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Improved rotor aeromechanics predictions using a fluid structure interaction approach
Aerospace Science and Technology 73 (2018) 118–128
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Aerospace Science and Technology www.elsevier.com/locate/aescte
Improved rotor aeromechanics predictions using a fluid structure interaction approach Younghyun You, Deokhwan Na, Sung N. Jung ∗ Department of Aerospace Information Engineering, Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul 05029, Republic of Korea
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Article history: Received 4 September 2017 Received in revised form 13 November 2017 Accepted 26 November 2017 Available online 2 December 2017 Keywords: HART I rotor CFD–CSD coupling Isolated rotor Rotor-fuselage model Airloads
a b s t r a c t The measured HART (Higher harmonic control Aeroacoustic Rotor Test) I data in a descending flight condition is validated using various numerical approaches including CFD (Computational Fluid Dynamics)–CSD (Computational Structural Dynamics) coupled analyses with isolated rotor model and rotor-fuselage model. A CSD-alone approach is also conducted for reference purpose. A three-dimensional (3D) compressible RANS (Reynolds Averaged Navier Stokes) flow solver is employed for the CFD code. Good convergence behavior is found for both coupling analyses. It is observed that the rotor-fuselage model improves the correlation significantly as compared with the measured data. Specifically, the highly oscillating section normal forces signals marked in the advancing and retreating sides of the rotor are captured accurately. Detailed harmonic analysis and the gradient of the airloads signals are observed to prove the validity of the prediction model. The upwash induced due to a fuselage as well as the increased vorticity over the rotor flow fields are attributed to the enhanced correlation. The predicted blade elastic motions and structural moments also indicate improvements with the present rotor-fuselage model. © 2017 Elsevier Masson SAS. All rights reserved.
1. Introduction In the perspective of rotorcraft aeromechanics disciplines, a low speed transition particularly in descending flight regimes is one of the critical conditions in generating abrupt impulsive rotor loadings leading to high vibration and noise [1]. Among other features, the blade-vortex interaction (BVI) phenomenon is of prime concern creating unsteady pressure fluctuations in the vicinity of the blade passage caused by the preceding blade motions and their trailed wakes. To understand the BVI flow characteristic more closely and suppress the noise and vibration actively, an international consortium is formed to carry out a wind tunnel test at the large low speed facility of the DNW (German–Dutch wind tunnel) in 1994 [2]. A 40% scaled BO-105 rotor model along with a fuselage is used for the test. A range of sophisticated measurement techniques are introduced to measure the noise level, blade surface pressure, tip vortices, blade motions, and structural moments with and without the application of HHC (Higher Harmonic Control) pitch control inputs. The measured data set of HART I rotor exhibits a wider spectrum compared to the follow-on HART II experiments. For instance, HART I rotor is installed with 124 pressure transducers for
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Corresponding author. E-mail address: [email protected] (S.N. Jung).
https://doi.org/10.1016/j.ast.2017.11.041 1270-9638/© 2017 Elsevier Masson SAS. All rights reserved.
chordwise airloads measurements at 3 different radial stations [3] whereas HART II allows only single radial station for chordwise airloads distributions with 51 pressure sensors [4]. In addition, 32 strain gages are used to measure blade structural moments (13 flap bending, 12 lag bending, and 7 torsion) for HART I rotor, as compared with 6 spanwise measurements (3 flap bending, 2 lag bending, 1 torsion moment) for the case of HART II [3,4]. These wide range of data sets need to be exploited to verify the prediction capability of an analysis system and to tailor analytical models for more reliable prediction methods. Despite the advantages, HART I rotor has been received less attention than the postdecessor program HART II rotor in terms of the volume of publications reported in the literature [5]. It is noted also that the structural properties of HART I blades are measured recently using the original set of blades tested in DNW [6]. This means, most of the earlier published works on HART I rotor (before 2013) are based on the estimated properties provided by the manufacturer of the blades. Taking these into consideration, there is an obvious gap in the literature to examine the quality of the measured HART I data. The CFD–CSD coupling in rotorcraft applications is pioneered by Tung et al. [7] for predicting rotor aerodynamic loadings in high speed conditions to take advantage of the first principlebased flow representation by CFD approach in the aeromechanics analysis. This innovative concept, however, has not been successful almost for two decades because of the difficulty in meeting a convergence and immature in computer hardware and software
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technologies [8]. Once the proper coupling method is established, the classic two unsolved problems such as a phase shift in section lifts and an underprediction in the section pitching moments [9] have been demonstrated to be resolved in the case of UH-60A rotor [10,11]. Even with a significantly increased computational burden, a CFD–CSD coupled approach is conceived to be desired particularly for airloads and structural loads prediction of a helicopter rotor. So far, very limited work has been found for the validation of HART I data using CFD–CSD coupling except the work of Lim et al. [12] where improvements on section airloads are demonstrated over a CSD approach. However, no structural loads correlation is presented and the effect of the fuselage is neglected in Lim et al. Furthermore, the blade structural properties used are necessary to be updated. Based on the aspects stated above, the present study is conducted to fill the gaps in the literature associated with HART I rotor. Major features of the present work are stated as: 1) improved correlations of the measured HART I rotor data are assessed using a loose CFD–CSD coupled approach; 2) the influence of a fuselage on HART I rotor is identified using both isolated rotor model and rotor-fuselage model; 3) the structural blade properties measured recently by Jung et al. [6] are implemented in the analysis; and 4) predictions on structural loads and blade elastic motions as well as the section airloads are validated against the measured data. 2. Analysis methodologies A 3D compressible RANS flow solver KFLOW [13] is used for the CFD analysis. For timewise flow simulations, a secondorder accurate, dual-time stepping scheme combined with a diagonalized alternating-directional implicit method is applied to compute the unsteady flow fields around a rotor. The inviscid fluxes are calculated using the fifth-order weighted essentially non-oscillatory (WENO) scheme, while the central differencing technique is applied to the viscous fluxes. The k–ω Wilkox–Durbin (WD+) scheme is adopted for the turbulence model. The characteristic boundary conditions using the Riemann invariant are applied to the far field boundary, whereas a no-slip condition is used at the solid wall surface. A moving overlapped Chimera grid system with the near body and the Cartesian off-body grid are employed. Either C-mesh topology grids or O-mesh based grids are formed respectively for the blade and the fuselage. Figs. 1a and 1b show the computational grid systems used for an isolated rotor model and a rotor-fuselage model, respectively, for the HART rotor. The blade grids extend 1.5 times of a chord length (c) in the normal direction, measured from the blade surface. The cell spacing for the first grid point from the wall boundary used is 1.0 × 10 − 5c. The offbody grids consist of an inner region which extends 4c upward, 3c below from the blade, and 1.5c away from the blade tip. The far field boundary is stretched up to 5R (blade radius), centered at the rotor hub. The cell spacing is 0.1c for the Cartesian off-body grids. The CFD computational grids consist of 6.4 M (million) cells for the blade grid, 29.1 M for the off-body grid, and another 2.5 M for the fuselage grid, leading to a total of about 35.0 M cells for the isolated rotor model and 37.5 M for the rotor-fuselage model, respectively. A rotorcraft comprehensive code CAMRAD II [14] is used as the CSD analysis. CAMRAD II is characterized by multibody dynamics, nonlinear finite elements, and various level of rotorcraft aerodynamics. For the structural analysis, the blade motion is composed of the rigid body motion and the elastic deformation. The rigid body motion describes the motion of one end of a beam element, and the elastic motion is measured relative to the rigid motion. The beam elements are represented by 6 degrees of freedom (DOF) for the rigid motion and 9 DOF for the elastic motion
