Aerodynamic characteristics of rigid coaxial rotor by wind tunnel test and numerical calculation

Jinghui DENG,Feng FAN,Ping'an LIU,Shuilin HUANG,Yongfeng LIN

National Key Laboratory of Science and Technology on Rotorcraft Aeromechanics,China Helicopter Research and Development Institute,Jingdezhen 333001,China

KEYWORDS Aerodynamic characteristics;High-speed helicopter;Lateral lift offset;Rigid coaxial rotor;Wind tunnel test

Abstract Focusing on aerodynamic characteristics of rigid coaxial rotor of a high-speed helicopter in hover and forward flight,a wind tunnel test is conducted in the 8 m×6 m low-speed straightflow wind tunnel of China Aerodynamics Research and Development Center.In the experiment,a 4 m diameter composite model rigid coaxial rotor is designed and manufactured,and firstorder flapping frequency ratio of the blade is 1.796 to ensure sufficient stiffness at the blade root.Rotor aerodynamic performance is measured under hovering and high advance ratio conditions.Also,the numerical method is used to calculate aerodynamic characteristics in typical states of the rigid coaxial rotor for analysis purpose.The rotor lift-drag ratio and lateral lift offset in the experiment are emphatically analyzed for the rigid coaxial rotor.The results indicate that in forward flight condition,the rotor lift-drag ratio first increases and then decreases with the increment of advance ratio and lift offset.When advance ratio remains constant,with the increment of lift offset,the lift-drag ratio of rigid coaxial rotor first increases and then decreases.

1.Introduction

The compound helicopter with rigid coaxial rotor is one of main configurations in the development of high-speed helicopters,and as the most important feature of the helicopter,the Advanced Blade Concept(ABC)rotor1is adopted.The advancing side of the rotor produces most of lift,while less for the retreating side of the rotor.Dynamic pressure is larger for the advancing side in forward flight,and the limitation of dynamic stall for the retreating side can be overcome.In this way,the maximum forward speed of helicopter will be increased.This type of rotor is characterized by its compactsized,good performance of aerodynamic characteristics,maneuverability and controllability,and performs well under both hovering and forward flight conditions.However,compared to a conventional single rotor,the coaxial rotor configuration suffers severe vortex-vortex interaction and bladevortex interaction due to the small separation between upper and lower rotor.Furthermore,lift offset is the unique aerodynamic phenomenon of rigid coaxial rotor.2In view of this,comprehensive understanding of complex aerodynamic characteristics for this rotor configuration is of great significance.

Harrington3conducted an aerodynamic experiment about conventional coaxial rotor in hovering state in early years.He compared the lift,torque and hovering efficiency between coaxial and single rotors.The Sikorsky Aircraft Corporation4-6developed the first helicopter with rigid coaxial rotor named XH-59A in the 1970s,and carried out wind tunnel tests to study the properties such as overall performance of rotor,hub drag and noise characteristics.McAlister et al.7conducted experimental study of a model coaxial rotor in NASA Ames Research Center about the influence of spacing parameter on coaxial rotor aerodynamic performance.Lim et al.8studied the relationship of aerodynamic performance between full size and scaled coaxial rotor model.Coleman summarized the early research results about aerodynamic performance of conventional coaxial rotor.9 In addition to experiment,numerical calculation is also an important way to research the aerodynamic performance.Wayne10used the software CAMARD to investigate the influence of lift offset on rotor aerodynamic performance,and the results indicated that lift offset could reduce induced power consumption in high-speed forward flight.Bagai11investigated the effect of design parameters such as chord length,twist angle,and airfoil distribution on the aerodynamic performance for the X2TM technology demonstrator main rotor blade.Brown and Kim12established an analytical method for the flow field of the coaxial rotor configuration based on viscous vortex transport model,and carried out the research about rotor aerodynamics and noise.In recent years,CFD methods derived from Navier-Stokes equations have been widely used in the studies of aerodynamic interactions of coaxial rotor.CFD methods can accurately describe the complex shape of rotor blade.Based on sliding and overset grid,Lakshminarayan et al.13conducted a research on aerodynamic interference characteristics for conventional coaxial rotor in hovering state and described the unsteady mechanism of vortex-vortex interaction as well as blade-vortex interaction.Ye and Xu14used self-adaptive grid technique to study the induced velocity field and spatial variation characteristics of wake vortices of conventional coaxial rotor.In order to address the problem of low computational efficiency which comes from the inherent property of moving overset grid method,Xu and Ye15established a numerical method for coaxial rotor flow field based on Euler equations to study the flow characteristics and overall aerodynamic performance for coaxial-rotor helicopter in hover.

