Validation of Comprehensive Analysis Performance Predictions for Coaxial Rotors in Hover

Jimmy C. Ho Hyeonsoo Yeo Mahendra Bhagwat Research Scientist Research Scientist Research Scientist Science and Technology Corporation U. S. Army Aviation Development Directorate – AFDD Ames Research Center Aviation & Missile Research, Development & Engineering Center Moffett Field, California Research, Development and Engineering Command (RDECOM) Ames Research Center, Moffett Field, California

ABSTRACT Comparisons of rotor aerodynamic performance parameters in hover, between rotorcraft comprehensive analysis pre- dictions using a free vortex wake model and measured data, for two model–scale and two full–scale coaxial rotors are provided. Predictions from a computational fluid dynamics analysis are also included for one of the full–scale rotors to provide additional insights. Test points evaluated form sweeps in both the coaxial rotor system thrust and the axial separation distance between the two rotors. The comprehensive analysis predictions are mostly in good agreement with measured data, which includes reflecting the same trends from all sweeps. While the comprehensive analysis predictions are mostly in good agreement with measured data and computational fluid dynamics predictions for individual rotor thrust, good agreement for individual rotor torque is more elusive. The comprehensive analysis predictions also show that even though the coaxial rotor figure of merit is not strongly dependent on the thrust sharing ratio between the two rotors, the figure of merit of the two individual rotors are highly sensitive to the thrust sharing ratio.

