A Simple Analytical Fuselage-Induced Velocity Model for Comprehensive Rotor Codes

st 41 European Rotorcraft Forum 2015

A SIMPLE ANALYTICAL FUSELAGE-INDUCED VELOCITY MODEL

FOR COMPREHENSIVE ROTOR CODES

* ** *** **** Berend G. van der Wall , Marc Wentrup , Ganesh Rajagopalan , Sung N. Jung * Institute of Flight Systems, DLR Braunschweig, Germany ** Institute of Aerodynamics and Flow Technology, DLR Braunschweig, Germany *** Department of Aerospace Engineering, Iowa State University, Ames, IA, US **** Department of Aerospace Engineering, Konkuk University, Seoul, Korea Abstract A simple analytical model to account for fuselage-induced velocities at rotor blade elements and at rotor wake nodes is described. The method is applied to three different fuselage configurations. Results obtained with a comprehensive rotor code show the fuselage effect on rotor trim controls, comparing the isolated rotor with inclusion of the fuselage for the same trim. This is compared to a simple analytical estimate of the fuse- lage effect using blade element/momentum theory. It is found that in forward flight the lateral control is main- ly affected by fuselage effects. Rotor thrust can be varied by the presence of the fuselage, depending on its angle of attack, and the fuselage influence generally increases with flight speed.

Nomenclature 𝐴 , 𝐵 Non - dimensional begin and end of the aerodynamic part of the blade 𝑣 Fuselage - induced velocity in 𝑧 - direction 𝑖𝑧𝑓 𝐴 , 𝐴 , 𝑒𝑡𝑐 . Magnitude and its coefficients of induced 𝑥 , 𝑦 , 𝑧 Shaft - fixed coordinate system, origin in velocity function rotor hub 𝑐 Polynomial coefficients 𝑥 , 𝑦 Coordinates of induced velocity peaks 𝑛𝑗 0 0 𝐶 , 𝐶 Thrust and weight coefficient 𝑧 Coordinate of fuselage centerline below 𝑇 𝑊 0 Interpolation factors the hub 𝑓 , 𝑓 𝛼 𝛽 𝛼 , 𝛽 Fuselage angle of attack, side - slip angle Mach number 𝑀 ∞ 𝛼 Blade element angle of atack 𝑅 , 𝑟 Radius, non - dimensional radial coord i- 𝑎 Θ , Θ , Θ Blade pitch angle, longitudinal and lateral nate 𝑆 𝐶 control angle 𝑆 , 𝑒𝑡𝑐 . Shape parameter 𝐴 in 𝑧 - direction 𝐴 0 Non - dimensional fuselage - induced veloc i- 𝜆 𝑆 , 𝑆 , 𝑆 , Shape parameters in 𝑥 and 𝑦 direction 𝑖𝑧𝑓 𝑥 𝑦 𝑥 0 ty, referenced to 𝑉 and their coefficients ∞ 𝑆 , 𝑒𝑡𝑐 .

𝑦 0 𝜇 Rotor advance ratio 𝑢 , 𝑑 , 𝑡 Subscripts denoting upwash, downwash 𝜎 Rotor solidity and tail boom contributions 𝜓 Rotor blade azimuth angle 𝑉 Free - stream velocity ∞ Ω Rotor rotational speed 𝑉 , 𝑉 Velocity tangential and perpendicular to 𝑇 𝑃 rotor blade section effort. A good overview of the multitude of interac- 1. INTRODUCTION tions is given by Sheridan [2] .

Rotorcraft comprehensive codes are used for de- tailed flight mechanics, aerodynamics, dynamics and In this paper, only the interaction between the fuse- acoustics research. They usually include separate lage and the rotor is addressed in this unidirectional sophisticated models for each component, like two- sense (the reverse interaction from the rotor to the dimensional unsteady blade section aerodynamics, fuselage is left for future studies). The problem is beam theory for elastic blade motion, free-wake for sketched in Fig. 1 (a). At any flight speed the fuse- the rotor-induced velocities, tabulated aerodynamic lage causes the air to pass around it and thus to characteristics for the fuselage, and other compo- generate an upwash in the front half of the rotor disk nent models. Interactions between these compo- and a downwash in the rear half of it. Since flight nents – and others obstacles like ground, buildings, speeds of conventional helicopters are theoretically trees, other aircraft – often are either ignored, or limited to 360 km/h (= 100 m/s, ≈ 200 kts) the Mach significantly simplified, or introduced by means of number does not exceed 0.3 and therefore this rep- any type of computational fluid dynamics (CFD) resents an incompressible flow.

code of low order (panel methods, for example [1] ) The rotor is operating outside the boundary layer of to high fidelity (Navier-Stokes solvers) at the ex- the fuselage in the outer potential flow; therefore pense of medium to huge additional computational panel methods may well be applied for many opera- st 41 European Rotorcraft Forum 2015 tional conditions of interest. One such application This paper tries to fill this gap and presents a simple was given in Stepniewski’s textbook on helicopter analytical model of fuselage-induced velocities for aerodynamics [3] and the computed deflection of the the fuselage-rotor interference and the fuselage- free-stream flow is sketched in Fig. 1 (b). wake interference, for usage at least in forward flight and descent conditions. The importance of interfer-

Thrust & downwash

ence models grows with the proximity of the rotor to upwash downwash

the fuselage or to other interfering bodies like wings in compound designs [2] , [6] . Fuselage-rotor inter-

V

ference can significantly degrade rotor performance  and adversely affect vibration [4] , [7] . To avoid this

already in the pre-design phase where a large Weight & download

(a) Principle amount of parameter variations needs to be done using comprehensive analysis codes a simplified method to represent the fuselage-rotor interference effects is needed since in this stage of development CFD is unaffordable.

The solution proposed to this problem is the genera- tion of a semi-empirical mathematical model that accounts for the specific fuselage flow field charac- teristics, the operational conditions, and the rotor- fuselage separation distances analytically. For this, a small set of isolated steady fuselage CFD compu- tations is sufficient to generate a data base of fuse- lage-induced velocities within the volume defined by the rotor blade motion. This may involve either panel codes, Euler methods, or Reynolds-averaged Navier Stokes (RANS) CFD methods including flow separa- (b) Free-stream flow deflection, adapted from [3] tion.

Fig. 1. Principle of fuselage-rotor interference.

Based on these data the parameters of the math model are identified. Then the model is ready for Depending on the shape of the fuselage, the angle being used in comprehensive analysis without the of attack towards the free-stream and the proximity need of further CFD computations. Because the of the rotor to it the local flow deflection may well model consists of a few lines of algebraic equations exceed 10 deg and modify blade element aerody- only, its evaluation is negligible in terms of computa- namic loads significantly relative to an isolated rotor.

tional effort compared to CFD and can be included An application using panel methods to investigate in all the parameter variation studies without penalty.

this effect for different rotor-fuselage separation distances was done by Huber [4] . It was found that Additional details on the modeling approach and the fuselage influence is highly non-linear with re- results presented herein may be found in [8] .

spect to the separation distance and that the fuse- 2. FUSELAGE MODELS AND CFD SETUP lage significantly increases vibratory loads, com- pared to the isolated rotor. No data about how much Within this study three fuselages will be investigated: trim controls or thrust are affected were given.

 the Large Rotor Test Apparatus (LRTA), Many investigations regarding fuselage-rotor and  the smaller Rotor Test Apparatus (RTA), rotor-fuselage interactions have been performed  the Higher Harmonic Control Aeroacoustic since then, nowadays mainly involving coupled Rotor Test (HART).

