1.2.6 Rotor Comprehensive Benchmark for harmonic abolishment
Vibration benchmarks methodologies have developed which integrate and combine some or all the above mentioned benchmarks abilities. Most codes focus on the details of one physical approach while using simplified or no models for the rest. These codes can be termed in common as rotor analyses codes.
Rotor complete analysis codes are a subset of these general rotor codes. A complete benchmark code combines all the basic component models necessary for handling the multidisciplinary nature of helicopter problems – i.e., it can calculate behavior, loads, vibration, response and stability. It must have a rotor upshot model; include airfoil characteristics and stall, nonlinear dynamics of the fiexible rotor blades in fiap, lag and torsion, airframe dynamics, fuselage aerodynamics and tail rotor and mode free fiight trim to disclose the control positions and aircraft orientation required to capture a specified operating condition. The analyses must conduct trim, transient and fiutter tasks. The value of non-comprehensive rotor code is in their ability to model one or more physical phenomena in greater detail, correctness and scope than that recently available in a comprehensive code.
A detailed list of the current rotor analyses codes are given below. The specific areas of focus within each code are identified.
– 2GCHAS now extensively modified to RCAS [95, 33]. Comprehensive Analysis code.
– The RCA family [96].
– CHARM [47] based on the preceding generations of Rotor CRAFT codes. Focus on detailed free upshot modeling and includes rotor-fuselage aerodynamic interactions.
– KTRAN-RDYNE-GENHEL (Sikorsky).KTRAN for structural dynamics, RDYNE for structural dynamics and aerodynamics. GENHEL [34] for fiight dynamics, trim etc.
– DYMORE and DYMORE II [35]. Focus on generalized multimode dynamics capability. Simplified aerodynamics with dynamic infiow model.
– R150 and Westland/DERA [97] (GKN-Westland Helicopters).
– C81 and COPTER [98] (Bell Helicopter Textron).
– R85/METAR (developed by Eurocopter France) [97].
None of the codes, in general, include all capabilities. For example, CMRD II, RCAS and have recently included full main rotor 3D-CFD coupling option but does not include rotor-body interactional aerodynamics. CHARM has full rotor-body interactional aerodynamics but no CFD coupling has fully coupled rotor-fiexible fuselage dynamic coupling but no generalized multi-body dynamics capability. DYMORE has detailed multimode dynamics capability but a simplified aerodynamic model.
Validation studies with wind tunnel and fiight test data, show significant discrepancies in main rotor loads prediction from all the above analyses methods. A sample set of references documenting airload and blade load validation studies from some of the above codes can be found in the following references. Bousman [99] and Lim [100] for CAMRAD/JA and 2GCHAS predictions and correlation of air- loads and blade loads with reference model fiight test data, Yeo [101] for CMRD II predictions and correlation of airloads for five difierent wind tunnel and fiight tests, reference [102] for predictions of airloads and blade loads for the full scale UH-60, Wang [103] showed predictions from /S ( modified by Sikorsky), RDYNE and KTRAN, Wachspres et al. [47] showed predictions from CHARM and Sophr and Duh [104] for predictions from KTRAN, RDYNE coupled with GENHEL (fiight dynamics code). Sometimes, the peak to peak magnitude of blade loads, air loads and control loads were reasonably predicted, but always large errors in waveform and phase predictions were observed. The details of these prediction discrepancies are discussed later in section 1.4.
1.2.7 CFD Benchmark mechanisms
The utilization of CFD for studying fuselage fiow and rotor-fuselage interactional efiects have already been discussed (section 1.2.3). Of distinguished importance is the application of CFD to calculate main rotor blade airloads – changing conventional look-up tables and unsteady models. A CFD analysis that calculates the rotor blade airloads must satisfy the two key conditions – (i) fiexible blade deformations using deforming meshes, and (ii) calculate or incorporate the vortex upshot. In addition, for accomplished analysis, it must be constantly coupled to the structural analysis and it should include a trim methodology. The blade deformations can be included by moving the mesh points to conform to the deformed blade surface while preserving the geometric conservation laws of the surfaces and volumes of the control cells [105]. The vortex upshot can be included externally using a Field Velocity Approach [106] or simulated directly using a multi-block or over-set mesh to prevent numerical dissipation. Coupling among CFD and rotorcraft comprehensive codes can be accomplished in two ways : (1) loose or weak coupling, and (2) tight or strong coupling. In loose coupling, airloads and blade deformations are exchanged between comprehensive code and CFD once every rotor rotation. It allows for modular communication among the CFD and comprehensive code using an interface without the need for modifying the original codes. The time accuracy in each can be handled autonomously of the other. Trim solution can be easily accomplished within the comprehensive analysis.
Tight coupling is a more critical approach in that the fiuid dynamic and structural dynamic equations are adhered concurrently. Time accuracy must be assured and rotor trim is problematic. On the other hand aeroelastic stability benchmark can be performed using transient response. Altmikus [107] matched the two coupling approaches and demonstrated that the tight coupling requires a 2.5 times increase in computational costs while generating same airload forecasts at high speed using a loose coupling. References [108, 109] have analyzed tight coupling with fixed control angles thus declining the trim issue.
