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Leading-edge slat optimization for maximum airfoil lift

A numerical procedure for determining the position (horizontal location, vertical location, and deflection) of a leading edge slat that maximizes the lift of multielement airfoils is presented. The structure of the flow field is calculated by iteratively coupling potential flow and boundary layer analysis. This aerodynamic calculation is combined with a constrained function minimization analysis to determine the position of a leading edge slat so that the suction peak on the nose of the main airfoil is minized. The slat position is constrained by the numerical procedure to ensure an attached boundary layer on the upper surface of the slat and to ensure negligible interaction between the slat wake and the boundary layer on the upper surface of the main airfoil. The highest angle attack at which this optimized slat position can maintain attached flow on the main airfoil defines the optimum slat position for maximum lift. The design method is demonstrated for an airfoil equipped with a leading-edge slat and a trailing edge, single-slotted flap. The theoretical results are compared with experimental data, obtained in the Ames 40 by 80 Foot Wind Tunnel, to verify experimentally the predicted slat position for maximum lift. The experimentally optimized slat position is in good agreement with the theoretical prediction, indicating that the theoretical procedure is a feasible design method.

Olson, L. E.↗

Performance Optimization of Plate Airfoils for Martian Rotor Applications Using a Genetic Algorithm

The Mars Helicopter Technology Demonstrator will be flying on the NASA Mars 2020 rover mission scheduled to launch in July of 2020. The goal is to demonstrate the viability and potential of heavier-than-air vehicles in the Martian atmosphere. Research is performed at the Jet Propulsion Laboratory and NASA Ames Research Center to extend these capabilities and develop the Mars Science Helicopter as the next possible step for Martian rotorcraft. The Mars Science Helicopter mass is scaled up to the 5 to 20 kg range, allowing a greater payload (approximately 0.5 to 2.0 kg), and greater range (approximately 3 km). Key to achieving these targets is careful aerodynamic rotor design. The Martian atmosphere’s low density and the small helicopter rotors result in very low chord-based Reynolds number flows, which reduces rotor performance. A continuous genetic algorithm is developed to optimize airfoil shapes at representative conditions for the Martian atmosphere. Previous research indicates that sharp leading edges and plate-like airfoils can out-perform conventional airfoil shapes. The present optimization allows for camber and thickness variation of curved and polygonal thin airfoils with sharp leading edges. The airfoil performance is evaluated at the highest attainable liftto- drag ratio near a moderate lift coefficient at compressible Mach numbers, as expected for Martian rotor application. Increases between 16% and 29% in airfoil lift-to-drag ratio at fixed lift coefficients are observed when compared with the Mars Helicopter Technology Demonstrator airfoils. Improvements in hover figure of merit are estimated to be between 4% and 10%, when applied to the Mars Helicopter Technology Demonstrator.

Koning, Witold J. F.↗

NASA technology program for future civil air transports

An assessment is undertaken of the development status of technology, applicable to future civil air transport design, which is currently undergoing conceptual study or testing at NASA facilities. The NASA civil air transport effort emphasizes advanced aerodynamic computational capabilities, fuel-efficient engines, advanced turboprops, composite primary structure materials, advanced aerodynamic concepts in boundary layer laminarization and aircraft configuration, refined control, guidance and flight management systems, and the integration of all these design elements into optimal systems. Attention is given to such novel transport aircraft design concepts as forward swept wings, twin fuselages, sandwich composite structures, and swept blade propfans.

Wright, H. T.↗

A Generic Nonlinear Aerodynamic Model for Aircraft

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

Grauer, Jared A.↗

System-Level Experimental Validations for Supersonic Commercial Transport Aircraft Entering Service in the 2018-2020 Time Period