computational structural dynamics and CFD solu- While the first two are used in the National Full- tions. It would exceed the scope of this paper to Scale Aerodynamics Complex (NFAC) at NASA outline a review of all this work, and a comprehen- Ames, California, the third one is used by DLR in the sive overview is found in [5] . Topics addressed were large low-speed facility of the German-Dutch wind the impingement of the rotor wake on the fuselage, tunnels in the Netherlands. All three of them are the variation of fuselage forces and moments due to sketched with their dimensions in Fig. 2 . Note that the rotor and those of the rotor due to the presence they are differently scaled; 𝑅 is the rotor radius and of the fuselage, and effects of the fuselage on the 𝑧 is the position of the fuselage centerline below the wake convection. No attempt, however, was made hub center, which forms the origin of the coordinate to simplify the physical modeling in an engineering system used.

way and always some kind of CFD was used to compute those effects.

st 41 European Rotorcraft Forum 2015 The LRTA flow field is computed using the DLR TAU In addition, the overall grid size and density was code, an unstructured compressible RANS solver very different and a comparison of these data is [9] , the RTA flow field by RotCFD, a structured in- given in Table 1 .

compressible RANS solver [10] , and the HART fuse- The attitudes of the LRTA and RTA are limited to the lage by a structured compressible RANS solver range −20° ≤ 𝛼 ≤ +15° and similar for the HART KFLOW [11] . Due to the incompressibility character used in the DNW, however, for this fuselage CFD of the flow field the fuselage-induced velocities with- computations were performed in the range −90° ≤ in the volume of rotor blade operation above the 𝛼 ≤ +90° . 𝛼 = −90° represents a vertical climb fuselage are linearly proportional to the wind speed where the flow is attacking the fuselage from the top, 𝑉 . Thus, the most interesting component of the ∞ as also is the case in hover due to the rotor down- fuselage-induced velocities normal to the rotor disk, wash. 𝛼 = −20° represents a steep climb, 𝛼 = −10° 𝑣 , can be made non-dimensional in the form 𝑖𝑧𝑓 either a moderate climb or high-speed level flight, 𝑣 𝑉 ⁄ which is independent of 𝑉 . Thus, only one 𝑖𝑧𝑓 ∞ ∞ 𝛼 = 0° a low speed forward flight or high speed dive, appropriate free-stream velocity can be used in CFD 𝛼 = +10° is characteristic for moderate to low speed computations. Different values were chosen for the descent, and finally 𝛼 = +90° resembles a vertical various computations that were performed inde- descent for the fuselage. The settings where data pendently by the contributors. The air data for all the were generated are also given in Table 1 .

CFD computations are standard atmosphere at sea level and 15°𝐶 temperature.

(a) LRTA for UH-60 size ( rotors 𝑅 = 26 . 83 𝑓𝑡 = 8 . 179 𝑚 ) ; 𝑧 𝑅 ⁄ = − 0 . 2676 (b) RTA for Bo105 size rotors ( 𝑅 = 16 . 11 𝑓𝑡 = 4 . 91 𝑚 ) ; 𝑧 𝑅 ⁄ = − 0 . 4 (c) HART for model-scale rotors ( 𝑅 = 6 . 56 𝑓𝑡 = 2 . 0 𝑚 ) ; ⁄ 𝑧 𝑅 = − 0 . 3 Fig. 2. Fuselage bodies investigated.

Table 1: Parameters used in CFD computations.

Fuselage (code used) LRTA (TAU) RTA (RotCFD) HART (KFLOW) Compressible yes no yes Solution type steady RANS steady RANS steady RANS Grid type unstructured structured structured Outer grid size, multiples of 𝑅 149 . 1 248 . 3 10 Total discretization, times 10 2 . 2 (points) 0 . 066 (cells) 31 . 5 (cells) Free - stream velocity, 𝑉 50 𝑚 𝑠 ⁄ 51 . 4 𝑚 𝑠 ⁄ 32 . 9 𝑚 𝑠 ⁄ ∞ Free - stream Mach number, 𝑀 0 . 147 0 . 151 0 . 097 ∞ Angles of attack computed, 𝛼 − 20° , ± 15° , ± 10° , − 20° , ± 15° , ± 10° , ± 90° , ± 60° , ± 30° , ± 5° , 0° ± 5° , 0° ± 10° , 0° st 41 European Rotorcraft Forum 2015 The reason for using steady RANS instead of un- equidistant samples (LRTA, RTA) or 84 (HART) in steady RANS is found in the application of the re- each 𝑥, 𝑦 direction.

sults: the goal is to create a mathematical model for Only in HART the flow separation effects affected the steady mean characteristics of the flow field.

the extracted data for angles of attack 𝛼 ≥ 0° . Due to Unsteady RANS will result in highly unsteady flow the rounded surface the separation line was pulsat- fields when flow separation occurs, which usually is ing and the CFD solution was unsteady. This re- the case when bluff bodies are being computed, quired special attention when fitting the math model such as helicopter fuselages. Unsteady results need to the data field since these unsteady disturbances a long-term averaging procedure to obtain averaged need to be eliminated from the parameter identifica- flow field characteristics. In addition, the steady tion process for a model that is supposed to repre- RANS is computationally much faster and thus more sent the time-averaged steady flow field.

efficient for the purposes of this study. For the mod- erate angles of attack in case of LRTA and RTA no Additionally to the main fuselage body the HART severe flow separation took place, but the more had a rearward sting adapter which was relatively extreme settings in case of HART caused strong thick in diameter and which covered the outer half flow separation on the leeward side of the fuselage.

rotor radius in the rear position. For angles of attack 𝛼 ≠ 0° its impact on the flow field could well be seen Data extraction for generating the math model was in the volume of rotor blade operation. Therefore, confined to the volume defined by the rotor blade this contribution was also modeled in addition to the operation. Assuming a typical coning of 3° and a contributions of the main fuselage body.

⁄ 1 𝑟𝑒𝑣 blade flapping with relatively large amplitude of 8° this volume can be defined by the following The different test rigs are used for different rotor cuboid in shaft axis coordinates, with 𝑥 pointing sizes, and to judge the relevance of individual fuse- downstream, 𝑦 to the starboard side and 𝑧 upwards lage shape characters on the flow field within the in rotor shaft direction: −1 ≤ 𝑥 𝑅 ⁄ , 𝑦 𝑅 ⁄ ≤ +1 and rotor disk the relative size and position of the volume −0.1 ≤ 𝑧 𝑅 ⁄ ≤ +0.2 with origin in the hub center. of interest to the fuselage dimension is important to know. This is shown in Fig. 3 for all three fuselages.

Data were extracted in four planes within this vol- ume 𝑧 𝑅 ⁄ = −0.1, 0, 0.1, 0.2 with a resolution of 65 Side view Rear view hub center hub center Side view Rear view (a) LRTA, UH-60 size rotor hub center hub center (b) RTA, Bo105 size rotor 0.3 R  (c) HART, model scale rotor Fig. 3: Relative dimensions of the rotor blade operating volume with respect to the fuselage.

st 41 European Rotorcraft Forum 2015 It is interesting to note that the lowest plane of data linearly from data for 𝛼 = −10° and −30° . In such a extraction, 𝑧 𝑅 ⁄ = −0.1 , is cut by the fuselage in case nose-down orientation the upwash in the front is of the LRTA and HART, but not so in case of the quite strong. The usual sign convention is used here RTA. Also, for the LRTA and HART there is some where downwash is positive and thus upwash is range where the fuselage surface is very close to negative.

the plane of data extraction and eventually large The peak values of upwash are close to 𝑣 𝑉 ⁄ = 𝑖𝑧𝑓 ∞ induced velocities will appear there.