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(3 axial, 2 flap, 2 lag, and 2 torsion) that results in a 15 DOF for each beam finite element. The aerodynamic model is based on the ONERA-EDLIN unsteady airfoil theory combined with C81 airfoil table look-up. For the vortex wake representation, a free wake geometry is assumed and the formation of the tip vortices is modeled using a free rolled-up wake model. The rolled-up wake model is based on the feature that a tip vortex forms at the blade tip. In this study, the blade structure is modeled using 15 beam finite elements while the airfoil blade region is divided into 17 non-uniform aerodynamic panels with finer segments toward the blade tip, as shown in Fig. 1c. Specifically, the centers of each aerodynamic panel are aligned to coincide with the measured airloads stations to minimize the discretization error. A loose coupling between CAMRAD II and KFLOW codes is used for the analysis [15]. The basic principle of the coupling is to exchange information between CSD-computed blade motions and CFD-computed airloads, per revolution base, to benefit the strength of the other code. The coupling iteration begins with CSD analysis using a built-in aerodynamic model. The resulting blade motions along with trim control angles are transferred to the CFD code to update the aerodynamic forces and moments. The difference in airloads between the two codes (i.e. delta airloads) is calculated and superposed to the CSD airloads for the updated blade motions and trim controls for the subsequent iteration stage. This process continues until the airloads and trim control angles indicate little or no noticeable difference compared to the previous iteration steps. It is remarked that the CFD results have a timewise interval of 0.2◦ (ψ = 0.2◦ ) while CSD having 5◦ resolutions. Due to the varying resolutions in both results, appropriate data regression schemes are required to transfer data between CFD and CSD analyses. For blade motions, the interpolation in the radial direction is represented using a polynomial with the seventh order while the timewise domain is interpolated using a Fourier series containing up to the eleventh components, following the approaches given in Refs. [16] and [17]. The airloads in the spanwise direction are interpolated using a cubic spline fit whereas a random data selection at every 5◦ azimuth angle is applied for the timewise airloads data. 3. Results and discussion The baseline case (BL; Dpt 140) of HART I rotor in low speed descent with an advance ratio μ = 0.15 and a shaft tilt angle αs = 4.5◦ aft (after the wind tunnel wall correction) is considered for the study. The target trim values specified are 3100 N, 11.2 Nm, and −20 Nm respectively for the thrust, hub roll, and pitching moments. The positive signs are defined respectively when the advancing side moves up and a pitch up is induced for the moments. A pitch bearing stiffness amounting 1,706 Nm/rad is adopted which has been chosen to match the measured nonrotating first torsion frequency and to represent the control system characteristic of HART I rotor. The detailed validation results are discussed in this section. 3.1. Trim convergence Fig. 2 shows the convergent behavior of CFD–CSD coupled computations on Mach-scaled, section normal forces M 2 C n (Fig. 2a) and delta section normal forces M 2 C n (Fig. 2b) obtained at 87% radial station (r / R = 0.87) with respect to the coupling iterations. The measured airloads data are presented for a comparison purpose. As can be seen, a clear convergence characteristic is reached with the advance of coupling steps considering that both section airloads results show no significant deviations after marching about six or seven coupling cycles. The section airloads at the initial stages of coupling present more flattened waveforms with
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Fig. 1. Computational grids used for CSD and CFD analyses.
some overshoots and phase-outs when compared with the measured data. As the cycles are stepped further, however, the predicted airloads signals become matched with the measured data. The other section airloads components (i.e. section chord forces and pitching moments) show a similar behavior (not shown explicitly). The blade elastic motions demonstrate also a convergence with the iteration cycles, as is depicted in Fig. 3. These results verify the robustness of the coupling algorithm adopted in the present analysis. Fig. 4 shows the variation of CFD trim forces and moments (denoted as continuous lines with symbols) against the measured target values (dotted lines) with the coupling iterations. Since the trim process is managed by the CSD code, the trim results are post-processed and computed using the CFD code at each iteration step. The resulting CFD trim values indicate a clear convergence after about 6 iteration cycles while slightly underestimating the trim forces and moments, as compared with the
measured results. It should be mentioned that the CSD trim values are exactly matched with the trim targets though not shown explicitly. In Fig. 5, the trim control angles (collective, and lateral and longitudinal cyclic angles) predicted using a CSD approach and CFD– CSD couplings with isolated rotor and rotor-fuselage model are compared against the measured HART I data. All predictions are obtained after the trim is converged. The CSD predictions overestimate the collective pitch by about 12.3% whereas both CFD–CSD coupled results correlate reasonably (maximum up to 1.8%) with the measured data. The rotor-fuselage model improves lateral and longitudinal cyclic pitch correlations than the isolated rotor model. This is due to enhancements in modeling to capture the upwash effect by a fuselage. Overall, the CFD–CSD coupled approach with a fuselage shows the best prediction capability in reference to the measured data.
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Fig. 2. Convergence behavior of airloads and delta airloads at r / R = 0.87 with coupling iterations.
3.2. Validation of airloads Figs. 6 and 7 show the predicted pressure distributions over the upper and lower surfaces of the blade for the three measurement locations (i.e. r / R = 0.75, 0.87, and 0.97) at the time when the reference (instrumented) blade is positioned at the azimuth angles of 60◦ and 120◦ , respectively, as compared with those of the measured data (denoted as hollow circles). Both predictions with isolated rotor (dotted lines) and rotor-fuselage model (continuous lines) are presented for a comparison. Note that a total of 44 pressure sensors are distributed at the radial stations of 0.75R and 0.97R while 24 sensors are used for the measurements at the station of 0.87R. The output signals from each pressure sensor are sampled at a rate of 2,048/rev and averaged for 64 rotor revolutions. Fair to good correlations are obtained at the specified azimuth angles. Both CFD results predict pressure fluctuations near the trailing-edge tab with a finite thickness of 0.9 mm. How-
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Fig. 3. Convergence behavior of blade tip displacements with coupling iterations.
ever, the measured data show no such indication since pressure sensors are not installed to verify the pressure variations possibly because of the limited space allowed in this region of the blade. The influence of a fuselage on the pressure loading is found to be substantial at both azimuth stations. It should be remarked that the results presented in Figs. 6 and 7 demonstrate the comparison between the present predictions against the measured data only at the selected azimuthal instants and should not be generalized for the global airloads behavior. Integrating all the local pressure loadings over the whole rotor disk at specific radial stations leads to the section airloads which will be discussed in the following paragraphs. Fig. 8 shows the comparison of the spanwise distribution of section airloads M 2 C n predicted using CSD analysis and CFD–CSD couplings with isolated rotor and rotor-fuselage model, against the measured data. The CSD results are depicted using dashed lines whereas CFD–CSD predictions with isolated rotor and rotor-
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Fig. 4. Convergence behavior of target trim values with coupling iterations.
