Performance analysis of variable speed tail rotors with Gurney flaps

Chen DONG,Dong HAN,Lei YU

National Key Laboratory of Rotorcraft Aeromechanics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

KEYWORDS Tail rotor;Variable speed;Performance;Gurney flap;Tail rotor thrust;Flap height;High speed flight

Abstract Gurney Flaps(GFs)are used for improving the performance of variable speed tail rotors.A validated analytical helicopter model able to predict the main and tail rotor power is utilized.The fixed height GF has substantially small influence on the tail rotor power in hover and low to medium speed forward flight,and can obtain significant power reduction in high speed flight.This ability can be enhanced by decreasing the tail rotor speed.With the deployment of GF,the collective pitch of the tail rotor decreases,and the maximum tail rotor thrust increases.The GF can compensate the reduction of the maximum thrust by the decrease in the tail rotor speed.The GF with a height of 5%of the chord length can almost remedy 50%of the thrust reduction introduced by decreasing 10%of the tail rotor speed.With the increase of GF height,the maximum thrust generated by the tail rotor increases.The GF with larger height can cause the increase in the tail rotor power in hover and low to medium speed flight.The retractable GF can obtain more power savings than the fixed height GF.However,the benefit is substantially small even in high speed flight.Considering the side effects introduced by the active GF,the fixed height GF may be more preferable.The mechanism for the retractable GF to generate more tail rotor thrust is to increase the lift in advancing side due to the higher dynamic pressure.

1.Introduction

Varying main rotor speed has been well studied to reduce helicopter power required and improve fight performance in hover and forward flight.1–6Changing the output shaft speed of the engine is one of the primary and effective means of changing the main rotor speed,which cannot avoid the simultaneous change of the tail rotor speed.The reduction of the tail rotor speed can reduce not only the tail rotor power,7but also the tail rotor noise.8However,the decrease in the tail rotor speed reduces the maximum tail rotor thrust due to the decrease in the dynamic pressure,which can deteriorate the capability of the tail rotor in balancing the main rotor torque and implementing the yaw control.This can adversely limit the application of variable speed tail rotors.In high speed flight,decreasing the tail rotor speed can even increase the tail rotor power required.7It is necessary to compensate the simultaneous increase in the power and decrease in the maximum thrust to maintain acceptable fuel consumption and handling quality.

The Gurney Flap(GF)is a lift enhancement device attached to the trailing edge perpendicular to the chord line on the pressure side of an airfoil,9invented by a race car driver named Dan Gurney in 1960s.The GF attracts lots of attention due to not only its efficiency and simplicity,but also its lower power consumption10.The GF has been extensively explored to improve the helicopter main rotor performance.11–16These investigations verified the effectiveness,especially at high thrust,high speed and/or high altitude.The retractable GF can change the height of GF following the variation of the aerodynamic environment,which can provide better performance improvement.Kinzel utilized deployable GFs to enhance rotorcraft performance.17In forward flight,the GFs were usually deployed in retreating side and retracted in advancing side.The maximum flight speed could be increased by 20%and rotor thrust by 6%.The computational investigation of the effect of GF on rotors in forward flight indicated that a 2/rev dynamic deployable GF resulted in a slight decrease in rotor power.18Less attention is paid to the application of GFs in the performance improvement of tail rotors.Baslamisli et al.applied a GF in a tail rotor for the increase in the tail rotor thrust.19The GF with a fixed height of 5%of the chord length was selected for the consideration of safety in operation and easiness in production.This height could decrease the lift to drag ratio,but it was effective to increase the thrust generated by the tail rotor.The previous research has not explored the potential of the GF in improving the performance of variable speed tail rotors,especially the GF with variable height.

In this work,the fixed height and retractable GFs are used to decrease the power and increase the maximum thrust of variable speed tail rotors.The mechanism of the GF enhancing tail rotor performance is explored.Parametric studies are utilized to determine the dominant parameters in power savings,maximum thrust enhancement,and performance improvement.To evaluate and compare the power savings and thrust increase by the GF,a helicopter model able to predict the main and tail rotor power is used,which includes a rigid blade model,look-up aerofoil aerodynamics,the Pitt-Peters in flow model,a rigid fuselage model,a tail rotor model and a propulsive trim method.The tail rotor power and corresponding thrust for the fixed and retractable GFs are analyzed to investigate the benefit of GF in improving the performance of variable speed tail rotors.