−0.11 . Both LRTA and RTA indicate a very small In addition, these effects are located at small radial magnitude of downwash downstream of the hub and positions from the hub center, mainly within the right and left of the fuselage, while the centerline still blade root cutout where no airfoil can experience it, indicates upwash. In contrast, the HART fuselage and up to a radial position of 0.3𝑅 any disturbances has a rather sharp curvature behind the hub that can be ignored anyway due to the extremely small generates even in this nose-down condition a dynamic pressure in these inner regions. All these downwash of up to 𝑣 𝑉 ⁄ = 0.03 . The sting support 𝑖𝑧𝑓 ∞ effects are ignored in the parameter identification seems to be responsible for the upwash in the cen- process later on since a blade attached to the hub terline at the downstream end of the data field at center will never experience these, even when flap- 𝑥 𝑅 ⁄ = 1 . In any case the asymptotic decay of the ping downwards.

induced velocity profiles in both 𝑥 and 𝑦 directions are clearly visible. In addition, the HART fuselage 3. FUSELAGE-INDUCED VELOCITIES COMPUT- generates the largest values both in upwash and in ED BY CFD downwash; the RTA seems to have the smallest Fuselage-induced velocity fields of all three fuselag- values, but differences to the LRTA are marginal.

es are presented next for three different angles of attack covering the range of LRTA and RTA atti- The next set of data is given for a nose-up attitude of tudes. First, the lower extreme with 𝛼 = −20° is 𝛼 = +10° in Fig. 5 . In this case the downwash shown in Fig. 4 for (a) the LRTA, (b) the RTA and (c) strength dominates the upwash, which is especially the HART fuselage. Since no data were available for visible for the HART fuselage.

HART at this angle of attack, they were interpolated 0.01-0.03 0.03 0.03 0.03 -0.01-0.01 0.01 0.01 0.01 -0.03--0.01 -0.01 -0.01 -0.01 -0.05--0.03 -0.03 -0.03 -0.07--0.05 -0.03 -0.05 -0.09--0.07 -0.05 -0.05 -0.07 -0.11--0.09 -0.07 -0.07 -0.09 -0.09 -0.09 0.5203 -0.11 0.0121 -0.11 -0.11 -0.4961 -1.0043 -1.00 -1.00 -1.0043 -0.75 -0.75 -0.50 -0.50 -0.7381 -0.25 -0.4719 0.00 -0.25 0.00 0.25 -0.2057 0.0605 0.25 0.50 0.50 0.3267 0.75 0.75 0.5929 1.00 1.00 0.8591 (a) LRTA (b) RTA (c) HART (interpolated) Fig. 4: Fuselage-induced velocity distribution, 𝛼 = − 20° , 𝑧 𝑅 ⁄ = 0 . 1 .

0.07-0.09 0.09 0.09 0.09 0.05-0.07 0.07 0.07 0.07 0.03-0.05 0.05 0.05 0.05 0.01-0.03 0.03 0.03 0.03 -0.01-0.01 0.01 0.01 0.01 -0.03--0.01 -0.01 -0.01 -0.01 -0.05--0.03 -0.03 -0.03 -0.03 0.5203 -0.05 -0.05 -0.05 0.0121 -0.4961 -1.00 -1.00 -1.00 -0.75 -0.75 -0.76 -0.50 -0.50 -1.0043 -0.52 -0.25 -0.25 0.00 0.00 -0.28 0.25 -0.04 0.25 0.21 0.50 0.50 0.45 0.75 0.75 0.69 1.00 1.00 0.93 (a) LRTA (b) RTA (c) HART ⁄ Fig. 5: Fuselage-induced velocity distribution, 𝛼 = + 10° , 𝑧 𝑅 = 0 . 1 .

st 41 European Rotorcraft Forum 2015 The large fuselage curvature aft of the hub gener- that all fuselage-induced velocities must die out for ates a strong peak in downwash of 𝑣 𝑉 ⁄ = 0.1 , large distance to the fuselage. The magnitude is 𝑖𝑧𝑓 ∞ inversely reducing proportional to about the square which is much larger than that of the LRTA or RTA of the distance to the center of the fuselage, as seen with 𝑣 𝑉 ⁄ = 0.07 . However, this also causes flow 𝑖𝑧𝑓 ∞ by the data Fig. 7 for the dependence on 𝑧 𝑅 ⁄ and by separation to develop and to show up in the data of the distributions shown in Fig. 4 to Fig. 6 for the the HART fuselage at the downstream end of the ⁄ ⁄ dependence on 𝑥 𝑅 and 𝑦 𝑅 . In all angle of attack figure around the centerline.

conditions shown, an upwash is found in the front The spikes there are caused by small-scale local region and a downwash in the rear region, their size turbulence and are the instant image of an otherwise and intensity depending on the angle of attack.

unsteady phenomenon that will occur periodically or Therefore, the hypothesis is made to make use of stochastically, depending on the nature of flow sepa- the superposition principle, i.e. , to model the upwash ration. The goal of the model to be developed is not and the downwash by separate functions and then to simulate such unsteady effects. Its goal is to adding their results. This suggests using a function model the time-averaged mean velocity field. There- such as fore, such fluctuations need to be eliminated during the parameter identification process either by ignor- v A izf  (1) ing the error in these regimes or by significantly re- 2 2 V x x y y        ducing it artificially.

0 0 1 S S   x y     R R     In any case the fuselage-induced velocity distribu- tions always show the asymptotic decay for increas- wherein 𝐴 represents the peak value, 𝑆 a decay 𝑥 ing distance to the fuselage. The next will be to in- factor for the profile of the fuselage-induced velocity vestigate the flow field behavior with increasing dis- distribution in 𝑥 -direction, 𝑆 respectively in 𝑦 - 𝑦 tance to the fuselage in the remaining z-direction.

direction, and 𝑥 is the peak position on the 𝑥 -axis.

This is done for the RTA only, but is representative Since in this specific setup without a side-slip angle for the general behavior of all fuselages, and shown the fuselage-induced velocities are symmetric in in Fig. 6 . It can be seen from the different scales that lateral direction (no side-slip) the respective 𝑦 - the maximum upwash and downwash peaks of the ⁄ coordinate of the peak value is zero: 𝑦 𝑅 = 0 .

fuselage-induced velocities reduce roughly by one Therefore, it can be eliminated from the formula. For half of the values with every increment away from each of the physical phenomena observed one for- the fuselage.

mula of type Eq. (1) is applied and given subscripts This is further demonstrated when plotting the peak 𝑢, 𝑑, 𝑡 denoting the upwash, downwash and tail values of upwash and downwash, as well as the boom contributions.

peak-to-peak or ∆𝑣 𝑉 ⁄ versus the distance from 𝑖𝑧𝑓 ∞ The parameter identification is performed in three the hub center as is done in Fig. 7 . The decay of ⁄ steps. First, every plane 𝑧 𝑅 = 𝑐𝑜𝑛𝑠𝑡 . for every a n- upwash and downwash appears to be inversely to gle of attack 𝛼 is modeled fully independently from the distance from the fuselage center and asymptot- each other using Eq. ( 1 ) . Therefore, the dependency ically approaching zero for larger distances, which of each of the four parameters 𝐴 , 𝑆 , 𝑆 , 𝑥 for both 𝑥 𝑦 0 represents the expected potential theory behavior.

the upwash function and the downwash function can In terms of their extremes in upwash and downwash be plotted versus 𝑧 𝑅 ⁄ for each angle of attack (in of fuselage-induced velocities the LRTA and RTA total: 8 parameters for every of the 8 angles of a t- are quite similar to each other, while the HART fuse- tack times 4 planes 𝑧 𝑅 ⁄ = 8 ⋅ 8 ⋅ 4 = 256 param e- lage generates larger peak velocities. This is due to ters). It is found that in general they show a depen d- larger curvatures of the HART fuselage in closer ency as shown in Fig. 7 while the peak position 𝑥 proximity to the rotor than in the other two cases.

found is essentially independent on 𝑧 𝑅 ⁄ . The magn i- Also, the upwash in the front of the LRTA and the tude and the decay factors all are dependent on the RTA fuselages is always larger than the downwash distance to the fuselage, such that they may be in the rear, while the HART fuselage generates up- modeled in t he form wash and downwash of comparable magnitude.

