**4. Results**

### *4.1. The Isolated UAV Wing*

The UAV wing is considered first, to focus on the presence of indirect drag reduction effects in three dimensions, but without the geometrical complexities implied by the interaction between wing and fuselage. The UAV finite isolated wing is considered at the cruise flight condition of *Re*<sup>∞</sup> <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup><sup>5</sup> . As always, locally optimal riblets with *l* + *<sup>g</sup>* = 10.5 are placed over the entire wing surface.

Figure 6 shows how drag reduction induced by riblets changes with the angle of attack. The friction component of the total drag reduction is nearly constant at 6.3%, whereas pressure and total drag change with *α*. At *α* = 0 ◦ , the total drag reduction rate is 3.7%, and diminishes at larger incidences. Clearly, the diminished total drag reduction goes hand in hand with the diminished pressure drag reduction. As already observed for the NACA 0012 airfoil in Section 3.2, riblets tend to modify the pressure distribution in such a way that lift is increased; this is confirmed here for the UAV wing. This phenomenon causes an increase in the lift-induced drag, which is not seen in two dimensions. This should not be regarded as a negative effect of riblets, since the aircraft has to achieve the same lift, and increased aerodynamic efficiency is always beneficial.

**Figure 6.** Riblets drag reduction vs. angle of attack for the UAV wing.

In fact, riblets' performance should be measured by adjusting *α* in such a way that the lift coefficient is unchanged. In Table 1, we compare the clean case and the riblets case at the same angle of attack, and at the same lift coefficient as well. Two configurations are considered, at a nominal angle of attack of *α* = 0 ◦ and *α* = 4 ◦ . Total drag is split into friction *CD*, *<sup>f</sup>* and pressure *CD*,*<sup>p</sup>* drag, as well as induced *CD*,*<sup>i</sup>* and profile *CD*,*pr* drag. As expected, comparing at the same *C<sup>L</sup>* provides larger drag reduction than comparing at the same *α*. At the same angle of attack, riblets produce a larger lift coefficient, and hence, a larger induced drag. It is worth noticing that the decrease in *CD*,*pr* is almost the same for the cases at constant *α* and constant *CL*, whereas the induced drag is larger when compared at the same *α*.

**Table 1.** Aerodynamic coefficients for the isolated UAV wing. Comparison between clean and riblets configurations is carried out at the same angle of attack and at the same lift coefficient for nominal angle of attack of *α* = 0 ◦ and *α* = 4 ◦ .


Drag breakdown is graphically shown at various *α* in Figure 7: the focus is on the total, induced, and profile drag on the left panel, and on the contributions to profile drag on the right panel. From the left panel, riblets are seen to mainly act on the profile drag, while the lift-induced drag is essentially unchanged. The right panel of Figure 7 focuses on the decomposition of profile drag, and shows that, besides the obvious reduction of friction drag, riblets additionally act upon form drag in a significant way. Depending on the angle of attack, the benefit of riblets in reducing *CD*,*pr* is in the 5–10% range. This is linked to the modifications on the pressure distribution on the wing, already observed in the NACA 0012 validation tests; see Figure 5. The pressure distribution at 2*y*/*b* = 0.52 for the UAV wing is shown in Figure 8, and confirms the larger pressure recovery and the increased expansion peak induced by riblets that are at the root of form drag reduction.

**Figure 7.** Drag breakdown for the isolated UAV wing (**left**), and focus on the profile drag (**right**). Solid lines with square markers indicate the clean configuration; dashed lines with triangular markers indicate the configuration with riblets.

Finally, Figure 9 plots the skin friction distribution at the spanwise station 2*y*/*b* = 0.52 of the wing, and compares clean and riblets configurations at different angles of attack. A decrease in the skin friction across the entire chord is observed. In particular, on the suction side friction is mainly reduced in the fore portion; at large angles of attack, friction reduction vanishes in the aft part. On the lower surface, the reduction in friction is almost constant when *α* is varied.

**Figure 8.** Pressure coefficient on the pressure and suction sides of the isolated UAV wing at 2*y*/*b* = 0.52, at *α* = 4 ◦ , for the clean case (black line) and difference with the riblets case (red dashed line).

### *4.2. The UAV*

The complete UAV is now considered in the configuration described above and shown in Figure 1. Consistently with the rest of this study, riblets are assumed to be locally optimal, with *l* + *<sup>g</sup>* = 10.5 and unitary slip length *λ* <sup>+</sup> = 1. The spatial distribution of the optimal riblet size, i.e., *l<sup>g</sup>* (which, for a given cross-sectional shape, leads immediately to the geometric dimensions of the riblets) is retrieved as a result of the simulations. It should be remarked, however, that previous work [10] indicates how the size of locally optimal riblets does not vary much, so that the drag reduction obtained adopting riblets with constant physical size is quite near to the maximum drag reduction.

