Slipstream Deformation of a Propeller-Wing Combination Applied for Convertible Uavs in Hover Condition

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Leng, Yuchen and Bronz, Murat and Jardin, Thierry and Moschetta, Jean-Marc Slipstream Deformation of a Propeller-Wing Combination Applied for Convertible UAVs in Hover Condition. (2020) Unmanned Systems, 8 (4). 295-308. ISSN 2301-3850

Any correspondence concerning this service should be sent to the repository administrator: [email protected] Slipstream Deformation of a Propeller-Wing Combination Applied for Convertible UAVs in Hover Condition

,†,‡,§ † Yuchen Leng* , Murat Bronz , Thierry Jardin*, Jean-Marc Moschetta*

*ISAE-Supaero, Universite de Toulouse, 10 Avenue Edouard Belin, Toulouse, 31400, France † ENAC, Universite de Toulouse, 7 Avenue Edouard Belin, Toulouse, 31055, France ‡ Delair, 676 Rue Max Planck, Labege, 31670, France

Convertible unmanned aerial vehicle (UAV) combines advantages of convenient autonomous launch/recovery and efficient long range cruise performance. Successful design of this new type of aircraft relies heavily on good understanding of powered lift generated through propeller-wing interactions, where the velocity distribution within propeller slipstream is critical to estimate aerodynamic forces during hover condition. The present research studied a propeller-wing combination with a plain flap. A 5-hole probe measurement system was built to construct three-dimensional (3D) velocity field at a survey plane after wing trailing edge. The study has found that significant deformation of propeller slipstream was present in the form of opposite transverse displacement on extrados and intrados. The deformation could be enhanced by flap deflections. Velocity differences caused by the slipstream deformation could imply local variation of lift distribution compared to predictions from conventional assumptions of cylindrical slipstream. An analytical method was developed to reasonably estimate the position of deformed slipstream centreline. The research underlined that the mutual aspect of propeller-wing interaction could be critical for low-speed aerodynamic design.

Keywords: Convertible UAV; aerodynamics; propeller-wing interaction.

1. Introduction efficiency of fixed-wing aircraft could improve mission performance of current UAV applications and eventually Small-scale unmanned aerial vehicle has recently attracted open up new types of missions. Rotor lifting system is in- much interest due to their autonomous capability to con- efficient for long-endurance flight, and thus mission range is duct highly repetitive or dangerous flight missions. Such limited. On the other hand, most current fixed-wing UAVs capability is realized through electrical propulsion system rely on crew and sometimes special systems for launch and and improved autoflight system. The current UAV lifting recovery, which limits the origin and destination to dedi- systems are generally derived by down-scaling manned cated ground stations. To perform a fully autonomous long- aircraft. The clear division of rotorcraft and fixed-wing range mission, a hybrid design called convertible drone is aircraft can still be seen in most professional UAV needed. applications. The key to an optimized design of convertible drone lies It has been seen however that a hybrid design that in the interaction between propulsion system and the lifting combines the vertical take-off/landing capability and the surfaces. An entirely independent design, such as shown in Fig. 1 requires lifting propellers that are not used in cruise flight, hence additional weight and drag are introduced. A fully integrated approach (Fig. 2) places lifting surfaces This paper was recommended for publi- cation in its revised form by editorial board member, Hriday Bavle. within propeller slipstream to take advantage of augmented § Email Address: [email protected] lift from blown wing. In this way, the propeller and wing are Y. Leng et al.

Fig. 1. Hybrid Drone [1].

Fig. 3. Convertible UAV Cyclone hovering with negative ﬂap deﬂection.