Fig. 5. Comparison of control trim angles.
fuselage model are represented by dashed-dot lines and continuous lines, respectively. The CSD analysis predicts the mean airloads response reasonably, however, much of the oscillatory peaks present either in the first or the fourth quadrant of the measured airloads are missed and a down-up pulse near the front edge of the rotor (around the azimuth of 180◦ ) is not captured as well. The highly oscillatory peaks are due to a close encounter between the blades and the nearby vortices formed by the preceding blade motions. This phenomenon is known as BVI leading to severe vibration and noise [18]. Inherent limitations in modeling capability and coarse time step sizes adopted in the CSD approach cause the discrepancy. The CFD–CSD coupled approach improves the correlation drastically, especially for BVI response apparent in both the first and the fourth quadrants, overall 2/rev (two per revolution) waveform, and the down-up pattern near the front edge noticed in the measured airloads signals. The CFD–CSD predictions with the isolated rotor model shows a phase lag of about 10◦ near the front edge with lager peak-to-peak magnitudes at 87% radial station of the rotor as compared with the measured data. The inclusion of a fuselage in the CFD analysis corrects the errors in magnitudes and phases of the predicted airloads at all three radial stations. A zoomed-up view of the signal is presented in Fig. 9 for closer look on the BVI events, particularly in the advancing side region. It is observed that the rotor-fuselage model captures the BVI encounters in terms of the number of counts, peak-to-peak amplitudes, and phases of the signals at different radial locations. The isolated rotor model captures the BVI response reasonably well at 75% radial station while underestimating the oscillatory peaks with
Fig. 6. Comparison of chordwise pressure distributions at azimuth location ψ = 60◦ .
substantially-decreased means at the two outermost stations of the blade. Similar behavior is observed in Lim et al. [12] where only isolated rotor model is used to predict much milder BVI encounters than the measured data at both 87% and 97% radial stations. The comparison results demonstrate that a fuselage model is vi-
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Fig. 7. Comparison of chordwise pressure distributions at azimuth location ψ = 120◦ . Fig. 8. Comparison of section normal forces M 2 C n with radial stations.
able in a CFD analysis to accurately predict the BVI events for a rotor in descending flight. The section normal force signals of Fig. 8 are harmonically broken down into lower harmonic (up to 10/rev) and higher harmonic (11/rev and higher) components in Figs. 10 and 11, respectively. The former dictates major blade loadings while the latter may represent the BVI characteristic of the rotor. The comparison of lower
harmonic signals (Fig. 10) shows that the rotor-fuselage model corrects the phase error while decreasing the peak-to-peak magnitudes at all radial stations of the isolated rotor model. With the exception of the case at 0.87R, an excellent agreement appears to be obtained for the lower harmonic loadings with the rotorfuselage model. It is noted that the predicted mean at 0.87R by
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Fig. 9. Enlarged view of the advancing side signals for M 2 C n with radial stations.
the rotor-fuselage model underestimates the measured value. One possible reason for the discrepancy is the use of much smaller number of pressure sensors (24) at 0.87R compared to the other two stations (44) in the rotor test, leading to relatively large integration error in the computation of section airloads. In a means to improve the correlation for the computation of CFD–CSD coupling
Fig. 10. Comparison of lower harmonic contents (up to 10/rev) for M 2 C n with radial stations.
with the rotor-fuselage model, the number of integration points are reduced to synchronize with that of the pressure measurement locations. Fig. 11 shows the effect of the integration methods on the section normal force predictions. The solid continuous line denotes the integration with complete data points (258 points),
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Fig. 11. Effect of integration methods on section normal forces M 2 C n at 0.87R for CFD–CSD with rotor-fuselage model.
whereas the dotted line represents that with the reduced set of data identical with the measured pressure locations. Using the reduced data set for computing M 2 C n is seen to improve slightly the correlation with the measured data, however, the predicted means in the second quadrant are still underestimated the measured values. This result may demonstrate the limitation of the measured airloads data at 0.87R and need to modify the current pressure sensor locations or increase the number of pressure sensors comparable to the other two radial stations of the rotor. With regard to the higher harmonic signals (Fig. 12), both CFD–CSD coupled predictions show comparable results with the measured data. The retreating side signals including the highest peak around the azimuth angle of 300◦ at 0.97R are accurately predicted using the rotor-fuselage model, whilst some of the advancing side signals are underestimated slightly with the present CFD–CSD approach. This is related with the aging of tip vortices [19] and more refinements in CFD grids may be necessary to capture the wake behavior. Other means to understand the BVI characteristic is to examine a partial derivative (slope) of air loading with time. Fig. 13 shows the comparison of predictions on gradients of the section normal forces with the azimuth angles against the measured data. It is noted that the timewise resolutions are 0.2◦ and 1◦ for the CFD computational results and measured data, respectively. For consistency of comparison, the measured data are interpolated using the cubic spline technique to match with the CFD resolutions (i.e. 0.2◦ ). As can be seen, reasonable agreements are obtained between the cases considered except the CSD results which appear not adequate due to overly large time intervals (15◦ ). The phase behavior of the gradient of the airloads signals is seen to be captured accurately by the rotor-fuselage model at all the blade radial locations, while underestimating the peak BVI pulses near the tip of the blade. The correlation is generally better in the retreating region of the rotor than the advancing side, as has been observed in the airloads comparison results. It should be mentioned that the location (instant) and peak values of the gradient signals are obtained correctly using the present CFD–CSD coupling approach with significant improvements with a fuselage. Fig. 14 presents the comparison of iso-surfaces of Q-criterion colored by vorticity when the reference blade is positioned at 20◦ (measured from the rear) obtained respectively by the isolated rotor and rotor-fuselage model. The predicted results clearly demonstrate the differences in the rotor wake by a fuselage. It is noted that the vorticity is clearly
Fig. 12. Comparison of higher harmonic contents (11/rev and higher) for M 2 C n with radial stations.
visible for over one and half revolutions of the rotor and the possible BVI encounters during the period are reflected accordingly in the airloads prediction results shown earlier. In summary, considering the comparison results on the chordwise pressure distribution, and section airloads and their harmonic contents and gradient sig-
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Fig. 14. Comparison of iso-surfaces of Q-criterion plots colored by vorticity.