NOTATION INTRODUCTION cd = airfoil drag coefficient In the United States, there is renewed interest in coaxial rotor cℓ = airfoil lift coefficient especially for high–speed applications. Sikorsky cm = airfoil pitching moment coefficient completed flight testing its X2 Demonstrator in July 2011 and CP,ideal = ideal rotor power coefficient is expected to begin flight testing its S–97 Raider this year. CT = rotor thrust coefficient Sikorsky and Boeing are partners on the U. S. Army’s Joint CT,L = rotor thrust coefficient of lower rotor Multi–Role Technology Demonstrator program in which they CT,U = rotor thrust coefficient of upper rotor are expected to fly their SB>1 Defiant design by 2017. In CQ = rotor torque coefficient Russia, continues to develop a navalised derivative CQ,L = rotor torque coefficient of lower rotor of its Ka–52 while Rumas completed first flight of its Ru- CQ,U = rotor torque coefficient of upper rotor mas 10 in September 2014. These recent activities involving D = rotordiameter the development of coaxial rotor helicopters indicate a strong FM = rotorfigureofmerit need for computational tools to accurately predict rotor aero- h = axial separation distance between rotors dynamic performance for coaxial rotors. The accuracy of a KD = Reynolds number correction factor for drag computationaltool needs to be validated by comparing its pre- M = Machnumber dictions against experimentally measured data. n = exponent in Reynolds number corrrection Coleman wrote a survey (Ref. 1) of experimental and an- Re = Reynoldsnumber alytical research, up to 1997, on the aerodynamics of coaxial Re = Reynoldsnumberof the C81 tables C81 rotors. The survey is excellent in describing the influence of V = rotortipspeed tip the primary factors, such as axial separation between the two α = angle–of–attack rotors, that determine coaxial rotor performance. σ = rotor solidity Comparisons of coaxial rotor performance, between pre- Presented at the AHS 71st Annual Forum, Virginia Beach, dictions and measured data, do exist for some modern com- Virginia, May 5–7, 2015. This is a work of the U. S. Gov- putational tools. Wachspress and Quackenbush (Ref. 2) pro- ernment and is not subject to copyright protection in the U. S. vided validations of the aerodynamics tool CHARM for sev- DISTRIBUTION STATEMENT A. Approved for public re- eral coaxial rotors. They included comparisons, between lease; distribution is unlimited. PR 1635 March 23, 2015 CHARM predictions and measured data, of rotor performance 1 and/or tip vortex position for the isolated coaxial rotors tested The next section is a description of the analytical mod- by Nagashima et al. (Refs. 3–5) and Andrew (Ref. 6), as eling used in the RCAS analysis. This is followed by vali- well as for the Kamov Ka–32 (Ref. 7) in flight. Lim et dations of RCAS performance predictions for coaxial rotors al. (Ref. 8) provided validations of the comprehensive analy- in hover. Most of the validations are comparisons between sis tool CAMRAD II for several coaxial rotors in hover. They RCAS predictions and measured data of model–scale rotors included comparisons, between CAMRAD II predictions and from Ramasamy (Ref. 18). Comparisons between RCAS pre- measured data, of rotor performance for the isolated coax- dictions and measured data of full–scale rotors from Harring- ial rotors tested by Harrington (Ref. 9) and McAlister and ton (Ref. 9) are also shown. Where available, OVERTURNS Tung (Ref. 10), as well as for the Sikorsky XH–59A (Ref. 11) predictions from Ref. 16 are also included to provide addi- in flight. Johnson (Ref. 12) provided validationsof CAMRAD tional insights. Following the validations is a section that II for coaxial rotors in forward flight. He included compar- compares rotor performance between single and coaxial ro- isons, between CAMRAD II predictions and measured data, tors. of rotor performance for the isolated coaxial rotor tested by Dingeldein (Ref. 13) as well as for the XH–59A (Ref. 14) in ANALYTICAL MODELING flight. Ruzicka and Strawn (Ref. 15) provided validations of the Reynolds–average Navier–Stokes (RANS) solver OVER- RCAS allows for numerous options in modeling the vortex FLOW 2 for the isolated coaxial rotor tested by McAlister and wake system of a rotor, the aerodynamic interference between Tung (Ref. 10) by showing comparisons, between predictions rotors, the airloads acting at a blade section, the dynamics of and measured data, of rotor performance. Lakshminarayan a multibody system, and the trim conditions of rotors. This and Baeder (Ref. 16) provided validations of the RANS solver section is restricted to only describing the models used in this OVERTURNS for “Rotor 2” of the isolated coaxial rotors paper. For interested readers, Ref. 22 describes the various tested by Harrington (Ref. 9) by showing comparisons, be- modeling options available in RCAS. tween predictions and measured data, of rotor performance. Rajmohan et al. (Ref. 17) provided validations of the vortex Vortex Wake Model particle method (VPM) as well as of a hybrid VPM solution, in which VPM is coupled with the computationalfluid dynam- The rotor blades are modeled as lifting lines, i. e., as bound ics (CFD) code OpenFOAM, for the coaxial rotor that was vortices located along the blade quarter chord lines. Each lift- tested by McAlister and Tung (Ref. 10). They compared VPM ing line is discretized into a series of spanwise aerodynamic predictions against measured data for both rotor performance segments, or “aerosegments.” The wake behind the blade is and velocity in the flow field. comprised of vortices trailing from the edge of each of the In addition to the experiments already mentioned, a recent aerosegments. Shed vortices can also be optionally included experiment by Ramasamy (Ref. 18) is especially useful for to model the effects of azimuthally varying blade circula- validating the aerodynamic performance predictions of coax- tion distribution. A small azimuthal region behind the blade ial rotors. This experiment included measurements of rotor called the “near–wake” includes all of these individual vor- performance for each individual rotor. It also included varia- tices over the entire blade span. For numerical efficiency, this tions in the axial separation h/D between the two rotors to an near–wake extends only a small number of azimuthal steps extent that is greater than previousexperiments. In this experi- (wake age) behind the blade, after which a simpler “far–wake” ment, Ramasamy tested model–scale rotors in both single and model is used. The far–wake is comprised of a discrete tip coaxial rotor configurations in hover. Two sets of rotor blades vortex, a root vortex, and a large–core vortex representing the were tested. One set used untwisted blades and the other set inboard wake sheet trailing from the entire blade span. The used highly twisted blades. Note that the highly twisted blades tip vortex strength and the relative strengths, between the root used are the same blades used in the experiment by McAlis- vortex and the sheet vortices, are all determined from the ac- ter and Tung (Ref. 10), but the rotor hubs from McAlister and tual loading distribution on the blade. An implementation of Tung were not used by Ramasamy. The experiment by McAl- the University of Maryland free vortex wake (Ref. 23) model ister and Tung featured significant blade coning, which were is used to allow the tip vortex to freely deform. The extent negligible in the experiment by Ramasamy due to the hub re- of the near–wake and far–wake are set to a wake age of 15◦ placements. and 20 revolutions, respectively. This same discretized wake The goal of this paper is to present validations of the per- model was consistently used for RCAS hover calculations of formance predictions of the Rotorcraft Comprehensive Anal- isolated rotors presented earlier by Jain et al. (Ref. 21). ysis System (RCAS, Refs. 19, 20) for coaxial rotors in hover. This is a naturalfollow–up to the work by Jain et al. (Ref. 21), Aerodynamic Interference Model who provided validations of RCAS performance predictions using vortex wake models for several isolated single rotors in In RCAS, the aerodynamic interference between two rotors hover and