wing lift for sections immersed in propeller slipstream, the accelerated freestream velocity and sometimes the circumferential swirl velocity are applied to calculate local angle of attack and dynamic pressure. The velocities in the slipstream are computed from a free propeller model, such as one based on blade element momentum theory. To improve accuracy, dual-coupling mode is sometimes used. The same calculation on wing sections still applies. A main difference is that the freestream condition of the propeller is also modified after the wing circulation distribution is solved, and induced velocity from the lifting sur- Fig. 2. Darko, ENAC drone research group. faces is added to flight speed for propeller calculation. Ideally, an iterative approach is used until both solutions both used during hover and cruise flight, and their sizes converge. must match to deliver the required aerodynamic perfor- Both analysis modes require an empirical coefficient to mance while minimizing the weight of combined system. attenuate propeller induced velocity before application in Unlike an independent design, hover lift is distributed wing calculation [3, 4]. This suggests that propeller induced between the vertical component of propeller thrust and velocity distribution might have changed due to the pres- wing lift augmented by rotor slipstream. Thus, flow inter- ence of the wing. The effect was treated semi-empirically ference between the wing and slipstream must be well [3], but a clear physical understanding is still absent. understood to ensure sufficient lift in hover. Recent studies on tractor propeller wake measurements To further augment wing lift and to provide flight con- have found that the influence of the wing on the propeller is trol, trailing edge flap is typically installed, such as shown in not limited to the flow upstream of the rotor disk. Deters Fig. 3. Propeller slipstream can therefore be deflected at a et al. [5] have used a seven-hole probe to make wake survey certain angle to generate additional aerodynamic force and at different downstream locations after three different moment. Sufficient pitch and roll control authority can be propellers. A flat plate wing is situated close to the pro- achieved with appropriate flap design. peller. The presence of the wing is significant that the upper During preliminary design, reduced-order models such and lower halves of the slipstream were observed to be as panel method, vortex lattice method, to name a few, are offset in opposite directions by a distance up to 1 propeller preferred, thanks to their capability of analyzing large radius at survey plane. The phenomenon was first observed amount of candidate configurations at a relatively small and analyzed by Witkowski et al. [6]. However, neither computational cost [2]. Veldhuis has identified two studies provided quantitative analysis. approaches in analyzing propeller-wing systems: single In this paper, a wake survey in static condition is pre- approach and dual-coupling approach. sented at different rotation speeds and flap deflection In single analysis mode, only the influence of propeller angles. The test equipment and condition will be introduced slipstream is taken into consideration. When calculating in Sec. 2. Results and quantitative analysis will be shown in Sec. 3. The test was also performed with flap deflection to behind the trailing edge or 1:7 times propeller diameters investigate the slipstream development when the wing was downstream of rotor plane. generating lift. At the center sphere, five holes were arranged in a cross In Sec. 4, an analytical model based on potential flow pattern with one in the center, a pair in vertical plane and analysis was developed to estimate the deformation of another pair perpendicularly arranged. A series of static propeller slipstream. ports were situated after the probe head. When air is blown, the velocity, pitch and yaw attitude of probe will produce pressure difference between center hole and static ports, 2. Test Set-up vertical pair and side pair holes. Honeywell analogue differential pressure sensors were 2.1. Test equipments used to measure the three pairs of pressure differences which were needed to resolve flow velocity. A calibration The test was conducted in the indoor flight arena at Ecole method proposed by Reichert and Weidt [7] were used to National de l’Aviation Civile (ENAC). The flight arena’s vol- take into consideration cross-product terms and to correct ume provides static ambient environment for simulating alignment errors. hover condition. The calibration was also analyzed for measurement The test equipments were divided into three sub- error. An uncertainty analysis was performed similar to the systems: (1) propeller-wing combination and their relevant one described by Reichert and Weidt, and fitting error as motion control system; (2) 5-hole probe and its data ac- well as pressure fluctuations were considered in uncer- quisition system; (3) motion control system for 5-hole tainty propagation. A validation test was performed in a probe. The test setup in shown in Fig. 4. wind tunnel with known wind velocity and probe attitude. 2.1.1. Propeller-wing model Flow angle measurement and its uncertainty is plotted in Fig. 5; flow speed measurement and its uncertainty is The wing tested was a semi-span model with 500 mm span. plotted in Fig. 6. fl The straight wing had a constant chord length of 150 mm From the validation case, uncertainty in ow speed was estimated at 0:3 m/s and error in flow angle was esti- and NACA0012 aerofoil section. A propeller nacelle was situated at 55 mm from plane of symmetry, where a mated to be less than 2 below 20 . CM2206 direct current brushless motor was enclosed. A full-span plain flap was installed for the last 50% chord, and 2.1.3. Motion control system a servo allowed symmetrical flap deflection of 15 in either direction. A two-axis linear motion frame was constructed to allow An APC 3-blade 5 4:6E propeller was tested. A tilt- automatic wake survey at a given plane perpendicular to rotor mechanism was designed to allow propeller install propeller axis. Three stepper motors controlled by I2C bus angle to change between 10 to 10 with respect to wing were used to move a cart on which the 5-hole probe was chord line. The tilt mechanism was fixed at 0 for this mounted within the survey plane. The measurement was experiment.

2.1.2. 5-hole probe

The wake survey was conducted with an Aeroprobe 5-hole probe. The center of the probe head was located 15 mm

Fig. 4. Test set-up in ENAC indoor ﬂight arena. Fig. 5. Flow angle measurement. Y. Leng et al.

vanish at wing tip, spanwise lift distribution is not uniform for a finite wing without propeller. Furthermore, an up- going propeller blade influences the wing section behind in adifferent way from the down-going blade, hence the influence of a single rotating propeller is not symmetrical. For this reason, both positive and negative flap deflections were tested.

3. Results

In this section, the results of 0 flap deflection will first be presented in Sec. 3.1, where the effect of rotation speed as well as the general flow structure of propeller-wing interference will be discussed. Further discussion will continue in Sec. 3.2 on the effect of flap deflection. Fig. 6. Flow speed measurement. 3.1. 0 Flap deflection

The configuration at neutral flap setting excluded the effect of different velocity and pressure profiles on the extrados and intrados. The wake survey therefore was only influ- enced by the fact that propeller slipstream was separated by a solid surface. The wake survey at 8000 rpm is presented in Fig. 8. The velocity field distribution in the survey plane is depicted as two components: the streamwise component u is perpen- dicularpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi to the survey plane and the transverse component ¼ 2 þ 2 Vt v w is situated within the survey plane. In Fig. 8, the background contour shows u distribution while the Fig. 7. Motion control system and survey pattern. transverse Vt is superposed by arrow symbols that give both magnitude and direction of Vt at sample points. made on a 15 15 grid using alternating survey pattern as depicted in Fig. 7. Mean velocity data was obtained from sample recorded at 700 Hz over a period of 5 s.

2.2. Test conditions

All tests were conducted at V1 ¼ 0 to analyze flow condition at hover flight. Different propeller rotation speeds and flap angles were tested, and the test matrix is given in Table 1. The rotation of the propeller in front of a finite wing made the situation no longer symmetrical. Since lift must

Table 1. Test parameters.