Although such high-resolution numerical analysis methods as CFD develop fast,it is still a challenge to calculate the aerodynamic performance of rigid coaxial rotor accurately.Experiment is still an important way to investigate the aerodynamics of this rigid coaxial rotor.Recently,Sikorsky conducts wind tunnel tests for S-97 high-speed helicopter.16However,there are few published literatures of rigid coaxial rotor experiments about aerodynamic interference in hover and lift offset in forward flight.Reliable experimental data for numerical calculation models are also lacking.Given this,this paper conducts a wind tunnel test research for rigid coaxial rotor aiming at aerodynamic performance in hovering and forward flight state.Moreover,numerical methods are also used to compute typical states of rigid coaxial rotor flow field.Aerodynamic interference characteristics in hover are analyzed.Emphatically,the variations of rotor lift-drag ratio with parameters such as lateral lift offset and advance ratio in forward flight are investigated.

2.Test and numerical method

2.1.Wind tunnel and model rotor description

The experiment is conducted in an 8 m×6 m low-speed straight- flow wind tunnel at Chinese Aerodynamic Research and Development Center,and the maximum wind speed of the test section is 70 m/s.A new rigid coaxial rotor teststand is built for the experiment,rotational shaft of the upper rotor is wrapped in the lower one,and the two rotors rotate synchronously in opposite direction through gear system.Conventional control system is used for lower rotor,while for upper rotor,mast components are wrapped in the hub of upper rotor to mount a supporting platform for control system.Control mechanisms like electric actuator,swashplate,pitch link and so on are installed within the hub of upper rotor,so the upper rotor can be controlled within the hub.This construction can reduce the size of hubs,thus reducing the drag of hubs.In addition,shaft angle variation of test-stand is controlled through hydraulic actuator.Two six-component balances are used to measure aerodynamic force of upper and lower rotor,respectively.Fig.1 gives the picture of rigid coaxial rotor test-stand in the wind tunnel.

The rigid coaxial rotor model is of 4 m diameter and built by composite material.The first-order fl ap frequency ratio is 1.796 to ensure sufficient rigidity at the root of blade.The hub system is hingeless,and flanges are used to connect blades to it.The main parameters are shown in Table 1,R is the rotor radius.

2.2.Definition of main variable symbols

The Definitions of main variable symbols are shown in Table 2.The subscripts UR and LR represent upper rotor and lower rotor,respectively.θ1sURand θ1sLRare positive if the rotor pitch moment is nose-down,and θ1cURand θ1cLRare positive if the rotor roll moment is toward the advancing side.The lateral lift offset is subject to upper rotor,and is positive if it is in the advancing side.

Thrust coefficient CT,power coefficient Qcoand hovering efficiency Mcoare de fined as follows:

Fig.1 Picture of rigid coaxial rotor test-stand in wind tunnel.

Table 1 Main parameters of model rotor.

Table 2 Definition of main variable symbols.

where ρ is air density,Ω is rotational speed,R is rotor blade radius,TURand TLRare the thrust of upper and lower rotor,respectively,and QURand QLRrepresent upper and lower rotor power,respectively.

Rotor lift-drag ratio L/D and Lift Offset(LOS)are de fined by

where Fzand Fxare rotor aerodynamic forces in wind axes,Fxis aerodynamic drag,and is positive if it is backward,Fzis perpendicular to direction of wind,and is positive if it is upward,P is rotor power,and V represents wind speed,MxURand FzURrepresent roll moment and vertical force,respectively.

2.3.Numerical calculation method and validation

To analyze the aerodynamic characteristics of rigid coaxial rotor in detail,a numerical calculation method is established based on CFD technique.The rotor flow field is simulated by solving Reynolds-averaged Navier-Stokes equations,17and the governing equations are as follows:

The expressions of conservation variables W,convection fluxes Fc,and viscous fluxes Fvare

In the formulas,u，v，w and p denote the fluid velocity in three directions and pressure,respectively.E and H are internal energy and enthalpy per unit mass.τ is the viscous stress,and U the velocity of rotor blade relative to the fluid.[nx,ny,nz]Tis the normal vector.Θ is the work of viscous stress and heat conduction on fluid.

Roe scheme18is used to solve the convection flux on the surface of the grid.To simulate the unsteady characteristics of rotor flow,the dual time stepping method is used.At each pseudo time step,implicit Lower-Upper Symmetric Gauss-Seidel(LU-SGS)scheme19is adopted.Moreover,Baldwin-Lomax(B-L)model is applied for turbulence closure.20

Considering the unsteady characteristics in forward flight,moving overset grid method21is used to simulate the rotor flow field in this paper.Fig.2 shows the grid used in the calculation(the number of blade for two pairs of rotors is 8),in which the rotor blade is C-O type grid,while the background is Cartesian type grid.In order to capture the rotor wake and reduce the computational complexity,the background grid is locally clustered around the rotor.