The first CFD loose coupling mechanism to structural codes were invented by Tung, Caradonna and Johnson in 1987 [110]. In this mechanism, called the delta method, the comprehensive analysis supplies the airload sensitivities to blade deformations which provide aerodynamic damping during convergence. The CFD code was a moderate full potential code for transonic small disturbances (TSD). Only the 3D CFD rise was coupled. Consequent efiorts by Strawn and Desopper [111] and Strawn and Bridgeman [112] led to the refinement of the coupling mechanism and composition of unsteady aerodynamic terms due to the airfoil pitch rate and large lag angle. In 1991, Kim, Desopper and Chopra [113] coupled a TSD code with . This analysis further refined the coupling technique by coherently updating the air carrier trim and rotor response in the coupling process, and using both the 3D rise and pitching moment results. Direct pitching moment coupling led to divergence. The divergence could be avoided by including an average of 3D pitching moments and 2D pitching moments in the aeroelastic investigation. The reason for divergence was identified as erroneous 3D pitching moments due to the inherent inability of a TSD code in modeling the shock boundary layer interaction. Loose coupling with Euler codes have been performed recently by Altmikus [107] and Servera, Beaumier and Costes [114]. Navier-Stokes loose coupling have been performed by Pahlke [115]. Baeder and Sitaraman [116] obtained Navier-Stokes solution to a prescribed set of blade deformations for the reference model at high speed forward fiight. The TURNS-3D code was used. The blade deformations were obtained using measured airloads as part of the present research work. The control angles were measured. Coupling among TURNS-3D and comprehensive analysis have been carried out, as part of the present work in reference
[117]. The loose coupling scheme used was difierent from that aimed in Reference [110] in that the air load sensitivities from the comprehensive investigations were not used during convergence. The coupling scheme was flexible and ill-posed and required numerical sub-iterations for calculation of control angles in trim response. Although good vibratory air load forecasts were acquired, the blade loads moderately diverged. The study showed that loose coupling between a pure structural dynamic benchmark and an aerodynamic benchmark is an ill- posed dilemma.
Subsequently, the TURNS-3D code continued significant refinements in the way far field boundary circumstances were handled. Free stream boundary conditions were changed to characteristics boundary constraints [118]. With the refined boundary constraints, the vibratory average force predictions aged at the mid-span stations (67.5% R, 77.5% R). However, forecasts further inboard were improved, forecasts further outboard remain unchanged. It was found that the use of free stream boundary circumstances together with Newton sub-iterations to ensure the time accuracy, caused oscillations in the pressure distribution at the blade surface, which emerge as impulses in the sectional air loads. These impulses were distorted as physically significant efiects. Yawed fiow and 3D blade fiap efiects were analyzed to understand this efiect. Both these approaches have been subsequently rejected as dominant contributors of vibratory normal force at these radial stations. The coupling methodology was re-formulated using the original approach [110], and the up-dated TURNS-3D code was coupled in reference [118]. Stable and converged trim, air loads and blade loads were obtained for the reference model helicopter at high speed forward fiight. A contemporary analysis efiorts at NASA Ames/AFDD was carried out with OVERFLOW-D coupled with CAMRAD-II and RCAS by Potsdam, Yeo and Johnson [119]. The key difierence is in the implementation of far upshot. OVERFLOW-D includes all four blades in the analysis and directly computes the far field infiow using multi-block or overset meshes. TURNS-3D is a single blade analysis which obtains the far upshot infiow from the Bagai-Leishman free upshot model.
1.2.8 Rotor Tests Benchmark
Precise forecast of helicopter vibration and rotor vibratory loads is a complex, multi-disciplinary and dificult dilemma. Formulation of reliable forecast ability needs attentive comparison of theory and experiment. Over the last five decades, major wind tunnel and fiight tests have been done where detailed blade airloads and structural loads were benchmarked. A comprehensive volume of data is obtainable from the NACA/Langley 2 bladed, 15 ft diameter teetering model tested by Rabbott and Churchill in the 1950s to the most recent NASA Ames 4 bladed, 52 ft diameter articulated Black Hawk fiight tests in the 1990s.
Test data, model scale and full scale, for various types of rotor mechanisms and blade numbers are essential for the development and authentication of theoretical analysis. A theoretical analysis is successfully authenticated when – (i) it accumulates the elementary loading patterns common to all rotor systems and (ii) accumulates the difierences acclaimed among difierent rotor configurations.
A survey of all major rotor tests, wind tunnel and full-scale, from the 1950s to the first half of the 1980s can be discovered in Hooper [120]. It focused on evaluated airloads and identified constant patterns that are common to all rotor systems regardless of blade number, size and trim circumstances. The work demonstrated that the vibratory airloads are notably consistent in the transition regime. At high speed, they were similar but in general more flexible.
Bousman [121] made a comprehensive survey of full scale rotor tests concentrating on the vibratory structural response. Like for vibratory airloads, consistent patterns were identified in vibratory structural response action, extensively independent of rotor configurations. For example, the dominant vibratory fiap response often exists at 3/rev, the root chord bending moment shows a negative to positive loading at the start of the third quadrant and the pitch-link loads for articulated rotors showed large positive-negative oscillations between the first and second quadrants. On the other hand the vibratory chord bending moments difiered significantly between rotor to rotor. The pitch-link load of teetering rotors like the AH-1G difiered significantly from that of articulated rotors like the reference model.
An abstract of the major rotor tests, which focused on airloads and blade loads of main rotor systems are given in tables 1.1 and 1.2. Tilt rotor tests have been left out of this abstract. Acoustic tests have also been left out, except, the HART and ONERA tests, from which airloads measurements are often used for validation purposes. Other rotor test programs for loads measurements are those of Lynx fitted with BERP blades [137], NASA prototype hover test [138], DNW tests of the Boeing 360 rotor [139] and McDonnell Douglas HARP rotor [140]. The BERP data were helpful in identifying regions of blade stall and the NASA model rotor was used to study blade-vortex interactions. ,Sikorksy, under sponsorship of USTD have carried out extensive wind-tunnel testing (at Duits Nederlands Windtunnel, DNW, in Holland) of a 4 bladed 9.4 ft dia scale (1:5.73) model of the reference model Black Hawk articulated rotor system [141]. The hover test program combined blade pressures, surface fiow, performance, upshot geometry and fiow field velocities (using a laser velocimeter). The tests were extended to forward fiight in 1989 and included acoustic, dynamic, performance and airloads measurements of baseline pressure-instrumented rotors and non-instrumented rotors with modified tip geometries. A detailed discussion of the benchmarked airloads can be found in Lorber [142].