Test variables

Rotation speed [rpm] 5770/8000/10000 Flap deﬂection []0,15 Fig. 8. Velocity distribution at survey plane for symmetrical conﬁguration at 8000 rpm. Slipstream Deformation for Convertible UAVs in Hover Flight

Above and below the wing, propeller slipstream can be identified as a semi-circular region of high energy airflow. Within the slipstream, both u and Vt are notably higher in magnitude than the surrounding flow region. The increase in axial velocity is expected as the propeller produces forward thrust by accelerating air in downstream direction. The transverse velocity is caused by the air resistance against blade rotation. Transverse induced velocity thus results from viscous effect, and is commonly referred to as swirl in rotary wing terminology. According to momentum theory [8], the induced axial velocity at propeller disk can be related to thrust coefficient: rffiffiffiffiffiffiffiffiffi ¼ 2CT ; ð Þ ui nD 1 where n is rotation speed in revolution per second and D ff ffi fi Fig. 9. Comparison of axial velocity distribution at di erent is propeller diameter. Thrust coe cient is de ned as rotation speeds. ¼ T CT n 2D 4 , and was obtained as tabulated data from propeller manufacturer at different rotation speeds [9]. After Plotted in nondimensional form, the contour lines of the rotor plane, contraction of slipstream accelerates flow three different cases generally overlap for most flow region. towards twice of u at downstream infinity. The flow sur- i Major differences lie close to the axial velocity peaks at vey is nondimensionalized using the induced axial velocity intrados and extrados. The general agreement of flow to- at ultimate wake. The benefit of such normalization is pology suggests that at hover condition, the wake devel- to remove the effects of thrust loading and rotational opment is scalable with thrust loading and blade rotation. speed. A circle in dashed line represents the undisturbed slipstream boundary obtained from vortex theory from 3.2. Effect of flap deflection McCormick [10], where qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffi In Sec. 3.1, the slipstream development in 0 flap deflection ðÞ¼ þ 2 þ 2; ð Þ fi R z Rp 1 z z 1 z 2 con guration was presented and analyzed. In this condition, the wing was not lifting, and thus the transverse slipstream where z is the distance from rotor disk plane normalized by displacement was purely caused by the presence of solid propeller radius Rp and z is negative downstream. Through surface between the extrados and intrados parts of slip- comparison with the actual high-speed regions, a distinct stream. separation of flow structures between the extrados and Results obtained at 8000 rpm are included and dis- intrados can be observed. cussed in this section, while the other results are included While increases in ui and Vt can be reasonably explained in Appendix A for simplicity. The effects discussed in this by free propeller theory, movement of the two slipstream section are similar at a different tested rotation speed. regions cannot be similarly explained. For a single propeller, Figure 10 demonstrated the wake survey in a similar the slipstream will stay together as in an approximate cy- fashion as in Fig. 8. The dashed line represents the flap lindrical shape. But when a wing is present, as seen in Fig. 8, trailing edge location when deflected. High speed region can the upper slipstream exhibited a general displacement to- still be observed in the velocity field, but the distribution wards the right (outboard) while the lower slipstream re- took a different shape because of the deflection of flap. gion moves oppositely towards the left (inboard). The Besides the transverse displacement in left and right directions of movement is associated with the direction of directions, the slipstream profiles also differ from each propeller, where in the test case, the inboard blade was other in their vertical expansion. On the extrados, the slip- turning upward relative to the wing chord. stream was displaced towards the right and took a slightly Axial velocity contours of cases from three different ro- narrower width. While the highest point of extrados slip- tation speeds are plotted in Fig. 9, where the solid line stream stayed close to 1 propeller radius, the region spread depicts u distribution at 5770 rpm, dashed line represents lower and generally followed the deflected trailing edge the one at 8000 rpm and dotted line is for 10,000 rpm. flap. The extended vertical expansion is consistent with the Y. Leng et al.

boundary of intrados slipstream is shown lower than 1 propeller radius.

4. Analytical Model of Wake Displacement

From flow survey behind propeller-wing combinations in Sec. 3, it has been observed that when separated by the wing, two halves of propeller slipstream were subjected to opposite transverse motions, or “transverse slipstream displacement”. The phenomenon was explained by Witkowski et al. [6] using a method of imagines. They have qualitatively demonstrated that a pair of streamwise vortices mirrored by the wing surface will induce the correct trend of fluid motion. Fig. 10. Velocity distribution at survey plane for 15 flap However, no quantitative results were given as the effect on deflection at 8000 rpm. a propeller-wing combination at high speed condition was estimated to be small. reduced lateral width, since flow continuity must be However, such phenomenon is significant at low-speed satisfied. regime, observed in Sec. 3. From the comparisons with two The intrados slipstream was wider and flatter compared recently developed reduced-order models, the phenomenon to the extrados slipstream and Fig. 8. The combined effect has not been included in performance estimation of pro- produced a distinct velocity difference for the wing section peller-wing combinations. after up-going blade (inboard section), while such differ- To include the transverse displacement in a potential ence was more subtle on the other side. The non-uniform model is not trivial. Consider the deformed slipstream velocity distribution could imply significant local lift varia- system in Fig. 12 where a series of vortex rings symbolize tion in the surveyed section. the blade tip vortices shed from one propeller blade. The Wake survey for negative flap deflection is depicted in vortex line is displaced in corresponding directions upon Fig. 11. The velocity distribution is generally axial sym- contact with the wing. metric of Fig. 10. However, the vertical extent of the intra- This simple model shows the discontinuity between dos slipstream is slightly larger than the extrados upper and lower halves of the helical vortex and their re- slipstream in positive flap deflection. In Fig. 11, the wake spective translations. Such model is not admissible in potential flow methods. A line vortex is needed to reconnect

Fig. 11. Velocity distribution at survey plane for with 15 ﬂap Fig. 12. Displaced propeller slipstream and connecting line deﬂection at 8000 rpm. vortex segments. Slipstream Deformation for Convertible UAVs in Hover Flight