in forward flight. A free vortex wake model is used is modularly included with several modeling options ranging to allow the wake geometry to deform accordingly. Usage of from a simple cylindrical vortex sheet to a free vortex wake a vortex wake model inherently allows it to calculate the in- model. This allows the user to include rotor–to–rotor inter- duced velocity effects from one rotor on the other. ference effects even with simpler rotor inflow models, such 2 as momentum theory or dynamic inflow. When the free vor- of the system must be balanced to zero while the thrust must tex wake model is used for modeling the rotor inflow, it can be equal to its desired value. The experiment, by Ramasamy, also be used to calculate the interference inflow velocity at included axial separation sweeps that consist of test points in the other rotor. However, there is another interference effect which the value of h/D was varied while the thrust of the en- whereby the wake of one rotor alters the wake geometry of the tire system was kept approximately constant. For some of other rotor. This is called the wake–to–wake interference and these test points, the experiment contained significant devia- is available as a user choice with the free vortex wake inflow tions from its targeted thrust value. Small imbalances in the option. The separation of these two effects allows complete system torque also exist (so that CQ,U =CQ,L)duetothe nature modularity in the choice of modeling options and allows one of physical testing. Therefore, for axial6 separation sweeps, the to analytically isolate these effects to better understand their two constraints are that the thrust and torque of the system are influence on performance. All calculations shown in this pa- set to its measured values from each test point. As a measure per include both rotor–to–rotor and wake–to–wake interfer- of the smallness of the torque imbalance, the % torque imbal- ence effects. CQ,U CQ,L ance is defined as 100% | − |. The largest % torque × CQ,U +CQ,L imbalance from all test points is 2.5% and most test points Airloads Model have a torque imbalance of less than 1%. Sectional lift, drag, and pitching moment along the blade are determined from C81 lookup tables with a Reynolds number RESULTS FOR MODEL–SCALE ROTORS correction on drag. The C81 tables contain values of cℓ, cd, and cm as functions of α and M. A correction is applied to ac- Ramasamy (Ref. 18) tested three–bladed, model–scale rotors count for mismatches in Reynolds number between its value inside the U. S. Army AFDD hover chamber at NASA Ames from the C81 tables and its value at a blade section. The Research Center. Rotors were tested in both the single and Reynolds number correction, that is applied in this paper, is coaxial rotor configurations. Figure 1 shows the experimental to modify the value of cd from the C81 tables by dividing it setup for the coaxial rotor configuration. As seen in the figure, n by the factor of KD = (Re/ReC81) . In this expression, Re is two identical, but independent rotor rigs were used. the Reynoldsnumber of the blade section of interest and ReC81 Two sets of blades were tested. One set used untwisted is the Reynolds number corresponding to the C81 tables. In blades featuring the NACA 0012 airfoil at all sections. The this paper, n is set to 0.2, which corresponds to the value for other set used highly twisted XV–15–like blades featuring a turbulent flat plate boundary layer. This Reynolds number NACA 64-series, five–digit airfoils. The airfoil thickness correction was suggested by Yamauchi and Johnson (Ref. 24). varies nonlinearly from the 64-X32 section at the blade root to With the exception of the C81 tables used in modeling the 64-X08 section at the blade tip. The airfoil at the tip is ro- the highly twisted blades from the experiment by Ramasamy tated relative to the root by 37◦ due to blade twist, which also (Ref. 18), the values of ReC81 are unknown for the C81 tables varies nonlinearly across the span. In the coaxial rotor config- used in this paper. In cases where ReC81 is unknown, the au- uration, the maximum rotor speed tested was 1200 RPM for thors chose its value for each set of blades so that RCAS per- both the untwisted and highly twisted blades. Table 1 com- formance predictions would be in good agreement with mea- pares some geometric parameters and hover operating condi- sured data for the isolated single rotor configuration. The C81 tions (at standard sealevel and 1200 RPM) between the differ- tables used in modeling the highly twisted blades from the ex- ent model–scale rotors. Asides from differences in the twist periment by Ramasamy were generated by Lim (Ref. 8), who and airfoil distribution, the two rotors are physically similar. used the airfoil analysis tool MSES to calculate the needed values specifically for modeling the rotors that were tested by McAlister and Tung (Ref. 10). Table 1. Model–scale rotor parameters in hover Parameter Untwisted Highly Twisted Dynamics and Trim Radius,ft 2.17 2.15 Bladenumberperrotor 3 3 The blades are modeled here as rigid with its sole motion be- Chord,in 2.29 2.0 ing its prescribed rotation about the hub center. Pitch hinges Rootcut–out 19.1% R 20.1% R are placed at blade root locations to allow for control of blade Single rotor solidity, σ 0.084 0.074 pitch. For single rotor configurations, the blade collective Coaxial rotor solidity, σ 0.168 0.148 pitch is varied to form a thrust sweep for comparison with Tip Re at1200RPM 331,000 286,000 measured data. Tip M at1200RPM 0.244 0.242 For coaxial rotor configurations, the blade collective pitch of each rotor is determined from a trim analysis. These two For coaxial rotors, the traditional definition of FM is used collective pitch angles are adjusted to simultaneously satisfy in this paper and it is given by constraints on the thrust and torque of the entire coaxial ro- 3/2 tor system. For thrust sweeps in which the thrust of the en- (CT U +CT L) FM = , , (1) tire system is varied, the two constraints are that the torque √2(CQ,U +CQ,L) 3 The definition that was used by Ramasamy in Ref. 18 is a thrust level, RCAS predictions are in good agreement with modified definition (Ref. 25) and it is given by measured data in coaxial rotor FM in spite of not being in good agreement for individual rotor FM. 3/2 3/2 CT U +CT L FM = , , (2) The results in Figs. 3, 4, and 5 reveal differences in the √2(CQ,U +CQ,L) sensitivity of FM, to deviations in thrust and torque, between an isolated, single rotor, the individual rotors from a coax- In cases where the torque of the coaxial system balances to ial rotor, and a coaxial rotor system. For an isolated, sin- zero (i. e., CQ,U = CQ,L), the modified definition simply re- gle rotor, plotting FM as a function of CT means that FM duces to being the average of the two individual rotor FM. is entirely determined by the rotor torque at the thrust level The reason for using the traditional definition in this paper is indicated. For coaxial rotors, an accurate determination of explained later in the section on comparing single and coax- CT,L/CT,U is needed for one to be able to accurately predict ial rotor performance. The choice of FM is insignificant to individual rotor FM. Prior to stall, increasing individual rotor the qualitative comparison in FM between measured data and thrust would also increase individual rotor FM. For the axial predictions. separation sweep at the lower thrust level in Fig. 4, the RCAS predictions of individual rotor thrust are consistently higher Model–Scale Rotors with Untwisted Blades and lower than measured data for the upper and lower rotor, respectively. Consequently, for this particular sweep, RCAS In the isolated single rotor configuration, experimental test predictions of individual rotor FM are consistently higher and points for the model–scale rotor with untwisted blades form lower than measured data for the upper and lower rotor, re- thrust sweeps at 800 and 1200 RPM. Figure 2 shows the com- spectively. This trend also exists, albeit with the RCAS pre- parison of FM between measured data and RCAS predictions. dictions being quite close to the measured data, for the axial As explained in the subsection on airloads