Again, this behavior is caused by the fuselage A A  shapes and especially their curvature. The general z z    behavior, however, is quite the same for all three 0 1 S  0 A   fuselages.

R   (2) 4. SEMI-EMPIRICAL MODEL OF FUSELAGE- S S 0 y 0 x ; S S   INDUCED VELOCITIES x y 2 2 z z z z       An in-depth description of the model is given in [5] .

0 0     Physical considerations from potential theory require R R     st 41 European Rotorcraft Forum 2015 0.06-0.10 0.05-0.07 0.02-0.06 0.03-0.05 0.10 0.07 -0.02-0.02 0.01-0.03 0.06 0.05 -0.06--0.02 -0.01-0.01 0.02 0.03 -0.10--0.06 -0.03--0.01 -0.02 0.01 -0.14--0.10 -0.05--0.03 -0.06 -0.01 -0.18--0.14 -0.07--0.05 -0.10 -0.03 -0.22--0.18 -0.09--0.07 -0.14 -0.05 -0.26--0.22 -0.11--0.09 -0.18 -0.07 -0.22 -0.09 -0.26 -0.11 -1.00 -1.00 -0.72 -0.72 -0.44 -0.44 -0.16 -0.16 0.13 0.13 0.41 0.41 0.69 0.69 0.97 0.97 ⁄ ⁄ (a) 𝑧 𝑅 = − 0 . 1 (b) 𝑧 𝑅 = 0 . 0 0.03-0.04 0.02-0.03 0.02-0.03 0.04 0.03 0.01-0.02 0.01-0.02 0.03 0.02 0.00-0.01 0.00-0.01 0.02 -0.01-0.00 0.01 0.01 -0.01-0.00 -0.02--0.01 0.00 0.00 -0.02--0.01 -0.03--0.02 -0.01 -0.04--0.03 -0.01 -0.02 -0.03--0.02 -0.05--0.04 -0.03 -0.02 -0.04--0.03 -0.06--0.05 -0.04 -0.03 -0.05 -0.06 -0.04 -1.00 -1.00 -0.72 -0.72 -0.44 -0.44 -0.16 -0.16 0.13 0.13 0.41 0.41 0.69 0.69 0.97 0.97 ⁄ ⁄ (c) 𝑧 𝑅 = 0 . 1 (d) 𝑧 𝑅 = 0 . 2 Fig. 6: Influence of 𝑧 𝑅 ⁄ on fuselage - induced velocity distribution, RTA, 𝛼 = 0° .

0.6 peak - to - peak 0.3 downwash upwash -0.3 -0.1 0 0.1 0.2 (a) LRTA (thin lines) and RTA (thick) (b) HART Fig. 7: Peak fuselage-induced velocities ’ dependence on 𝑧 𝑅 ⁄ , 𝛼 = 0° .

Therein, 𝑆 represents the respective decay factor these fuselage bodies will be pl aced on their respe c- 𝐴 0 for the variation of 𝐴 in 𝑧 - direction, with 𝐴 as the tive centerline. By intention 𝑆 , 𝑆 become infinite at 0 𝑥 𝑦 amplitude at 𝑧 = 𝑧 and 𝑧 is the position of the ma x- 𝑧 = 𝑧 , which allows a smooth variation from upwash 0 0 imum of 𝐴 on the 𝑧 - axis, which is considered the on the upper side of the fuselage to downwash on center of the fuselage, measured from the hub ce n- the lower side because then the fuselage - induced ter as the reference coordinate system. The reason velocity becomes zero at 𝑧 = 𝑧 to avoid a singular i- for doing so is found in potential theory: the distrib u- ty. While the LRTA and RTA model are sufficiently tion of sources and sinks to generate a contour of represented by the upwas h and downwash function, st 41 European Rotorcraft Forum 2015 the HART has a stronger influence of the tail boom fully analytical model with a few parameters only, support and accordingly a third function of the type thus increasing the overall error. However, it is still as given by Eq. (1) is added to represent this effect. below the goal of 5% relative error.

The second step of parameter identification is to Also, due to the nature of the functions used, see combine Eqs. (1) and (2) in order to achieve an ana- Eqs. (1) and (2), the fuselage-induced velocities lytical representation for the entire (𝑥, 𝑦, 𝑧) -domain. asymptotically approach zero for ( 𝑥 , 𝑦 , 𝑧 ) 𝑅 ⁄ → ± ∞ This adds one parameter for each upwash and as required by potential theory. Therefore, the model downwsh function to a total of 10 parameters for can also be used outside of the volume of data it is each of the 8 angles of attack (reducing the total based on. If it is desired to also compute approx i- number to 10 ⋅ 8 = 80 parameters). All those param- mately the fuselage - induced velocities below the eters are then plotted versus the angle of attack to fuselage – although no data are extracted to build up identify this last dependency. The angle of attack a separate model for this region – the following co n- has been made non-dimensional through division by sideration can be applied. Due to the approximate 90° , such that in the extreme angles of 𝛼 = ±90° symmetry of the fuselage body with respect to the ⁄ (HART data are available up to these) the non- plane 𝑧 𝑅 the flow field below it can be assumed to be dimensional values become −1 and +1 . It is found that most of the parameters are essentially linear or v v izf izf quadratic in 𝛼 within the range −20° ≤ 𝛼 ≤ +15° , (4) ( , ) ( , ) z z z z        0 0 such that the following relations can be used to ap- V V   proximate them (LRTA and RTA; either 𝛼 or 𝛼 90° ⁄ may be used therein). The CFD data of the HART fuselage cover a much wider range of angle of attack −90° ≤ 𝛼 ≤ +90° for A A A A      0 00 01 02 no side-slip, 𝛽 = 0° , and also for the range of side- slip angles 0° ≤ 𝛽 ≤ +90° for no angle of attack, S S S    0 00 01 A A A 𝛼 = 0° . The behavior of the parameters with respect S S S S      to 𝛼 thus is much more non-linear; as representative (3) 0 00 01 02 y y y y example the factors influencing the shape in 𝑥 and S S S    0 00 01 x x x 𝑦 -direction are given in Fig. 10 .

x x x    The position of the upwash and downwash extremes 0 00 01 is found to vary about linearly with angle of attack.

The third and final step of parameter identification is Most of the other parameter’s dependencies with thus to identify these additional parameters, wherein respect to 𝛼 show an asymptotic behavior for large 𝐴 is the magnitude for 𝛼 = 0° , 𝐴 the variation 00 01 angles with a continuous variation between them.

linear proportional to 𝛼 and 𝐴 the variation propo r- This behavior can be described by two generic func- tional to the square of 𝛼 , etc., as given in Eq. (3).

tions, where 𝑋 is a placeholder for the parameter Similarly, 𝑥 is the peak position for 𝛼 = 0° , 𝑥 the 00 01 symbols.

variation linear proportional to 𝛼 . In total, only 22 paramete rs are resulting that all have a physical   1 1  X X   interpretation .

