A CFD-Based Approach to Coaxial Rotor Hover Performance Using Actuator Disks

Jonathan Chiew

AE4699 - Spring 2007

Dr. Lakshmi Sankar

Georgia Institute of Technology

2

Table of Contents

Table of Contents 2

Introduction 3

Methodology 5

Results 8

Conclusions and Recommendations 11

Acknowledgements 11

References 12

3

Introduction

Up until Igor Sikorsky successfully flew the VS-300 in 1939, symmetric rotor

systems were preferred by early designers, but now the single main rotor and tail rotor

design is nearly ubiquitous in the helicopter industry. Boeing has successfully used the

tandem rotor arrangement on the CH-47 Chinook and other helicopters, while Kamov is

the only company to have put a coaxial helicopter in production. However, the coaxial

rotor has been making a recent resurgence, especially with the need for maneuverable,

high-speed helicopters as well as heavy-lift rotorcraft.

A coaxial rotor has several significant advantages over other configurations. First,

the counter-rotating coaxial rotors automatically conserve angular momentum; hence, no

anti-torque system is required and the power that a single-rotor helicopter uses to drive

the tail rotor is “recovered” and used to generate useful lift and thrust in the coaxial

system. The removal of the tail rotor also allows a coaxial helicopter to be designed with

a smaller footprint since the long tail boom is no longer required for rotor separation,

which is especially important for maritime operations. Furthermore, a coaxial helicopter

is inherently directionally stable and thus safer to fly at low speeds in close quarters. The

restrictions on sideward flight in single-rotor helicopters to prevent the tail rotor from

entering vortex-ring state can be relaxed or removed in a coaxial design.

There are advantages of a coaxial rotor configuration beyond those of involving

the removal of the anti-torque device. A coaxial rotor system is aerodynamically

symmetric and therefore immune to the retreating blade stall problems of a single-rotor

system, allowing coaxial helicopters the potential fly at much high advance ratios. In

addition, coaxial rotors can achieve higher thrust coefficients making them much more

4

maneuverable than conventional single-rotor helicopters. The pilot’s workload is also

reduced in because constant pedal input is not required for longitudinal flight and the

cross coupling of controls is removed.

However, coaxial rotor systems are not without their disadvantages. There is a

significant increase in the amount of mechanical linkages and supports necessary for the

rotor control systems. Also, there must be enough separation between the two rotors so

that the blades can flap without hitting each other or the fuselage. Both of these factors

increase the parasitic drag of the aircraft as well as construction and maintenance costs.

Furthermore, there are undesirable interference effects between the coaxial rotors

increasing induced power; finally there are significant vibration and weight issues.

Despite these disadvantages, coaxial rotor systems impart many benefits over

other helicopter rotor designs. This study is a preliminary step in creating a model for

considering the hover performance of a coaxial rotor system. The XV-15 rotor tested by

McAlister, Tung, et al. (Ref. 1) was examined in FLUENT using momentum theory. In

this study a coaxial rotor system was tested at various separation distances to determine if

the model could match the experimental data.

5

Methodology

This study uses a combination of generic momentum theory and a blade element

method to calculate the power required for hover. An unstructured, axisymmetric grid

comprising approximately 240,000 tetrahedral cells was created in GAMBIT, and the

corresponding flow field was solved using FLUENT 6.2.16. The coaxial rotor system

was modeled as two actuator disks acting on an inviscid fluid, using the “fan” boundary

condition in FLUENT. The other outer surfaces of the flow field were designated as the

pressure far field, while the pressure jump applied to the fluid by the disk was set equal to

the rotor’s disk loading and constant over the disk area:

Area

ThrustLoadingDisk =

The thrust data was interpolated from the coaxial rotor plot of thrust versus non-

dimensional separation distance, S/D (Ref. 1) and the rotor area was calculated to be

approximately 1.2 m2.

The flow was given a small, initial velocity in the negative z-direction,

perpendicular to the actuator disks. FLUENT was used to solve the 3D flow field and

compute the average velocity over each disk. The calculated induced power was:

( ) ( )AvgIndind VelThrustPwr ,=

Profile power was calculated using a blade element model. Table 1 describes the

properties of each blade. All

dimensions were scaled down to

match the tip chord tested at

Ames (Ref. 1) resulting in a scale

Table 1: XV-15 Rotor and blade properties (Ref. 2)

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factor of approximately 1/7. Because the collective pitch was referenced at the blade tip,

the inflow angle, zero lift line angle, and effective angle of attack were each calculated in

the following manner:

)(1

r

VelTanAngleInflow directionz

Ω== −−φ

twistlocaltipcollectiveAngleLineLiftZero θθθ +== ,

φθα −== effAttackofAngleEffective

Using the calculated value for αeff, the local section lift (cl) and drag (cd)

coefficients were interpolated from the airfoil polars. Since Abbott and Doenhoeff report

(Ref. 3) only had a polar for the NACA 64-208 airfoil, XFOIL 6.96 and Javafoil were

used to determine the other airfoil polars. Using the section coefficients, the section

torque was calculated:

( )[ ][ ] drrcccVelrQTorqueSection ldInd )sin()cos(2

1'

22φφρ ++Ω== ∞

where ρ∞ is 1.2 kg/m3 and c is the local chord length at that particular radial position. The

total torque was then calculated as follows:

∑=Tip

Cutout

Total TorqueSectionTorque

Since the model had a 17% root cutout, only nine of the ten points were used in

the computation. The resulting profile and total power equations are

( )( )Ω= Totalofile TorquePwrPr

( )( ) ( )( )Ω+=+= TotalAvgIndofileIndTotal TorqueVelThrustPwrPwrPwr ,Pr

This total power was then compared the actual power required, given by

7

( ) ( )Ω= ActualActual TorquePwr

The actual torque was interpolated from the plot of torque versus S/D. The

predicted and actual power required comparisons were made at various separation

distances between 0.1 and 0.8. The coaxial rotor thrust was computed using the following

formulas.