In order to verify the numerical method,the numerical example on the rigid coaxial rotor used in the present experiment is calculated.The hover performance of the rigid single rotor and coaxial rotor is simulated.The trim strategy is that the upper rotor's collective pitch is fixed,and lower rotor's collective pitch is changed to maintain the torque of lower rotor equal to that of upper rotor.The total gird number is about 18000000.Fig.3 shows the calculated rotor thrust and torque coefficients(CT,CQ)with different collective pitch and com-pares the calculated results with the experimental data.It can be seen from the figure that,for both single and coaxial rotor,the calculated rotor thrust and torque coefficients agree well with experimental data,which indicates that the established calculation method can be used reliably to analyze the aerodynamic characteristics for rigid coaxial rotor.

Fig.2 Schematic of grid system.

Fig.3 Comparison of hover performance of rigid single and coaxial rotor between calculated results and experiment.

3.Analysis of aerodynamic interference characteristics in hover

In this section,experiments of collective pitch scanning and torque trim for rigid coaxial rotor are carried out.Aerodynamic force and moment of upper and lower rotors are measured and then compared with the single rotor case to analyze the hovering performance and aerodynamic interference characteristics.

In order to analyze the interactions between upper and lower rotor,collective pitch scanning for the coaxial rotor is conducted firstly.During this experiment,the same collective pitch is applied to upper and lower rotors.Fig.4 presents the variation of thrust coefficient with collective pitch θ when the rotational speed is 778 r/min.It shows that the thrust of upper rotor is larger than that of the lower one.Fig.5 gives percentage of thrust of each rotor against total thrust coefficient.It can be seen that percentage of thrust for upper rotor decreases with the increment of collective pitch,while lower rotor changes inversely.The thrust of upper rotor is always larger than that of the lower rotor.This is because the effective angle of attack of lower rotor is decreased when it is in the downwash of upper rotor,so the thrust generated by lower rotor is less than the upper one.

Fig.4 Thrust coefficient for upper and lower rotors in experiment.

Fig.5 Percentage of thrust for upper and lower rotors in experiment.

Fig.6 Performance curves for upper and lower rotors in experiment.

Fig.6 presents the hover performance curves for each rotor.As can be seen from the figure,at the same thrust coefficient,power consumption of lower rotor is larger than that of the upper one,and the absolute value of torque difference also increases with the increment of thrust coefficient.The percent-age of torque for each rotor is given in Fig.7,and CQis the total torque coefficient of the coaxial rotor system.It shows that percentage of torque for upper rotor decreases slowly,while increases for lower rotor,with the increase of total thrust coefficient and tends to be a constant.The torque moment reflects the power consumption of rotor.That is to say,the absolute value of torque difference will increase,while its relative value will decrease,with the increment of thrust coefficient.

In order to analyze the aerodynamic interference between two rotors,CFD method is used to simulate the test case.Fig.8 presents the change of transient thrust coefficient of upper and lower rotors with azimuthal angle φ when the total thrust coefficient is trimmed to 0.02.The trim strategy is giving an initial value of the collective angle of upper rotor,adjusting the collective angle of lower rotor to keep the same torque,and then changing the collective angle of upper rotor and the corresponding value of lower rotor until the total thrust coefficient is equal to the objective value.In the figure,eight periodic changes in rotor thrust can be seen in one circle because the blades of upper and lower rotors meet each other at every 45°,while the thrust of single rotor remains unchanged due to the quasi-steady flow condition in hover.The bound vortices of blade will induce upwash on another blade when the two blades rotate close to each other,leading to the increase of thrust.The upwash turns into downwash when the two blades rotate away from each other,so the thrust decreases.

In the normal operation state of the rigid coaxial rotor,torques of coaxial rotor are trimmed to maintain the stability of the helicopter flight.In this paper,the performance test of rotors in hover is carried out in the condition of torque balanced.During the test,the collective pitch of upper rotor is taken as the baseline,and the torque balance is achieved by adjusting differential collective pitches of two rotors.Fig.9 shows both the variation of collective pitches and the thrust coefficient share of the upper and lower rotors.As the induced downwash of upper rotor impacts on lower rotor directly,the collective pitch of lower rotor becomes greater.However,it still produces less thrust.As the thrust increases,the difference of collective pitches between two rotors is maintained at about 1.6°,while the torque of the upper and lower rotor is trimmed to the same.In the total coefficient of thrust,the upper rotor accounts for about 53.5%,while the lower one accounts for about 46.5%.