0 6   (1 / 90) 1 1 X X     1 1   Now the entire flow field within the volume of the data given ( −1 ≤ 𝑥 𝑅 ⁄ ≤ + 1 , − 1 ≤ 𝑦 𝑅 ⁄ ≤ + 1 , − 0 . 1 ≤   1 1  (5) or X X   0   𝑧 𝑅 ⁄ ≤ + 0 . 2 ) can be analytically represented by the 6 (1 / 90 ) 1 1 X X     1 1   math model for all angles of attack − 20° ≤ 𝛼 ≤ + 15° and any in between. The 𝑥 - position of the tail boom w , ith , , X A S S S  0 0 0 0 A x y function used only in the HART model, however, is x x x    ⁄ fixed to 𝑥 𝑅 = + 1 since it is extending also aft of 0 00 01 𝑡 the rotor. A sufficient degree of accuracy if in ave r- The exponent therein is empirical and gives best fit age is obtained, if the error relative to the peak - to - to the curves found here. This is applied to all the peak data range within each individual plane is less parameters of the upwash, downwash and tail boom equal 5% . This goal is achieved as seen in Fig. 8 , ⁄ functions, except for 𝑥 𝑅 = 1 as mentioned before 𝑡 where the mean relative error is shown after the first and for the magnitude, which is modeled by a Sine step of parameter identification, and in Fig. 9 of the function.

final model after step 3.

(6) sin A A A    The smallest errors are obtained in step 1 since this 0 00 01 t t t allows the largest degree of freedom with one pa- The side-slip conditions were computed for the rameter set for each individual plane 𝑧 𝑅 ⁄ . Step 3 HART fuselage only and the procedure of parameter combines all dependencies on 𝑥 , 𝑦 , 𝑧 and 𝛼 in one st 41 European Rotorcraft Forum 2015 identification is the same as for the angle of attack. and the second one is only present for 𝛽 ≠ 0 . The Note that in side-slip conditions the tail boom- reason is that when a pure angle of attack is present induced velocity field is represented by two func- the tail boom generates only upwash or only dow n- tions, where one of them is part of the modeling in α wash abo ve it, depending on the sign of 𝛼 .

5 5 5 0.2 4 0.2 4 0.2 0.1 0.1 0.1 3 3 3 0.0 0.0 0.0 -0.1 rror, % 2 -0.1 rror, % 2 rror, % 2 -0.1 e e e Rel. Rel. Rel.

1 1 1 0 0 -20 -15 -10 -5 0 5 10 15 -20 -15 -10 -5 0 5 10 15 -20 -15 -10 -5 0 5 10 15 (a) LRTA (b) RTA (c) HART Fig. 8: Mean relative error after step 1 of parameter identification.

5 5 5 0.2 4 0.2 4 0.2 0.1 0.1 0.1 3 3 3 0.0 0.0 0.0 -0.1 rror, % 2 -0.1 rror, % 2 2 -0.1 rror, % e e e Rel. Rel. Rel.

1 1 1 0 0 -20 -15 -10 -5 0 5 10 15 -20 -15 -10 -5 0 5 10 15 -20 -15 -10 -5 0 5 10 15 (a) LRTA (b) RTA (c) HART Fig. 9: Mean relative error after step 3 of parameter identification.

12 3 Sxu0 Syu0 Syd0 Sxd0 8 2 Syt0 Sxu-s 4 1 0 0 -90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90 (a) Shape factor, 𝑦 (b) Shape factor, 𝑥 Fig. 10: Dependence of shape factors on 𝛼; 𝛽 = 0° .

In side-slip, the tail boom generates an upwash on step 2 vary essentially proportional either to sin | 𝛽 | the windward side and a downwash on the leeward or to 1 − cos 𝛽 .

side, such that one function of the type of Eq. (1) is needed for each of these. When plotting the results of step 2 of the parameter identification versus the side-slip angle 𝛽 in the same way as done in Fig. 10 for 𝛼 , it appears that all parameters identified within st 41 European Rotorcraft Forum 2015 s function using 𝑓 and 𝑓 as given in Eq. ( 8 ) , which 𝛼 𝛽 sin | | X X X    0 1 leads to a continuous variation from pure 𝛼 to pure c (7) or (1 cos ) X X X     𝛽 . However, this blending is purely empirical and 0 1 needs verification by CFD computation for some with , , , , , X S A S S x y  0 0 0 0 0 0 A x y combined 𝛼 , 𝛽 conditions .

In side-slip all the upwash areas move to the wind- The accuracies achievable in this large range of ward side and all the downwash areas to the lee- angles including partly massive flow separation is of ward side, therefore the function centers also move course worse than in the small angle of attack towards these sides and 𝑦 ≠ 0 in Eq. (1). Step 3 of 0 range. The separated flow regimes needed to be both the angle of attack range formulation and of the ignored during the parameter identification in a side-slip angle formulation is set up in a way such proper way, and of course are ignored in the error that the model for 𝛼 = 𝛽 = 0° is the same in both computation as well. The error thus refers only to the and all variations of this basic model due to 𝛼 and 𝛽 areas of clean undisturbed flow. Nevertheless, it was are superimposed to it . In addition, any combin a- possible to remain essentially with an accuracy of tions of 𝛼 and 𝛽 – though not supported by CFD 6% of the peak-to-peak data range within each data – should be possible to predict in a meaningful plane 𝑧 𝑅 ⁄ as shown in Fig. 11 .

way as well. This is achieved by a proper blending v v v v   izf izf izf izf ( , ) ( 0 ) ( , 0 ) ( 0 , ) f f                     V V V V     (8) | |  1 cos f f f        | | | | 0.0001     0.2 0.1 0.0 -0.1 rror, % rror, % e e Rel.

Rel.

-90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90 (a) 𝛼 -variation (b) 𝛽 -variation Fig. 11: Mean relative error after step 3 of parameter identification.

It is obvious that the model is able to reconstruct the 5. COMPARISON: MODEL VERSUS CFD DATA CFD data to a high degree of accuracy sufficient at A sample result is given in Fig. 12 , comparing the least for use in comprehensive rotor codes. The CFD-generated data on the left with data reconstruc- mean values, and especially the magnitude and tion using the math model developed to the right; the shape of inflow variations experienced at the revolv- wind is always from the left. The angle of attack is ing rotor blades can therefore be taken into account zero common for all fuselages, showing the individ- in a proper, easy and reliable way. More data are ual differences due to the fuselage shapes and also given in the Appendix for angles of attack of that the model is able to adapt to these specifies in a 𝛼 = −20° in Fig. 21 and for +10° in Fig. 22 .

⁄ plane 𝑧 𝑅 = 0.1 above the hub center. Note the different peak values of upwash in the front and For the HART fuselage, extremes in angle of attack downwash in the rear, as well as the slightly different 𝛼 = ±90° are also of interest and shown in Fig. 13 .

shapes. The large circles indicate the rotor radius Again, the essential features of the CFD data are and the contour inside represent the specific fuse- well represented by the model. In case of hover or lage of the LRTA, RTA and HART. Also note that the vertical climb, 𝛼 = −90° shown in Fig. 13 (a), the scale range for the fuselage-induced velocities in fuselage is blown from top and the rotor operates in case of HART is larger than for the LRTA and RTA.

clean flow, partly blocked by the fuselage especially st 41 European Rotorcraft Forum 2015 in the center. To the right the tail boom blockage is through the entire volume of rotor operation, but is well visible and also represented by the model in confined to the centerline. The model can only rep- size and intensity. In vertical descent, 𝛼 = +90° resent the mean flow features without these turbu- shown in (b), the fuselage is blown from bottom up- lent separated structures, but the magnitude and wards and thus upon it separated flow and associat- distribution indicate this is achieved sufficiently well.

ed turbulence is found in the CFD data that passes (a) LRTA, CFD data (b) LRTA, model reconstruction (c) RTA, CFD data (d) RTA, model reconstruction (e) HART, CFD data (f) HART, model reconstruction ⁄ Fig. 12. Comparison of CFD data with the model. 𝛼 = 0°, 𝑧 𝑅 = 0.1 , wind from left.

st 41 European Rotorcraft Forum 2015 -0.02-0.02 -0.02-0.02 -0.06--0.02 0.5 0.5 -0.06--0.02 -0.1--0.06 -0.14--0.1 -0.10--0.06 -0.18--0.14 0 0 -0.14--0.10 -0.22--0.18 -0.26--0.22 -0.18--0.14 - 0.5 - 0.5 -0.22--0.18 -0.26--0.22 - 1 - 1 - 1 - 0.5 0 0.5 1 - 1 - 0.5 0 0.5 1 (a) 𝛼 = − 90° : CFD data (left), model (right); wind from top.