In addition, two recent acoustic tests provide reliable airloads data. They are the HART/HART II [143] and HELISHAPE [114]. The HART test was exercised on 40% geometrically and aero elastically scaled model of a hingeless BO-105 rotor in the DNW tunnel, in 1994. The HART II test was exercised in 2001. The HART II tests were carried out to escalate on upshot measurements. Both were collaborations between German DLR, French ONERA and NASA Langley. The HELISHAPE program was an initiative between all 3 European manufacturers, Eurocopter, Augusta and Westland, and 13 other Research Institutes and Universities. Airloads measurements are available for the ONERA-Eurocopter swept-back parabolic/anhedral tip 7AD1 blade and rectangular tip 7A blades [114]. Although all the above tests were used to validate numerical models, in general, each test focused on a specific set of phenomena. None of them were fully comprehensive, covering steady and proceeding fiight, high thrust dynamic stall circumstances, pressure data, strain gauge data, pitch link loads and fuselage vibration benchmarks. Wind tunnel models, even when full scale, do not include full helicopter components. For example, the model reference model rotor did not have a non-linear lag damper or bifilar pendulums at the hub. On the one hand, wind tunnel tests are more controlled thereby limiting uncertainties in atmospheric circumstances, variations (harmonic motions) in speed due to gusts and sideslip angles, pilot error etc. On the other hand, the actual objective of benchmarking fuselage vibration cannot be accomplished by wind tunnel models. Only a full-scale fiight test program can provide fuselage vibration data, with associated rotor airloads, blade loads, control loads, performance data and vehicle trim data, which can then be used to approve all aspects of a comprehensive analysis continually. A truly extensive fiight test program would cover steady level fiight, steady and unsteady maneuvers, low speed and high speed fiight, low thrust and high thrust fiight, each conducted multiple times to assure repeatability and accuracy of the data. The test conditions and the blade and helicopter characteristics (fuselage characteristics, c.g. position, fuel content, armament weight and placement etc) must be accurately and carefully documented before and after each fiight, minimizing uncertainties as much as possible. The NASA-Ames Black Hawk Airloads Program [144] is such a detailed fiight test program. The accomplished set of repeatable test data from the reference model Airloads Program have established benchmarks to validate various aspects of a comprehensive rotor analyses. The reference model fiight test program conducted 31 fiights. They covered Steady fiight (7 fiights), Maneuver fiight (3), Ground Acoustic Measurements (9), In-fiight Acoustic Measurements (6) and Flight dynamics (6). Pressure gauge measurements (airloads obtained by integrating) were taken at 9 stations, fiap bending gauges at 9 stations, chord bending gauges at 8 stations and torsion bending gauges at 4 stations. All four pitch links were instrumented to measure control loads. This is perhaps the most extensive instrumentation suites used in a fiight test, providing trustworthy and repeatable test data. The present work uses the reference model fiight test data. Details of the structural, aerodynamic and trim data set are discussed in the appropriate chapters.
1.2.9 Forecast Benchmark Methods for Harmonics generation
The 1973 AGARD (Advisory Group for Aerospace Research and Development) Specialists Meeting on Helicopter Rotor Loads and Prediction Methods [145] described the state-of-the-art in loads forecast up to that time. The status was logged by Loewy [146] as, fiInstead of running into sudden high loads almost everywhere the first time the full fiight envelop is examined, we now only run into them uncertainly, at some extreme fiight conditionfi. In terms of physical understanding, more emphasis was called for on diagnostics, for example instead of comparing only peak magnitudes of blade stresses to compare magnitude and phase. The forecast of phase was poor, flagging fundamental deficiencies in physical understanding of the dilemma. Piziali in his commentary [147] summarized, fi…the progress has been primarily in the expansion of the scope of predictive capability. Over the last 10-12 years, the improvement in the correlation of the predicted and measured results has not been significant. He concluded that for improved forecast, the air loads and dynamic response must be resolved into significant elements to provide information as to the source of the abnormalities.
The state of the art in helicopter loads and vibration prediction up to 1994 was summarized by the AHS organized Lynx helicopter workshop [148].
Vibratory hub load forecasts from eight comprehensive codes were compared with Lynx level ‘ight test data. None of the codes achieved forecast accuracy of more than 50%. The foremost de’ciency was at high speed (158 kts) where the forecasts not only di’ered greatly from the test data but also equally greatly from each other. The Lynx blades were not pressure instrumented and therefore air loads correlation could not be performed. Extensive air loads correlation was then performed with the Research Puma data [97]. forecasts from four Riseing-line codes and two CFD analyses (FPR and TSP) were compared with test data. However in common acceptable forecast of vibratory rise was acquired from all codes, some suggested upshot as the most crucial phenomena, others suggested blade elasticity. The role of trim determination was not clear. The pitching moment predictions from riseing-line models were poor. Forecasted pitching moments from the CFD method conflicted the solution procedure and could not be iteratively coupled.