modeling, the value separation sweep at the higher thrust level in Fig. 5. For the of ReC81 was adjusted so that RCAS predictions would be in thrust sweep in Fig. 3, with the exception of the case of CT good agreement with measured data. = 0.0041, the trends are reversed due to RCAS predictions In the coaxial rotor configuration, a thrust sweep was per- of individual rotor thrust being lower and higher than mea- formed at the test conditions of h/D = 0.07 and 1200 RPM. sured data for the upper and lower rotor, respectively. With Figure 3 shows the comparison between measured data and the compensating effects of RCAS predicting higher values of RCAS predictions for the individual rotor thrust CT , individ- FM than measured data for one rotor and lower values of FM ual rotor torque CQ, the thrust sharing ratio CT,L/CT,U , the than measured data for the other rotor, the coaxial rotor FM individual rotor FM, and the coaxial rotor FM. All of these ends up showing good agreement between RCAS predictions quantities are plotted as functions of the total coaxial rotor and measured data for all three sweeps. In summary, individ- system thrust CT . The RCAS predictions reflect all general ual rotor FM is sensitive to changes in CT,L/CT,U , but coaxial trends found in the measured data. Good qualitative agree- rotor FM is not. The latter half of the previous sentence is ment, between measured data and RCAS predictions, exists corroborated by experimental data (Ref. 5) and CHARM pre- for individual rotor thrust and torque. RCAS predictions for dictions (Ref. 2). FM of the upper rotor is generally lower than the measured data (particularly at the higher thrust values) in spite of the Model–Scale Rotors with Highly Twisted Blades good qualitative agreement in both thrust and torque, which is a reflection of the sensitivity of FM to small deviations in In the isolated single rotor configuration, experimental test thrust or torque. Measured data and RCAS predictions are in points for the model–scale rotor with highly twisted blades good agreement for the coaxial rotor FM. form thrust sweeps between 800 and 1400 RPM at increments Axial separation sweeps were performed for two levels of of 100 RPM. Figure 6 shows the comparison of FM between thrust and at a rotor speed of 800 RPM. The targeted thrust measured data and RCAS predictions. Prior to stall, there is value from the experiment for the lower and higher thrust lev- good agreement between measured data and RCAS predic- tions. els were CT 0.007 and 0.014, respectively. The compari- son between≈ measured data and RCAS predictions for rotor In the coaxial rotor configuration, a thrust sweep and an performance parameters are shown in Figs. 4 and 5 for the axial separation sweep were performed. The thrust sweep was lower and higher thrust levels, respectively. These quantities performed at the test conditions of h/D = 0.07and 1200RPM, are plotted here as functions of axial separation h/D. The which are the same conditions as the thrust sweep from the RCAS predictions here are not as smooth as those from the model–scale rotor with untwisted blades. The axial separa- thrust sweep (e. g., the coaxial rotor FM is highly discon- tion sweep was performed at a rotor speed of 800 RPM and tinuous at values of h/D 0.75 for the higher thrust level), its targeted thrust value from the experiment was CT 0.014, because of deviations from≤ the targeted thrust values in the which correspond to the same conditions as the axial≈ sepa- experiment. As with the thrust sweep, RCAS predictions re- ration sweep at the higher thrust value from the model–scale flect all general trends found in the measured data. For the rotor with untwisted blades. Figure 7 shows the comparison, higher thrust level, RCAS predictions are in good agreement between measured data and RCAS predictions, of rotor per- with measured data for all parameters shown. For the lower formance parameters for the thrust sweep as functions of the 4 total coaxial system thrust CT . Likewise, Fig. 8 shows the comparison of rotor performance parameters for the axial sep- Table 2. Full–scale rotor parameters in hover aration sweep as functions of axial separation h/D. Except Parameter “Rotor1” “Rotor2” for the test point at CT = 0.0039 from the thrust sweep, the Radius,ft 12.5 12.5 RCAS predictions are in good agreement with measured data Bladenumberperrotor 2 2 for individual rotor thrust for both sets of sweep. However, Chordattip,ft 0.316 1.5 the RCAS predictions for individual rotor torque are higher Rootcut–out 20% R 20% R than the measured data. This leads to RCAS predictions being Axial separation, h/D 0.0932 0.08 lower than measured data for all forms of FM. The authors Single rotor solidity, σ 0.027 0.076 currently do not have an explanation for the higher torque pre- Coaxial rotor solidity, σ 0.054 0.152 dictions. Tip Re at max Vtip 1,005,000 3,740,000 Tip M at max Vtip 0.448 0.351 As mentioned in the Introduction, Ref. 8 provides compar- isons, between measured data and CAMRAD II predictions, Harrington “Rotor 1” of rotor performance for the coaxial rotor tested by McAlister and Tung (Ref. 10). Given that the experiment by McAlister In the isolated single rotor configuration, experimental test and Tung and the experiment by Ramasamy shared the same points for “Rotor 1” form a thrust sweep at Vtip = 500 ft/sec. highly twisted blades, it would be of interest to compare the Figure 10 shows the comparison of FM between measured measured data from both experiments along with predictions data and RCAS predictions. The value of ReC81 was adjusted by both RCAS and CAMRAD II. The experiment by McAl- so that RCAS predictions would be in good agreement with ister and Tung also included an axial separation sweep at the measured data prior to stall. rotor speed of 800 RPM, but at higher levels of total coaxial In the coaxial rotor configuration, experimental test points system thrust than the corresponding sweep from the experi- form thrust sweeps at Vtip = 450 and 500 ft/sec. Figure 11 ment by Ramasamy. Figure 9 shows the comparison, between shows the comparison of the coaxial rotor FM between mea- measured data and predictions from both experiments, for the sured data and RCAS predictions. For Vtip = 450 ft/sec, good two individual rotor thrusts CT as functions of h/D. Note the agreement exists between measured data and RCAS predic- vast amount of scatter in the measured data by McAlister and tions. For Vtip = 500 ft/sec, the agreement is mostly good Tung. The CAMRAD II predictions are consistently near or although RCAS predictions are slightly higher than measured above the upper bound of this scatter for both rotors. data in the range of 0.0046 CT 0.0056. ≤ ≤ Harrington “Rotor 2” RESULTS FOR FULL–SCALE ROTORS In the isolated single rotor configuration, experimental test points for “Rotor 2” form thrust sweeps at Vtip = 262 and Harrington (Ref. 9) tested two–bladed, full–scale rotors inside 392 ft/sec. Figure 12 shows the comparison of FM between a full–scale wind tunnel at what was then NACA Langley Re- measured data and RCAS predictions. Once again, the value search Center. Rotors were tested in both the single and coax- of ReC81 was adjusted so that RCAS predictions would be in ial rotor configurations. For coaxial rotors, thrust and torque good agreement with measured data. of the entire system were measured but not for each individual In the coaxial rotor configuration, experimental test points rotor. form thrust sweeps at Vtip = 327 and 392 ft/sec. Figure 13 Two sets of blades were tested. Abiding by Harrington’s shows the comparison of the coaxial rotor FM between mea- terminology, rotors tested with one set of blades are referred sured data, RCAS predictions, and OVERTURNS predictions (Ref. 16). At the lower thrust levels (i. e., CT 0.0050), to as “Rotor 1” while rotors tested with the other set of blades ≤ are referred to as “Rotor 2”. Both sets of blades are untwisted RCAS predictions are in good agreement with measured data. and feature symmetric NACA four-digit airfoils. The chord However, at thrust levels of CT > 0.0055, RCAS predictions distribution of the blades on “Rotor 1” and “Rotor 2” is lin- are higher than the measured data and the