domain: spi phys

text:
Ronan Boisard

Numerical Analysis of Rotor / Propeller aerodynamic interactions on a high speed compound helicopter

In the context of the development of high-speed compound helicopters, the main rotor may not be an efficient propulsive device at high speeds and adding a propulsive propeller is a means to enable higher speed. On such configuration, at low speed, the propellers are in strong interactions with the main rotor wake which affects their performance and aircraft maneuverability. The present work numerically investigates the aerodynamics of the rotor / propeller interaction on rotorcraft similar to the Racer from Airbus Helicopters. Through the comparison of two different levels of fidelity for three different advance ratios it is shown that at high advance ratio, a simple free wake model is suitable to give most of the interaction effects, while in hover, a full Comptational Fluid Dynamics (CFD) unsteady computation is necessary to better capture all the unsteadiness of the interaction. The detailed analysis of CFD results also outlines the different behaviors of the propeller when it is fully inside the rotor wake or out of it, and therefore the need for a precise control of the rotorcraft in the transition between hover to fast forward flight. Nomenclature c Blade chord, m R Rotor radius, m r/R Non dimensional spanwise location V o Freestream velocity, m/s V tip Blade tip rotation velocity, m/s µ advance ratio, 𝑉 𝑜 𝑉 𝑡𝑖𝑝 Ω Rotational velocity, rad/s b Number of blades σ Rotor solidity, 𝜎 = 𝑏 𝑐 𝜋 𝑅 ρ Freestream air density, kg/m 3 a Speed of sound, m/s M Mach number S Rotor disk surface, m² F x Axial force, N F z Thrust, N C T Thrust coefficient, 𝐶 𝑇 = 𝐹 𝑍 𝜌 𝑆 (𝑅 Ω) 2 𝑍 ̅ Thrust coefficient, 𝑍 ̅ = 100 𝐹 𝑍 1 2 ⁄ 𝜌 𝑆 𝜎 (𝑅 Ω) 2 F n Local force normal to the blade section (N) C n M 2 Section normal force coefficient 𝐶 𝑛 𝑀 2 = 𝐹 𝑛 1 2 𝜌𝑎 2 𝑐 F c Local force align with the blade section chord(N) C c M 2 Section chordwise force coefficient 𝐶 𝑐 𝑀 2 = 𝐹 𝑐 1 2 𝜌𝑎 2 𝑐 RMS Root Mean Square: 𝑅𝑀𝑆 = √ 𝐴 2 ̅̅̅ -𝐴 ̅ 2 θ 0 blade collective pitch angle (positive up) θ 1c blade lateral cyclic pitch angle θ 1s blade longitudinal cyclic pitch angle β 0 blade coning angle (positive down) β 1c blade longitudinal cyclic flap angle β 1s blade lateral cyclic flap angle δ 0 blade lead-lag angle (positive lead) δ 1c blade longitudinal cyclic lead-lag angle δ 1s blade lateral cyclic lead-lag angle

Introduction

Helicopters have typically more than one rotor. While a conventional helicopter has a main rotor and a tail rotor, tandem, coaxial, and tiltrotor aircraft have multi-rotors to ensure both lifting and propulsive forces. In the context of the development of high-speed compound helicopters, the main rotor may not be an efficient propulsive device at high speed and one or more propeller have to be added in order to reach high advancing velocities. The simultaneous use of a main rotor and lateral propellers adds a lot of aeromechanical complexity and can lead to complex unsteady interactions between the wakes emitted from the rotor and propellers. It is legitimate to assume that such interactions, of aerodynamic nature, can have a significant impact on vibrations, radiated noise and aerodynamic performance, especially in low speed conditions. Aerodynamic interactions between rotor and fixed airframe surfaces have been studied for a long time. Main rotor / fuselage interactions are now well understood and can be predicted thanks to numerical tools which were validated against experimental results (Ref. 1 and 2). Main rotor/tail rotor interactions are also well documented, they were for example the main focus of the European project GoAhead involving several European organizations (Ref. [START_REF] Barakos | CFD for Rotorcraft Recent Progress and new Challenges with the GoAhead case[END_REF]). Literature about rotor / rotor interactions is also available, but usually with a very limited scope. For example, US Army carried out an experimental study simulating co-axial and tandem configurations (Ref. [START_REF] Ramasamy | Measurements Comparing Hover Performance of Single, Coaxial, Tandem, and Tilt-Rotor Configurations[END_REF]) which was limited to hover cases. The first extensive analysis of a compound helicopter with side propellers was performed back in the sixties (Ref. [START_REF] Bain | Investigation of Compound Helicopter Aerodynamic Interference Effects[END_REF]). The study was limited to relatively high advance ratios for which wakes interactions were minimal, mainly focusing on vibratory loads with a full aircraft (main rotor, fuselage, wing and propeller).