Fig. 13. Side view of an aerofoil section after up-going propeller blade. the ends of upper and lower vortex semi-rings. The addition of the line vortex segment is significant in three ways: First, it completes the vortex system so that Helmholtz theorem is again respected. The solution is thus admissible in potential methods. Second, the circulation has physical meaning of streamwise velocity difference between the upper and lower surfaces. In Fig. 13, an aerofoil section after up-going blade is Fig. 14. Imaginary propeller distributed vortex system. shown. According to Fig. 12, at the upper surface, the aerofoil section is situated outside of the propeller slipstream and 8 > ¡ thus experiences a smaller velocity component in streamwise > 0 r R ; 0 <<; x ¼ 0 > 2r p direction. At lower surface, the streamwise component is < ¼ ¡ ; ð Þ however augmented because of the induced velocity within r 0 ;<<; ¼ 4 > r Rp 2 x 0 ff > 2r propeller slipstream. The velocity di erence means :> additional circulation exists around the aerofoil section. 0 otherwise Third, the direction of the vortex segment has the effect 8 > ¡ cos of attenuating the overestimation of propeller-wing inter- < 0 r ¼ R ; x < 0 ¼ 2R p ; ð Þ action. The up-going blade induces increased local angle-of- > p 5 ¡ : attack and thus wing circulation w is enhanced. However 8 0 otherwise ¡ from the previous discussion in Fig. 13, the bound line > 0 sin ¼ ; <<; < > r Rp 0 x 0 vortex segments add an opposing circulation, and hence <> 2 Rp ff ¡ mitigate the e ect of increasing w. ¼ ¡ sin ; ð Þ x 0 ¼ ;<<; < 6 To correctly place the bound vortex segments so that > r Rp 2 x 0 > 2 Rp they affect the corresponding wing sections, an estimation :> of the transverse slipstream displacement is needed. The 0 otherwise: next sections present a qualitative estimation of centerline deformation for a propeller slipstream on a flat plate. Note that circumferential distributed vortices do not change sign, so that Helmholtz theorem at the surface is satisfied. Nonpenetration condition is still assured as the circumferential component does not induce normal velocity 4.1. Imaginary distributed slipstream vortex field at the surface. The upper half of imaginary distributed When the wing is present, the normal velocity at the lifting vortex system represents the upper propeller slipstream surface must vanish. This nonpenetration condition can be with wing leading edge situated exactly at rotor plane. satisfied by reversing the direction of axial and radial It is apparent that the axial induced velocity along cen- distributed vortex elements. The imaginary system is given terline does not change in the imaginary distributed vortex in Eqs. (4)–(6), and illustrated in Fig. 14. In Eqs. (4)–(6), system. Furthermore, it will be assumed that the induced angle refers to wake helix angle, which is the angle be- velocity does not vary much around centerline, such that tween the tangent of shed tip vortex centerline and the the centerline value could be used to trace the deformed trajectory. During the process, slipstream boundary will propeller rotor plane. Here the slipstream contraction is fi neglected. remain as a straight semi-in nite cylinder. The problem then reduces into solving centerline transverse induced ° ¼ð ; ; Þ; ð Þ r x where 3 velocity viy. Y. Leng et al.

fi Velocity viy comes from two parts: a rst part induced by where the expression takes negative sign above the surface rotor plane vortex v ; and a second part from axial vor- (<<2). Similar to the situation with rotor plane in- iyr tices in trailing wake v . duced velocity, the result from upper vortex elements is iyx doubled to obtain full component of transverse induced velocity. 4.1.1. Rotor plane induced transverse velocity viy° r Relative position vector from an arbitrary downstream ; ¼ position A is given in Eq. (12): At rotor plane where r Rp x 0, an elementary vortex segment is expressed in Eq. (7): ¼ ½ ^ þ ^ þ Δ ^; ð Þ r¡xA Rp cos i sin j Ak 12 ¡ ¼ ^ d r rrd drir Δ ¼ Δð Þ¼ ¡ where A xA x xA ¼ 0 ^ d drir Differential transverse induced velocity is obtained from 2 ¡ Biot–Savart law: ¼ 0 ddrðcos î þ sin ^jÞ: ð7Þ 2 ðr¡ ¡ Þ dv ðx Þ¼ xA x y where the expression takes negative sign above the surface ixx A 3=2 4r ¡ (0 <<). Because of symmetry, the contribution from xA ¡ sin sin ddx vortex elements above the surface is identical as that from ¼ 0 : ð13Þ 2 ð þ Δ 2Þ3=2 below. Thus, the induced velocity from upper vortex ele- 8 Rp 1 A ments is doubled to obtain the full component. fi Relative position vector from an arbitrary downstream Integrate on the upper semi-in nite cylinder and double position A is given in Eq. (8): the result, the transverse induced velocity from trailing wake vortex distribution is obtained: ^ ^ ^ ¡ ¼ ð þ Þ : ð Þ r rA r cos i sin j Rp xAk 8 Z ¡ sin 0 v ðx Þ¼ 0 ð1 þ Δ 2Þ3=2dx where x is x coordinate normalized by propeller radius. iyx A 2 A 2 R 1 Differential transverse induced velocity is obtained from p ¡ – 0 sin xA Biot Savart law: ¼ 1 : ð14Þ 2 2 Rp A ðr¡ ¡ Þ ð Þ¼ rA r y dvix xA r 3=2 Finally, the centerline transverse induced velocity can be 4 r ¡ A r obtained by combining Eqs. (10) and (14): ¡ x sin ddr ¼ 0 A : ð9Þ 2 2 2 = 8 Rp ðr þ x Þ3 2 ¡ x 1 A v ðx Þ¼ 0 1 A sin : ð15Þ iy A 2 Integrate on the upper half rotor plane and double the 2 Rp A x A result, the transverse induced velocity from rotor plane vortex distribution is obtained: Z Z 4.2. Deformed centerline equation ¡ 1 2 ð Þ¼ 0 xA sin d dr viy xA r 2 2 2 3=2 4 Rp 0 ðr þ x Þ To obtain an analytical approximation of centerline equa- Z A ¡ 1 tion, axial induced velocity v obtained from vortex system ¼ 0 xA dr ia 2 2 2 = is needed. It is calculated in a similar way, and a detailed 2 Rp ðr þ x Þ3 2 0 A derivation can also be found in McCormick [10]. For brevity, ¡ 1 ¼ 0 ; ð10Þ the expression is given in Eq. (16): 2 2 Rp xA A pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¡ cos x ¼ ð Þ¼ þ 2 ðxÞ¼ 0 1 : ð16Þ where parameter A xA 1 x A. via 4 Rp