0.55-0.65 0.55-0.65 0.45-0.55 0.5 0.5 0.45-0.55 0.35-0.45 0.25-0.35 0.35-0.45 0.15-0.25 0.25-0.35 0.05-0.15 -0.05-0.05 0.15-0.25 -0.5 - 0.5 0.05-0.15 -0.05-0.05 -1 - 1 - 1 - 0.5 0 0.5 1 - 1 - 0.5 0 0.5 1 (b) 𝛼 = + 90° : CFD data (left), model (right); wind from bottom.

⁄ Fig. 13. Comparison of CFD data with the model for extreme angles of attack, HART, 𝑧 𝑅 = 0.1 .

Finally, the side-slip conditions are of interest. These end of the graphs for 𝛽 ≥ 30° . The associated im- are given in Fig. 14 for 𝛽 = 10°, 30°, 90° . Again, the pact on the downwash is more visible for smaller model performs well in representing the important side-slip angles 𝛽 ≤ 30° , but is still present for larger features of the CFD data. Due to the symmetry of ones. However, it is hidden in the larger scale range the fuselage, negative angles need not be modeled of fuselage-induced velocities at large side-slip an- separately; the flow field only needs to be mirrored gles.

at 𝑦 𝑅 ⁄ = 0: 𝑣 (𝑥, 𝑦, 𝑧, −𝛽) = 𝑣 (𝑥, −𝑦, 𝑧, 𝛽) . For 𝑖𝑧𝑓 𝑖𝑧𝑓 6. EFFECT OF FUSELAGE-ROTOR INTERFER- 𝛽 = 10° no flow separation takes place, this begins ENCE ON ROTOR TRIM at 𝛽 = 30° and progressively increases in intensity Analytic results can be obtained from simple blade and space covered towards 𝛽 = 90° , especially in element theory assuming constant inflow, linear the lowest plane 𝑧 𝑅 ⁄ = −0.1 . The model, of course, steady incompressible 2D aerodynamics, no flap- cannot represent these separated flow turbulent ping motion, and centrally hinged blades trimmed for structures and only the estimated mean (as if time zero hub moments [5] . Results shown in the follow- averaged) values are represented. The maximum ing are for a given thrust coefficient of 𝐶 = 𝐶 = 𝑇 𝑊 upwash peak on the windward side is found much 0 . 00484 with the rotor solidity assumed as 𝜎 = 0 . 07 , closer to the fuselage centerline than the downwash which is representative for a 2 . 2 ton Bo105 helico p- peak on the leeward side which appears at a much ter. Ana lytical results require a polar coordinate re p- larger lateral distance to the fuselage. Also, the vari- resentation of the fuselage - induced velocity field, ation of the x-position of the peak is matched well.

which so far is formulated in Cartesian coordinates, Finally, the tail boom effect shows up in an exten- see Eqs. ( 1 ) and ( 2 ) .

sion of the upwash on the windward side to the rear st 41 European Rotorcraft Forum 2015 (a) 𝛽 = 10° : CFD data (left), model (right) (b) 𝛽 = 30° : CFD data (left), model (right) (c) 𝛽 = 90° : CFD data (left), model (right) Fig. 14. Comparison of CFD data with the model for side-slip angles, HART, 𝑧 𝑅 ⁄ = 0.1 .

For this, the model is evaluated at equidistant radial the Fourier coefficients dependence on the radial and azimuthal positions first, then for each radial coordinate are approximated by a polynomial of third position a Fourier analysis is performed and finally order (𝐽 = 3) .

st 41 European Rotorcraft Forum 2015 Due to the lateral symmetry of the flow field in pure Using blade element velocities tangential to the rotor angle of attack settings only Cosine terms result; in disk 𝑉 and perpendicular to it 𝑉 to compute the 𝑇 𝑃 case of side-slip angles both Cosine and Sine terms ⁄ local dynamic pressure (simplified as 𝑉 𝜌 2 ), and 𝑇 will show up until in quartering flight 𝛽 = ±90° the the blade element angle of attack 𝛼 from Eq. ( 10 ) 𝑎 Sine terms will dominate the result, but the Cosine ( sin ) V R r      will not be zero since the front part of the fuselage is T different to the rear part, which causes a non- ( , ) V R r     P izf symmetry of the flow field with respect to the plane (10) ⁄ 𝑥 𝑅 = 0 . Considering pure α variations, the fuse- arctan( / ) V V     a P T lage-induced inflow, referenced to the tip speed, can cos sin / V V        C S P T be written as given in Eq. (9) (for a given 𝛼 and a ⁄ fixed value of 𝑧 𝑅 ): an expression for the thrust increase or decrease  due to the fuselage-induced inflow can be derived, ( , ) v r  izf which is given in Eq. (11) ( 𝐴 and 𝐵 are the effective ( ) cos( ) r n   



izfn V 0 n  non-dimensional radii of the beginning and the end  (9) J of the airfoiled section of the blade, the approxima- j tion makes use of 𝐴 = 0, 𝐵 = 1 ) ( ) r c r  



izfn nj 0 j  2 B  1 C dC  T T d  

 

0 A 2 C C  W W (11) 2 2 2 2 j j   J J c      B A B A      0 j   S c             

0 S j    

2 2 2 2 2 C j C j     0 0 j j   W W     The cyclic controls required to keep hub moments lage appears widely linear in the advance ratio 𝜇 , the same as for the isolated rotor results are given in since they are affected by the upwash in the front Eq. (12) (the approximations again are obtained and the downwash in the rear. In contrast, the longi- using 𝐴 = 0, 𝐵 = 1 ): tudinal control is affected by 𝜇 due to the asym- metry of dynamic pressure on the advancing and 3 3 j j   J B A  retreating side. However, physical consideration c



1 j already suggests that the ∆Θ will be very small 𝑆 3 j  0 j     compared to ∆Θ due to lateral symmetry of the 𝐶 C 4 4 2 2 B A B A   fuselage-induced flow field when 𝛽 = 0° .

  4 8 The evaluation of the coefficients of the fuselage- J c induced flow field 𝑐 can be done for different angle 8  𝑛𝑗 1 j 



2 of attack 𝛼 and for different separation distances 2 3 j    0 j  ⁄ 𝑧 𝑅 of the rotor to the fuselage to investigate the (12) 2 2 j j J   individual effects. In the following the effect of 𝛼 is c B A    2 j c  shown at a representative rotor position of 𝑧 𝑅 ⁄ =



0 j   2 2 j  0 j  2   0.05 .

   S 4 4 2 2 B A B A   The change in thrust as estimated by simple blade 3   element/momentum theory exemplarily is shown 4 8 2 next in Fig. 15 for a rotor of UH-60 size on the J 2 c c  4  0 2 j j LRTA, a rotor of Bo105 size on the RTA, and a 



2 3 2 j    model scale sized rotor on the HART test rig for the 0 j  range of attitudes in wind tunnel operation. Following As can be seen from these analytical results, the Eq. (11) the mean part of the fuselage-induced ve- fuselage impact on thrust requires the radial distribu- locities is the dominant contribution to the rotor tion of the steady part of fuselage-induced flow (ex- thrust. Nose-down attitudes cause the generation of pressed by 𝑐 in Eq. (11)) and also the change in more upwash than downwash, thus the thrust is 0𝑗 longitudinal control ∆Θ . This, in reverse, requires increasing and vice versa, the effect grows propor- 𝑆 tional to wind speed, and the magnitude is depend- the steady and the 2/rev part in 2𝑐 − 𝑐 , see Eq.