This report describes the work conducted under NASA funding for the Boeing N+2 Supersonic Experimental Validation project to experimentally validate the conceptual design of a supersonic airliner feasible for entry into service in the 2018 -to 2020 timeframe (NASA N+2 generation). The primary goal of the project was to develop a low-boom configuration optimized for minimum sonic boom signature (65 to 70 PLdB). This was a very aggressive goal that could be achieved only through integrated multidisciplinary optimization tools validated in relevant ground and, later, flight environments. The project was split into two phases. Phase I of the project covered the detailed aerodynamic design of a low boom airliner as well as the wind tunnel tests to validate that design (ref. 1). This report covers Phase II of the project, which continued the design methodology development of Phase I with a focus on the propulsion integration aspects as well as the testing involved to validate those designs. One of the major airplane configuration features of the Boeing N+2 low boom design was the overwing nacelle. The location of the nacelle allowed for a minimal effect on the boom signature, however, it added a level of difficulty to designing an inlet with acceptable performance in the overwing flow field. Using the Phase I work as the starting point, the goals of the Phase 2 project were to design and verify inlet performance while maintaining a low-boom signature. The Phase II project was successful in meeting all contract objectives. New modular nacelles were built for the larger Performance Model along with a propulsion rig with an electrically-actuated mass flow plug. Two new mounting struts were built for the smaller Boom Model, along with new nacelles. Propulsion integration testing was performed using an instrumented fan face and a mass flow plug, while boom signatures were measured using a wall-mounted pressure rail. A side study of testing in different wind tunnels was completed as a precursor to the selection of the facilities used for validation testing. As facility schedules allowed, the propulsion testing was done at the NASA Glenn Research Center (GRC) 8 x 6-Foot wind tunnel, while boom and force testing was done at the NASA Ames Research Center (ARC) 9 x 7-Foot wind tunnel. During boom testing, a live balance was used for gathering force data. This report is broken down into nine sections. The first technical section (Section 2) covers the general scope of the Phase II activities, goals, a description of the design and testing efforts, and the project plan and schedule. Section 3 covers the details of the propulsion system concepts and design evolution. A series of short tests to evaluate the suitability of different wind tunnels for boom, propulsion, and force testing was also performed under the Phase 2 effort, with the results covered in Section 4. The propulsion integration testing is covered in Section 5 and the boom and force testing in Section 6. CFD comparisons and analyses are included in Section 7. Section 8 includes the conclusions and lessons learned.

Magee, Todd E.↗

Anti-Phase Vortex Reduction Control for Rotor Noise Suppression

An investigation is conducted in 2019 under the NASA Ames Center Innovation Funds (CIF) project entitled “Anti-Phase Vortex Reduction Control for Rotor Noise Suppression“ to experimentally validate an anti-phase rotor noise suppression concept. The first objective of the investigation is to conduct computational fluid dynamics (CFD) simulations to investigate the noise characteristics of several anti-phase rotor designs. The second objective is to conduct a series of acoustic tests of anti-phase rotors in an anechoic chamber at Pennsylvania State University (PSU) to evaluate the merit of the anti-phase rotor concept. The CFD investigation seeks to optimize the anti-phase alternating trailing edge patterns for rotor noise suppression. The design objective is to maximize the noise reduction while maintaining the aerodynamic thrust. The investigation is performed using a three-dimensional (3D) Unsteady Reynolds-Averaged Navier-Stokes (URANS) commercial solver STAR-CCM+ together with the Ffowcs-Williams and Hawkings (FW-H) formula to obtain the aerodynamic thrust and far-field noise level. An acoustic study is conducted for 13 anti-phase design candidates based on a proprietary rotor design. The CAD geometry of the rotor is furnished by PSU. These design candidates include different alternating trailing edge (TE) waveforms, TE segment lengths, TE deflection amplitudes, and transition characteristics. The best design candidate among those explored is an anti-phase rotor that has a four-period TE waveform which results in a reduction in far-field noise level of 2.1 dB in the hover condition and a reduction of 1.1 dB in the forward flight condition at 9.7 m/s. A further acoustic study is conducted for a different rotor manufactured by APC. Five APC rotor design candidates are simulated. The best anti-phase design candidate for the APC rotor results in a reduction in far-field noise level of 4.0 dB in the hover condition. An in-phase design candidate is also studied. This in-phase design provides a noise reduction of 2.5 dB. A series of acoustic experiments in the PSU anechoic chamber have been conducted in July 2019 and October 2019. Both anti-phase and in-phase rotors fabricated for the left-hand and right-hand rotations are tested. In the hover condition, all the rotors do not provide sufficient evidence of improved acoustic performance. However, the experimental data in the hover condition are deemed to be inconclusive due to the flow recirculation in the anechoic chamber caused by the rotor downwash. In the forward flight condition at 9.7 m/s, the anti-phase right-hand rotor produces a noise reduction by as much as 6.5 dB in the frequency range of 2000-4000 Hz, while the in-phase right-hand rotor produces a noise reduction by as much as 5 dB in the same frequency range. Both the anti-phase and in-phase left hand rotors offer no evidence of noise reduction. The difference in the acoustic performance of the left-hand and right-hand rotors could be explained by the location of the microphone array which is placed to the left side of the rotors. This microphone array location could create a bias in the sound pressure level in favor of the right-hand rotor. Using the average noise reduction values, the anti-phase 4H rotor could offer a noise reduction by as much as 3.25 dB while the in-phase 4I rotor could produce up to a 2.5 dB noise reduction. Both the computational and experimental results have provided sufficient evidence to support the noise suppression capability of the proposed anti-phase rotor concepts.