4.1.2. Trailing wake induced transverse velocity v With Eqs. (15) and (16), the deformed centerline can be iy°x expressed by considering it to be a surface streamline, ¼ ; < At wake boundary where r Rp x 0, streamwise ele- where mentary vortex segment is expressed in Eq. (11): dy dx ¡ ¼ : ð17Þ 2 ^ 0 Rp sin ^ ðÞ ðÞ d¡ ¼ R ddxi ¼ ddxk: ð11Þ vy x vx x x x p x 2 Slipstream Deformation for Convertible UAVs in Hover Flight

< Local transverse velocity vy and axial velocity vx is given Solving the integral and also consider all x 0, the in Eq. (18): complete static deformed centerline equation is given in Eq. (22), where c is chord length normalized by propeller v ðxÞ¼v ðxÞ; y iy radius. ðÞ¼ þ ðÞ: ð Þ vx x V1 via x 18 8 > ; > 0 xLE x The negative sign in front of V1 is because positive x is > > 2 defined to be opposite direction of freestream. Local de- > ð ÞΔ ; > sec tan LE xTE x flection angle is given in Eq. (19): > > > v ðxÞ > 2 ðxÞ¼ iy : ð19Þ > þ sec x < x þ ðÞ > LE LE V1 via x > > > Thus, the deformed centerline Eq. (20) can be approxi- > xLE 1 > þ ln mated by integrating Eq. (17): > x 1 8 > LE > > 0 xLE x > <> Z < 2 ð Þ x sec tan cTE yðxÞ¼ ð Þ < : ð20Þ yðxÞ¼ : ð22Þ > s ds xTE x xLE > > > : xLE > þ Δ < > 2 yTE TE TE x xTE > þ sec x < x > TE LE TE > Equation (20) contains two parts: the first term repre- > > sents the deformation on top of the wing starting from > þ xLE 1 TE > ln nondimensional leading edge xLE until trailing edge xTE; the > x 1 > TE LE second term assumes constant centerline deviation angle > > from rotation axis after trailing edge, and thus the trans- > 2 Δ > sec sin LE verse displacement is linear with downstream location x. > > The analytical expression of deformed centerline equa- > > Δ tion will be presented in two parts: the first part is for static :> TE x ð x 2 Þ case where V1 ¼ 0 and the second part is for cases where TE TE TE V1 > 0.

4.2.2. Deformed centerline equation in forward ﬂight 4.2.1. Deformed centerline equation in hover condition

When V1 > 0, the slipstream will be convected in stream- When V1 ¼ 0 and x < x ,Eq.(20) simplifies to Eq. 21: TE wise direction, which tends to attenuate centerline defor- Z x TE mation. From Eq. (20), the integral term is expanded: ðÞ¼ ð Þ þ Δ y x s ds TE TE x LE Z " x 2 IðxÞ¼ ðsÞds ¼ sec sin Δ TE xLE Z # x sec Z 2 tan sðsÞ Δ xTE ¼ ; ð Þ TE ds sec ds 23 : ð Þ þ 21 x LE 1 ¡ ð Þ x ð x Þ sð sÞ 0 s TE TE TE xLE ¡ 0 Before proceeding further, it is worth mentioning that where the nondimensional circulation ¡ ¼ . Since ¡ 0 4 V1 Rp 0 the different factors affecting centerline deformation can be is associated with the total propeller thrust, the centerline clearly observed in Eq. (21). The first term includes all deformation in forward flight condition is determined by contribution from streamwise vortices in the trailing wake, both disk loading and total thrust condition. The relations and it is a linear term in streamwise coordinate with pro- between propeller thrusting condition and slipstream ¡ portional constant determined by helix angle. The second parameters , 0 are related from vortex theory [10], and term represents the influence from blade circulation. This demonstrated in Appendix B. term grows with the proximity from leading edge to rotor rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! plane. It is interesting to conclude that for a given geometry V1 þ v 1 8C (x and x ) in static condition, the deformed centerline tan ¼ ia ¼ T þ J 2 J : ð24Þ LE TE R 2 shape only depends on wake helix angle . p Y. Leng et al.