Fig.7 Percentage of torque for upper and lower rotors in experiment.

Fig.8 Thrust coefficients for upper and lower rotors in calculation.

Fig.9 Variation of both collective pitches and thrust coefficient share of upper and lower rotors with total thrust in experiment.

Fig.10 Performance comparison of coaxial rotor and single rotor with the same solidity in experiment.

In order to compare the aerodynamic performance of the rigid coaxial rotor and the conventional single one,the collective pitch scanning test of the isolated single rotor is also carried out.Fig.10 shows a comparison of the hover performance among the upper and lower rotors,as well as the isolated single rotor in hover.It can be seen from the figure,with the same thrust coefficient and rotor solidity,the torque of the upper rotor is greater than that of the single rotor,while the lower rotor requires greater torque than the upper one.Namely,hover performance of the upper or lower rotor is worse than that of the isolated rotor,while the upper rotor is better than the lower one.The reason lies in the fact that the separation of coaxial rotors is close,and hence there is strong aerodynamic interference.Compared to single rotor,the in flow of coaxial rotor increases much more,especially for the lower one.In order to produce the same thrust as single rotor,greater collective pitches are needed for the coaxial rotor.As a conclusion,the aerodynamic interference of coaxial rotor causes that the hover performance of both upper and lower rotor is less than that of isolated single rotor,and the influence on lower rotor is even worse.

In order to explain the phenomenon further,Fig.11 gives a comparison of the induced velocity field of the coaxial rotor and single rotor obtained by CFD simulation.The thrust coefficient of single rotor is half of the rigid coaxial rotor.It can be seen from the figure that the wake contraction rate of the coaxial rotor is much less than that of the single rotor.

Fig.12 gives a comparison of the Figure of Merit(FM)between the rigid coaxial rotor and single rotor,in which the symbol CTand σ indicate the rotor thrust coefficients and rotor solidity,respectively.As can be seen from the figure,with the same blade load,FM of the rigid coaxial rotor model is about 10.5%higher than that of the isolated single rotor.However,due to the presence of the interference,the upper and lower rotors require more power than the single rotor(see Fig.6),which weakens the advantage of coaxial configuration on FM.This phenomenon can also be explained as larger equivalent rotor disk area of coaxial rotor when compared with the single rotor under the condition of the same blade loads.

4.Aerodynamic characteristics of rigid coaxial rotor in forward flight

In forward flight,the lift of rigid coaxial rotor is mainly provided by blades at the advancing side,accompanied by the unique lift offset phenomenon.In high-speed flight,the rotational speed of rigid coaxial rotor will be usually reduced.The reduction of rotational speed has an important effect on the aerodynamic performance of rigid coaxial rotor.This paper carried out the wind tunnel test of rigid coaxial rotor in forward flight with trim of control settings.The rotor liftdrag ratio and lateral lift offset are given to evaluate the rotor performance.Also,the influence of parameters such as advance ratio on the forward flight performance is analyzed.

Fig.11 Induced velocity field comparison of coaxial rotor and single rotor in calculation.

Fig.12 Comparison of FM between single rotor and coaxial rotor.

Rigid coaxial rotor has six control settings.During wind tunnel test,the rotor differential collective pitches and differ-ential longitudinal cyclic pitches are set to zero.Collective pitches are trimmed to a specified vertical force coefficient,while the lateral and longitudinal cyclic pitches are adjusted to control the pitching and rolling moments.Meanwhile,differential lateral cyclic pitches are used to control the lateral lift offset.Due to the speed limit of the wind tunnel,the method of reducing the rotor rotational speed is used to improve the rotor advance ratio.The test condition is shown in Table 3.

4.1.influence of lateral lift offset on aerodynamic performance

The LOS is an important parameter of the rigid coaxial rotor,and different LOS has a significant effect on the aerodynamic performance of the rotor.Fig.13 presents the influence of the LOS on L/D performance at different advance ratios.It can be seen from the figure that,at different advance ratios μ,the L/D increases first and then decreases with the increment of LOS.Each advance ratio has an optimal LOS,making the L/D reach a maximum value.The test results show that the best L/D performance is obtained at advance ratio of 0.4.

In order to analyze the reason,the variation of the rotor forward flight drag and the power equivalent drag with different LOS is given in Fig.14.From the figure,as the LOS increases,the forward flight drag also increases,while the power equivalent drag decreases rapidly and then increases slowly,which makes the total equivalent drag(the sum of forward flight drag and power equivalent drag)exhibit a tendency of decreasing first and increasing later.

