TR represents the location of turbulent reattachment. The region encapsulated between the laminar separation (LS) point and the turbulent reattachment (TR) point constitutes the laminar separation bubble. As evidenced by this figure, it is apparent that at low Reynolds numbers, a distinct laminar separation bubble exists on the upper surface of the airfoil. In comparison to the experimental outcomes, the calculated errors are sufficiently minute, thereby validating the high accuracy of the unsteady numerical simulation method employed in this study for predicting the locations of laminar separation and turbulent reattachment at low Reynolds numbers. The calculation result shows that when the angle of attack is 3°, the time-averaged length of the laminar separation bubble is 22.2%
c. The substantial extent of the laminar separation bubble suggests a significant impact on the airfoil’s aerodynamic performance.
4.2. Influence of the Oscillation Frequency
In this segment, we examine the impact of oscillation frequency on the airfoil’s aerodynamic properties through numerical simulations. The oscillating surfaces are positioned at P = 0.1c and P = 0.6c, with an amplitude of 0.001c. Based on the unsteady computations of the rigid airfoil, it is revealed that the frequency of the flow field around the rigid airfoil is approximately 5.5 Hz. Consequently, this study elects to investigate oscillation frequencies in the vicinity of the rigid airfoil’s flow field frequency, with a range of 1–10 Hz, which corresponds to Strouhal numbers St = 0.23–2.3.
Figure 10 depicts the time-averaged lift coefficient (
CL), drag coefficient (
CD) and lift-to-drag ratio (
K) for varying oscillation frequencies, where “rig” refers to the rigid airfoil within the illustration.
Figure 10 demonstrates the significant impact of oscillation frequency on the aerodynamic properties of the airfoil. When the oscillation position is set at 0.1
c, it is observed that as the oscillation frequency increases, the lift coefficient (
CL) of the airfoil initially rises before declining, whereas the drag coefficient (
CD) experiences a decrease followed by an increase. Consequently, the lift-to-drag ratio of the airfoil exhibits an ascending and then descending trend. At the oscillation frequency of
f = 6 Hz, the lift-to-drag ratio attains its peak value. Relative to a rigid airfoil, partial oscillation leads to a 4.9% enhancement in the lift coefficient, a 15.3% reduction in the drag coefficient and, correspondingly, a substantial boost of 23.8% in the lift-to-drag ratio. At an oscillation position of 0.6
c, similar trends in variation are noted for the airfoil’s
CL,
CD and
K as the frequency increases, paralleling the scenario when the oscillation position is at 0.1
c. It is noteworthy that when the frequency hits
f = 4 Hz, the lift-to-drag ratio attains its peak value. Under these conditions, the partial oscillation leads to a 4.9% boost in the lift coefficient, a 15.2% reduction in the drag coefficient and thereby a significant 23.7% enhancement in the lift-to-drag ratio of the airfoil.
The aforementioned research demonstrates that partial oscillation can lead to a substantial decrease in the airfoil’s drag coefficient. To delve into the underlying mechanisms of this drag reduction, the total drag on the airfoil is partitioned into its pressure drag and viscous drag components. At an oscillation position of 0.6
c,
Figure 11 depicts the time-averaged pressure drag coefficient (
CDp) and viscous drag coefficient (
CDv) for varying frequencies. This figure reveals that, relative to the rigid airfoil, the pressure drag coefficient of the oscillating airfoil diminishes, while its viscous drag coefficient experiences an increase. These data highlight that as the oscillation frequency rises, the pressure drag coefficient of the airfoil initially dips before climbing back up, whereas the viscous drag coefficient follows a pattern of initially increasing and then subsequently decreasing. At the point where
f = 4 Hz, the viscous drag coefficient peaks, registering an 11.6% boost, whereas the pressure drag coefficient hits its lowest point, witnessing a notable drop of 23.3%. Taking into account the fluctuations in both pressure and viscous drags, the overall drag coefficient for the oscillating airfoil sees a reduction of 15.2% in comparison to its rigid counterpart.
Figure 12 illustrates the position of transition and the extent of the LSB along the airfoil under varying oscillation frequencies, with the oscillation position fixed at 0.6
c.
Figure 12a depicts that for the rigid airfoil, the transition position is located at 0.656
c; however, when subjected to oscillation, this transition point shifts forward. At a frequency of
f = 4 Hz, the transition position shifts to 0.602
c. In
Figure 13, the friction coefficient
Cf along the upper surface of the airfoil is depicted. Evidently from the illustration, partial oscillation induces an earlier transition effect, thereby causing a shift in the frictional characteristics on the airfoil’s surface. As gleaned from
Figure 13, the
Cf value upstream of the oscillation zone remains unaffected by the partial oscillation. Conversely, within the downstream area of the oscillation,
Cf values escalate due to the oscillation and rise above those of the rigid airfoil. This phenomenon constitutes the primary driver behind the fluctuation in the viscous drag coefficient.
Figure 12b illustrates that the length of the LSB on a rigid airfoil amounts to 0.215
c, and the implementation of partial oscillation significantly reduces this LSB dimension. At a frequency of
f = 4 Hz, the LSB length reaches its minimum at 0.185
c, demonstrating a 14.0% reduction in comparison to the length of the LSB on the rigid airfoil. From
Figure 13, one can discern the changes in the LSB, where the regions marked by
Cf values lower than zero denote the LSB’s location.