Complete integrations of tan and sec terms: can be approximated by Gaussian function. The jet boundary corresponds to where the extrema of shear stress exists. 2 ¡ sin @ ðÞ¼ 0 ½Δ þ If streamwise partial derivatives ( ) are assumed to be I x LE LE @x 2a 1 small compared to cross-flow derivatives, the cross-flow ðÞ¡ 2 2 p0ffiffiffiffiffiffiffiffiffiffiffiffiffifficos tan sec ½ ðÞ shear stress can therefore be determined as x LE 2a 1 2a 1 a @u þ ðxÞ ¼ ; ð27Þ LE xy @y ¡ þ 0 1 LE 1 þ ln ; ð25Þ @u a þ 1 1 ¼ : ð28Þ LE xz @z pffiffiffiffiffiffiffiffiffi where a ¼ 1 þ ¡ cos , ðxÞ¼tan1 x 2a1, and ðxÞ¼ The wake boundary was then determined to be the locus pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0 a of maximum transverse shear stress, drawing analogy from ð Þð þ Þ 1 2a 1 1 x 2 tan a1 . conclusions of turbulent jet theory: The complete deformed centerline equation in forward qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð ; Þ : 2 þ 2 : ð Þ flight condition is in Eq. (26). y z max xy xz 29 yðxÞ 8 The vertical extrema of the slipstream boundary were > ; chosen as the radius of contracted wake R, as shown in > 0 xLE x > Fig. 15. The angular and radial position of the closest points > > 2 ¡ sin ½Δ þ of slipstream boundary to rotational axis were determined > 0 LE LE > 2a 1 as R and . From geometry relations, the slipstream center > 1 1 > can then be determined as > ¡ cos sin 1 > þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi0 ; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > xTE x > 2a 1 2a 1 a y ¼ R 2 ðR sin Þ2 þ R cos : ð30Þ > c w 1 1 1 1 > > ½ ðÞþ ðÞ > x x LE LE x xLE > > The displacement of slipstream center from propeller > 1 1 þ 1 > ln LE ; > þ axis can therefore be found, and the results for three test <> 2a 1 LE 1 cases can be found in Table 2. ¼ 2 sin ; From Table 2, it can be concluded that the three cases > ¡ ½ þ < > 0 c TE LE x xTE have nearly identical wake displacement. A theoretical re- > 2a 1 > sult was also calculated for each case. This value is based on > > ¡ cos sin 1 the previously derived potential flow method. > þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi0 > > 2a 1 2a 1 a > > > ½ þ > TE TE LE LE > > þ > 1 TE 1 LE 1 > ln þ > 2a TE 1 LE 1 > > > 2¡ sin ðÞ x 1=x :> 0 TE TE TE Δ ðÞþ TE a TE xTE xTE ð26Þ

4.3. Comparison with wake survey in hover condition Fig. 15. Geometry relations to determine slipstream center.

fi A quanti able measurement is made by determining the Table 2. Centerline displacement at different rotation speeds. centers of extrados and intrados slipstreams. Due to the presence of wing wake, the slipstream center cannot be RPM CT yc=Rp Theoretical yc=Rp Error % easily defined. An indirect method was used to determine : : : : slipstream center through shear stress at the boundary. 5770 0 1907 0 4290 0 4252 0 9 : : : : From turbulent jet theory, it can be concluded that the 8000 0 1908 0 4086 0 4253 3 9 10; 000 0:1906 0:4017 0:4252 5:5 axial velocity profile of a round jet surrounded by static air Slipstream Deformation for Convertible UAVs in Hover Flight

The results contrast with most reduced-order model of propeller-wing interaction where propeller wake was assumed to retain its cylindrical shape. Comparison with a theoretical model suggests that wing influence on propeller slipstream velocity distribution can be accurately modeled using method of reflection on slipstream streamwise vorticity. The influence of wing on velocity distribution within slipstream was observed to be different between upper and lower surfaces when flap deflection was present, with the deformation being stronger on the wing surface opposite to flap deflection. This paper is a first step towards more accurate pre- diction of forces and moments on convertible UAVs via reduced order models. Fig. 16. Velocity distribution at survey plane for symmetrical configuration at 8000 rpm, with displaced slipstream boundary. Acknowledgments ¼ = The resulting model for centerline displacement yc yc Rp ¼ = is a function of downstream location z z Rp, with blade The research was conducted as a cooperation between tip vortex shedding angle as a parameter. The centreline research institutes ISAE-Supaero, ENAC and Delair compa- displacement is given in Eq. (22) at static condition. ny, with partial funding from Association Nationale Angle can be calculated from momentum theory using Recherche Technologie. The authors would like to express ffi thrust coe cient, and zLE, zTE are leading edge and trailing gratitude to Mr. Stephane Terrenoir for his coordination of edge locations divided by propeller radius with origin at the project, to engineers at Delair, Mr. Alexandre Lapadu, rotor center and negative direction pointing downstream. Mr. Clement Pfiffer and collegues at ENAC, Mr. Michel In Fig. 16, slipstream boundary from momentum theory Gorraz, Mr. Xavier Paris, Mr. Nicolas Peteilh for their pro- was displaced by the predicted amount from Table 2. The fessional assistance and expertise during the implementa- deformed boundary appeared to include both high-speed tion and execution of wind tunnel experiment. flow regions at extrados and intrados. The results confirm that at static condition, displaced centerline can be accurately calculated using the theoretical model. The results seem to Appendix A. Wake Surveys with Flap affirm that the presence of wing serves as an imaginary plane for slipstream vortex system, and its induced transverse ve- Wake surveys with 15 flap deflections are depicted in locity component explains centerline displacement. Figs. A.1 and A.2 for propeller rotation speed at 5770 rpm. Wake surveys with 15 flap deflections are depicted in Figs. A.3 and A.4 for propeller rotation speed at 10,000 rpm.

5. Conclusion

In this paper, a wake survey was presented immediately after a propeller-wing combination to investigate the flow interaction for a convertible UAV under hover condition. A sym- metric wing profile was tested in ENAC indoor flight arena at calm wind condition. Velocity magnitude and direction were measured by a 5-hole probe at a plane perpendicular to streamwise direction and downstream of trailing edge. The test was conducted with zero flap deflection, as well as with flap deflection of 15 in either direction. The results demonstrated that the presence of wing influences velocity distribution within propeller slipstream compared to a free propeller. In the experiment, the upper half slipstream was observed to translate towards outboard while the lower half slipstream translates towards inboard. Fig. A.1. 15 flap deflection. Y. Leng et al.