3.3. Validation of blade structural responses
Fig. 13. Comparison of the gradient of section normal forces d(M2 C n )/dψ with radial stations.
nals, the quality of the measured airloads data of HART I rotor appears excellent and deserves to exploit further for cross-validating any analysis system. It is repeated that much less effort has been paid on HART I rotor than its postdecessor program HART II [20] and more study is needed to tap the potential of the full spectrum of HART I data [21].
In Fig. 15, the predicted blade elastic deformations at the tip using CFD–CSD with isolated rotor and rotor-fuselage model as well as CSD with a rolled-up wake model are compared against the measured data. It is seen that all predicted results capture the general trends of the measured data. Among other cases, a 2/rev waveform apparent in the measured flap motion is correctly predicted using the rotor-fuselage model. The comparison of tip elastic torsion results shows a similar behavior where improved predictions on magnitudes and phases of the elastic torsion are met with the rotor-fuselage model, even though the mean is underestimated significantly as compared with the measured data. The discrepancy in the mean is induced by the fact that the structural properties of HART I blades are not measured using the instrumented (blade No. 1) blade but from one (blade No. 3) of the blades [6]. Furthermore, the instrumented blade is heavier by about 6% compared to the other blades and the rotor encounters substantial bladeto-blade dissimilarities. For lag mode deformation results, a 4/rev behavior present in the measured signals is not captured in any of the analyses. An assessment of uncertainty quantification [22] may be helpful to understand the blade response. However, this is be-
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Fig. 15. Comparison of elastic deformations at the blade tip.
yond the scope of the present work. Therefore, the source of the discrepancy is remained unclear at this moment. Finally, the predicted flap bending, lag bending, and torsion moments obtained at an outboard blade station (around r / R = 0.45) are validated against the measured data in Fig. 16. The mean is removed for a convenience. As expected, the CSD predictions with
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Fig. 16. Comparison of structural moments at blade outboard stations (mean removed).
rolled-up free wake model show only marginal correlations with the measured data. The oscillatory patterns in the measured flap bending are correlated poorly with the CSD analysis while predicting opposite phases in the second quadrant of the measured torsion moments. The CSD–CFD coupled approaches improve the
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correlation significantly, especially with the rotor-fuselage model. The mismatched waveforms in the second quadrant of the disk are corrected somewhat for both flap bending and torsion moments. However, the first peak in the measured flap bending along with a 4/rev harmonic behavior in the measured lag bending are not captured by any of the present analysis models. Some degree of uncertainties in the blade structural properties (in association with the instrumented blade) may cause the discrepancies. 4. Conclusions In this work, an extensive validation for HART I rotor in descending flight condition is studied using CFD–CSD coupled approaches with an isolated rotor and rotor-fuselage model as well as a CSD analysis with rolled-up free wake model. For the CFD–CSD coupling, a 3D compressible RANS flow solver KFLOW is looselycoupled with a CSD code CAMRAD II. Main conclusions drawn from the present study are summarized as: 1) The predicted results using a CSD approach indicate only fair to poor correlation against the measured HART I data with the benefit of high computational efficiency. The CFD–CSD with an isolated rotor model improves the correlation significantly with limited prediction capabilities as: underestimation of BVI peaks, about 10◦ phase offsets near the rotor front edge for lower harmonic contents of the section normal forces, and overestimations of the peak magnitudes in the second quadrant of the flap bending moments. Most of the deficiencies become fixed with a fuselage in the CFD model. 2) The incorporation of a fuselage is shown to capture the BVI characteristic correctly in terms of the number of counts, peak amplitudes, and phases of the measured airloads data. The predicted gradient signals show close agreements with the measured data and clear improvements with a fuselage for the three blade measurement locations. 3) The blade tip motions predicted using the rotor-fuselage model indicate reasonable accuracy solutions while showing some offsets in the mean as compared with the measured data. A dissimilarity in the structural properties between the blades is the probable source of the deviation in the mean. 4) The comparison of flap bending moments show fair agreements especially in the first quadrant signals. Use of other than the instrumented blade in the measurement of blade structural properties is attributed to the discrepancy. Since the properties of the instrumented blade appear final, some uncertainties in the structural moments of HART I rotor remain unsolved. Conflict of interest statement None of the authors have no conflict of interest. Acknowledgements This work was conducted at High-Speed Compound Unmanned Rotorcraft (HCUR) research laboratory with the support of Agency for Defense Development (ADD). This paper resulted from the