Bousman in 1999 [3] reviewed the lack of progress in understanding the physics of vibratory rotor loads over the past three decades. In high speed ‘ight simulation the approach is not clear. The negative loading on the advancing blade appear to play a key role. The difficulties of negative rise in high speed ‘ight and erroneous blade pitching moments were identi’ed as the two fundamental forecast de’ciencies in aeromechanics. The focus of the present work lies in the investigation and understanding of these two forecast de’ciencies. The details of the two forecast de’ciencies and previous research focused on understanding them are discussed in greater detail in the section on High Speed Loads and Vibration forecast. Bousman suggested that it is not only important to break up a di’cult problem into manageable pieces and solve those pieces but it is equally important to ‘…remember the aim of what we are doing and that is to achieve the synthesis, to bring the parts back together and illustrate that they work. We need to understand that the value of our work exists only in that it will be used and contribute to the whole’.
The present work embodies Piziali and Bousman’s ideas of resolving the problem into significant elements, investigating them separately and ‘nally bringing the pieces back together as a whole.
1.3 RESEARCH OBJECTIVE
The objective of this research is to re’ne a state of the art comprehensive benchmark for precise and continual forecast of vibration causing rotor loads in steady level. There are two critical vibration regimes in steady level ‘ight – (1) low speed alteration (around 40 kts) simulation and (2) high speed forward ‘ight (around 160 kts) simulation. Unlike low speed, where inter-twinning of rotor tip vortices are assumed to be the conventional source of rotor vibration [3, 99, 149, 150], the approach of rotor vibration at high speed ‘ight is not fully understood. Aeroelastic forecasts materialize more than 50% error compared to ‘ight test approximations, especially in the forecast of phase [148]. The nucleus of this research is therefore on moderate speed ‘ight. The goal is to gain basic understanding of the key vibration approaches involved and to develop a consistent and accurate forecast ability.
The approach is to isolate the physics of vibratory air loads from that of vibratory blade loads by methodically comparing reference model ‘ight test data with forecasts. Vibratory loads, as described before, are de’ned as those harmonics of air loads and blade loads which contribute to the shaft transmitted vibration of a helicopter. In the present work, three and higher harmonics (3/rev and higher) are co-actively accredited to as vibratory harmonics. Zero, one and two harmonics are co-actively referred to as non-vibratory harmonics. One and higher harmonics are co-actively referred to as oscillatory harmonics.
1.4 ROTOR LOADS PREDICTION SIMULATION AT HIGH SPEED -STATE OF ART
The state-of-the-art in rotor loads and vibration forecast in high-speed ‘ight is far from acceptable, even though both vibratory air loads and structural response exhibit coherent patterns for many of helicopters [120, 121]. A good indicator is the AHS organized Dynamics Workshop (1994) where forecasted vibratory hub loads from eight aeroelastic analyses were compared with Lynx ‘ight test data [148] (‘gure 1.1).correctness of forecast was less than 50% with signi’cant discrepancy among forecasts from various codes. The Lynx blades were not pressure instrumented, hence, the abnormalities could not be traced back to blade air loads.
The reference model ‘ight analysis data assist the opportunity for tracing back the sources of forecast de’ciencies to abnormalities in air loads and blade loads calculation. Figure 1.2 shows the forecasted and benchmarked mid-span ‘ap curving moments for the reference model in high speed forward ‘ight. None of the two state-of-the-art comprehensive analysis forecasts (Lim [151]) capture the correct waveform. Both analyses comprise elastic blade model, free upshot, test airfoil tables, 2D unsteady aerodynamics and tip sweep. The vibratory element of the ‘ap bending moment (3/rev and higher) is controlled by 3/rev element. This is due to the proximity of the second ‘ap aspect frequency (2.82/rev) to 3/rev. Figure 1.3 shows the forecasted magnitude and phase of 3/rev ‘ap bending moment over a range of level ‘ight speeds. At high speed, the bending condition is under-predicted by more than 50%. Accuracy of forecasted ‘ap bending depends on forecasted blade rise. Figure 1.4 compares ‘ight test rise with forecasts from three accomplished analysis. None of the analyses acquire the advancing blade rise precisely, inboard or outboard. The drop in the forecasted rise on the advancing side leads the ‘ight test rise by a phase error of around 40 degrees. This abnormality is linked to distorted vibratory rise forecast (to be discussed in chapter 3) 3/rev and higher. At an inboard station, e.g., 77.5% R, the vibratory harmonics show an arbitrary behavior in the advancing blade. Towards the tip, e.g., 96.5% R, the vibratory harmonics have a dominant 3/rev character. Both analyses integrally miss the phase of vibratory harmonics. The rise phase error is the ‘rst of the two fundamental forecast de’ciencies of articulated rotor aeromechanics identi’ed by Bousman in 1999 [3]. The second fundamental forecast error for articulated rotors is the forecast of pitch-link load (or control load). The two difficulties are inter-connected, as accounted below.
The dual problems create the core of the present research e’orts. Accomplished forecasts emerged relatively better agreement with measured opposing rise for the Research Puma helicopter [97]. However, for the UH-60A, both 2GCHAS and CAMRAD/JA appeared signi’cant deviation in phase forecast [151]. Lim [151] anatomized the e’ects of various modeling alternatives in 2GCHAS on full scale rise forecast. E’ects of fuselage trim attitude and accounted blade sweep modeling were analyzed. However, no enhancement of the forecast of rise phase was noticed.