Recently, a renewed interest for rotor/propeller aerodynamic interactions raised, linked to either Airbus Helicopter X3 (Ref 6) and RACER (Ref 7, 8, 9 and 10) or Sikorsky X2 (Ref 11 and 12) and S97 ( Ref 13,14 and 15). In either cases, wake interaction issues are tackled in a manufacturer point of view. Experiments or numerical simulations are always performed on a relatively complex configuration (including fuselage, wings, tails, …), and focus not only on aerodynamics but also often on flight mechanics. This makes it difficult to clearly identify the ins and outs of the interactions phenomena. On a more theoretical point of view, it sounds important for us to be able to isolate the effect of each component on the others in order to be able to improve the efficiency and stability of the rotorcraft. One way to achieve this goal is to reproduce the phenomena on a simpler configuration.

The objective of this paper is to investigate the aerodynamics of rotor/propeller wake interactions on a rotorcraft similar to the X3 or the Racer demonstrators of Airbus Helicopters.

The configuration was simplified at its maximum up to the definition of an academic case to be able to clearly identify the effect of each component on the other, and to make it easy to reproduce either numerically or experimentally by anyone. This study will provide some insight on the effects of the propeller and main rotor interactions and also provides the results necessary to judge whether simple approaches like lifting line methods are sufficient to capture the phenomena or a full URANS (Unsteady Reynolds-Averaged Navier-Stokes Simulation) Computational Fluid Dynamics (CFD) computation is mandatory. Some work on the same rotor / propeller setup was already published in 2018 in Ref. [START_REF] Boisard | Aerodynamic investigation of rotor / propeller interactions on a fast rotorcraft[END_REF]. However, the present work is a synthesis using improved URANS CFD computations.

Studied configuration

The studied configuration is representative of the X3 prototype and uses the main rotor and propeller geometry from the ONERA interactional test rig tested in wind tunnel in mid-2021 (Fig. 1).

The main rotor is based on a Dauphin helicopter test rig which was already extensively used to study rotor / fuselage interactions more than a decade ago (Ref. 17 In order to isolate the aerodynamic effect from the main rotor and the propeller, in this numerical study only the main rotor and the propeller will be modeled. The main rotor is 4 bladed one with a diameter of 1.5m and a blade root cutoff at 27% radius. The rotor shaft is tilted 4° forward (nose down). The blades are rectangular with a constant OA209 airfoil, a chord of 0.05m and a linear twist of -12°/R. The rotor is not Mach-scaled. It rotates clockwise seen from above at 1272 RPM and its tip speed is 100m/s. However, this is not an issue since the main goal here is to study wake interactions at low advance ratios where compressible effects are not so important.

The propeller was chosen in order to be consistent in terms of diameter, thrust and tip speed with the main rotor compared to an actual rotorcraft of this type (Airbus Helicopter X3 or RACER). It is a four bladed, fixed pitch, puller propeller of 28cm diameter referenced as APC11x9 by APC Propellers. Details of the blade geometry were kindly provided by the manufacturer. The rotation speed of the propeller was set to 6 times the main rotor RPM in order to be able to have a periodic setup in the computations to ease the postprocessing and analysis of the results. For this study the propeller was set 0.14m (one propeller radius) ahead of the rotor center, on the rotor advancing side (0.375m from the rotor center, i.e. mid span of the main rotor blade) and 0.28m (one propeller diameter) below the rotor head. This positioning is approximately what was used on the X3 helicopter from Airbus Helicopters.

Concerning the flight conditions, a target value of 𝑍 ̅ = 14.5 (equivalent to C T /σ=0.0725) was chosen for the main rotor. This corresponds to a medium thrust condition for which wake interactions are expected to be relatively important. The rotor trim values of the rotor pitch, flap and lead-lag angles, are obtained from a comprehensive analysis code (Table 1) and used throughout all the computations. Note that the trim conditions were obtained for each advance ratio on an isolated rotor and re-used for the installed configurations. The author acknowledge that it is not representative of an actual flying rotorcraft. However, this approach enables to isolate pure aerodynamic effect which are of interest for this study. Concerning the advance ratio, three different operating conditions are detailed in the present work: hovering condition (μ=0.00) for which the propeller is fully inside the main rotor wake, an advance ratio of 0.05 for which the propeller is partialy inside the propeller wake, and an advance ratio of 0.15 for which the propeller is outside the main rotor wake.

Numerical methodology

In this study, two different numerical methodologies are used. The first one is a fast response method based on a lifting line approach coupled with an unsteady free wake model. The second one is much more computationally expensive and relies on URANS CFD using elsA solver.