Konkuk University research support program. The authors thank HART I test team for the data. References [1] W.G. Bousman, Rotorcraft airloads measurements-extraordinary costs, NASA/TP-2014-218374, extraordinary benefits, Moffett Field (CA): National Aerospace and Space Administration 2014. [2] Y.H. Yu, B. Gmelin, H. Heller, J.J. Philippe, E. Mercker, J.S. Preisser, HHC aeroacoustics rotor test at the DNW – the joint German/French/US HART project, in: Proceedings of the 20th European Rotorcraft Forum, 1994. [3] W.R. Splettstoesser, R. Seelhorst, U. Kube, W. Wagner, A. Boutier, F. Micheli, E. Mercker, K. Pengel, Higher Harmonic Control Aeroacoustic Rotor Test (HART) – Test Documentation and Representative Results, Institute Report IB-129-95/28, German Aerospace Center (DLR), Braunschweig, Germany, 1995. [4] B.G. van der Wall, 2nd HHC Aeroacoustic Rotor Test (HART II) – Part I: Test Documentation, Institute Report IB-111-2003/31, German Aerospace Center (DLR), Braunschweig, Germany, 2003. [5] B.G. van der Wall, A comprehensive rotary-wing data base for code validation: the HART II international workshop, Aeronaut. J. 115 (1164) (2011) 91–102. [6] S.N. Jung, Y.H. You, B.H. Lau, W. Johnson, J.W. Lim, Evaluation of rotor structural and aerodynamic loads using measured blade properties, J. Am. Helicopter Soc. 58 (4) (2013) 1–12. [7] C. Tung, F.X. Caradonna, W. Johnson, The prediction of transonic flows on an advancing rotor, J. Am. Helicopter Soc. 31 (3) (1986) 4–9. [8] R.A. Ormiston, Revitalizing advanced rotorcraft research – and the compound helicopter, J. Am. Helicopter Soc. 61 (1) (2016) 1–23. [9] W.G. Bousman, Putting the aero back into aeroelasticity, in: Proceedings of the Eighth ARO Workshop on Aeroelasticity of Rotorcraft Systems, University Park, PA, 1999, pp. 18–20. [10] M. Potsdam, H.S. Yeo, W. Johnson, Rotor airloads prediction using loose aerodynamic/structural coupling, J. Aircr. 43 (3) (2006) 732–742. [11] A. Datta, M. Nixon, I. Chopra, Review of rotor loads prediction with the emergence of rotorcraft CFD, J. Am. Helicopter Soc. 52 (4) (2007) 287–317. [12] J.W. Lim, T.A. Nygaard, R. Strawn, M. Potsdam, Blade-vortex interaction airloads prediction using coupled computational fluid and structural dynamics, J. Am. Helicopter Soc. 52 (4) (2007) 318–328. [13] J.W. Kim, S.H. Park, Y.H. Yu, Euler and Navier–Stokes simulations of helicopter rotor blade in forward flight using an overlapped grid solver, in: Proceedings of the 19th AIAA Computational Fluid Dynamics Conference, San Antonio, TX, 2009. [14] W. Johnson, CAMRAD II, Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics, Johnson Aeronautics, 1992. [15] S.N. Jung, J.H. Sa, Y.H. You, J.S. Park, S.H. Park, Loose fluid–structure coupled approach for a rotor in descent incorporating fuselage effects, J. Aircr. 50 (4) (2013) 1016–1026. [16] B.G. van der Wall, Mode Identification and Data Synthesis of HART II Blade Deflection Data, Institute Report IB-111-2007/28, German Aerospace Center (DLR), Braunschweig, Germany, 2007. [17] J.H. Sa, J.W. Kim, S.H. Park, J.S. Park, S.N. Jung, Y.H. Yu, KFLOW results of airloads on HART-II rotor blades with prescribed blade deformation, Int. J. Aeronaut. Space Sci. 10 (2) (2009) 52–62. [18] Y.H. Yu, Rotor blade-vortex interaction noise, Prog. Aerosp. Sci. 36 (2) (2000) 97–115. [19] B.G. van der Wall, C.L. Burley, 2nd HHC Aeroacoustic Rotor Test (HART II) – Part II: Representative Results, Institute Report IB-111-2005/03, German Aerospace Center (DLR), Braunschweig, Germany, 2005. [20] B.G. van der Wall, J.W. Lim, M.J. Smith, S.N. Jung, J. Bailly, J.D. Baeder, D.D. Boyd Jr., The HART II international workshop: an assessment of the state-of-the-art in comprehensive code prediction, CEAS Aeronaut. J. 4 (3) (2013) 223–252. [21] B.G. van der Wall, J. Yin, Cruise-speed BVI noise computation by comprehensive code and validation with HART I data, in: Proceedings of the 2nd International Forum on Rotorcraft Multidisciplinary Technology, Seoul, Korea, 2009. [22] S. Murugan, R. Ganguli, D. Harursampath, Aeroelastic response of composite helicopter rotor with random material properties, J. Aircr. 45 (1) (2008) 306–322.
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Improved rotor aeromechanics predictions using a fluid structure interaction approach Younghyun You, Deokhwan Na, Sung N. Jung ∗ Department of Aerospace Information Engineering, Konkuk University, 120 Neungdong-ro, Gwangjin-gu, Seoul 05029, Republic of Korea
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Article history: Received 4 September 2017 Received in revised form 13 November 2017 Accepted 26 November 2017 Available online 2 December 2017 Keywords: HART I rotor CFD–CSD coupling Isolated rotor Rotor-fuselage model Airloads
a b s t r a c t The measured HART (Higher harmonic control Aeroacoustic Rotor Test) I data in a descending flight condition is validated using various numerical approaches including CFD (Computational Fluid Dynamics)–CSD (Computational Structural Dynamics) coupled analyses with isolated rotor model and rotor-fuselage model. A CSD-alone approach is also conducted for reference purpose. A three-dimensional (3D) compressible RANS (Reynolds Averaged Navier Stokes) flow solver is employed for the CFD code. Good convergence behavior is found for both coupling analyses. It is observed that the rotor-fuselage model improves the correlation significantly as compared with the measured data. Specifically, the highly oscillating section normal forces signals marked in the advancing and retreating sides of the rotor are captured accurately. Detailed harmonic analysis and the gradient of the airloads signals are observed to prove the validity of the prediction model. The upwash induced due to a fuselage as well as the increased vorticity over the rotor flow fields are attributed to the enhanced correlation. The predicted blade elastic motions and structural moments also indicate improvements with the present rotor-fuselage model. © 2017 Elsevier Masson SAS. All rights reserved.
1. Introduction In the perspective of rotorcraft aeromechanics disciplines, a low speed transition particularly in descending flight regimes is one of the critical conditions in generating abrupt impulsive rotor loadings leading to high vibration and noise [1]. Among other features, the blade-vortex interaction (BVI) phenomenon is of prime concern creating unsteady pressure fluctuations in the vicinity of the blade passage caused by the preceding blade motions and their trailed wakes. To understand the BVI flow characteristic more closely and suppress the noise and vibration actively, an international consortium is formed to carry out a wind tunnel test at the large low speed facility of the DNW (German–Dutch wind tunnel) in 1994 [2]. A 40% scaled BO-105 rotor model along with a fuselage is used for the test. A range of sophisticated measurement techniques are introduced to measure the noise level, blade surface pressure, tip vortices, blade motions, and structural moments with and without the application of HHC (Higher Harmonic Control) pitch control inputs. The measured data set of HART I rotor exhibits a wider spectrum compared to the follow-on HART II experiments. For instance, HART I rotor is installed with 124 pressure transducers for
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Corresponding author. E-mail address: [email protected] (S.N. Jung).
https://doi.org/10.1016/j.ast.2017.11.041 1270-9638/© 2017 Elsevier Masson SAS. All rights reserved.