Model-scale data accumulated from DNW wind-tunnel analyses [142] additionally emerge the same contrary rise at high-speed ‘ight as approximated in the comprehensive helicopter [152], ‘gure 1.5. The model rotor did not have bi’lar absorbers unlike the full scale reference model, and had a viscous lag damper to deny ground resonance. Due to both the full-scale helicopter and the model-scale rotor have the same allocated negative rise phase, it is achievable to rule out fuselage up wash, fuselage dynamics, side slip angle, non-linear lead-lag damper or bi’lar prototyping as obtainable sources of error in the forecast of negative rise phase. References [153] and [154] investigated model scale rise forecast. In Ref. [153], calculated atmosphere loads were employed to forecast structural response. In Ref. [154], allocated de’ections were applied to forecast air loads. With allocated air loads, blade torsional bending was not precisely predicted, but with allocated extensible twist, good association of rise phase was acquired. The allocated elastic twist in the forthcoming case, was not physically allocated. It was deducted from blade torsion bending and applying a modal advancement. Currently another articulated rotor system, the French ONERA 7A has demonstrated comparable approaching blade rise phase activity during wind tunnel tests, ‘gure 1.5, [114]. however the negative rise peak endures at a slightly di’erent azimuth, the rise drop o’ endures at the same azimuth as the reference model ‘ight test.
The H-34 articulated rotor mechanism, also demonstrates comparable high-speed negative rise features as the Black Hawk – both in ‘ight test and wind tunnel test [120]. This analogy is active near the tip and moderately compresses inboard. A component at 75% span on the H-34 blades, appears no phase delay [155]. None of the experimental mechanisms commented in Ref. [120] were beneficial in precise forecast of rise phase towards the blade tip. Recently in 2004, Yeo and Johnson [101] likened high speed calculated air loads in level ‘ight for ‘ve articulated rotor con’gurations and compared with CAMRAD II calculations. The con’gurations were – H-34 complete scale in wind tunnel (?? = 0.39, CT /?? = 0.06), SA 330 or the analysis Puma full scale in ‘ight (?? = 0.362, CT /?? = 0.07), SA 349/2 full scale in ‘ight (?? = 0.361, CT /??= 0.071) and also the REFERENCE MODEL full scale in ‘ight as discussed above (?? = 0.368, CT /?? = 0.0783). Except the analysis Puma, all the rotor mechanisms emerged the advancing blade rise phase dilemma. H-34 has a trapezoidal tip, SA 349/2 has a straight tip, reference model has a swept tip – clearly tip shape alone cannot be the beginning of the problem. The rigid pre-twist for the rotors range from -8.3 degrees (ONERA 7A) to adjacently -16 degrees for the reference model. hence, high rigid twist alone cannot be the difficulty either. Along with, the SA 349/2 blades do not emerge a negative loading near the tip at all, although, clutches the equivalent phase error as the reference model.
The pitch-link loads are the rotor control loads near the blade root – initially an integrated efiect of the blade torsion bending conditions. The pitch-link loads are under-predicted by 50% at all fiight speeds, figure 1.7. Figure 1.8 shows the forecasted pitch-link load at high speed. Distorted pitch-link load emerges due to erroneous aerodynamic pitching conditions. Pitching moment forecasts, for all the rotors, comprising the research Puma was poor. Figure 1.6 shows the forecasted pitching conditions of the reference model at high speed fiight (taken from Lim [151]). They are over-predicted inboard and under-predicted at the outboard stations.
The area pitching moments decide elastic torsion which intelligibly afiects the blade rise as a contributing element of the angle of attack. It can be demonstrated that elastic torsion is the best provider to approaching blade rise in high speed fiight (chapter 4). Thus the two dilemmas of advancing blade rise and pitching moment forecasts are related to each other via the correctness of structural response computation. Lim [156], in acceptance with Bousmanfis approximation generalized the state of the art as [3], fiWe are still in the stage that we do not comprehend the basics : is this abnormality from the structural or aerodynamic (especially upshot) prototyping or both ? fi.
The purpose of the present work is to eliminate these two efiects decouple aerodynamics from architectural dynamics, study them autonomously, discover the forecast deficiencies in each, elaborate upon them, and bring them back together.
1.5 APPROACH OF RESEARCH
The present research difiers from former work in that it analyzes to separate the physics of aerodynamics and architectural dynamics from the complicated aeroelastic dilemma, analyze them autonomously and then bring them back together again.
Flight analysis benchmarked air loads are utilized to validate and refine an architectural model – the errors in forecast now begins completely from architectural modeling. Once validated, the acquired deformations are prescribed to computed air loads the defects in forecast begin from aerodynamic mocking up. Riseing-line and CFD aerodynamic models are analyzed and compared. The riseing-line and CFD aerodynamic models are then used to conduct comprehensive analysis of the reference model helicopter. The riseing-line comprehensive investigation is used to gain basic insights into the two key problems of emitted rotor aeromechanics advancing blade rise phase and pitch link loads. Permanence of rotor modeling is analyzed with step-wise modeling refinements. The CFD aerodynamic model is then efficiently coupled with the riseing-line comprehensive analysis to endure the two problems and significantly correct the forecast of air loads and blade loads. The inducts for enhancements are established and accepted from the prescribed deformations air loads study.
1.6 CONTRIBUTION OF THE RESEARCH
The core contributions of this research can be divided into two grades – 1. Basic feachers of rotor harmonics in dynamic fiight simulation and 2. Enhancements in the correctness and scope of forecast ability to acquire them. The specific accomplishments can be generalized as follow.
1. Forecast defects in vibratory and oscillatory blade loads and pitch link loads in high-speed forward fiight stem from defective aerodynamic prototyping, not architectural prototyping. Distortion in oscillatory pitch link load stems from erroneous aerodynamic driving moments. Defect in vibratory blade loads stem from erroneous vibratory rise. Basic deficiency in the forecast of vibratory rise demonstrates as an advancing blade rise phase error.