Unsteady Free Wake Method

Free wake computations are based on the PUMA (Potential Unsteady Methods for Aerodynamics) code, which has been developed at ONERA since 2013. It is built on a coupling between an aerodynamic module and a kinematic module. The aerodynamic module relies on lifting line method with a free wake model. The free wake model is based on Mudry theory (Ref.

19) which rigorously describes the unsteady evolution of a wake modelled by a potential discontinuity surface. The lifting line method relies on 2D airfoils characteristics through lookup tables. Concerning the kinematic module, it is based on a rigid multi-body system approach using a tree-like structure with links and articulations. PUMA is used at ONERA for various aerodynamic studies of fixed wings and rotating wings configurations. It has been successfully applied for helicopter rotors wake in interactions with obstacles as discussed in Ref. [START_REF] Gallas | Experimental and numerical investigation of the aerodynamic interactions between a hovering helicopter and surrounding obstacles[END_REF] and Ref.

21.

The airfoil data needed for the PUMA computations were computed using ONERA elsA CFD solver (Ref. [START_REF] Cambier | The Onera elsA CFD software: input from research and feedback from industry[END_REF]) for a constant Reynolds number over Mach number corresponding to the rotor scale.

While for isolated cases and installed case at advance ratio 0.15 convergence is easy to reach, installed cases for which the main rotor wake is directly interacting with the propeller blade are extremely unstable. Sometimes numerical parameters have to be tuned in order to avoid singularities and numerical issues. In hover, 14 rotor revolutions where computed and the overall loads were averaged over the last 5 rotor revolutions, while for other cases only 11 revolutions were computed with an averaging of the 3 last revolutions for the loads. Free wake methods are relatively fast responding methods. However, due to the difference in terms of rotational speed between the propeller and the rotor, the required computational time could still be of the order of a few hours.

elsA CFD solver

All the URANS CFD computations are performed using the ONERA elsA software (Ref.

22

). The computations are based on structured grids with overset approach.

The rotor and propeller blades grids are built using the Pointwise® software. The rotor blade surface grid counts 151 points per blade side in the chordwise direction and 231 points in the spanwise direction. The propeller blade surface grid counts 159 points per blade side in the chordwise direction and 171 points in the spanwise direction. Extension of the grids around the blade is approximately 0.5 to 1.0 blade chord for a total number of mesh points of roughly 3.9 million per propeller blade and 5.8 million for each rotor blade. To be fully consistent with the free wake computations, the fuselage was not taken into account.

The background mesh is a Cartesian grid automatically generated using an Octree approach.

The full grid counts 9 grid levels with a two cell size increase between each level. The background grid extends up to roughly 10 rotor diameters in the farfield. The mesh is refined in the vicinity of the blades and in the wakes up to a level of approximately 9% of the blade chord.

Depending on the test cases, the final meshes count from 300 million points to 440 million points.

Computational parameters used are based on ONERA best practices on such kind of configurations. The time scheme used is a 2 nd order implicit backward finite difference scheme solved by a Newton algorithm. In order to ensure good accuracy the number of Newton sub- While for the isolated rotor and propeller computations, the convergence criteria is easy to define (no significant variations of mean thrust between two revolutions) and can be reached in relatively few rotor revolutions, it is much more difficult for the interactional setup. The hover case even seems to never reach a periodic state due to the strong interactions involved. In hover, 15 rotor revolutions were computed, 9 for other advance ratio values and the loads were averaged over the last one (six propeller revolutions).

iterations

PostProcessing convention

In the following sections, the thrust and power will be defined as forces and moments with respect to the vertical axis for the rotor and the horizontal axis for the propeller. In-plane forces and moments, along with azimuthal blade positions will be defined with the convention given in

Numerical results

Fig. 3 summarizes the interactional effect on the rotor and propeller performance as a function of advance ratio. For both rotor and propeller, the variations of thrust and torque are expressed in percent of the nominal value obtained in isolated conditions. It clearly outlines the three different interactional conditions:

 Hover case: The propeller is fully immersed in the rotor wake, with no freestream velocity to push the rotor and propeller wake backward from the helicopter. It seems to induce large changes in torque and thrust on the propeller and only small effects on the main rotor. However, there is some large discrepancy between the two simulations.

 Low advance ratio case, µ=0.05: The propeller is partially immersed in the rotor wake, but both wakes are pushed away from the rotor due to the free stream velocity.

This condition is somewhat a transitional condition between hover and forward flight.

The effect on the main rotor seems larger than in the hover case and the propeller is affected in a very different way as described in the section below. But once again a large discrepancy is observed between the different numerical approaches.

propeller blades and minor wake interactions can be seen. It seems to induce a very small increase in propeller thrust with almost no change in the propeller power along with small effects on the main rotor. In the following sections a detailed analysis of the three different advance ratios (µ=0.15, hover and µ=0.05 ) will be performed.