chordwise airloads measurements at 3 different radial stations [3] whereas HART II allows only single radial station for chordwise airloads distributions with 51 pressure sensors [4]. In addition, 32 strain gages are used to measure blade structural moments (13 flap bending, 12 lag bending, and 7 torsion) for HART I rotor, as compared with 6 spanwise measurements (3 flap bending, 2 lag bending, 1 torsion moment) for the case of HART II [3,4]. These wide range of data sets need to be exploited to verify the prediction capability of an analysis system and to tailor analytical models for more reliable prediction methods. Despite the advantages, HART I rotor has been received less attention than the postdecessor program HART II rotor in terms of the volume of publications reported in the literature [5]. It is noted also that the structural properties of HART I blades are measured recently using the original set of blades tested in DNW [6]. This means, most of the earlier published works on HART I rotor (before 2013) are based on the estimated properties provided by the manufacturer of the blades. Taking these into consideration, there is an obvious gap in the literature to examine the quality of the measured HART I data. The CFD–CSD coupling in rotorcraft applications is pioneered by Tung et al. [7] for predicting rotor aerodynamic loadings in high speed conditions to take advantage of the first principlebased flow representation by CFD approach in the aeromechanics analysis. This innovative concept, however, has not been successful almost for two decades because of the difficulty in meeting a convergence and immature in computer hardware and software
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technologies [8]. Once the proper coupling method is established, the classic two unsolved problems such as a phase shift in section lifts and an underprediction in the section pitching moments [9] have been demonstrated to be resolved in the case of UH-60A rotor [10,11]. Even with a significantly increased computational burden, a CFD–CSD coupled approach is conceived to be desired particularly for airloads and structural loads prediction of a helicopter rotor. So far, very limited work has been found for the validation of HART I data using CFD–CSD coupling except the work of Lim et al. [12] where improvements on section airloads are demonstrated over a CSD approach. However, no structural loads correlation is presented and the effect of the fuselage is neglected in Lim et al. Furthermore, the blade structural properties used are necessary to be updated. Based on the aspects stated above, the present study is conducted to fill the gaps in the literature associated with HART I rotor. Major features of the present work are stated as: 1) improved correlations of the measured HART I rotor data are assessed using a loose CFD–CSD coupled approach; 2) the influence of a fuselage on HART I rotor is identified using both isolated rotor model and rotor-fuselage model; 3) the structural blade properties measured recently by Jung et al. [6] are implemented in the analysis; and 4) predictions on structural loads and blade elastic motions as well as the section airloads are validated against the measured data. 2. Analysis methodologies A 3D compressible RANS flow solver KFLOW [13] is used for the CFD analysis. For timewise flow simulations, a secondorder accurate, dual-time stepping scheme combined with a diagonalized alternating-directional implicit method is applied to compute the unsteady flow fields around a rotor. The inviscid fluxes are calculated using the fifth-order weighted essentially non-oscillatory (WENO) scheme, while the central differencing technique is applied to the viscous fluxes. The k–ω Wilkox–Durbin (WD+) scheme is adopted for the turbulence model. The characteristic boundary conditions using the Riemann invariant are applied to the far field boundary, whereas a no-slip condition is used at the solid wall surface. A moving overlapped Chimera grid system with the near body and the Cartesian off-body grid are employed. Either C-mesh topology grids or O-mesh based grids are formed respectively for the blade and the fuselage. Figs. 1a and 1b show the computational grid systems used for an isolated rotor model and a rotor-fuselage model, respectively, for the HART rotor. The blade grids extend 1.5 times of a chord length (c) in the normal direction, measured from the blade surface. The cell spacing for the first grid point from the wall boundary used is 1.0 × 10 − 5c. The offbody grids consist of an inner region which extends 4c upward, 3c below from the blade, and 1.5c away from the blade tip. The far field boundary is stretched up to 5R (blade radius), centered at the rotor hub. The cell spacing is 0.1c for the Cartesian off-body grids. The CFD computational grids consist of 6.4 M (million) cells for the blade grid, 29.1 M for the off-body grid, and another 2.5 M for the fuselage grid, leading to a total of about 35.0 M cells for the isolated rotor model and 37.5 M for the rotor-fuselage model, respectively. A rotorcraft comprehensive code CAMRAD II [14] is used as the CSD analysis. CAMRAD II is characterized by multibody dynamics, nonlinear finite elements, and various level of rotorcraft aerodynamics. For the structural analysis, the blade motion is composed of the rigid body motion and the elastic deformation. The rigid body motion describes the motion of one end of a beam element, and the elastic motion is measured relative to the rigid motion. The beam elements are represented by 6 degrees of freedom (DOF) for the rigid motion and 9 DOF for the elastic motion
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(3 axial, 2 flap, 2 lag, and 2 torsion) that results in a 15 DOF for each beam finite element. The aerodynamic model is based on the ONERA-EDLIN unsteady airfoil theory combined with C81 airfoil table look-up. For the vortex wake representation, a free wake geometry is assumed and the formation of the tip vortices is modeled using a free rolled-up wake model. The rolled-up wake model is based on the feature that a tip vortex forms at the blade tip. In this study, the blade structure is modeled using 15 beam finite elements while the airfoil blade region is divided into 17 non-uniform aerodynamic panels with finer segments toward the blade tip, as shown in Fig. 1c. Specifically, the centers of each aerodynamic panel are aligned to coincide with the measured airloads stations to minimize the discretization error. A loose coupling between CAMRAD II and KFLOW codes is used for the analysis [15]. The basic principle of the coupling is to exchange information between CSD-computed blade motions and CFD-computed airloads, per revolution base, to benefit the strength of the other code. The coupling iteration begins with CSD analysis using a built-in aerodynamic model. The resulting blade motions along with trim control angles are transferred to the CFD code to update the aerodynamic forces and moments. The difference in airloads between the two codes (i.e. delta airloads) is calculated and superposed to the CSD airloads for the updated blade motions and trim controls for the subsequent iteration stage. This process continues until the airloads and trim control angles indicate little or no noticeable difference compared to the previous iteration steps. It is remarked that the CFD results have a timewise interval of 0.2◦ (ψ = 0.2◦ ) while CSD having 5◦ resolutions. Due to the varying resolutions in both results, appropriate data regression schemes are required to transfer data between CFD and CSD analyses. For blade motions, the interpolation in the radial direction is represented using a polynomial with the seventh order while the timewise domain is interpolated using a Fourier series containing up to the eleventh components, following the approaches given in Refs. [16] and [17]. The airloads in the spanwise direction are interpolated using a cubic spline fit whereas a random data selection at every 5◦ azimuth angle is applied for the timewise airloads data. 3. Results and discussion The baseline case (BL; Dpt 140) of HART I rotor in low speed descent with an advance ratio μ = 0.15 and a shaft tilt angle αs = 4.5◦ aft (after the wind tunnel wall correction) is considered for the study. The target trim values specified are 3100 N, 11.2 Nm, and −20 Nm respectively for the thrust, hub roll, and pitching moments. The positive signs are defined respectively when the advancing side moves up and a pitch up is induced for the moments. A pitch bearing stiffness amounting 1,706 Nm/rad is adopted which has been chosen to match the measured nonrotating first torsion frequency and to represent the control system characteristic of HART I rotor. The detailed validation results are discussed in this section. 3.1. Trim convergence Fig. 2 shows the convergent behavior of CFD–CSD coupled computations on Mach-scaled, section normal forces M 2 C n (Fig. 2a) and delta section normal forces M 2 C n (Fig. 2b) obtained at 87% radial station (r / R = 0.87) with respect to the coupling iterations. The measured airloads data are presented for a comparison purpose. As can be seen, a clear convergence characteristic is reached with the advance of coupling steps considering that both section airloads results show no significant deviations after marching about six or seven coupling cycles. The section airloads at the initial stages of coupling present more flattened waveforms with
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Fig. 1. Computational grids used for CSD and CFD analyses.