To understand the influence of LOS on the aerodynamic characteristics of rigid coaxial rotor,the auxiliary analysis is conducted by using CAMARD II software.The rotor disk lift coefficient CLdistributions of the rigid coaxial rotor model in different LOS are calculated,as shown in Fig.15.It can be seen from the figure,when the LOS is not limited(i.e.differential lateral cyclic pitch equals 0),the lift loading mainly lies on the advancing side,and concentrates in the vicinity of 90°azimuth.After altering LOS through control,the lift begins to move toward the longitudinal center.When the lift offset equals 20%,the lift is still mainly loaded on the advancing side,but no longer concentrated in the vicinity of 90°azimuth,while there are two high lift areas in the first and second quadrants.When the lift offset is equivalent to 10%,the lift is concentrated near the azimuth of 0°and 180°,while there is an obvious negative lift zone in the blade tip region of the 90°azimuth.It should be pointed out that the excessive lift offset can lead to a larger alternating torque load on the blade root,which will have an adverse effect on the structural strength and fatigue life of the blade.

Figs.13 and 15 show that LOS can directly affect the rotor forward flight performance and the lift distribution of therotor disk.An appropriate lift offset according to the flight condition can significantly improve the aerodynamic performance of rigid coaxial rotor.

Table 3 Test status of forward flight.

Fig.13 influence of LOS on experimental L/D of coaxial rigid rotor.

Fig.14 Variation of drag components of coaxial rigid rotor with different LOS in experiment(μ=0.4).

Fig.16 shows the experimental results of the variation of the lateral lift offset of rigid coaxial rotor with differential lateral cyclic pitches.As can be seen from the figure,for a given advance ratio,the increment of the lateral lift offset of rotor shows approximately a linear decreasing trend with the increase of differential lateral cyclic pitch.In addition,as the advance ratio increases,the slope gradually decreases.This phenomenon implies that the increase of advance ratio makes the lift offset more difficult to be adjusted.

4.2.Rotor performance at different advance ratios

Fig.17 presents the variation of the L/D of rigid coaxial rotor against the advance ratio.It should be pointed out that the L/D in the figure is the optimal value among the different lateral lift offsets for each forward flight condition.The L/D shows a trend of increasing first and decreasing later.Under the present test condition,the maximum L/D of the rigid coaxial rotor model can reach 8.3 at the advance ratio of 0.4.

Fig.15 Lift distribution on upper rotor with different LOS in calculation.

Fig.16 Variation of LOS with change of differential lateral cyclic pitch in experiment.

Fig.17 Variation of L/D with different advance ratios in experiment.

Fig.18 Variation of control settings with different advance ratios in experiment.

Fig.18 shows the variation of trimming control settings with different advance ratios.It can be seen from the figure that with the increment of the advance ratio,the collective pitch required for trimming is decreased.However,this decrease is not obvious when the advance ratio is greater than 0.6,which reflects the same change tendency of rotor power consumption.With the increment of advance ratio,the lateral cyclic pitches almost keep steady in a very small value(-1°).This is because that the rotor lift offset makes the rolling moment be balanced in forward flight.The rotor longitudinal cyclic pitch firstly decreases and then increases,while the overall change is small,basically maintained at about 6°.

5.Conclusions

In this paper,wind tunnel test and numerical calculation are carried out to study the aerodynamic characteristics of a rigid coaxial rotor for high-speed helicopter.The rotor aerodynamic performance such as lift,drag and power is measured in hover and high-advance-ratio forward flight conditions.The numerical method is used to calculate aerodynamic characteristics in typical states of rigid coaxial rotor.Through the analysis of the experimental data and the numerical results,the following conclusions can be drawn:

(1)Aerodynamic interference of rigid coaxial rotor between the upper and lower rotors is significant in hover.The upper rotor shows superior hover performance than the lower one,while it is not better than isolated single rotor with the same solidity.And the figure of merit of coaxial rotor is greater than that of the corresponding single rotor.

(2)The rotor L/D shows a trend of increasing first and decreasing later with the increase of advance ratio.Under current test condition,the maximum L/D of the rigid coaxial rotor model can reach 8.3 at the advance ratio of 0.4.

(3)Lift offset has an important influence on forward flight efficiency of rigid coaxial rotor.With the same advance ratio,L/D of rigid coaxial rotor increases first and then decreases,and there is an optimal lift offset which can make the L/D reach a locally maximum value.

(4)With the increase of advance ratio,the collective pitch required for the balance of the rigid coaxial rotor decreases,and the lateral cyclic pitch maintains at a very small value,keeping constant as the forward speed changes.