Appendix B. Relation Between Propeller and Slipstream Parameters

In the derivation of deformed centerline equations, it has been observed that the centerline profile is associated with propeller working condition by two parameters: wake helix ¡ angle and rotor plane circulation 0. The two parameters can be related to propeller thrust condition by the application of momentum theory. Consider the centerline velocity induced by the vortical system at propeller plane, from Eq. (16) where ¡ cos v ð0Þ¼ 0 : ðB:1Þ ia 4R From momentum theory [8], the rotor plane induced Fig. A.2. 15 flap deflection. velocity can be concluded, and is applicable for both static and forward flight condition, as rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! 0 nD 8C v ð0Þ¼ T þ J 2 J : ðB:2Þ ia 2

By setting the two velocities equal, the rotor plane circulation can be solved: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! 4R2n 8C ¡ ¼ T þ J 2 J ; ðB:3Þ 0 cos

or in nondimensional form as used in the discussion before. ¡ ¡ ¼ 0 0 4V1R sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! sec 8C ¼ T þ 1 1 : ðB:4Þ 2 J 2

Fig. A.3. 15 flap deflection. The wake helix angle can be found using velocity geometry relations: þ ¼V1 via tan rRffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! 1 8C ¼ T þ J 2 J : ðB:5Þ 2

Appendix C. Useful Integrations Z z2 ds (a) pffiffiffiffiffiffiffiffiffiffiffiffiffi ð þ 2 Þ z1 s 1 s s After rationalization, the integral can be simplified, Z Z rffiffiffiffiffiffiffiffiffiffiffiffiffiffi z2 1=sds z2 1 pffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1 þ 1 þ ds 2 2 z 1 þ s s z s 1 1 Z rffiffiffiffiffiffiffiffiffiffiffiffiffiffi z2 1 ¼ z z þ 1 þ ds: ðC:1Þ 2 1 s2 Fig. A.4. 15 flap deflection. z1 Slipstream Deformation for Convertible UAVs in Hover Flight R qffiffiffiffiffiffiffiffiffiffiffiffiffi z2 þ 1 The second integral is solved using a change of variable For the integral 1 2 ds, make a change of variable qffiffiffiffiffiffiffiffiffi z1 s pffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ¼ 1 ¼ 1 ¼ þ 2 ¼ a 2 s tan , and let 1 tan z1, 2 tan z2. The integral is 1 s , and let b 2a1, then solved by parts: rffiffiffiffiffiffiffiffiffiffiffiffiffi Z pffiffiffiffiffiffiffiffiffiffiffiffiffi Z Z z2 2 z2 2 1 s 1 þ s 1 2 I ¼ ds 1 þ ds ¼ cscsec d 2 2 þ 2 2 2a 1 z s b z s 1 1 1 Z Z 1 2 2 2 ¼ ¼ j 2 þ 2 2 d csc tan csc d 2a 1 þ b 1 1 1 1 qffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 2 2 2 ¼ 2 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1 þ z 1 þ z þ lnjjj csc cot b 1tan 2 1 1 2a 1 b2 1 1 z 1 ð Þð Þ ¼ þ 1 2 ; ð : Þ 2 1 a 1 2 1 2 1 ln C 2 ¼ ; ðC:7Þ z2 1 1 2a 1 ð2a 1Þ3=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 where ¼ 1 þ z . ð2a1Þð1þz 2Þ where ¼ tan1 . Thus, the complete integral is solved as a1 Z Thus, the integral is solved as z2 = pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 sds z1 1 2 Z pffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ z z þ þ ln : z2 1 þ s2 s z z ð Þ 2 2 1 2 1 2 1 2 1 z 1 þ s s z2 1 1 pffiffiffiffiffiffiffiffiffiffiffiffiffi ds ¼ 1 2 z a 1 þ s ða 1Þs 2a 1 ðC:3Þ 1 Z pffiffiffiffiffiffiffiffiffiffiffiffiffi a 1 z2 1 þ s2 s þ ð (b) pffiffiffiffiffiffiffiffiffiffiffiffiffi ds ð2a 1Þ3=2 2 1 a 1 þ s2 ða 1Þs z1 þ Þ: ð : Þ ¼ þ ¡ 2 1 C 8 Rationalize the integral, and a 1 0 cos is assumed to Z fl z2 be larger than unity for normal ight condition pffiffiffiffiffiffiffiffiffiffiffiffiffids pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi (c) Z Z s½a 1 þ s2 ða 1Þs z2 1 þ s2 s z2 s2 s 1 þ s2 þ a z1 pffiffiffiffiffiffiffiffiffiffiffiffiffi ds ¼ ds Rationalize the integral, and a ¼ 1 þ ¡ cos is assumed to a 1 þ s2 ða 1Þs ð2a 1Þs2 þ a2 0 z1 Zz1 be larger than unity for normal flight condition: z2 s2 ¼ ds Z Z pffiffiffiffiffiffiffiffiffiffiffiffiffi ð2a 1Þs2 þ a2 z2 ds z2 ða 1Þs þ a 1 þ s2 zZ1 pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi ds ¼ ds z 2 ½ð Þ 2 þ 2 2 s 1 þ s2 z s½a 1 þ s ða 1Þs z s 2a 1 s a ds 1 Z 1 ð2a 1Þs2 þ a2 z2 a 1 zZ1 ¼ ds z ð Þ 2 þ 2 2 ds z 2a 1 s a þ a Z1 pffiffiffiffiffiffiffiffiffiffiffiffiffi ð2a 1Þs2 þ a2 z2 a 1 þ s2 z1 þ ds ¼ þ : ð : Þ s½ð2a 1Þs2 þ a2 I1 I2 aI3 C 4 z1 ¼ð Þ þ : ð : Þ The first and third integrations are trivial: a 1 I3 aI4 C 9 Z z2 s2 Integral I is trivial. I ¼ ds 3 1 ð2a 1Þs2 þ a2 Now only I remains to be solved. Make a change of z1 p4ffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 z2 variable ¼ 1 þ s 1 a 2a 1 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 s tan s pffiffiffiffiffiffiffiffiffiffiffiffiffi 2a 1 2a 1 a z Z Z 1 z2 1 þ s2ds 1 2 d ð Þ ¼ z2 z1 a 2 1 ds 2 ¼ ; ðC:5Þ s½ð2a 1Þs2 þ a2 a2 1 2a 1 ð2a 1Þ3=2 z1 1 pffiffiffiffiffiffiffiffiffi ða 1Þ2 þ where ¼ tan 1ðz 2a 1Þ, and a2ð2a 1Þ Z a z Z 2 ds 2 d I ¼ 3 ð Þ 2 þ 2 2 2 z 2a 1 s a þða 1Þ =ð2a 1Þ p1ffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 z 2a 1 2a 1 2 1 1 þ 1 ¼ 1 ¼ ln 2 1 tan s 2 þ að2a 1Þ a 2a 1 1 2 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi z1 ð Þð Þ 2a 1 þ a p1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 1 : ð : Þ ¼ ð Þ: ðC:6Þ C 10 a 2 1 a2 2a 1 Y. Leng et al.