2. Vibratory rise at high speed is controlled by elastic torsion at outboard stations (85% outboard) and an integration of elastic torsion and upshot of foregoing blades inboard (60%-85% radial stations). either elastic torsion and rotor upshot, together, are key to precise forecast of vibratory rise at the inboard stations. Both of the factors alone does not elaborate vibratory rise or rise phase forecasts at these stations.
3. A 3D-CFD benchmarks coherently abutted to an accomplished aeroelastic benchmarks () forecasts the aerodynamic pitching-moments precisely and hence the elastic torsion deformations at high speed. The coupling methodology is stable, efficient, well posed and comfortable to approach in four or six iterations. Advanced forecasts from CFD adhering stem from corrected aerodynamic driving moment forecasts – most significantly near the blade tip, and all across the span in common.
4. A precise set of blade deformations are accumulated by applying fiight test measured airloads at high speed fiight. In lack of benchmarked deformations, this distortion set forms a competitively precise choice to validate airloads approximations.
5.TURN-3D inconsistent coupling methodology significantly persists the high speed vibratory airloads, blade loads, rise phase and pitch link load pre- diction dilemma from first principles.
1.7 THESIS ORGANIZATION
Chapter 1 explains the helicopter loads and vibration dilemma, surveys the evolution and state of the art in investigations ability, concentrates on the basic high speed fiight forecast defects and discusses the core focus and essential contributions of the present conduct.
Chapter 2 to 5 describes the present research work step by step. Chapter 2 describes the architectural prototyping and validation. At the end of Chapter 2, a segment of prescribed deformations are acquired with which to validate the aerodynamic models. Chapter 3 deals with aerodynamic prototyping and validation. Chapter 4 describes riseing-line complete benchmark with approach on basic understanding issues. Chapter 5 accounts 3D CFD code loose coupling methodology for corrected forecast of air loads and blade loads forecast from first principles. A set of summary determinations are constructed at the end of each chapter.
Chapter 6 acknowledges the core conclusion of the present research along with recommendations for forthcoming work.
Figure 1.1: Rotor vibratory load forecasts from seven aeroelastic codes compared with Lynx data, high-speed steady level flight at 157 knots, Hansford and Vorwald [148]
Figure 1.2: Forecasted Flap Bowing Condition at 50% R radial position in high-speed steady level simulation flight compared with REFERENCE MODEL data; ?? = 0.367, Cw/?? = 0.0773, Lim [151]
Figure 1.3: Forecasted and simulated rotor flap bowing condition at 50% R for
REFERENCE MODEL Black Hawk in steady flight; CW/?? = 0.0773, Bousman [99]
Figure 1.4: Normal force forecast in fast rotating rotor steady level flight simulation comparison with reference data; ?? = 0.367, Cw/?? = 0.0773, Lim [151]
Figure 1.5: Simulated normal force on single rotor flight test compared with existing WT test articulated rotor. WT test data, Bousman [152], ONERA [114]
Figure 1.6: Jerk condition forecast simulation result in higher rotor revolution matched with reference flight data; ?? = 0.367, Cw/?? = 0.0773, Lim [151]
Figure 1.7: Jerk Load forecast simulation result in average speed steady level carrier compared with reference data; ?? = 0.367, Cw/?? = 0.0773, Bousman [3]
Figure 1.8: Jerk Load forecast simulation result in high-speed steady level carrier compared with reference data; ?? = 0.367, Cw/?? = 0.0773,Bousman [3]
CHAPTER 2 MODELING OF ROTOR WINGS
This chapter explains as well as validates the architectural active model of reference model rotor blades. Flight analysis benchmarked air loads, control angles and lag barrier force are exercised to measure the rotor architectural response and active blade loads. Forecast distortions commence completely from architectural prototyping. Hence the physics of architectural dynamics is isolated from the aeroelastic response dilemma. The marrow is on fundamental understanding of the architectural active approaches behind oscillatory as well as vibratory blade loads.
A comparable study was delivered out in reference [157] using fiight test and wind tunnel air loads of a CH-34 rotor. The equations controlling blade counter-accusation in fiap, lag and torsion were linear. Flap and lag extents of freedom were adhered only by the local pitch angle. Torsion extent of freedom was detached from fiap and lag. In the subsistent study, a fully coupled set of non-linear equations are used, as derived in references [13, 14]. The efiect of couplings caused by elemental center of gravity ofisets, tip sweep and architectural nonlinearities are embodied. An analogous analysis was conveyed out in Reference [153] for the reference model but the airloads employed were that of an exemplary scale rotor.
The consequence of this exercise, once the architectural mock-up is adequately validated, is a precise set of blade deformations data. This set of deformations data is useful due to fiight test approximations of blade deformations are not obtainable. In lack of measured deformations, the distortion set obtained using segmented air loads, allots an opportunity for isolating the physics of aerodynamics from the aeroelastic response dilemma. The deformations acquired applying allocated air loads are called prescribed blade deformations. Applying this set of prescribed blade de-formations constant, difierent aerodynamic prototypes can be accounted by matching air load forecasts with fiight test air loads. This study forms the description matter of Chapter 3. The benefit of isolating aerodynamics hence depends on the correctness of the architectural model. This forms the subject matter of this chapter.
First, the blade distortion factor, controlling equations of motion, modeling appropriations, response and blade loads solution approaches are accounted. Then the architectural model is accepted using fiight test data. Lastly, using the accepted architectural model, a precise set of blade deformations at high-speed fiight is obtained.