2.Modeling

A helicopter power prediction model is used in this work.The main rotor blade model is based on a rigid beam with a hinge offset and a hinge spring,which are used to match the fundamental flap-wise blade frequency.Look-up table aerofoil aerodynamics is used to calculate the lift and drag coefficients of blade elements according to the local resultant Mach number and angle of attack.The induced velocity over the rotor disk is predicted by the Pitt-Peters in flow model,which captures the first harmonic azimuthal variation of induced velocity.The hub forces and moments of the main rotor are derived from the resultant root forces and moments of rotor blades by the blade element theory.The fuselage is treated as a rigid body with aerodynamic forces and moments.These forces and moments acting on the main rotor,tail rotor and fuselage contribute to the equilibrium equations of the helicopter,which are solved to get the trimmed pitch controls of main and tail rotors,and attitude angles of fuselage.The tail rotor thrust countering the main rotor torque is determined by the torque divided by the distance from the hub center of the tail rotor to the main rotor shaft.The tail rotor thrust and power are obtained by performing a numerical integration over the blade elements along the radial and azimuthal directions with the uniform in flow model.This model has been validated by comparing the UH-60A flight test data with the results generated by the present model,and used to analyze the helicopter performance improvement by dynamic blade twist and variable tail rotor speeds.7,20For the performance analysis,usually just considering the aerodynamic drag in the fuselage model is enough for acceptable helicopter performance prediction.21The flowchart of the performance prediction is shown in Fig.1.

Fig.1 Flowchart of performance prediction.

Fig.2 Configuration of an airfoil with a GF.

The parameters of an airfoil with a GF are shown in Fig.2.In the figure,α is the angle of attack,V∞is the far field flow velocity,d is the height of GF,and c is the chord length.For a retractable GF,the mounting angle β is 90°,and the height is given as a prescribed value.In the following analysis,the maximum ratio of d/c is limited to be less than 5.0%,and the GF extends from 70%to 90%of the rotor radius.The method in Ref.11is utilized to calculate the aerodynamic characteristics of NACA0012 airfoil with a GF.The comparison of the lift coefficients between the test data in Ref.22and the results generated by the C81 airfoil table is shown in Fig.3,which shows that the prediction is generally in good agreement with the test data.

The power reduction ratio is defined to measure the benefit in saving tail rotor power as

where P is the tail rotor power to be compared with,and Pbis the baseline tail rotor power.The baseline power is defined as the power at sea level and 100%Ω(nominal tail rotor speed)without any GF.In the following analysis,the baseline helicopter weight is 8322.3 kg,and the corresponding weight coefficient is 0.0065.

The parameters of the baseline main and tail rotors similar to the UH-60A helicopter are from Refs.23–26For the performance analysis,only the aerodynamic drag is considered in the fuselage model.The airfoil of the tail rotor is changed to NACA0012 for better calculating the aerodynamic characteristics of the tail rotor with a GF.The distance from the hub center of tail rotor to the rotor shaft is 9.93 m.The vertical distance from the mass center of the helicopter to the rotor hub is 1.78 m.

Fig.3 Comparison between test data and prediction.

3.Fixed height GF

Figs.4 and 5 show the tail rotor power and corresponding power reduction with and without the fixed height GF(H)for different rotor speeds(V).The height of the GF is 2%of the chord length(2%c).In hover,decreasing the tail rotor speed has substantially small influence on the tail rotor power.Decreasing the speed by 10%or 20%can reduce the power by 2.1%or 3.1%.With the GF,the power reduction changes to 2.3%or 3.6%.The increment by the GF is 0.2%or 0.5%,which indicates that the speed reduction dominates the power savings,and the GF has a second effect.At a speed of 150 km/h,decreasing the tail rotor speed can significantly reduce the power,and decreasing the speed by 20%can reduce the power by 25.1%.Since the rotor speed has stronger effect on the rotor profile power,decreasing the tail rotor speed in this flight speed can obtain more power savings.With the GF,the difference is not distinguishable in hover and low to medium speed forward flight.At a high speed of 290 km/h,the power reduction by the GF for decreasing the speed by 0%,10%or 20%is 7.2%,9.7%or 21.5%,respectively.The GF shows stronger ability in power saving in high speed flight,especially at lower rotor speeds,since the GF is a lift enhancement device with better lift to drag ratio in high lift.For the performance improvement,decreasing tail rotor speed is more suitable for medium speed flight,and the deployment of GF is more suitable for high speed flight.