0𝑗 2𝑗 ing on rotor size relative to the fuselage dimensions (12). The change in lateral control ∆Θ only depends 𝐶 as well as to the vertical separation of the hub from on the 1/rev part of the fuselage flow field, 𝑐 . The 1𝑗 the fuselage. Depending on the shape of the fuse- change in thrust and lateral cyclic due to the fuse- st 41 European Rotorcraft Forum 2015 lage the changes in thrust can reach from −4% to large distances to it. It is of interest, how large a +5% of the helicopter weight (LRTA, HART) and distance between fuselage and rotor hub need to be in order to have negligible influence of the fuselage.

even 10% in case of the RTA at the highest advance In the following the effect of the rotor’s distance to ratio, but for angles of attack 𝛼 ≈ 0° the fuselage the fuselage is investigated for a separation up to effect is negligible.

two radii away from it, all following figures are for an Fig. 16 shows the major fuselage impact on rotor advance ratio of 𝜇 = 0.5 where the largest impact on trim, namely on the lateral control angle. The strong rotor trim was found so far. The fuselage impact on variation of upwash in the front and downwash in the rotor thrust is indeed asymptotically decreasing as rear represents a 1/rev Cosine variation in blade seen in Fig. 18 .

element angle of attack and thus needs a 1/rev lat- At a distance of two radii the maximum change of eral control angle in order to compensate the fuse- thrust is about 1% for either extremes of angle of lage-induced flow field to maintain trim, as given by Eq. (12). The radial location of the maximum in- attack, and practically zero for 𝛼 = 0° . As in case of ground effect about three rotor radii are sufficient to duced velocities plays a role here, in addition to its magnitude. The smallest impact is found for the ignore fuselage effects on rotor thrust.

LRTA, while the RTA and the HART are quite simi- This is even more pronounced when looking at the lar. Nose-up attitudes generate a larger increase in lateral control in Fig. 19 . For half a radius distance to downwash than the upwash is reduced, thus a larger the fuselage the change in control has already 1/rev variation and consequently a larger lateral shrunk to about 0.2° , from 1.2° at the regular hub control to compensate this. For nose-down attitudes ⁄ position. For 𝑧 𝑅 = 2 the changes in lateral control this is opposite and less control is needed.

are far below 0.1° and negligible, which is similar to The longitudinal control is much less affected than a rotor in ground effect, where 3𝑅 distance are con- the lateral control due to the lateral symmetry of the sidered as the limit of being out of ground. The longi- fuselage-induced flow field in forward flight. It de- tudinal control angle was much less affected by the pends on the mean and the 2/rev part of the flow presence of the fuselage than the lateral control as field, see Eq. (12). As can be seen from Fig. 17 the sown before. An increasing distance to the fuselage changes in control needed to retrim the rotor are further reduces this effect as shown in Fig. 20 (note about one magnitude smaller than the lateral control the smaller scale compared to Fig. 19 ). Again, two shown before. The potential induced flow field out- rotor radii will result in control angle changes of sig- side the fuselage asymptotically approaches zero for nificantly less than 0.1° and thus negligible effects.

0.10 0.10 0.10 -20 0.05 0.05 0.05 -10 0.00 0.00 0.00 -0.05 -0.05 -0.05 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 (a) LRTA (b) RTA (c) HART ⁄ Fig. 15. Prediction of fuselage-induced velocities on change of rotor thrust, 𝑧 𝑅 = 0.05 .

1.2 1.2 1.2 1.0 1.0 -20 1.0 0.8 0.8 0.8 -10 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 (a) LRTA (b) RTA (c) HART ⁄ Fig. 16. Prediction of fuselage-induced velocities on change of lateral control, 𝑧 𝑅 = 0.05 .

st 41 European Rotorcraft Forum 2015 0.1 0.1 0.1 -20 0.0 0.0 0.0 -10 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 (a) LRTA (b) RTA (c) HART Fig. 17. Prediction of fuselage-induced velocities on change of longitudinal control, 𝑧 𝑅 ⁄ = 0.05 .

0.10 0.10 0.10 -20 0.05 0.05 0.05 0.00 0.00 0.00 -0.05 -0.05 -0.05 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 (a) LRTA (b) RTA (c) HART Fig. 18. Prediction of fuselage-rotor separation on change of rotor thrust, 𝜇 = 0.5 .

1.2 1.2 1.2 1.0 1.0 1.0 -20 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0.0 0.0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 (a) LRTA (b) RTA (c) HART Fig. 19. Prediction of fuselage-rotor separation on change of lateral control, 𝜇 = 0.5 .

0.1 0.1 0.1 -20 0.0 0.0 0.0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 (a) LRTA (b) RTA (c) HART Fig. 20. Prediction of fuselage-rotor separation on change of longitudinal control, 𝜇 = 0.

7. CONCLUSIONS volume of rotor blade operation for the entire range It is shown that the nonlinear fuselage-induced flow of angle of attack), which is deemed sufficient for field can be reconstructed by a simple analytical helicopter comprehensive code environments. Indi- model with good accuracy (an average error less vidual characteristics of fuselage shapes can cor- than 5% of the peak-to-peak data range within the rectly be represented by the model and it can easily st 41 European Rotorcraft Forum 2015 be extended to include the effects of further compo- and thus increasingly affects the longitudinal control nents like tail booms, horizontal stabilizers, wings, with increasing side-slip angle, while the impact on etc. This allows the inclusion of fuselage-rotor and the lateral control simultaneously is reducing.

fuselage-wake interference at almost no extra cost Future studies using wake deformation due to the within comprehensive rotor codes.

fuselage may investigate this effect on blade-vortex The purpose of usage is within comprehensive rotor interaction (BVI) locations and thus rotor noise radia- codes such as CAMRAD II, DLR’s S4 or similar. tion, but this effect is assumed to be minor since Two applications are considered for this model: these BVI locations are at lateral positions farer away of the fuselage where the fuselage-induced a. Blade element aerodynamics: modification of velocities are rather small and therefore the wake local angle of attack and dynamic pressure.

perturbations as well.

b. Rotor wake: prescribed or free-wake perturba- 8. REFERENCES tions due to fuselage presence.

[1] Yamauchi G K, and Johnson W. Analysis of axi- symmetric body effects on rotor aerodynamics using The first application will modify blade loading, espe- modified slender body theory. Proc. AIAA 2nd Ap- cially in fast flight since the fuselage-induced veloci- plied Aerodynamics Conference , Seattle, WA, Aug.

ties scale with flight speed. They will change rotor 21-23, 1984.

thrust and moments and thus trim control angles.