A series of simulations with/without riblets is carried out to provide data points to build the polar of the aircraft (Figure 10). Owing to the already highlighted lift increase provided by riblets, the angle of attack necessary to provide the required lift in cruise conditions slightly decreases from *α* = 2.85◦ to 2.81◦ . The drag reduction obtained for the entire aircraft is an interesting 3%, which derives from a combination of a (less important) friction drag reduced by 6.1% and a (more important) pressure drag reduced by 1.5%.

**Figure 9.** Friction coefficient for the isolated UAV wing, at spanwise location 2*y*/*b* = 0.52 and four angles of attack.

**Figure 10.** *CD*(*α*) and polar curves of the UAV, in clean/riblets configurations.

Figure 11 helps determining where the largest percentage changes of the skin friction take place over the surface of the aircraft. ∆*C<sup>f</sup>* /*C<sup>f</sup>* ,0 is about 6% almost everywhere, roughly as expected for a flat plate at this value of *Re*, except for the region near the trailing edge and for the aft part of the fuselage: here, the absolute value of *C<sup>f</sup>* approaches zero, and its percentage variations become less meaningful.

**Figure 11.** Percentage of skin friction reduction on the upper (**left**) and lower (**right**) parts of the aircraft in cruise condition.

Figure 12 shows the computed height distribution for the locally optimal riblets, by assuming that the cross-sectional riblet shape is a standard V groove, for which *s* <sup>+</sup> = *h* <sup>+</sup> = √ 2*l* + *g* . The optimal riblets height is about 0.2 mm nearly everywhere, except for the trailing edge of the wing, and for the aft part of the fuselage. This provides graphical evidence for the previous statement that riblets of properly chosen constant physical height would provide drag reduction that is very close to the maximum.

Riblets are then tested in off-design situations, i.e., at various incidences different from the cruise angle of attack, to check for robustness and to verify that riblets do not cause unwanted effects on the UAV aerodynamics during manoeuvrers or the climb/descent phases of a typical mission. As already noted for the UAV wing, Figure 13 shows that, although drag reduction is maximum in cruise, the performance degrades only mildly when the angle of attack differs from the cruise value. Again, it is confirmed that friction drag reduction remains nearly constant when *α* ranges from −2 ◦ to 5◦ .

**Figure 12.** Spatial distribution of the computed optimal riblets height in physical units, for symmetric V groove riblets. **Left**: upper part of the aircraft in cruise conditions; **right**: lower part.

Finally, the aerodynamic drag is broken down into profile drag and induced drag in the left plot of Figure 14, while the right plot decomposes further profile drag into friction and form drag. The most obvious difference between clean and riblets configurations is the reduced profile drag, which derives from a sizable reduction in the friction component, joint with a comparable contribution from the form drag.

**Figure 13.** Drag reduction rate vs. angle of attack. The largest drag reduction is achieved in cruise condition.

**Figure 14.** Drag breakdown (**left**) and decomposition of profile drag (**right**). Solid lines with square markers refer to clean configuration; dashed lines with triangular markers refer to riblets configuration.

### *4.3. Partial Coverage*

Perhaps the most interesting consequence of the availability of a simple yet accurate boundary condition to model riblets within RANS simulations is the ability to carry out quick numerical studies to address practical problems related to their use. For example, since riblets produce limited benefits and imply costs and penalties, an elementary cost/benefit analysis should start by addressing the simple question of which area of the aircraft surface would yield the largest benefits after riblets installation. To this aim, we have designed a further set of simulations to explore partial coverage of the aircraft surface with riblets. The amount of coverage is quantified by the ratio *β* between the riblets-covered area and the total area, with *β* = 1 indicating total coverage. In these simulations, the full aircraft is considered, but riblets coverage varies according to Table 2, where case I is the full-coverage case described above. Outcomes of the simulations are shown in Table 3 and graphically represented in Figure 15. Figure 16 schematically illustrates where riblets are applied on the surface of the UAV.



**Table 3.** Drag breakdown for the UAV in cruise condition, for different configurations of riblets coverage, and percentage changes with the clean case.

**Figure 15.** Drag reduction contributions for different configurations of riblets coverage from highest (I-full coverage) to lowest (V-wing only, suction side) coverage.