Moderate advance ratio (μ =0.15)

Fig. 4 shows the time average and RMS of the velocity for both isolated rotor and installed configurations from the URANS computations. As it was stated before, the isolated computations clearly outline the fact that the main rotor wake is passing above the propeller position (in pink in the left figure). However, the flowfield around the propeller positions shows some decrease of velocities for an amount of eight to ten percent with a small vertical gradient.

Moreover, the direction of the flowfield is not purely axial, it has an angle of 4° with also some variations along the vertical and lateral axes. At last, the absolute value of the velocity and its directions is almost steady in time.

The installed configuration results confirm that wake interactions (right figure) only occur far from the main rotor and propeller planes. It also outlines the fact that the propeller is operating a suction on the flow which is accelerated in front of the propeller disc. On the opposite, between the main rotor plane and the propeller wake, the flow velocity is reduced compared to the isolated computation. However, the propeller inflow seems to remain constant in time. rotor even if there is no direct impact of its wake. Moreover, the propeller loads should become unsteady due to the almost steady but non axisymmetric inflow.

Effects on the main rotor

The effect of the interactions on the main rotor loads (C n M 2 ) as a function of blade azimuth is shown in Fig. 5 along with the position of the propeller disc (pink line). Spanwise load distribution in isolated and installed configuration is also detailed in Fig. 6 for different azimuth of interest (40°, 80°, 130°).

First thing to notice is that URANS (elsA) and free-wake (PUMA) are in very good agreement with each other in terms of installation effect. Free wake computation only overestimates the changes when tip or root vortices are involved, like on the centerline at the back of the rotor disc. Concerning the absolute values (Fig. 6), it is overestimating the loads, which is rather common for such low-fidelity approach. On the advancing side, two different areas can be identified. The first one, at the back of the propeller disc, is characterized by an increase of the main rotor loading ranging from 2% to 4% using elsA, and 2% to 8% using free wake model. In this region, there is some blocking effect, the propeller wake is slowing down the flow (as seen in Fig. 4). The velocity through the rotor disc is reduced producing a local increase of the angle of attack at the rotor blade section. The area of increase of loads extends all over the propeller wake path, up to the rear of the disc, due to the relatively high advance ratio. At 40° azimuth (Fig. 6-a), all the main rotor blade is encountering an increase of loads. At 80° azimuth (Fig. 6-b), the increase of loads only appear between 40% to 75% of the blade radius. The outer part of the blade, which is not above the propeller wake is actually featuring a small loss of loads due to a change in the BVI patterns.

The second area of interest on the advancing side is located in front of the propeller disc. In this region, the main rotor blade is encountering a loss of loads of roughly 4% in both computations. The propeller has a suction effect on the flowfield leading to an increase of the velocity going through the rotor plane which induces a decrease of angle of attack and therefore a loss of loads. The influence of the propeller suction is relatively large and not limited to the close vicinity of the propeller disc. In Fig. 6-c it can be seen that at 130° azimuth, the decrease of loads occurs over the whole blade radius. This area is also actually extending slightly behind the propeller disc, but this behavior is only due to the vicinity of a blade tip vortex. While these changes in loads are clearly non negligible, they are limited to a small part of the rotor disc, leading to only small changes in terms of time average rotor loads (Table 2). In URANS computation, the main rotor thrust is reduced by only 0.54% and the power is increased by 0.56%. Using the free-wake approach the effects on time averaged loads are also small: 0.05% on the thrust and 1.23% on the power. While both computations were leading to very similar local behavior, discrepancies on the time average loads are mainly due to the discrepancies observed in the capture of blade root vortices change in terms of strength and path.

The free-wake approach remains perfectly able to correctly capture the interaction effects at moderate advance ratio in a cost effective way. At last, this outlines the need for a precise analysis of the local loads. In such configuration, looking only at the integrated thrust and power would have concluded to no effects of the propeller on the main rotor which would have been misleading.

Effects on the propeller

Effect of the interactions on the propeller loads (C n M 2 ) as a function of blade azimuth is shown in Fig. 7. Spanwise load distribution in isolated and installed configuration is also detailed in Fig. 8 for different azimuth of interest (45°, 170°, and 315°).