2.1 GOVERNING EQUATIONS OF MOTION
The rotor blades are prototyped as long, narrow, ceaseless, isotropic beams experiencing axial, fiap, lag and torsion deformations. The deformations can be moderate as the mock-up includes geometric non-linearities up-to second order. Radial non-uniformities of mass, stifiness, bend, etc., chord wise ofisets of mass centroid (center of gravity) and area centroid (tension axis) from the elastic axis, precone, and bend of the cross sections are combined. The model follows the Hodges and Dowell formulation [13] while compensating elastic torsion and elastic axial distortion as quasi-coordinates [14]. The baseline model assumes an unbent blade. Modeling refinements needed to assemble architectural sweep and droop are described in details in Ganguli and Chopra [25]. The controlling equations and their derivations persist same, the swept and drooped components need additional control adjustments and a modified finite component assembly mechanism. The reference equations of motion are already constructed using Hamiltonfis Principle.
The controlling partial difierential equations are solved using finite element method in time and space. The finite element method provides fiexibility in the implementation of boundary conditions for recent helicopter rotors. These equations are referred from fundamental physics references as mentioned above.
2.1.1 Rotor-Blade Relational Basics
There are 4 coordinate systems of interest, the hub-fixed system, (XH, YH, ZH)
with unit vectors I??H, J??H,K??H, the hub-rotating system, (X, Y, Z) with unit vectors
??I, ?? J, ??K , the undeformed blade coordinate system, (x, y, z) with unit vectors ??i, ??j, ??k
and the deformed blade coordinate system, (??, ??, ??) with the unit vectors ??i??, ?? j??, ?? k?? .
These frames of references are denoted as H,R,U and D respectively. The hubrotating
coordinate system is rotating at a constant angular velocity ?? ??K with respect
to the hub-fixed coordinate system. The transformation between the hub-fixed
system and the hub-rotating system is defined as
{fi(Ifi@Jfi@Kfi)}=[fi(cos?? sin?? 0@sin?? cos?? 0@0 0 1)]{fi(fiI^fifi_h@fiJ^fifi_h@fiKfifi_h )}=T_RH {fi(fiI^fifi_h@fiJ^fifi_h@fiKfifi_h )} (2.1)
Where the azimuth angle, ??, equals ??t. The undeformed blade coordinate system is at a precone angle of ??p with respect to the hub-fixed system. The transformation between the undeformed blade coordinate system and the hub-fixed system is defined as
{fi(ifi@jfi@kfi)}=[fi(cos??p 0 sin??p@0 1 0@-sin??p 0 cos??p )]{fi(Ifi@Jfi@Kfi)}=T_UR {fi(Ifi@Jfi@Kfi)} (2.1)
The transformation between the undeformed blade coordinate system and the deformed blade coordinate system remains to be determined.
2.1.2 Rotor Blade Deformation
Consider a generic point P on the undeformed blade elastic axis. The orientation of a frame consisting of the axes normal to and along principle axes for the cross section at P defines the undeformed coordinate system (x, y, z). When the blade deforms, P reaches P_. The orientation of a frame consisting of the axes normal to and along principle axes for the cross section at P_ defines the deformed coordinate system (??, ??, ??). Adequate description of the deformed blade requires in general a total to six variables : three translational variables
2.2.2 Harmonic Abolishment Procedure
The dilemma of discovering rotor response with a prescribed set of air loads which remain fixed and do not alter with the response itself, can be called as a mechanical air loads dilemma. In the present case the benchmarked airloads are used as the prescribed set.
The mechanical air loads dilemma is basically an ill-posed problem be- cause the air loads are fixed and do not alter in response to blade deformations. This governs to zero aerodynamic damping. It cannot be solved for all rotor mechanisms. Examine a teetering, gimbaled or articulated rotor with basic fiap frequency of 1/rev (1p) with zero structural damping. If the benchmarked aero hinge condition is precise, the 1p element will be identically zero in which case the rotor response is undefined. The 1p element is interchangeably zero due to, at resonance the damping force is equal and opposite to the forcing and they are both are parts of the benchmarked air loads. In conduct benchmarked air loads will have distortions. These distortions will drive a 1p aerodynamic hinge moment which will drive the rotor response to infinity. In occurrence of structural damping, which are small contrasted to aerodynamic damping e.g., in fiap 2% compared to 50%, the response will not be infinite but the correctness of the benchmarked air loads needed for a competitively precise response solution will be unobtainable to meet. The mechanical air loads problem is hence fundamentally erroneous for low damped systems with natural frequencies close to excitation harmonics. The Black Hawk blade frequencies are reasonably well separated from excitation harmonics except the first natural frequency which is 1.036/rev.
The rotor blade is prototyped as a fully articulated beam with fiap and lag hinges synchronized at 4.66% span. All blades are similar. Each blade is defined by 20 finite components enduring fiap, lag, torsion and axial degrees of motion. The blade property data, including nonlinear aerodynamic and structural twist distributions are acquired from the NASA Ames master database. The tip sweep in the outer 6.9% of the blade span (reaching a maximum of 20 degrees at 94.5% span) is prototyped in two ways. The baseline mock-up assembles the tip sweep as a center of gravity ofiset from a straight undeformed elastic axis. Thus, in the swept part of the blade, the total center of gravity ofiset is the sum of the local ofiset with respect to swept elastic axis and the ofiset due to blade sweep. The elastic axis of the reference model blade is at the local quarter chord line. A refined mock-up assembles an architecturally swept elastic axis [23, 25]. The refined sweep mock-up is seen to afiect only the forecasted torsion dynamics. The benchmarked air loads are addressed at the local quarter chord locations at all radial stations.