disparity increases ear (ratio of tip chord to root chord is 0.35) and constant, re- with increasing thrust. spectively. For “Rotor 1,” the thickness to chord ratio varies OVERTURNS predictions are generally in good agree- nonlinearly with the airfoil being the NACA 0031 and NACA ment with measured data (especially for CT 0.0060) for ≥ 0012 at blade root and tip, respectively. For “Rotor 2,” the the coaxial rotor thrust sweep at Vtip = 392 ft/sec; thus, it thickness to chord ratio varies linearly with the airfoil being is meaningful to compare the predictions between OVER- the NACA 0031 and NACA 0015 at blade root and tip, re- TURNS and RCAS of parameters, which require knowledge spectively. The maximum tip speed, as tested, was Vtip = 500 of individual rotor performance, to gain additional insights. and 392 ft/sec for “Rotor 1” and “Rotor 2,” respectively. Table Figure 14 shows the comparison, between OVERTURNS pre- 2 compares some geometric parameters and hover operating dictions and RCAS predictions, of rotor performance for the conditions (at standard sealevel and maximum tip speed as thrust sweep as functions of the total coaxial system thrust tested) for these full–scale rotors. CT . Predictions in individual rotor thrust are close with RCAS 5 predicting slightly less and more than OVERTURNS for the required even for a coaxial rotor. However, FM is also fre- upper and lower rotor, respectively. RCAS predictions for in- quently used as a metric for comparing the hover performance dividual rotor torque are less than OVERTURNS and the dis- between different rotors. In spite of requiring less torque than parity increases with increasing thrust. For the upper rotor, the the single rotor, Fig. 15 shows that the modified definition effects of lower predictionsby RCAS in both thrust and torque yields values that are significantly lower than the single rotor. offset each other so that predictions in FM is close between A major reason for this is that the ideal power neglects inter- RCAS and OVERTURNS. For the lower rotor, the effects of ference effects between the two rotors, so the ideal power is higher and lower predictions by RCAS in thrust and torque, drastically lower than the actual power. (A situation that does respectively, both lead to higher predictions in FM relative not exist for single rotors.) If one insists on using FM as a to OVERTURNS. As discussed previously, the thrust sharing metric for comparing hover performance between single and ratio CT,L/CT,U influences individual rotor FM but does not coaxial rotors, then it appears that the modified definition is have a strong influence on coaxial rotor FM. Regarding the not useful. For this reason, the traditional definition of FM higher values of coaxial rotor FM that RCAS predicts com- was used in previous sections of this paper. pared to measured data for CT > 0.0055, the primary issue remains the simple idea that RCAS is predicting less torque CONCLUDING REMARKS than required at a given thrust. Nevertheless, RCAS predic- tions do reflect all general trends found in both measured data Predictions from a rotorcraft comprehensive analysis code, and OVERTURNS. namely RCAS, of rotor performance parameters in hover are compared with measured data and CFD/OVERTURNS predictions (where available) for model–scale and full–scale COMPARING SINGLE AND COAXIAL coaxial rotors. Main features of the RCAS analytical model- ROTOR PERFORMANCE ing include a free vortex wake model, the usage of this vor- tex wake model as the aerodynamic interference model, C81 An oft cited advantage of coaxial rotor configurations is that lookup tables with Reynolds number correction, and trim con- it requires less torque to generate a given thrust in hover than straints on the thrust and torque of the coaxial rotor system. single rotor configurations of equivalent rotor solidities. In For each rotor, RCAS predictions of rotor performance pa- the experiment by Ramasamy (Ref. 18), the model–scale ro- rameters in the single rotor configuration are compared with tor with untwisted blades was also tested with six blades in the measured data and deemed satisfactory prior to performing σ single rotor configuration; thus, its solidity is = 0.168 and coaxial rotor simulations. Test points for the model–scale ro- equal to that of the coaxial rotor. Figure 15 shows both mea- tors, which include one rotor with untwisted blades and an- sured data and RCAS predictions of performance parameters other rotor with highly twisted blades, form thrust sweeps and for the coaxial rotor and six–bladed, single rotor. The per- axial separation sweeps. Test points for the full–scale rotors, formance parameters, which are the total system torque CQ which include one rotor with linearly tapered blades and one and system figure of merit FM, are shown as functions of the rotor with constant–chord blades, form thrust sweeps. The system thrust CT . For coaxial rotors, both the traditional and comparisons and results from this paper lead to the following modified definitions of FM corresponding to Eqs. (1) and (2), conclusions: respectively, are shown. The plotted values for the traditional definition of FM correspond to what is already shown in Fig. 1) For all thrust and axial separation sweeps, RCAS pre- 3. The figure confirms that coaxial rotors have a lower torque dictions reflect the same trends as found in the measured data requirement than single rotors and hence also higher values and CFD predictions. The majority of the RCAS predictions for the traditional figure of merit. are also in good agreement with measured data. These com- parisons provide readers with an idea of the level of accuracy The RCAS predictions also correctly reflect the lower of RCAS performance predictions for coaxial rotors in hover. torque requirementfor coaxial rotors. Furthermore, the RCAS 2) Previous studies demonstrated that the thrust sharing ra- predictions show good agreement with measured data for the tio C /C does not have a strong influence on the overall six–bladed, single rotor. These results, along with the good T,L T,U coaxial rotor performance. The RCAS predictions not only agreement for the three–bladed case in Fig. 2, is a demonstra- confirm the previous statement, but it also demonstrate that tion that the RCAS free vortex wake model is able to accu- individual rotor performance is highly sensitive to the thrust rately capture the effects of changing blade number. sharing ratio. This point is most vivid in the results for the FM is often thought of as the ratio of the ideal to actual model–scale rotor with untwisted blades. power required to hover for a given thrust. For a coaxial ro- 3) RCAS predictions for individual rotor thrust are mostly tor, the ideal power is found from assuming a uniform dis- in good agreement with both measured data and CFD pre- tribution of inflow over each rotor disk with no loss in effi- dictions, but this is less frequently the case for individual ciency due to interferenceeffects between the two rotors. This rotor torque. For the model–scale rotor with highly twisted 3/2 3/2 √ yields CP,ideal = CT,U +CT,L / 2. The nondimensional ac- blades, RCAS predictions for torque are consistently higher tual power required is CQ,U +CQ,L. Therefore, the modified than measured data. For the full–scale rotor with constant– definition of coaxial FM from Eq. (2) is valid if one main- chord blades, RCAS predictions for torque are lower than tains that FM is defined as the ratio of ideal to actual power CFD predictions. Not by coincidence, these are also the two 6 rotors in which RCAS predictions show the most amount of 9Harrington, R. D., “Full–Scale–Tunnel Investigation of the difference from measured data in terms of coaxial rotor FM. Static–Thrust Performance of a Coaxial Rotor,” 4) For the model–scale rotor with untwisted blades, mea- NACA TN 2318, Mar. 1951. sured data confirms that coaxial rotors require less torque 10 compared to single rotors, of equivalent rotor solidities, to McAlister, K. W., and Tung, C., “Performance and Flow hover for a given thrust. This is also correctly predicted by Field Measurements for a Hovering Coaxial Rotor with RCAS. Highly Twisted Blades,” USARDECOM AMR–CS–08–487, Mar. 2008.