Once again URANS and free-wake computations are in very good agreement with each other in terms of installation effects, even if the absolute values are overestimated using the lifting line approach. The spots of larges changes observed near the blade root for URANS computations in Overall, the upper part of the propeller disc, which is closer to the main rotor wake is featuring some increase of loads of the order of 10% over most of the blade radius (Fig. 8-c). The main rotor wake is reducing the inflow velocity near the propeller disc (Fig. 4) leading to a higher angle of attack at the blade section and higher loads. The slight downwash and sideslip produced by the main rotor wake explain the non-axisymmetric of the flowfield and the fact that the propeller blade going up (Fig. 8-c) is encountering a slightly larger increase than the blade which is going down (Fig. 8-a). When the blade is further away from the rotor wake (in the lower part of the propeller disc), it is almost out of its influence and there is very few changes in the propeller blade loads (Fig. 8-b). While the increase of loads is of the order of 10% on the upper part of the propeller disc, it is partly balanced by the lower part of the disc where there is almost no increase. This leads to an increase of the time averaged thrust of only 3.52% using the free-wake approach and 4.34% using URANS which goes along with an increase of power of respectively 1.49% and 1.96%. The non-axisymmetry of the propeller inflow leads to some asymmetry in the blade loads and therefore to in-plane forces and moments. While in-plane forces (Fy and Fz) remain very small, the moments are larger. Both computations agrees on a pitching moment (My) of roughly 6% to 8% of the propeller torque in installed conditions which is non negligible and has to be taken into account in the design of an actual rotorcraft.

Table 3. Installation effect on the propeller time averaged thrust and power, and in plane loads on the propeller in installed configuration at advance ratio 0.15.

Hover conditions (μ=0.00) Fig. 9 is showing the time average and RMS of the velocity for both isolated rotor and installed configurations from the URANS computations. As it was expected, in hover the propeller is fully immersed in the main rotor wake. It encounters an almost vertical flowfield with velocities up to 10 m.s -1 . In front of the propeller, the flow is slightly accelerated due to the propeller suction effect, however, this increase of velocity seems to be very limited in the vicinity of the main rotor disc. At the back of the propeller, the main rotor wake velocity is reduced due to its interaction with the propeller wake up to almost 1.5 propeller diameter downstream. Despite the important interactions that occur, the propeller inflow remains relatively steady. Larges unsteadiness is only observed in the propeller wake and at the edges of the main rotor wake, far from the propeller area.

Effects on the main rotor

The effect of the interactions on the main rotor loads (C n M 2 ) as a function of blade azimuth is shown in Fig. 10 along with the position of the propeller disc (pink line). While both URANS and free-wake computations shows similar patterns, the amount of changes is quite different between the two. The free-wake computation largely overestimated the interaction effects.

As it was the case for advance ratio 0.15, the propeller wake is producing some blocking effect leading to an increase of the main rotor loads over it, up to 5% using URANS approach and 10% using free-wake. For azimuth between 30° to 60°, the change in the main rotor loads is very small since in this area the propeller wake is pushed down (Fig. 9) and its effect on the main rotor disc becomes negligible. The propeller is also producing a very small suction effect leading to a decrease of main rotor loads in front of it of less than 1% for free-wake and up to 3% using to the change in tip vortices strength and path due to the change in loads. At last, on the retreating side, there is almost no effect of the interaction, except near the blade root and tip, once again due to the change in vortices path and strength. The change in blade loads involves a very small part of the rotor disc. Therefore, as it is shown in Table 4, the changes in time average loads are quite small. Both computation states that these changes are below 1% Table 4. Installation effect on the main rotor time averaged thrust and power in hover.

Thrust 1 [%] Power 1 [%]
PUMA (Free-Wake) -0.68%% 0.62% elsA (URANS) 0.04% 0.34%

1 Time average over one rotor revolution (six propeller revolutions) for elsA, five rotor revolution for PUMA downwash and is not a function of the main rotor blade passage. On Fig. 11, one can notice that there is an important increase on the URANS computation (less visible on the lifting line computation) at the tip of the blade from azimuth 270° up to azimuth 330° and also at 80% radius from azimuth 300° up to azimuth 60°. As it is shown in Fig. 13, in hover the propeller blade tip vortices are pushed downward by the main rotor wake leading to strong blade vortex interactions in the upper part of the propeller disc. The vortex encountering shows up on the blade spanwise load distributions as two peaks, which are moving inboard as the blade is rotating. This BVI phenomenon may produce strong noise radiations in hover conditions. Table 5 summarizes the change in time averaged thrust and power of the propeller due to the interactions. It also gives the amount of in-plane forces and moments in the installed configuration with respect to the axial force and moment. It can be seen that the increase of thrust on one side of the propeller disc is not balanced by the decrease of thrust on the other side.

The resulting time averaged thrust is actually, increased by 10% in the URANS computation, while the power remains almost unchanged. Using lifting line approach, the gain of thrust is of 2% only and the power is largely increased by 12%. This is because in the lifting line methodology the BVI is not correctly captured. While the blade tip vortex may be stronger, its interactions with the blade lead to lower thrust and higher power due to the use of 2D airfoil tables, which assumed that the blade is in stall conditions, which is not truly the case due to 3D effects and weaker tip vortices in the URANS. However, both URANS and free-wake method agree very well on the in-plane forces and moments. Due to the non-symmetrical loads between the right and left part of the disc, there is a resulting vertical force of about 7% to 8% of the thrust. Effect of the uneven loading is even much larger on the moments since the pitching moment is about 20% of the torque and the yawing moment reaches 70% of the torque.