some overshoots and phase-outs when compared with the measured data. As the cycles are stepped further, however, the predicted airloads signals become matched with the measured data. The other section airloads components (i.e. section chord forces and pitching moments) show a similar behavior (not shown explicitly). The blade elastic motions demonstrate also a convergence with the iteration cycles, as is depicted in Fig. 3. These results verify the robustness of the coupling algorithm adopted in the present analysis. Fig. 4 shows the variation of CFD trim forces and moments (denoted as continuous lines with symbols) against the measured target values (dotted lines) with the coupling iterations. Since the trim process is managed by the CSD code, the trim results are post-processed and computed using the CFD code at each iteration step. The resulting CFD trim values indicate a clear convergence after about 6 iteration cycles while slightly underestimating the trim forces and moments, as compared with the
measured results. It should be mentioned that the CSD trim values are exactly matched with the trim targets though not shown explicitly. In Fig. 5, the trim control angles (collective, and lateral and longitudinal cyclic angles) predicted using a CSD approach and CFD– CSD couplings with isolated rotor and rotor-fuselage model are compared against the measured HART I data. All predictions are obtained after the trim is converged. The CSD predictions overestimate the collective pitch by about 12.3% whereas both CFD–CSD coupled results correlate reasonably (maximum up to 1.8%) with the measured data. The rotor-fuselage model improves lateral and longitudinal cyclic pitch correlations than the isolated rotor model. This is due to enhancements in modeling to capture the upwash effect by a fuselage. Overall, the CFD–CSD coupled approach with a fuselage shows the best prediction capability in reference to the measured data.
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Fig. 2. Convergence behavior of airloads and delta airloads at r / R = 0.87 with coupling iterations.
3.2. Validation of airloads Figs. 6 and 7 show the predicted pressure distributions over the upper and lower surfaces of the blade for the three measurement locations (i.e. r / R = 0.75, 0.87, and 0.97) at the time when the reference (instrumented) blade is positioned at the azimuth angles of 60◦ and 120◦ , respectively, as compared with those of the measured data (denoted as hollow circles). Both predictions with isolated rotor (dotted lines) and rotor-fuselage model (continuous lines) are presented for a comparison. Note that a total of 44 pressure sensors are distributed at the radial stations of 0.75R and 0.97R while 24 sensors are used for the measurements at the station of 0.87R. The output signals from each pressure sensor are sampled at a rate of 2,048/rev and averaged for 64 rotor revolutions. Fair to good correlations are obtained at the specified azimuth angles. Both CFD results predict pressure fluctuations near the trailing-edge tab with a finite thickness of 0.9 mm. How-
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Fig. 3. Convergence behavior of blade tip displacements with coupling iterations.
ever, the measured data show no such indication since pressure sensors are not installed to verify the pressure variations possibly because of the limited space allowed in this region of the blade. The influence of a fuselage on the pressure loading is found to be substantial at both azimuth stations. It should be remarked that the results presented in Figs. 6 and 7 demonstrate the comparison between the present predictions against the measured data only at the selected azimuthal instants and should not be generalized for the global airloads behavior. Integrating all the local pressure loadings over the whole rotor disk at specific radial stations leads to the section airloads which will be discussed in the following paragraphs. Fig. 8 shows the comparison of the spanwise distribution of section airloads M 2 C n predicted using CSD analysis and CFD–CSD couplings with isolated rotor and rotor-fuselage model, against the measured data. The CSD results are depicted using dashed lines whereas CFD–CSD predictions with isolated rotor and rotor-
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Fig. 4. Convergence behavior of target trim values with coupling iterations.
Fig. 5. Comparison of control trim angles.
fuselage model are represented by dashed-dot lines and continuous lines, respectively. The CSD analysis predicts the mean airloads response reasonably, however, much of the oscillatory peaks present either in the first or the fourth quadrant of the measured airloads are missed and a down-up pulse near the front edge of the rotor (around the azimuth of 180◦ ) is not captured as well. The highly oscillatory peaks are due to a close encounter between the blades and the nearby vortices formed by the preceding blade motions. This phenomenon is known as BVI leading to severe vibration and noise [18]. Inherent limitations in modeling capability and coarse time step sizes adopted in the CSD approach cause the discrepancy. The CFD–CSD coupled approach improves the correlation drastically, especially for BVI response apparent in both the first and the fourth quadrants, overall 2/rev (two per revolution) waveform, and the down-up pattern near the front edge noticed in the measured airloads signals. The CFD–CSD predictions with the isolated rotor model shows a phase lag of about 10◦ near the front edge with lager peak-to-peak magnitudes at 87% radial station of the rotor as compared with the measured data. The inclusion of a fuselage in the CFD analysis corrects the errors in magnitudes and phases of the predicted airloads at all three radial stations. A zoomed-up view of the signal is presented in Fig. 9 for closer look on the BVI events, particularly in the advancing side region. It is observed that the rotor-fuselage model captures the BVI encounters in terms of the number of counts, peak-to-peak amplitudes, and phases of the signals at different radial locations. The isolated rotor model captures the BVI response reasonably well at 75% radial station while underestimating the oscillatory peaks with
Fig. 6. Comparison of chordwise pressure distributions at azimuth location ψ = 60◦ .
substantially-decreased means at the two outermost stations of the blade. Similar behavior is observed in Lim et al. [12] where only isolated rotor model is used to predict much milder BVI encounters than the measured data at both 87% and 97% radial stations. The comparison results demonstrate that a fuselage model is vi-
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Fig. 7. Comparison of chordwise pressure distributions at azimuth location ψ = 120◦ . Fig. 8. Comparison of section normal forces M 2 C n with radial stations.
able in a CFD analysis to accurately predict the BVI events for a rotor in descending flight. The section normal force signals of Fig. 8 are harmonically broken down into lower harmonic (up to 10/rev) and higher harmonic (11/rev and higher) components in Figs. 10 and 11, respectively. The former dictates major blade loadings while the latter may represent the BVI characteristic of the rotor. The comparison of lower
harmonic signals (Fig. 10) shows that the rotor-fuselage model corrects the phase error while decreasing the peak-to-peak magnitudes at all radial stations of the isolated rotor model. With the exception of the case at 0.87R, an excellent agreement appears to be obtained for the lower harmonic loadings with the rotorfuselage model. It is noted that the predicted mean at 0.87R by
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Fig. 9. Enlarged view of the advancing side signals for M 2 C n with radial stations.
the rotor-fuselage model underestimates the measured value. One possible reason for the discrepancy is the use of much smaller number of pressure sensors (24) at 0.87R compared to the other two stations (44) in the rotor test, leading to relatively large integration error in the computation of section airloads. In a means to improve the correlation for the computation of CFD–CSD coupling
Fig. 10. Comparison of lower harmonic contents (up to 10/rev) for M 2 C n with radial stations.
with the rotor-fuselage model, the number of integration points are reduced to synchronize with that of the pressure measurement locations. Fig. 11 shows the effect of the integration methods on the section normal force predictions. The solid continuous line denotes the integration with complete data points (258 points),
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Fig. 11. Effect of integration methods on section normal forces M 2 C n at 0.87R for CFD–CSD with rotor-fuselage model.