ACKNOWLEDGMENTS 11Arents, D. N., “An Assessment of the Hover Performance The authors are grateful to Dr. Manikandan Ramasamy, of the of the XH–59A Advancing Blade Concept Demonstration He- U. S. Army ADD–AFDD, for providing the measured data licotper,” USAAMRDEL–TN–25, May 1977. from his experiment (Ref. 18) and for useful discussions re- 12Johnson, W., “Influence of Lift Offset on Rotorcraft Per- lated to the subject of this paper. The authors are also grate- formance,” NASA TP–2009–215404, Nov. 2009. ful to Dr. Joon Lim, of the U. S. Army ADD–AFDD, and Dr. Wayne Johnson, of NASA Ames Research Center, for 13Dingeldein, R. C., “Wind–Tunnel Studies of the Per- providing details of the analytical models from their work formance of Configurations,” NACA TN 3236, (Refs. 8,12). The authors also appreciate Dr. Vinod K. Laksh- Aug. 1954. minarayan, of Science and Technology Corporation, for pro- 14 viding OVERTURNS predictions from his work (Ref. 16). Ruddell, A. J., “Advancing Blade Concept (ABC) Technology Demonstrator,” USAAVRADCOM TR–81–D–5, REFERENCES Apr. 1981. 15 1Coleman, C. P. , “A Survey of Theoretical and Experimen- Ruzicka, G. C., and Strawn, R. C., “Computational tal Coaxial Rotor Aerodynamic Research,” NASA TP 3675, Fluid Dynamics Analysis of a Coaxial Rotor Using Overset 1997. Grids,” American Helicopter Society Specialists’ Conference on Aeromechanics, San Francisco, CA, Jan. 2008. 2Wachspress, D. A., and Quackenbush, T. R., “Impact of Ro- tor Design on Coaxial Rotor Performance, Wake Geometry 16Lakshminarayan, V. K., and Baeder, J. D., “High– and Noise,” American Helicopter Society 62nd Annual Fo- Resolution Computational Investigation of Trimmed Coaxial rum, Phoenix, AZ, May 2006. Rotor Aerodyanmics in Hover,” Journal of the American He- licopter Society, Vol. 54, (4), Oct. 2009, pp. 042008. 3 Nagashima, T., Shinohara, K., and Baba, T., “A Flow Visu- doi: 10.4050/JAHS.54.042008 alization Study for the Tip Vortex Geometry of the Co–axial Rotor in Hover,” Journal of the Japan Society for Aeronautical 17Rajmohan, N., Zhao, J., and He, C., “A Coupled Vor- and Space Sciences, Vol. 25, (284), Sep. 1977, pp. 442–445. tex Particle/CFD Methodology for Studying Coaxial Rotor doi: 10.2322/jjsass1969.25.442 Configurations,” American Helicopter Society 5th Decennial Aeromechanics Specialists’ Conference, San Francisco, CA, 4Shinohara, K., “Optimum Aerodynamic Character of the Jan. 2014. Coaxial Counter Rotating Rotor System,” Ph. D. thesis, Na- tional Defense Academy, Feb. 1977. 18Ramasamy, M., “Measurements Comparing Hover Perfor- 5Nagashima, T., Ouchi, H., and Sasaki, F., “Optimum Perfor- mance of Single, Coaxial, Tandem, and Tilt-Rotor Configu- mance and Load Sharing of Co–axial Rotor in Hover,” Jour- rations,” American Helicopter Society 69th Annual Forum, nal of the Japan Society for Aeronautical and Space Sciences, Phoenix, AZ, May 2013. Vol. 26, (293), June 1978, pp. 325–333. 19Saberi, H., Khoshlahjeh, M., Ormiston, R. A., and doi: 10.2322/jjsass1969.26.325 Rutkowski, M. J., “Overview of RCAS and Application to 6Andrew, M. J. , “Co–axial Rotor Aerodynamics in Hover,” Advanced Rotorcraft Problems,” American Helicopter Soci- Vertica, Vol. 5, (2), 1981, pp. 163–172. ety 4th Decennial Specialists’ Conference on Aeromechanics, San Francisco, CA, Jan. 2004. 7Akimov, A. I., Butov, V. P., Bourtsev, B. N., and Se- lemenev, S. V., “Flight Investigation of Coaxial Rotor Tip Vor- 20Saberi, H., Hasbun, M. J., Hong, J., Yeo, H., and Ormis- tex Structure,” American Helicopter Society 50th Annual Fo- ton, R. A., “Overview of RCAS Capabilities, Validations, and rum, Washington, DC, May 1994. Rotorcraft Applications,” American Helicopter Society 71st Annual Forum, Virginia Beach, VA, May 2015. 8Lim, J. W., McAlister, K. W., and Johnson, W., “Hover Per- formance Correlation for Full–Scale and Model–Scale Coax- 21Jain, R., Yeo, H., Ho, J. C., and Bhagwat, M., “An Assess- ial Rotors,” Journal of the American Helicopter Society, ment of RCAS Performance Prediction for Conventional and Vol. 54, (3), July 2009, pp. 032005. Advanced Rotor Configurations,” American Helicopter Soci- doi: 10.4050/JAHS.54.032005 ety 70th Annual Forum, Montr´eal, Canada, May 2014. 7 22Anonymous, “RCAS Theory Manual,” USAAM- COM/AFDD TR 02–A–005, Mar. 2005. 23Leishman, J. G., Bhagwat, M. J., and Bagai, A., “Free– Vortex Filament Methods for the Analysis of Helicopter Ro- tor Wakes,” Journal of Aircraft, Vol. 39, (5), Sep.–Oct. 2002, pp. 759–775. doi: 10.2514/2.3022 24Yamauchi, G. K., and Johnson, W., “Trends of Reynolds Number Effects on Two–Dimensional Airfoil Characteris- tics for Analyses,” NASA–TM–84363, Apr. 1983. 25Leishman, J. G., and Syal, M., “Figure of Merit Definition for Coaxial Rotors,” Journal of the American Helicopter So- ciety, Vol. 53, (3), July 2008, pp. 290–300. doi: 10.4050/JAHS.53.290