Table 5. Installation effect on the propeller time averaged thrust and power, and in-plane loads on the propeller in installed configuration in hover.

Thrust 1 [%] Fy 2 [%] Fz 2 [%] Power 1 [%] My 3 [%] Mz 3 [%]
PUMA (Fraa-Wake)

Low advance ratio (μ =0.05)

The last case investigated in this study is for advance ratio 0.05. As seen in Fig. 14, this is a transient condition since the propeller disc is only partly inside the main rotor wake. On the isolated rotor results, the propeller position is shown in pink along with a contour line (in green)

showing where the local axial velocity is equal to the freestream one. This line can be interpreted as the edge of the main rotor wake. It outlines the fact that the upper part of the propeller disc is ingesting the main rotor wake which has a velocity 20% higher than the freestream one and impinges the propeller at an angle of roughly 45° with small temporal unsteadiness. On the opposite, the lower part of the propeller is undergoing a constant horizontal flowfield at the freestream velocity with no time variations. As it was already the case in the two other cases, the propeller suction leads to an acceleration of the flow through the rotor upstream of its location.

The velocity through the rotor disc is at the contrary reduced above the propeller wake. There is a sharpening of the loads due to the interaction and a slight increase of loads in the inboard sections (Fig. 16-c). Table 6 summarizes the installation effect on the main rotor time averaged loads. In the current condition, there is no loss of loads in front of the propeller disc to compensate the gain above the propeller wake. Therefore, the overall main rotor thrust and power are increased.

However, this increase remains relatively low (1%) in the URANS computation. Due to the overestimation of the increase of loads in the BVI area in the free-wake computation those increases are larger and reaches 2% on the thrust and 3.6% on the power.

Effects on the propeller

Interaction effect on the propeller loads (C n M 2 ) as a function of blade azimuth is shown in Fig. 17. Spanwise load distribution in isolated and installed configuration is also detailed in Fig. 18 for different azimuth of interest (315°, 45°, 150° and 240°). While for other cases both computations were giving similar trends, at advance ratio 0.05, discrepancies are larger. Using URANS computation there is an oscillation between large increase and large decrease of loads, while from free-wake computation the load changes are very smooth. For the part of the propeller disc inside the main rotor wake, trends are relatively clear. There is an increase of loads when the blade is going up with some interaction with its own tip vortices near the tip (Fig. 18-a). At 315° azimuth using free-wake the gain of loads is only located on the outer part of the blade while in URANS, the blade root load is also increased. It should be due to the main rotor wake, which seems to impinge the propeller on a different location. As seen in Fig. 17, in free-wake approach the blade root is outside of the main rotor wake, while using URANS it is inside. This outlines the importance of correctly capturing the main rotor wake spatial position in order to accurately capture the effect on the propeller. As it was the case in hover condition, when the blade is going down in the main rotor wake, there is a decrease of the loads over the whole span (Fig. 18-b). In this area, the propeller blade behavior is dominated by the main rotor wake downwash. Out of the main rotor wake, free-wake computation shows a smooth decrease of the loads over the whole blade of the order of 10%. However, in the URANS computation, things are more chaotic. In Fig. 18-c, it can be seen that at 150° azimuth, the loads are decreasing on the inboard part of the blade, as in free-wake computations, but there is an increase near the tip which is suffering from blade vortex interactions. At azimuth 240° (Fig. 18-d) gain and loss of loads are spread over the blade span. A large part of the changes in URANS computation on the propeller loads out of the main rotor wake seems to be due to the load oscillations along the blade which are already present in the isolated computation. The APC propeller design is based on airfoils similar to Clark Y ones, which have some important camber leading to a production of lift mainly from the recirculation of the flow near the trailing edge. An axial velocity of 5 m.s -1 seems to be critical for this propeller, with some important instabilities. Even the isolated computation is featuring some oscillations of the load along the span which should not be the case with uniform flowfield. Moreover, instabilities from flow recirculation are highly sensitive to the turbulence model used in the computation. Induced velocity from the main rotor wake tends to move these oscillations along the span, leading to the spot of load changes for the part of the disc outside of the main rotor wake in URANS computation. This kind of behavior is not seen in the free-wake computation since it relies on steady airfoil data.

Table 7. Installation effect on the propeller time averaged thrust and power, and in plane loads on the propeller in installed configuration.