Thus, the complete integral is obtained as 32nd AIAA Applied and Aerodynamics Conf. (2014) doi: 10.2514/ Z 6.2014-2152. z2 þ ds 1 2 1 1 1 [4] K. Epema, Wing optimisation for tractor propeller configurations: pffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ln 2 þ Validation and application of low-order numerical models adapted to z s½a 1 þ s ða 1Þs 2a 1 1 2 1 1 include propeller-induced velocities (Master’s Thesis, Delft Univer- ð Þ þ paffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 ð sity of Technology, Delft, Netherlands, 2017). 2 1 a 2a 1 [5] R. W. Deters, G. K. Ananda and M. S. Selig, Slipstream measurements þ Þ: ð : Þ of small-scale propellers at low reynolds numbers, 33rd AIAA Applied 2 1 C 11 Aerodynamics Conf. (2015), p. 2265. [6] D. P. Witkowski, A. K. Lee and J. P. Sullivan, Aerodynamic interaction between propellers and wings, J. Aircr. 26(9) (1989) 829–836. [7] B. A. Reichert and B. J. Wendt, A new algorithm for five-hole probe References calibration, data reduction, and uncertainty analysis (Technical Memorandum NASA-TM-106458, NASA Lewis Research Center Cle- [1] Falcon vertigo hybrid unmanned aerial vehicle https://www.uasvi- veland, CH, United States, 1994). sion.com/wp-content/uploads/2017/02/Falcon-Vertigo.png, acces- [8] G. J. Leishman, Principles of Helicopter Aerodynamics with CD Extra sed 21 May 2019. (Cambridge university press, 2006). [2] L. Veldhuis, Review of propeller-wing aerodynamic interference, [9] Apc propeller performance data https://www.apcprop.com/techni- 24th Int. Congress of the Aeronautical Sciences, Vol. 6, No. 1 (Japan, cal-information/performance-data/, accessed 21 May 2019. – 2004), pp. 1 21. [10] B. McCormick, Aerodynamics, Aeronautics, and Flight Mechanics fl [3] G. K. Ananda, R. W. Deters and M. S. Selig, Propeller-induced ow (Wiley, 1994). effects on wings of varying aspect ratio at low reynolds numbers,

Yuchen Leng is a third year PhD candidate at ISAE- Thierry Jardin is a Research Associate at ISAE- Supaero/ENAC and aerodynamic engineer at Tou- Supaero, Toulouse, France. He received his Master louse-based drone company Delair. He has received Degree in Mechanical Engineering from INSA Tou- his Bachelor Degree in aircraft design from Beihang louse and PhD Degree in Aerodynamics from ISAE- University, China and later received his Master ENSMA (Pprime institute). His research principally Degree in applied aerodynamics from Purdue Uni- focused on low Reynolds number aerodynamics. versity, US. Recent contributions concern flight in low pressure His main research interests concern low-speed environments (stratosphere, Mars planet), highly aerodynamics, particularly in the application for maneuverable UAVs and aeroacoustics of low vertical/short take-off and landing aircraft. He is Reynolds number rotors. currently working on the thesis “Aerodynamic Design of Long Endurance Convertible UAV”. Jean-Marc Moschetta graduated from ISAE- SUPAERO in 1987 and obtained his PhD Degree in Murat Bronz received his Masters degree from Aerodynamics in 1991. Since 2000, he has been a Istanbul Technical University on Aeronautical and full Professor of Aerodynamics at ISAE-SUPAERO Astronautical Engineering. Later, he received his and a Consultant at ONERA. From 2001, he orga- PhD on “Long Endurance Mini-UAV Design” from nized or co-organized several MAV conferences and ISAE in 2012. Since April 2013, he has been will host next year edition in Toulouse, France. He working as an Assistant Professor at ENAC. is currently the Head of the UAV program at ISAE- His main research concentrates on applied SUPAERO and Director of the MAV Research Center, aerodynamics and aircraft design. His recent con- a French research network on MAVs, which fosters tributions are on the mission oriented optimization a dozen research laboratories in the South West of of flight vehicles applied to conventional config- France. Jean-Marc Moschetta has published numerous papers on the design urations, VTOLs, Solar-powered vehicles, and au- and the aerodynamics of MAVs and is currently a member of the editorial tonomous soaring machines. board for the International Journal of MAVs.