8 Fig. 1. Physical setup for testing the coaxial, model–scale rotor.

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4 FM FM 0.3 0.3 Test, 800 RPM Test, 1200 RPM 0.2 RCAS, 800 RPM 0.2 RCAS, 1200 RPM

0.1 0.1

0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -2 -2 CT x 10 CT x 10

Fig. 2. Performance of single, model–scale rotor with untwisted blades.

9 0.7 8

0.6 7

6 0.5 5 -4 -2 0.4 4 x 10x x 10 x T Q C 0.3 C 3 Test, upper rotor Test, upper rotor 0.2 Test, lower rotor Test, lower rotor RCAS, upper rotor 2 RCAS, upper rotor RCAS, lower rotor RCAS, lower rotor 0.1 1

0 0 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 -2 -2 System Thrust, CT x 10 System Thrust, CT x 10

1 0.8

0.7 0.8 0.6

0.5 0.6 T,U

/C 0.4 FM T,L C 0.4 Test 0.3 Test, upper rotor RCAS Test, lower rotor 0.2 RCAS, upper rotor 0.2 RCAS, lower rotor 0.1

0 0 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 -2 -2 System Thrust, CT x 10 System Thrust, CT x 10

0.8

0.7

0.6

0.5

0.4 FM

0.3 Test, coaxial RCAS, coaxial 0.2

0.1

0 0 0.2 0.4 0.6 0.8 1 1.2 -2 System Thrust, CT x 10

Fig. 3. Performance of coaxial, model–scale rotor with untwisted blades, h/D = 0.07, and 1200 RPM.

10 1 5

0.8 4

0.6 3 -4 -2 x 10x x 10 x T Q C 0.4 C 2 Test, upper rotor Test, lower rotor RCAS, upper rotor 0.2 Test, upper rotor 1 Test, lower rotor RCAS, lower rotor RCAS, upper rotor RCAS, lower rotor 0 0 0 0.3 0.6 0.9 1.2 1.5 0 0.3 0.6 0.9 1.2 1.5 h/D h/D

1 0.7

0.6 0.8 0.5

0.6 0.4 T,U /C FM T,L

C 0.3 0.4 Test RCAS 0.2 0.2 Test, upper rotor 0.1 Test, lower rotor RCAS, upper rotor RCAS, lower rotor 0 0 0 0.3 0.6 0.9 1.2 1.5 0 0.3 0.6 0.9 1.2 1.5 h/D h/D

0.7

0.6

0.5

0.4 FM 0.3 Test, coaxial 0.2 RCAS, coaxial

0.1

0 0 0.3 0.6 0.9 1.2 1.5 h/D

Fig. 4. Performance of coaxial, model–scale rotor with untwisted blades, 800 RPM, CT 0.007, and various h/D. ≈

11 1 10

0.8 8

0.6 6 -4 -2 x 10x x 10 x T Q C 0.4 C 4 Test, upper rotor Test, upper rotor Test, lower rotor Test, lower rotor RCAS, upper rotor RCAS, upper rotor 0.2 RCAS, lower rotor 2 RCAS, lower rotor

0 0 0 0.3 0.6 0.9 1.2 1.5 0 0.3 0.6 0.9 1.2 1.5 h/D h/D

1 0.8

0.7 0.8 0.6

0.5 0.6 T,U

/C 0.4 FM T,L C 0.4 Test 0.3 RCAS 0.2 0.2 Test, upper rotor Test, lower rotor 0.1 RCAS, upper rotor RCAS, lower rotor 0 0 0 0.3 0.6 0.9 1.2 1.5 0 0.3 0.6 0.9 1.2 1.5 h/D h/D

0.8

0.7

0.6

0.5

0.4 FM

0.3 Test, coaxial RCAS, coaxial 0.2

0.1

0 0 0.3 0.6 0.9 1.2 1.5 h/D

Fig. 5. Performance of coaxial, model–scale rotor with untwisted blades, 800 RPM, CT 0.014, and various h/D. ≈

12 0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4 FM FM 0.3 0.3 Test, 800 RPM Test, 900 RPM 0.2 RCAS, 800 RPM 0.2 Test, 1000 RPM Test, 1100 RPM RCAS, 900 RPM 0.1 0.1 RCAS, 1000 RPM RCAS, 1100 RPM 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 -2 -2 CT x 10 CT x 10

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4 FM FM 0.3 0.3 Test, 1200 RPM Test, 1300 RPM 0.2 RCAS, 1200 RPM 0.2 Test, 1400 RPM RCAS, 1300 RPM RCAS, 1400 RPM 0.1 0.1

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 -2 -2 CT x 10 CT x 10

Fig. 6. Performance of single, model–scale rotor with highly twisted blades.