Table 7 summarizes the installation effects on the main propeller time averaged loads. As it could be expected from what was seen on the spanwise loads, there is more discrepancies between the URANS and free-wake computations on the time averaged loads. While both of them are expecting a loss of power, there is an opposite trends on the thrust. URANS computation shows a gain of 1.64% while free-wake approach is showing a loss of 5.4%, mainly due to the differences from the region of the propeller out of the main rotor wake. Concerning the in-plane loads, even if the free-wake computation is overestimating them, both numerical approaches agrees on the trends. There are some important vertical loads and yawing moments due to the asymmetry of the loads between the blade up and down side of the propeller disc.

CONCLUSIONS

In this study, rotor / propeller wake interactions were analyzed for a given propeller position at different advance ratios and using two different levels of physical fidelity.

All the computations agree on the fact that for all advance ratios the main rotor is only slightly affected by the propeller in terms of time-averaged loads. However, when the blade is moving over the propeller wake, sectional loads increase due to the blocking effect of the propeller wake. On the part of the disc in front of the propeller, the loads are lowered due to the suction effect of the propeller in hover, and to a lower extent for moderate advance ratio. Effects on the retreating side (the propeller is located on the advancing side) result only from differences in the root and tip vortices strengths and path. This trend is amplified at advance ratio 0.05 compared to the hover case or moderate advance ratio 0.15.

The aerodynamic behavior of the propeller is much more complex and depends on the advance ratio. In hover conditions there is some extreme fluctuations of loads (up to 50%) in an almost sinusoidal way, not depending on the main rotor blade passage, along with important inplane forces and moments. The propeller is also encountering some blade vortex interactions on the upper part of the disc which could be of importance in noise signature.

At moderate advance ratio (0.15), the propeller encounters a smaller induced effect from the main rotor wake with increase of loads below 5% along with a asymmetry over the disc producing some more acceptable in-plane loads. It is expected that as the advance ratio is increasing, the effect will be reduced.

Advance ratio 0.05, is a transition between other cases, leading to an effect similar to hover for the part of the propeller inside the wake and more similar to higher advance ratio when the blade is out of the wake.

Regarding the two numerical methods used, the free-wake approach is perfectly able to capture the aerodynamics of the interaction at moderate advance ratio. For hover and low advance ratio, it also gives very good results concerning the main rotor, even if it tends to overestimate some phenomena. Regarding the propeller, it only gives some trends at a much lower computational cost than URANS computations, but the full CFD computation remains necessary to capture all the details of the aerodynamics.

At last, it should be kept in mind that all the computations were performed at the prescribed trim from an isolated main rotor computation with a rigid blade assumption. On a real rotorcraft the blades are not rigid, the flap and lead-lag motion of the blade may be largely affected by the fluctuations of loads changing the interactions and also introducing some vibrations. Moreover, only one propeller was modeled. Introducing a second propeller on the retreating side will increase the complexity of the interactions. The different loads on both propellers would produce a change in yawing and maybe rolling moments, which require a re-trim of the full rotorcraft. At last no rotor head,fuselage or wings were used. Introducing the full rotorcraft will likely increase the complexity of the interactions and make it more difficult to isolate each component contribution to the interactions.

The author also acknowledges APC propellers for providing the geometrical description of the propeller blades.

  ). The propeller part is based on an off-the-shelf propeller designed for remotely controlled aircraft by APC Propellers (Ref. 18).

Fig. 1 .

 1 Fig. 1. ONERA interactional test rig.

  was set to 25 and a physical time step corresponding to an azimuthal angle of 0.1° on the main rotor was used throughout the whole computations. Due to the low velocities involved in these computations, a version of the 2 nd order AUSM+P scheme adapted to low Mach number flow (Ref. 23) was used. K-ω Kok (Ref. 24) model was used for the turbulence with Zheng limiter and SST correction. Computations were performed in the absolute velocity formulation using an absolute reference frame.

Fig. 2 WhenFig. 2 .

 22 Fig.2

Fig. 3 .

 3 Fig. 3. Interaction effect on rotor and propeller performances.

Fig. 4 .

 4 Fig. 4. Time average (top) and RMS (bottom) of the velocity for isolated (left) and installed

Fig. 5 .

 5 Fig. 5. Installation effect from URANS (left) and free-wake (right) computations on the main rotor blade loads (C n M 2 ) over one revolution. (Pink line: propeller disc position) at advance ratio

Fig. 6 .

 6 Fig. 6. Main rotor blade load comparison between isolated and installed configuration at azimuth

Fig. 7

 7 Fig.7are due to the fact that the blade section is very thick near the root, leading to some

Fig. 7 .

 7 Fig. 7. Installation effect from URANS (left) and free-wake (right) computations on the propeller blade loads (C n M 2 ) over one revolution at advance ratio 0.15.

Fig. 8 .

 8 Fig. 8. Propeller blade load comparison between isolated and installed configuration at azimuth

Fig. 9 .