The second application will modify the wake geome- [2] Sheridan P F, and Smith R P. Interactional Aerody- namics - a New Challenge to Helicopter Technology.

try according to the fuselage influence. Results J. Am. Helicopter Soc. , Vol. 25, No. 1, pp 3-21, 1980.

found by using this model are (angle of attack varia- tions only): [3] Stepniewski, W Z, and Keys C N. Rotary-Wing Aero- dynamics . Dover Publications, 1984.

a. Effect on thrust (or collective control): The mean value of fuselage-induced velocities is [4] Huber H, and Polz G. Studies on Blade-to-Blade and about zero for zero angle of attack, thus the im- Rotor-Fuselage-Tail Interferences. Aircraft Engineer- pact on thrust or collective to re-trim thrust is ing and Aerospace Technology , Vol. 55, No. 10, pp about zero as well. Nose-down (negative) an- 2-12, 1983.

gles of attack cause an upwash in average and [5] van der Wall B G, Bauknecht A, Jung S N, and You thus a thrust increase, or smaller collective to Y H. Semi-Empirical Modeling of Fuselage-Rotor In- re-trim the rotor; nose-up (positive) angles act terference for Comprehensive Codes: The Funda- opposite. The effect is essentially linear in ad- mental Model. CEAS Aeronautical Journal , Vol. 5, vance ratio and non-linear in angle of attack. No. 4, pp 387-401, 2014.

b. Lateral cyclic control: The upwash in the front [6] Dreier M E . Introduction to Helicopter and Tiltrotor Flight Simulation . AIAA Education Series, 2007.

half of the disk, combined with the downwash in the rear half of the disk, requires large lateral [7] Leoni R D. Black Hawk: The Story of a World Class cyclic control angles up to 1° and more to re- Helicopter. AIAA Library of Flight, 2007.

trim the rotor. The effect is essentially linear in [8] van der Wall, B.G., Jung, Sung N., Rajagopalan, G., advance ratio and non-linear in angle of attack.

Solis, E. Castro, A.: Fuselage-Induced Velocity Mod- In the extremes, when 𝛼 = ±90° , the fore-aft el for LRTA, RTA, and HART Fuselages. Report asymmetry almost vanishes (upwash or down- NASA/CR-2015-218840, Moffett Field, CA, 2015.

wash everywhere with only little fore-aft imbal- ance). [9] Gerhold T, Galle M, Friedrich O, and Evans J. Calcu- lation of Complex Three-Dimensional Configurations c. Longitudinal cyclic control: Compared to the Employing the DLR-TAU-Code, Proc. 35th AIAA lateral control the fuselage effect on longitudinal Aerospace Sciences Meeting & Exhibit , Reno, NV, control is much less. This is due to the lateral Jan. 6-9, 1997.

symmetry of the fuselage-induced velocitiy field.

[10] Rajagopalan R G, Baskaran V, Hollingsworth A, The effect is essentially quadratic in the ad- Lestari A, Garrick D, Solis E, and Hagerty B.

vance ratio and non-linear in angle of attack; it RotCFD, a Tool for Aerodynamic Interference of Ro- vanishes for 𝛼 = ±90° because then no differ- tors: Validation and Capabilities. Proc. AHS Future ence in dynamic pressure on the advancing and Vertical Lift Aircraft Design Conference , San Francis- retreating side exists any more. co, CA, Jan. 18-20, 2012.

The impact of fuselage-induced flow on rotor trim [11] Kim J W, Park S H, and Yu Y H. Euler and Navier – Stokes simulations of helicopter rotor blade in for- asymptotically decays with increasing distance of ward flight using an overlapped grid solver. Proc.

the rotor to the fuselage. About three rotor radii are 19th AIAA CFD Conference , San Antonio, TX, June sufficient to ignore the effects. In side-slip operating 22 – 25, 2009.

conditions, up to quartering flight, the fuselage- induced flow field is no longer laterally symmetric st 41 European Rotorcraft Forum 2015 APPENDIX 0.005-0.015 0.005-0.015 -0.005-0.005 -0.005-0.005 0.5 -0.015--0.005 -0.015--0.005 0.5 -0.025--0.015 -0.025--0.015 -0.035--0.025 -0.035--0.025 -0.045--0.035 -0.045--0.035 -0.055--0.045 -0.055--0.045 -0.065--0.055 -0.065--0.055 -0.075--0.065 -0.085--0.075 -0.075--0.065 -0.5 - 0.5 -0.095--0.085 -0.085--0.075 -0.105--0.095 -0.095--0.085 -0.105--0.095 -1 - 1 - 1 - 0.5 0 0.5 1 - 1 - 0.5 0 0.5 1 (a) LRTA: CFD data (left), model (right), 𝛼 = − 20° 0.005-0.015 0.005-0.015 -0.005-0.005 -0.005-0.005 0.5 -0.015--0.005 0.5 -0.015--0.005 -0.025--0.015 -0.025--0.015 -0.035--0.025 -0.035--0.025 -0.045--0.035 -0.045--0.035 0 -0.055--0.045 -0.055--0.045 -0.065--0.055 -0.075--0.065 -0.065--0.055 -0.085--0.075 -0.075--0.065 -0.5 - 0.5 -0.095--0.085 -0.085--0.075 -0.105--0.095 -0.095--0.085 -0.105--0.095 -1 - 1 - 1 - 0.5 0 0.5 1 - 1 - 0.5 0 0.5 1 (b) RTA: CFD data (left), model (right), 𝛼 = − 20° -0.01-0.01 -0.01-0.01 -0.03--0.01 -0.03--0.01 0.5 0.5 -0.05--0.03 -0.07--0.05 -0.05--0.03 -0.09--0.07 -0.07--0.05 -0.11--0.09 -0.13--0.11 -0.09--0.07 -0.15--0.13 -0.11--0.09 - 0.5 -0.5 -0.13--0.11 -0.15--0.13 - 1 -1 - 1 - 0.5 0 0.5 1 - 1 - 0.5 0 0.5 1 (c) HART: CFD data (left), model (right), 𝛼 = − 30° ⁄ Fig. 21. Comparison of CFD data with the model, nose-down 𝛼 , 𝑧 𝑅 = 0.1 .

st 41 European Rotorcraft Forum 2015 0.065-0.075 0.065-0.075 0.055-0.065 0.055-0.065 0.5 0.045-0.055 0.5 0.045-0.055 0.035-0.045 0.035-0.045 0.025-0.035 0.025-0.035 0.015-0.025 0.015-0.025 0.005-0.015 0.005-0.015 -0.005-0.005 -0.005-0.005 -0.015--0.005 - 0.5 - 0.5 -0.015--0.005 -0.025--0.015 -0.035--0.025 -0.025--0.015 -0.035--0.025 - 1 - 1 - 1 - 0.5 0 0.5 1 - 1 - 0.5 0 0.5 1 (a) LRTA: CFD data (left), model (right) 0.065-0.075 0.065-0.075 0.055-0.065 0.055-0.065 0.5 0.045-0.055 0.5 0.045-0.055 0.035-0.045 0.035-0.045 0.025-0.035 0.025-0.035 0.015-0.025 0.015-0.025 0.005-0.015 0.005-0.015 -0.005-0.005 -0.005-0.005 -0.015--0.005 - 0.5 - 0.5 -0.015--0.005 -0.025--0.015 -0.035--0.025 -0.025--0.015 -0.035--0.025 - 1 - 1 - 1 - 0.5 0 0.5 1 - 1 - 0.5 0 0.5 1 (b) RTA: CFD data (left), model (right) 0,07-0,08 0,065-0,075 0,06-0,07 0,055-0,065 0,05-0,06 0.5 0.5 0,045-0,055 0,04-0,05 0,03-0,04 0,035-0,045 0,02-0,03 0,025-0,035 0,01-0,02 0,015-0,025 -0,01-0,01 -0,02--0,01 0,005-0,015 -0,03--0,02 -0,005-0,005 -0.5 - 0.5 -0,015--0,005 -0,025--0,015 -0,035--0,025 -1 - 1 - 1 - 0.5 0 0.5 1 - 1 - 0.5 0 0.5 1 (c) HART: CFD data (left), model (right) Fig. 22. Comparison of CFD data with the model, 𝛼 = +10°, 𝑧 𝑅 ⁄ = 0.1 .