Fig.4 Tail rotor power for different rotor speeds and heights of GF.

Fig.5 Power reduction for different rotor speeds and heights of GF.

Fig.6 shows the collective pitch of the tail rotor with forward speed.Decreasing the tail rotor speed increases the collective pitch.With the 2%c height GF,the collective pitch decreases.The change of the collective pitch by the rotor speed is generally larger than that by the GF.Fig.7 shows the distribution of angle of attack(AoA)for different rotor speeds with and without the 2%c height GF at a speed of 300 km/h.The AoA in advancing side is distinctly larger than that in retreating side,which is essentially different from that of helicopter main rotors.Since tail rotors do not employ cyclic pitch controls and the balance of lateral moments is not available,the blades in advancing side generate much more thrust than the ones in retreating side.The GF decreases the AoA due to the increase in the lift coefficient of the airfoil with the GF.The speed reduction causes the increase in the AoA due to the decrease in the dynamic pressure.The GF can counteract the increase in the AoA due to the reduction of the tail rotor speed.

Fig.6 Collective pitch for different rotor speeds and heights of GF.

Fig.8 shows the thrust required to balance the main rotor torque,and the maximum thrust for different tail rotor speeds with and without GF.The thrust required is very large in hover,decreases with increasing forward speed,and then increases in medium to high speed flight.It is due to the change of the main rotor power with forward speed.The maximum thrust decreases with decreasing tail rotor speed due to the decrease in the dynamic pressure.At a speed of 300 km/h,reducing the speed by 20%almost makes it difficult to implement the yaw control.In high speed flight,it is necessary to compensate the decrease in the maximum thrust by the reduction of tail rotor speed.With the GF,the maximum thrust increases due to the increase in the lift coefficient,and the increase in the amplitude is moderate.The 2%c height GF has not the potential in remedying the decrease in the thrust caused by the speed reduction.

Fig.9 shows the power reduction for the GF with different heights at 90%Ω.In hover and low to medium forward speed flight,it is obvious that the speed reduction dominates the power saving.The power reduction decreases with increasing GF height in hover and low to medium speed forward flight,and then increases in high speed flight.It is because that the GF decreases the lift to drag ratio of the airfoil in low to medium lift but increases it in high lift.9At a speed of 150 km/h,the power reduces by 13.9%with the 10%speed reduction.With the 5%c height GF,the value changes to 11.8%.The 5%c height GF increases the power by 2.1%.At a speed of 290 km/h,the 2%c and 5%c height GFs can reduce the power by 9.7%and 13.5%,respectively.In high speed flight,larger height GF is preferred,since it can obtain more power saving than the smaller one.

Fig.10 shows the available maximum thrust for different GF heights and rotor speeds.It is obvious that decreasing the tail rotor speed by 10%can significantly reduce the maximum thrust,which can significantly deteriorate the yaw control ability.The maximum thrust increases with the GF height.The 5%c GF height can remedy almost 50%of the decrease in the thrust introduced by the 10%speed reduction.This effect can be enhanced by increasing the GF height.However,a too high GF is not preferred for the consideration of the performance penalties in hover and medium speed flight.

4.Retractable GF

The previous analysis is based on fixed height GF,which is simple and easy for production and maintenance.However,the required optimal height of the GF corresponding to the optimal tail rotor performance changes with the variation of helicopter flight states(speed,altitude,or weight).The active GF emerges as a better candidate for tail rotor performance improvement.In the following analysis,the height of the retractable GF is prescribed as

where A is the average GF height,n is the harmonic number,and φ is the phase of the harmonic input.