 9 Fig. 9. Time average (top) and RMS (bottom) of the velocity for isolated (left) and installed

Fig. 10 .

 10 Fig. 10. Installation effect from URANS (left) and free-wake (right) computations on the main rotor blade loads (C n M 2 ) over one revolution. (pink line: propeller disc position) in hover.

Fig. 12 .

 12 Fig. 12. Propeller blade load comparison between isolated and installed configuration at azimuth

Fig. 13 .

 13 Fig. 13. Blade vortex interaction on the upper part of the propeller disc in hover. (left Q-

Fig. 14 .

 14 Fig. 14. Time average (top) and RMS (bottom) of the velocity for isolated (left, front and side

Fig. 16 .

 16 Fig. 16. Main rotor blade load comparison between isolated and installed configuration at

Fig. 17 .

 17 Fig. 17. Installation effect from URANS (left) and free-wake (right) computations on the propeller blade loads (C n M 2 ) over one revolution at advance ratio 0.05.

Fig. 18 .

 18 Fig. 18. Propeller blade load comparison between isolated and installed configuration at azimuth

Table 1 .

 1 Rotor trim as a function of advance ratio.

				Pitch			Flap			Lead-Lag
	µ	Shaft Angle
			θ 0	θ 1c	θ 1s	β 0	β 1c	β 1s	δ 0	δ 1c	δ 1s
	0.00	-4°	9.9°	-0.21°	3.77°	-2.93° 3.95° 0.00°	-4.85°	-0.05° -0.21°
	0.05	-4°	9.6°	1.20°	2.70°	-3.04° 3.68° 0.00°	-4.56°	0.03°	-0.21°
	0.15	-4°	7.34°	2.17°	1.64°	-2.76° 3.74° 0.00°	-2.60°	0.10°	-0.18°

Table 2 .

 2 Installation effect on the main rotor time averaged thrust and power at advance ratio 0.15.

		Thrust	1 [%]	Power	1 [%]
	PUMA (Free-Wake)	0.05%	1.23%
	elsA (URANS)	-0.54%	0.56%

1 Time average over one rotor revolution (six propeller revolutions) for elsA, 3 rotor revolutions for PUMA

Table 6 .

 6 Installation effect on the main rotor time averaged thrust and power at advance ratio 0.05.

		Thrust	1 [%]	Power	1 [%]
	PUMA (Free-	2.06%	3.62%
	Wake)
	elsA (URANS)	0.94%	1.00%
	1 Time average over one rotor revolution (six propeller revolutions) for
	elsA and three rotor revolution for PUMA

Time average installed value as a percent of the mean installed torque

Acknowledgments

Part of this work was granted access to the HPC resources of CINES under the allocation 2017-A0032A10264 made by GENCI.

Effects on the propeller

The effect of the interactions on the propeller loads (C n M 2 ) as a function of blade azimuth is shown in Fig. 11. Spanwise load distribution in isolated and installed configuration is also detailed in Fig. 12 for different azimuth of interest (90°, and 270°). As it could have been expected, due to the strong vertical flow produced by the main rotor, there is a clear asymmetry in the change in loads between the blade going up (from 180° to 360° azimuth) and the blade going down (0° to 180° azimuth). Both numerical methodologies are predicting an increase of loads when the blade is going up of an amount of roughly 50% over the whole blade span (Fig. 12-a). This is because the main rotor downwash is adding to the propeller rotational velocity leading to an increase of the local angle of attack and increase of dynamic pressure. On the other side, when the blade is going down the main rotor downwash is lowering the velocity seen by the blade section leading to a decrease of local angle of attack and dynamic pressure and a reduction of the loads in almost the same amount (Fig. 12-b). It should be mentioned that this sinusoidal variation of propeller loads is only due to the main rotor

Effects on the main rotor

The effect of the interactions on the main rotor loads (C n M 2 ) as a function of blade azimuth is shown in Fig. 15 along with the position of the propeller disc (pink line). Details of the spanwise loads at different azimuth of interest are also shown in Fig. 16. Even if large changes are seen near the blade vortex interactions path, with some overestimation from the lifting line computation, one can still observe the same effect as in the two previous cases above the propeller wake. Both computations show an increase of the main rotor loads from azimuth 30° to 100° (Fig. 16-a, Fig. 16-b). At 80° azimuth the tip of the rotor blade is encountering a loss of loads due to the blade vortex interactions which is different in isolated and installed case (Fig. 16-b). In front of the propeller disc, the behavior is different than in the previous cases. Only half of the propeller is ingesting the main rotor wake and it is not sufficient to produce enough acceleration in the main rotor disc to decrease its loading. In this area, the interaction effect seems to be dominated by the BVI that occurs near 80% of the rotor