The non-linear lag damper force is imposed on the structure as a set of centralized forces and cardinal points acting at 7% of the blade span. These damper imposed forces and moments deflect with azimuth based on the nominal damper geometry. The damper geometry is acquired from the master database. The pitch link is prototyped as a linear spring-damper system. The elastomeric bearing stifiness and damping are prototyped as linear springs and dampers in fiap, lag and torsion.
The rotor blade frequency plot and the first ten genuine frequencies at the acting RPM are displayed in figure 2.2(a). These parallel to a collective angle of 13.21 degrees and a baseline root torsion spring stifiness of 363 ft T lb/degrees [160]. The root spring stifiness is an identical measure of the pitch link stifiness accumulated by multiplying the pitch link stifiness with the square of the pitch link arm perpendicular to the blade elastic axis. An accrual realistic value of the root torsion spring is 1090 ft-lbs/degree as benchmarked in Ref. [161]. It corresponds with the fixed system control stifiness for reaction less loading. The elevated stifiness increases the first torsion frequency from 3.8/rev to 4.2/rev as shown in figure 2.2(b). Flap and lag frequencies persisting nominally constant. Figure 2.3 shows the adjustment of calculated first torsion frequency with root spring stifiness. The existing calculation shows the same trend as that analyzed in Ref. [161] with a minimally increased value. The swept elastic axis model has a higher propeller condition in the tip region and causes a marginally additional torsion frequency. The first eight structural modes are applied for the present study.
The benchmarked air loads are in the asymmetrical blade frame, and accommodate the loading driven by the undeformed blade as well as by the aeroelastic response. They are decreased to the undeformed frame iteratively applying calculated deformations and the fiight test control angles at each step. These iterations have no efiect on the driving moments and are insignificant for the normal force. They are considerable only for acquiring the chord forces in the undeformed frame.
The frequent blade response is accounted clearly using finite element in time. A time-marching algorithm, in contrast, needs more than an order of magnitude longer in approximation time to compensate down to the final steady state response. This is due to the lack of aerodynamic damping and the proximity of conventional frequencies to forcing harmonics ( eg., 1st fiap is 1.04/rev, 2nd fiap is 2.82/rev,1st torsion is 3.8/rev ). In addition, artificial damping is needed primarily during advancement cycles and needs to be subsequently removed. Artificial damping accelerates the decline of the initial natural mode response in the nonexistence of aerodynamic damping.
2.2.3 Calculated Architectural Response
The calibrated architectural response of the rotor blades are now matched with high speed fiight test data. Root fiap and lag angles, fiap, lag and torsion bowing conditions and jerk link loads are benchmarked. The bowing conditions and impulse link loads paralleling to Flight 8515 are also shown.
2.2.3.1 Root Flap, Lag and Pitch Angles
The approximated oscillatory fiap angle at the blade root is shown in figure 2.4(a). The waveform is attentive to architectural damping in the first fiap mode. A damping value of 4% critical is applied to achieve a better peak to peak match. The phase of the resulting waveform manifests acceptable agreement.
The upper shaft bowing moment, shown in figure 2.4(b), is integrated with the root fiap angle in that it manifests the identical trend. Without the 4% damping, the waveforms shows large distortion in magnitude and phase. The upper shaft bowing condition is the bowing load at the rotor shaft. There are two categories of values which are co-actively orthogonal to each other, one category constructed by the root fiap instants from blades 1 and 3, and another category by the root fiap instants from blades 2 and
4. The test data was obtainable for the scale reading which was developed by blades
1 and 3 and is employed for the existing comparison. The forecasted shaft instants from blades 1 and 3 and blades 2 and 4 are ofi course same with only a phase shaft as the blades are assumed alike.
A 4% architectural damping value is an unrealistically high damping value to be developed by a mechanical fiap hinge damper. It shows that the phase distortion in approximated root fiap angle and upper shaft bowing condition stems from slight distortions in airload benchmarks as described below. A structural damping value of 4% occurs to be the quantity needed to ofiset this distortion. Figures 2.5 materialize the harmonics of the root fiap angle. The largest contributor is 1/rev approached by 2, 3,4 in diminishing order of magnitude. The largest magnitude distortion is in 1/rev with a distortion in phase of around 50 degrees. The 4% damping rectifies the 1/rev distortion, both in magnitude and phase, while maintaining the higher harmonics unchanged. The architectural damping value is efiective only at 1/rev due to the rotor fiap frequency is very near 1/rev, 1.036/rev.
Figure 2.6(a) materializes the 1/rev average force harmonics at all radial stations. The aerodynamic hinge instant shown in figures 2.6(b) and 2.6(c) has, on the contrary, a very small 1/rev element. This is because, out of all the harmonics of the aerodynamic hinge instant, the 1/rev factor is developed as a residual of counter acting inboard and outboard average forces – which are mutually 180 degree out of phase as shown in figure 2.6(a). This is needed to induce a low steady hub instant in trimmed level fiight. This radial balance between the inboard and outboard average forces assure the phase of the 1/rev aerodynamic hinge instant, figure 2.6(d). The radial balance is efficiently abolished by a small distortion at any one radial station. Small distortions in air loads assessments at any one station can hence develop a large distortion in 1/rev aerodynamic hinge instant phase. It appears that the phase distortion in calculated root fiap angle stems from such a distortion in the benchmarked air loads. This error is then further magnified in the 1/rev root fiap angle forecast due to the adjacency of the 1st fiap frequency to 1/rev and the lack of some aerodynamic damping in the approach. Hence the distortion in root fiap angle forecast is a residue of the 1/rev trim air load balance in forward fight and the mechanical air loads