Fig.11 shows the effect of the phase on the tail rotor power for different harmonic inputs with an average 2%c height GF at a speed of 250 km/h.With the increase of the harmonic number,the variation of the amplitude of the power decreases.The 1/rev input can achieve much more power reduction than the other harmonics.The 3/rev and 4/rev inputs have little effect on the tail rotor power.Lower harmonic input is preferred for power savings.When the phase of the 1/rev input shifts to 0°,it can obtain the maximum power reduction.For the 2/rev input,the corresponding phase is 270°.

Fig.7 Distribution of angle of attack for different rotor speeds with and without GF.

Fig.8 Maximum thrust for different rotor speeds and heights of GF.

Fig.12 shows the GF height with the azimuth.For the 1/rev input,the GF has the maximum height in advancing side and the minimum value in retreating side.For the 2/rev input,the GF has the maximum value at both advancing and retreating sides.To generate more thrust,the tail rotor sufficiently takes advantage of the higher dynamic pressure in advancing side.The mechanism for the GF to improve the tail rotor performance is completely different from that to improve the main rotor performance.17

Fig.9 Power reduction for GF with different heights at a speed of 90%.

Fig.13 shows the comparison of the power reduction by the fixed height and 1/rev retractable GF.The average height of both is 2%c,and the 1/rev GF is shifted to the phase of 0°.Generally,the difference is substantially small except in very high speed flight.At the rotor speeds of 100%Ω,90%Ω and 80%Ω and a forward speed of 300 km/h,the differences of the power reduction between the fixed height GF and the retractable GF are 1.9%,2.8%and 9.2%.It is obvious that the retractable GF does not exhibit significant advantages over the fixed height GF.However,the retractable GF has to consume power to actuate the GF.The actuation system and the power supply device add extra weight to the rotor system.The blade structure has to be strengthened to bear more loads.

Fig.10 Maximum thrust for different GF heights and rotor speeds.

Fig.11 Effect of phase on power for different harmonic input(250 km/h,100%,2%c).

Fig.12 GF height with azimuth for 1/rev and 2/rev input.

Fig.13 Comparison of power reduction by fixed height and 1/rev retractable GF.

These sub-systems increase the complexity of the rotor system,and the system reliability decreases.Considering these side effects introduced by the active GF,the fixed height GF may be more feasible and preferable.This is similar as the technology of variable speed rotor,and the change of rotor speed can also introduce problems.27–29When we apply a new technology,it is better to balance the positive and side effects.

5.Conclusions

A validated helicopter model able to predict the main and tail rotor power was used to explore the performance improvement of variable speed tail rotors by GFs.The analyses yielded the following conclusions:

(1)The GF has substantially small influence on the tail rotor power in hover and low to medium speed forward flight.In high speed flight,it can significantly decrease the tail rotor power,since the GF is a lift enhancement device with better lift to drag ratio in high lift.This benefit increases with the reduction of the tail rotor speed.

(2)The collective pitch of the tail rotor decreases by the deployment of GF,and the maximum tail rotor thrust increases,since the blade section with the GF can generate more lift.

(3)In high speed flight,a larger height GF is preferred,and it can obtain much more power saving than a smaller one.At a speed of 290 km/h,the 2%c and 5%c height GFs can further reduce the power at 90%Ω by 9.7%and 13.5%,respectively.

(4)The GF can compensate the decrease in the maximum thrust of the tail rotor due to the increase in the lift generated by the blade section with the GF.The 5%c height GF can almost remedy 50%of the thrust reduction introduced by decreasing 10%of the tail rotor speed.

(5)The retractable GF can obtain more power saving than the fixed height GF,since it can optimize the GF height following the variation of the aerodynamic environment.However,the benefit is substantially small even in high speed flight.Considering the side effects caused by the retractable GF,the fixed height GF may be more feasible and preferable.

(6)The retractable GF takes advantage of the higher dynamic pressure in advancing side to generate more tail rotor thrust.This mechanism for the active GF to improve the tail rotor performance is completely different from that to improve the main rotor performance.

Acknowledgements

This work was supported from the National Natural Science Foundation of China(No.11472129),the Science and Technology on Rotorcraft Aeromechanics Laboratory Foundation of China(No.6142220050416220002),the Foundation of Graduate Innovation Center in NUAA of China.(No.KFJJ20170102),the Fundamental Research Funds for the Central Universities of China,and a project funded by the Priority Academic Program Development of Jiangsu Higher Educational Institution of China.