whereas the dotted line represents that with the reduced set of data identical with the measured pressure locations. Using the reduced data set for computing M 2 C n is seen to improve slightly the correlation with the measured data, however, the predicted means in the second quadrant are still underestimated the measured values. This result may demonstrate the limitation of the measured airloads data at 0.87R and need to modify the current pressure sensor locations or increase the number of pressure sensors comparable to the other two radial stations of the rotor. With regard to the higher harmonic signals (Fig. 12), both CFD–CSD coupled predictions show comparable results with the measured data. The retreating side signals including the highest peak around the azimuth angle of 300◦ at 0.97R are accurately predicted using the rotor-fuselage model, whilst some of the advancing side signals are underestimated slightly with the present CFD–CSD approach. This is related with the aging of tip vortices [19] and more refinements in CFD grids may be necessary to capture the wake behavior. Other means to understand the BVI characteristic is to examine a partial derivative (slope) of air loading with time. Fig. 13 shows the comparison of predictions on gradients of the section normal forces with the azimuth angles against the measured data. It is noted that the timewise resolutions are 0.2◦ and 1◦ for the CFD computational results and measured data, respectively. For consistency of comparison, the measured data are interpolated using the cubic spline technique to match with the CFD resolutions (i.e. 0.2◦ ). As can be seen, reasonable agreements are obtained between the cases considered except the CSD results which appear not adequate due to overly large time intervals (15◦ ). The phase behavior of the gradient of the airloads signals is seen to be captured accurately by the rotor-fuselage model at all the blade radial locations, while underestimating the peak BVI pulses near the tip of the blade. The correlation is generally better in the retreating region of the rotor than the advancing side, as has been observed in the airloads comparison results. It should be mentioned that the location (instant) and peak values of the gradient signals are obtained correctly using the present CFD–CSD coupling approach with significant improvements with a fuselage. Fig. 14 presents the comparison of iso-surfaces of Q-criterion colored by vorticity when the reference blade is positioned at 20◦ (measured from the rear) obtained respectively by the isolated rotor and rotor-fuselage model. The predicted results clearly demonstrate the differences in the rotor wake by a fuselage. It is noted that the vorticity is clearly
Fig. 12. Comparison of higher harmonic contents (11/rev and higher) for M 2 C n with radial stations.
visible for over one and half revolutions of the rotor and the possible BVI encounters during the period are reflected accordingly in the airloads prediction results shown earlier. In summary, considering the comparison results on the chordwise pressure distribution, and section airloads and their harmonic contents and gradient sig-
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Fig. 14. Comparison of iso-surfaces of Q-criterion plots colored by vorticity.
3.3. Validation of blade structural responses
Fig. 13. Comparison of the gradient of section normal forces d(M2 C n )/dψ with radial stations.
nals, the quality of the measured airloads data of HART I rotor appears excellent and deserves to exploit further for cross-validating any analysis system. It is repeated that much less effort has been paid on HART I rotor than its postdecessor program HART II [20] and more study is needed to tap the potential of the full spectrum of HART I data [21].
In Fig. 15, the predicted blade elastic deformations at the tip using CFD–CSD with isolated rotor and rotor-fuselage model as well as CSD with a rolled-up wake model are compared against the measured data. It is seen that all predicted results capture the general trends of the measured data. Among other cases, a 2/rev waveform apparent in the measured flap motion is correctly predicted using the rotor-fuselage model. The comparison of tip elastic torsion results shows a similar behavior where improved predictions on magnitudes and phases of the elastic torsion are met with the rotor-fuselage model, even though the mean is underestimated significantly as compared with the measured data. The discrepancy in the mean is induced by the fact that the structural properties of HART I blades are not measured using the instrumented (blade No. 1) blade but from one (blade No. 3) of the blades [6]. Furthermore, the instrumented blade is heavier by about 6% compared to the other blades and the rotor encounters substantial bladeto-blade dissimilarities. For lag mode deformation results, a 4/rev behavior present in the measured signals is not captured in any of the analyses. An assessment of uncertainty quantification [22] may be helpful to understand the blade response. However, this is be-
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Fig. 15. Comparison of elastic deformations at the blade tip.
yond the scope of the present work. Therefore, the source of the discrepancy is remained unclear at this moment. Finally, the predicted flap bending, lag bending, and torsion moments obtained at an outboard blade station (around r / R = 0.45) are validated against the measured data in Fig. 16. The mean is removed for a convenience. As expected, the CSD predictions with
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Fig. 16. Comparison of structural moments at blade outboard stations (mean removed).
rolled-up free wake model show only marginal correlations with the measured data. The oscillatory patterns in the measured flap bending are correlated poorly with the CSD analysis while predicting opposite phases in the second quadrant of the measured torsion moments. The CSD–CFD coupled approaches improve the
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correlation significantly, especially with the rotor-fuselage model. The mismatched waveforms in the second quadrant of the disk are corrected somewhat for both flap bending and torsion moments. However, the first peak in the measured flap bending along with a 4/rev harmonic behavior in the measured lag bending are not captured by any of the present analysis models. Some degree of uncertainties in the blade structural properties (in association with the instrumented blade) may cause the discrepancies. 4. Conclusions In this work, an extensive validation for HART I rotor in descending flight condition is studied using CFD–CSD coupled approaches with an isolated rotor and rotor-fuselage model as well as a CSD analysis with rolled-up free wake model. For the CFD–CSD coupling, a 3D compressible RANS flow solver KFLOW is looselycoupled with a CSD code CAMRAD II. Main conclusions drawn from the present study are summarized as: 1) The predicted results using a CSD approach indicate only fair to poor correlation against the measured HART I data with the benefit of high computational efficiency. The CFD–CSD with an isolated rotor model improves the correlation significantly with limited prediction capabilities as: underestimation of BVI peaks, about 10◦ phase offsets near the rotor front edge for lower harmonic contents of the section normal forces, and overestimations of the peak magnitudes in the second quadrant of the flap bending moments. Most of the deficiencies become fixed with a fuselage in the CFD model. 2) The incorporation of a fuselage is shown to capture the BVI characteristic correctly in terms of the number of counts, peak amplitudes, and phases of the measured airloads data. The predicted gradient signals show close agreements with the measured data and clear improvements with a fuselage for the three blade measurement locations. 3) The blade tip motions predicted using the rotor-fuselage model indicate reasonable accuracy solutions while showing some offsets in the mean as compared with the measured data. A dissimilarity in the structural properties between the blades is the probable source of the deviation in the mean. 4) The comparison of flap bending moments show fair agreements especially in the first quadrant signals. Use of other than the instrumented blade in the measurement of blade structural properties is attributed to the discrepancy. Since the properties of the instrumented blade appear final, some uncertainties in the structural moments of HART I rotor remain unsolved. Conflict of interest statement None of the authors have no conflict of interest. Acknowledgements This work was conducted at High-Speed Compound Unmanned Rotorcraft (HCUR) research laboratory with the support of Agency for Defense Development (ADD). This paper resulted from the
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