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

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1 A CFD-Based Approach to Coaxial Rotor Hover Performance Using Actuator Disks Jonathan Chiew AE Spring 007 Dr. Lakshmi Sankar Georgia Institute of Technology

2 Table of Contents Table of Contents Introduction 3 Methodology 5 Results 8 Conclusions and Recommendations 11 Acknowledgements 11 References 1

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 3

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. 4

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 40,000 tetrahedral cells was created in GAMBIT, and the corresponding flow field was solved using FLUENT 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: Thrust Disk Loading = Area The thrust data was interpolated from the coaxial rotor plot of thrust versus nondimensional separation distance, S/D (Ref. 1) and the rotor area was calculated to be approximately 1. m. 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: ( Thrust) ( ) Pwr =, ind Vel Ind Avg 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. ) 5

6 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: Inflow Angle φ Zero Lift Line Angle Velz ( Ωr 1 direction = = Tan = = θcollective, tip θ + θ ) local twist Effective Angle of Attack = α eff = θ φ Using the calculated value for α eff, the local section lift (c l ) and drag (c d ) coefficients were interpolated from the airfoil polars. Since Abbott and Doenhoeff report (Ref. 3) only had a polar for the NACA airfoil, XFOIL 6.96 and Javafoil were used to determine the other airfoil polars. Using the section coefficients, the section torque was calculated: SectionTorque [( Ωr) + Vel ][ c cos( φ) c sin( φ ] crdr 1 Q' = ρ d + = Ind l ) where ρ is 1. kg/m 3 and c is the local chord length at that particular radial position. The total torque was then calculated as follows: Torque Total = Tip Cutout Section Torque 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 Pwr Pr ( Torque )( Ω) ofile = Total ( Thrust)( Vel ) + ( Torque )( Ω) Pwr Total = PwrInd + PwrPr ofile = Ind, Avg Total This total power was then compared the actual power required, given by 6

7 Pwr Actual ( Torque )( Ω) = Actual 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. T ' 1 ρ = [( Ωr) + Vel ][ c cos( φ) c sin( φ ] cdr Ind l d ) Thrust = Tip Cutout T ' 7

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 101,35 Pa and 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 006 with a single rotor (Figure 1) shows a significant disturbance in flow properties near the lower boundary which was approximate.5 radii below the disk. Figure 1: The rotor wake has not reached farfield conditions Figure : 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. 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 5% 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. 8

9 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 Induced Power Total Power Actual Total Power - Calculated Power Required (HP) Rotor Separation Distance (S/D) Figure 3: Computed and actual power required for the lower rotor Upper Rotor - Power Required Induced Power Total Power Actual Total Power - Calculated Power Required (HP) Rotor Separation Distance (S/D) Figure 4: Computed and actual powers required for the upper rotor 9

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 Theoretical Predictions CFD Computation Inflow Velocity (λ) Radial Station (r/r) Figure 5: Rotor inflow comparison Figure 6: Streamlines and velocity profile near rotor 10

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. 11

12 References 1 McAlister, K. W., Tung, C., Rand, O., Khromov, V., and Wilson, J.S., Experimental and Numerical Study of a Model Coaxial Rotor, Proceedings of the 6 nd Annual AHS Forum, Phoenix, Arizona, May, 006. Coffin, C. D., Tilt Rotor Hover Aeroacoustics, NASA CR , June, Abbott, I. H.; von Doenhoff, A. E.; and Stivers, L. S., Summary of Airfoil Data, NACA Report 84, Leishman, J., Ananthan, S., Aerodynamic Optimization of a Coaxial Proprotor, Proceedings of the 6 nd Annual AHS Forum, Phoenix, Arizona, May,

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