Figure 14 presents the precise outline of the LSB on the airfoil. Combining insights from
Figure 13 and
Figure 14, it becomes evident that the oscillation does not have a significant influence on the onset of laminar separation; however, it visibly causes the reattachment point to advance. Consequently, the LSB shortens, which in turn results in a reduction in the pressure drag coefficient.
4.3. Influence of the Oscillation Position
In this segment, we examine the impact of oscillation position on the aerodynamic properties of the airfoil, maintaining a constant oscillation frequency of
f = 5 Hz and an amplitude of
A = 0.001
c throughout the study. The aerodynamic attributes of the airfoil subject to various oscillation positions are illustrated in
Figure 15. This graphical representation highlights that when the oscillation position is at
P = 0.1
c and
P = 0.6
c, the airfoil experiences a reduction in its drag coefficient, concurrent with a significant boost in both the lift coefficient and the lift-to-drag ratio. Specifically, when
P = 0.1
c, there is a 4.87% increase in
CL, a 15.29% decrease in
CD and a remarkable 23.79% augmentation in
K, all in comparison to the rigid airfoil. With
P = 0.6
c, there is a notable augmentation of 4.94% in
CL, a substantial reduction of 15.15% in
CD and a considerable surge of 23.68% in
K. From the foregoing analysis, it is evident that the changes in the aerodynamic coefficients exhibit similar patterns when
P = 0.1
c and
P = 0.6
c, thus substantiating that partial oscillations at both 0.1
c and 0.6
c exert comparable flow control effects.
From
Figure 15, it is discerned that the time-averaged location of laminar separation lies at 0.506
c, while the time-averaged reattachment point is situated at 0.721
c. Consequently, the oscillation position at 0.6
c is proximate to the centroid of the LSB on the airfoil. The research demonstrates that when oscillation occurs in close proximity to the leading edge or the central region of the LSB, the enhancement in lift and the reduction in drag resulting from partial oscillation are most pronounced.
Figure 16 presents time-averaged streamline patterns and velocity distributions for the oscillating airfoil at various positions. Time averaging entails computing the temporal mean of flow field parameters over multiple cycles, yielding a result that represents the averaged conditions. This approach serves as a pivotal technique widely adopted in the study of unsteady flows at low Reynolds numbers [
23].
From this figure, it is discernible that multiple LSBs exist across the upper surface of the rigid airfoil within the span of 0.506c to 0.721c. Under a Reynolds number of 3 × 105, the cumulative length of these LSBs measures 0.215c. At P = 0.5c, a significant extent of laminar separation persists. However, when P assumes values of 0.1c and 0.6c, multiple smaller separation bubbles coalesce into a single larger bubble within the laminar separation region on the upper surface of the airfoil, resulting in a visibly reduced separation area. On the other hand, these velocity contours reveal that when the oscillation positions are at 0.1c and 0.6c, the acceleration of airflow over the upper surface of the airfoil is reduced compared to the rigid airfoil case and the scenario where oscillation occurs at 0.5c. Concurrently, the formation of low-velocity regions indicative of recirculation is diminished. These observations suggest that local oscillation at positions 0.1c and 0.6c exert a controlling effect on the laminar separation bubble over the upper surface of the airfoil.
The pressure distribution on the upper surface of both the rigid airfoil and airfoils with surface oscillation at different locations is depicted in
Figure 17. As illustrated by the distribution curves of pressure coefficients, remarkable fluctuations in pressure coefficients are observed over the separation bubble region on the upper surface of the rigid airfoil, a phenomenon attributed to the presence of multiple vortex structures in this area. However, when oscillation occurs at positions 0.1
c and 0.6
c, the pressure fluctuations within the separation bubble region are notably mitigated. This further suggests that oscillation at these two specific locations exerts a certain degree of control over the laminar separation bubble.
The mechanism underlying the aforementioned phenomena is as follows: When the oscillation position is at 0.1c, proximate to the airfoil’s leading edge, the oscillation serves to efficiently infuse energy into the boundary layer, influencing a broader downstream area, thus effectively managing the LSB. In contrast, when the oscillation occurs at 0.6c, situated within the LSB itself, it directly supplies energy into the low-velocity airflow within the separation bubble, thereby efficaciously controlling laminar separation.
At
P = 0.1
c and
P = 0.6
c,
Figure 18 depicts the peak displacement of the oscillating surface, denoted as △
ym, alongside the aerodynamic forces recorded at distinct instants across two complete oscillation cycles. This figure demonstrates that as the airfoil undergoes partial skin deformation, both its lift and drag coefficients exhibit periodic fluctuations. Over the course of one oscillation cycle, the lift coefficient of the airfoil surpasses that of its rigid counterpart, and, concurrently, the drag coefficient is found to be less than that of the rigid airfoil. Therefore, the introduction of partial oscillation enhances the aerodynamic performance of the airfoil at low Reynolds numbers. The magnitude of the aerodynamic coefficients when the position
P = 0.6
c exceeds that observed at
P = 0.1
c, suggesting that the influence of oscillation on the LSB is more pronounced at the former position. Consequently, the unsteady nature of the aerodynamic forces is more evident when
P is 0.6
c.
Illustrated in
Figure 19 are the varying shapes of the LSB on the upper surface of the airfoil at distinct moments within a single oscillation cycle when
P = 0.6
c. From the figure, it becomes evident that the LSB assumes diverse configurations at different instants during the oscillation cycle. This cyclical transformation of LSB shapes directly contributes to the periodic fluctuations in the aerodynamic forces exerted upon the airfoil.