Since, at the trailing edge of the wing, riblets do not provide significant reductions in skin friction (Figure 11) while locally enforcing a substantial change from the optimal size, in configuration II riblets are removed from the trailing edge of the entire wing. The reduction of the riblets-covered surface is minimal (less than 5%) but, as expected, there is no appreciable decrease in terms of performance. Configuration III has riblets removed from the booms that connect the wing to the tail. Again, the overall drag reduction is essentially unchanged, with 6.5% savings in covered areas: pressure drag reduction remains unchanged since the boom is not an aerodynamic body, whereas friction reduction decreases, but minimally so, because the surface of the boom is small. Together, cases II and III suggest that removing riblets from both the trailing edge and the booms would avoid difficult areas, and save over 10% of application surface without incurring insignificant performance degradation.

**Figure 16.** Schematic drawing of various riblets coverage configurations, cases II–V.

Configuration IV has riblets applied on the wing only, and is motivated by the observation that, in this application, pressure drag is approximately 2/3 of the whole drag, and that riblets placed on the wing produce pressure drag reduction in addition to friction drag reduction. With configuration IV, performance indeed degrades from 3% to 2%, but the saving in coverage area is more than proportional, with riblets surface shrinking down to one half at *β* = 0.524. As expected, pressure drag reduction remains almost unchanged at

1.4%, and friction drag reduction is seen to diminish from 6.1% to 3.3%: indeed, the area of the wing is approximately one half of the total area. Perhaps the most interesting configuration is configuration V, where only the suction side of the wing (and the entire winglet) is equipped with riblets, leading to *β* = 0.289. In contrast, the riblets-induced benefit remains more than one half, i.e., 1.7% instead of 3.0%.

### **5. Conclusions**

The drag reduction potential of riblets deployed on a fixed-wing, low-speed Unmanned Air Vehicle (UAV) has been assessed with RANS simulations, with the aim of determining an optimal coverage policy. While riblets are fully characterised in low-speed flows over plane walls, and studies are available for aeronautical configurations in transonic flow (commercial mid- or long-range passenger aircraft), a low-speed aircraft such as the present one (for which the cruise speed is only 22 m/s) is considered here for the first time. Since the friction component of the aerodynamic drag of the UAV is modest, the effectiveness of riblets in this specific application needs to be assessed.

The RANS simulations, which employ a standard OpenFOAM setup, are unable to describe riblets directly. Thus, the presence of riblets is accounted for via a suitable slip condition enforced at the planar wall. The chosen amount of slip is constant in viscous units, and corresponds to riblets that locally possess optimal size in viscous wall units. The slip length model has been validated in the simple flows over a flat plate and around a subsonic airfoil, where results agree with available information.

Once applied to the UAV, the simulated riblets have brought out indirect and favourable effects, which go beyond the local reduction of friction drag, and also render the deployment of a friction-reduction device definitely interesting in such a low-speed application. Indeed, riblets significantly change the pressure distribution across the wing of the aircraft, which translates into an additional reduction of form drag, and in a lift increment as well. Although the latter obviously causes an increase in lift-induced drag, the requirement for the aircraft in cruise to fly at a given lift leads to a reduced angle of attack, and thus, to a further contribution to drag reduction. In the end, riblets provide up to 3% reduction of the total drag of the aircraft at cruise speed: a noticeable result, especially when the low-flight Reynolds number of the UAV is considered.

Once a cheap computational model is available to reliably compute the global effect of riblets on the aerodynamic drag, varying the riblets coverage policy becomes a computationally affordable task; relatively inexpensive simulations can help determine what drag benefit can be achieved with a given extent and location of the coverage of the aircraft surface. Thanks to the importance of secondary effects on pressure drag reduction induced by riblets, as a consequence of the significant pressure drag component, up to 1.7% of total drag reduction is achieved by placing riblets on the upper surface of the wing only. In this configuration, the total drag reduction is almost 2/3 of the maximum obtained with full coverage, but it is obtained with a coverage of less than 1/3 of the total area. Since riblets costs (for application and maintenance) are directly linked to the amount of riblets-covered surface, the wing-only configuration offers a reduced cost–benefit ratio, and does not touch the UAV fuselage, where systems (sensors, cameras, and transmitters) are designed to be installed. Further analysis can determine the practicality of riblets removal from high-wear areas (e.g., the leading edge), which would further add to the practical appeal of riblets in this application. Such calculations are made possible by the simplicity of the slip-length model, whose validity goes beyond riblets, since it can be used to simulate a generic drag-reducing device which locally reduces the skin friction.

**Author Contributions:** Conceptualization and methodology, C.M. and M.Q.; software and validation, C.B., L.C. and B.M.; writing—original draft preparation, C.B. and L.C.; writing—review and editing, F.G. and M.Q.; data curation, F.G.; supervision, M.Q.; project administration, C.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflicts of interest.