13 0.8 10

9 0.7 8 0.6 7 0.5 6 -4 -2 0.4 5 x 10x x 10 x T Q C C 4 0.3 Test, upper rotor Test, upper rotor Test, lower rotor 3 Test, lower rotor 0.2 RCAS, upper rotor RCAS, upper rotor RCAS, lower rotor 2 RCAS, lower rotor 0.1 1

0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -2 -2 System Thrust, CT x 10 System Thrust, CT x 10

1 0.8

0.9 0.7 0.8 0.6 0.7 0.5 0.6 T,U

/C 0.5 0.4 FM T,L C 0.4 Test 0.3 Test, upper rotor RCAS 0.3 Test, lower rotor 0.2 RCAS, upper rotor 0.2 RCAS, lower rotor 0.1 0.1

0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -2 -2 System Thrust, CT x 10 System Thrust, CT x 10

0.8

0.7

0.6

0.5

0.4 FM

0.3 Test, coaxial RCAS, coaxial 0.2

0.1

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -2 System Thrust, CT x 10

Fig. 7. Performance of coaxial, model–scale rotor with highly twisted blades, h/D = 0.07, and 1200 RPM.

14 1 10

0.9 9

0.8 8

0.7 7

0.6 6 -4 -2 0.5 5 x 10x x 10 x T Q C 0.4 C 4 Test, upper rotor 0.3 3 Test, lower rotor RCAS, upper rotor 0.2 Test, upper rotor 2 Test, lower rotor RCAS, lower rotor 0.1 RCAS, upper rotor 1 RCAS, lower rotor 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 h/D h/D

1 0.8

0.9 0.7 0.8 0.6 0.7 0.5 0.6 T,U

/C 0.5 0.4 FM T,L C 0.4 Test 0.3 0.3 RCAS 0.2 0.2 Test, upper rotor Test, lower rotor 0.1 0.1 RCAS, upper rotor RCAS, lower rotor 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 h/D h/D

0.8

0.7

0.6

0.5

0.4 FM

0.3 Test, coaxial RCAS, coaxial 0.2

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 h/D

Fig. 8. Performance of coaxial, model–scale rotor with highly twisted blades, 800 RPM, CT 0.014, and various h/D. ≈

15 1.2

1

0.8 -2 0.6 x 10 x T

C McAlister and Tung, upper rotor McAlister and Tung, lower rotor 0.4 CAMRAD II, upper rotor CAMRAD II, lower rotor Ramasamy, upper rotor 0.2 Ramasamy, lower rotor RCAS, upper rotor RCAS, lower rotor 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 h/D

Fig. 9. Individual rotor thrust of coaxial, model–scale rotors with identical highly twisted blades, 800 RPM, and various h/D. Both measured data, from the experiment by McAlister and Tung, and CAMRAD II predictions are courtesy of Joon Lim (Ref. 8)

0.7

0.6

0.5

0.4 FM 0.3

Test, Vtip = 500 ft/sec 0.2 RCAS, Vtip = 500 ft/sec

0.1

0 0 0.1 0.2 0.3 0.4 -2 CT x 10

Fig. 10. Performance of single, full–scale, Harrington “Rotor 1”.

16 0.7

0.6

0.5

0.4 FM 0.3

Test, Vtip = 450 ft/sec 0.2 Test, Vtip = 500 ft/sec RCAS, Vtip = 450 ft/sec RCAS, V = 500 ft/sec 0.1 tip

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -2 CT x 10

Fig. 11. Performance of coaxial, full–scale, Harrington “Rotor 1”.

0.7

0.6

0.5

0.4 FM 0.3

Test, Vtip = 262 ft/sec 0.2 Test, Vtip = 392 ft/sec RCAS, Vtip = 262 ft/sec RCAS, V = 392 ft/sec 0.1 tip

0 0 0.2 0.4 0.6 0.8 1 -2 CT x 10

Fig. 12. Performance of single, full–scale, Harrington “Rotor 2”.

17 0.7

0.6

0.5

0.4 FM 0.3

Test, V = 327 ft/sec 0.2 tip Test, Vtip = 392 ft/sec

OVERTURNS, Vtip = 392 ft/sec 0.1 RCAS, Vtip = 327 ft/sec RCAS, Vtip = 392 ft/sec 0 0 0.2 0.4 0.6 0.8 1 -2 CT x 10

Fig. 13. Performance of coaxial, full–scale, Harrington “Rotor 2”. OVERTURNS predictions are courtesy of Vinod K. Lakshminarayan (Ref. 16).

18 0.6 6

0.5 5

0.4 4 -4 -2 0.3 3 x 10x x 10 x T Q C C

0.2 2

OVERTURNS, upper rotor OVERTURNS, upper rotor 0.1 OVERTURNS, lower rotor 1 OVERTURNS, lower rotor RCAS, upper rotor RCAS, upper rotor RCAS, lower rotor RCAS, lower rotor 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 -2 -2 System Thrust, CT x 10 System Thrust, CT x 10

1 0.6

0.5 0.8

0.4 0.6 T,U

/C 0.3 FM T,L C 0.4 OVERTURNS 0.2 RCAS OVERTURNS, upper rotor 0.2 0.1 OVERTURNS, lower rotor RCAS, upper rotor RCAS, lower rotor 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 -2 -2 System Thrust, CT x 10 System Thrust, CT x 10

0.7

0.6

0.5

0.4 FM 0.3

Test, coaxial 0.2 OVERTURNS, coaxial RCAS, coaxial 0.1

0 0 0.2 0.4 0.6 0.8 1 -2 System Thrust, CT x 10

Fig. 14. Performance of coaxial, full–scale, Harrington “Rotor 2”, with Vtip = 392 ft/sec. OVERTURNS predictions are courtesy of Vinod K. Lakshminarayan (Ref. 16).

19 Test, single 8 0.7 Test, coaxial, traditional Test, coaxial, modified 7 0.6 RCAS, single RCAS, coaxial, traditional RCAS, coaxial, modified

-4 6 0.5 x 10 x

Q 5 0.4 4 FM 0.3 3 Test, single Test, coaxial 0.2 System Torque,C System 2 RCAS, single RCAS, coaxial 1 0.1

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -2 -2 System Thrust, CT x 10 System Thrust, CT x 10

Fig. 15. Comparison of system performance, between coaxial and single rotor configurations of equivalent rotor solidi- ties, for the model–scale rotor with untwisted blades at 1200 RPM. For the coaxial rotor, h/D = 0.07.

20