( )[ ][ ] drcccVelrT dlInd )sin()cos(2

1'

22φφρ −+Ω= ∞

∑=Tip

Cutout

TThrust '

8

Results

The ambient conditions were set to closely match those of McAlister’s

experiments for a coaxial rotor in hover out of ground effect. Specifically, the angular

velocity of the disks was 800RPM while the pressure far field was set to 101,325 Pa and

294.261 K (70°F). For each case of S/D, FLUENT calculated 4000 iterations, which was

sufficient to generate a converged solution. Initial research conducted in 2006 with a

single rotor (Figure 1) shows a significant disturbance in flow properties near the lower

boundary which was approximate 2.5 radii below the disk.

Figure 1: The rotor wake has not reached farfield conditions

Figure 2: New grid size

After several experiments with a variety of grid sizes, the lower boundary was

moved to 100 radii beneath the lower actuator disk, as shown in Figure 2.

The computational model consistently overpredicted the power required for hover

by approximately 50% and 30% for the lower and upper rotors, respectively. Upon

further analysis, the model was found to be producing around 25% more thrust than the

coaxial rotor in the wind tunnel experiments. This brings into question whether the two

rotors are actually at the same test conditions.

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In order to compensate for this discrepancy in the model, the collective pitch of

the rotor was adjusted in the blade element code to match the thrust output of the rotor in

the experiment. The resulting induced power and total power required are plotted in

figures 3 and 4 for the lower and upper rotor respectively.

Lower Rotor - Power Required

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Rotor Separation Distance (S/D)

Po

wer

Req

uir

ed

(H

P)

Induced Power Total Power Actual Total Power - Calculated

Figure 3: Computed and actual power required for the lower rotor

Upper Rotor - Power Required

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Rotor Separation Distance (S/D)

Po

wer

Req

uir

ed

(H

P)

Induced Power Total Power Actual Total Power - Calculated

Figure 4: Computed and actual powers required for the upper rotor

10

This thrust matching adjustment gives closer correlation between the computed

and actual power required for hover. The average overprediction errors are 35% for the

lower rotor and 15% for the upper rotor. Finally, figure 5 shows a comparison between

theoretical (Ref. 4) and calculated non-dimensional inflow velocities on the upper rotor,

and figure 6 shows the streamlines superimposed on the flow velocity profile (S/D = 0.1).

Upper Rotor Inflow

0

0.02

0.04

0.06

0.08

0.1

0.12

0.0 0.2 0.4 0.6 0.8 1.0

Radial Station (r/R)

Infl

ow

Velo

cit

y ( λλ λλ

)

Theoretical Predictions CFD Computation

Figure 5: Rotor inflow comparison

Figure 6: Streamlines and velocity profile near rotor

11

Conclusions and Recommendations

For a coaxial rotor in hover out of ground effect, the hybrid momentum

theory and blade element method do not closely model actual rotor data. Even with thrust

matching, the model is not accurate enough to do hover performance predictions. It is

likely that the assumption of constant pressure over the actuator disk is the cause of the

computation errors. It is known that pressure varies along the span of the rotor blade.

FLUENT can model this using a boundary profile specification of the pressure increase

across the fan. Preliminary investigation shows a significant increase in accuracy using

this method (only 1-5% error) but more research needs to be done with this model. In

addition, FLUENT can specify a swirl velocity to be added to the fluid as it crosses the

fan. It may be possible to account for wake swirl in this fashion. Finally, an actual rotor

blade could be modeled and imported into FLUENT as a periodic wedge with a mixing

plane model between the upper and lower rotors in order to compare accuracy with actual

wind tunnel tests.

Acknowledgements

Dr. Sankar, Byung-Young Min, and Alan Egolf have been a tremendous help in

giving advice over the duration of this research project.

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References

1McAlister, K. W., Tung, C., Rand, O., Khromov, V., and Wilson, J.S., “Experimental

and Numerical Study of a Model Coaxial Rotor,” Proceedings of the 62nd

Annual AHS

Forum, Phoenix, Arizona, May, 2006.

2Coffin, C. D., “Tilt Rotor Hover Aeroacoustics,” NASA CR 177598, June, 1992.

3Abbott, I. H.; von Doenhoff, A. E.; and Stivers, L. S., “Summary of Airfoil Data,”

NACA Report 824, 1945

4Leishman, J., Ananthan, S., “Aerodynamic Optimization of a Coaxial Proprotor,”

Proceedings of the 62nd

Annual AHS Forum, Phoenix, Arizona, May, 2006.