Rotor noise↗

Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun Yuan↗

Probabilistic Unsteady Aerodynamic Analysis

Probabilistic CFD design is needed because we are asked to do more with less. To cost effectively accomplish the design task, we need to formally quantify the effect of uncertainties (variables) in the design. Probabilistic design is one effective method to formally quantify the effect of uncertainties. Our objective is to establish a revolutionary new early design process, by developing non-deterministic physics-based probabilistic design tools, which will include all the life cycle processes. This work was concerned with the usefulness of parametric optimization method coupled with a Navier-Stokes analysis code for the aero-thermodynamic design of turbomachinery combustor liner. The interconnection between the CFD code and NESSUS codes will facilitate the coupling between the thermal profiles and structural design. We have developed new concepts for reducing the computational cost of unsteady, three-dimensional, compressible aerodynamic analyses for multistage turbomachinery flows. The flow was modeled by the three-dimensional Favre-Reynolds-averaged Navier-Stokes equations using the k-E turbulence closure, which was integrated using an implicit third-order upwind solver. The methodology developed in this work is expected to lead to the design optimization of turbomachinery blades.

Gorla, Rama S. R.↗

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

Taylor, Arthur C., III↗

Structural tailoring of advanced turboprops

A computer program has been developed for the performance of numerical optimizations of highly swept propfan blades by minimizing an objective function that is defined either as direct operating cost or the aeroelastic difference between a blade and its scaled model. Three component analysis categories are employed: an optimization algorithm, approximate analysis procedures for objective function and constraint evaluation, and refined analysis procedures for optimum design validation. The analyses conducted by the program encompass aerodynamic efficiency evaluation, finite element stress and vibration analysis, acoustics, flutter, and forced response life prediction.

Brown, K. W.↗

Conceptual Design Oriented Wing Structural Analysis and Optimization

Airplane optimization has always been the goal of airplane designers. In the conceptual design phase, a designer's goal could be tradeoffs between maximum structural integrity, minimum aerodynamic drag, or maximum stability and control, many times achieved separately. Bringing all of these factors into an iterative preliminary design procedure was time consuming, tedious, and not always accurate. For example, the final weight estimate would often be based upon statistical data from past airplanes. The new design would be classified based on gross characteristics, such as number of engines, wingspan, etc., to see which airplanes of the past most closely resembled the new design. This procedure works well for conventional airplane designs, but not very well for new innovative designs. With the computing power of today, new methods are emerging for the conceptual design phase of airplanes. Using finite element methods, computational fluid dynamics, and other computer techniques, designers can make very accurate disciplinary-analyses of an airplane design. These tools are computationally intensive, and when used repeatedly, they consume a great deal of computing time. In order to reduce the time required to analyze a design and still bring together all of the disciplines (such as structures, aerodynamics, and controls) into the analysis, simplified design computer analyses are linked together into one computer program. These design codes are very efficient for conceptual design. The work in this thesis is focused on a finite element based conceptual design oriented structural synthesis capability (CDOSS) tailored to be linked into ACSYNT.

Lau, May Yuen↗

Potential for Integrating Entry Guidance into the Multi-Disciplinary Entry Vehicle Optimization Environment

The state-of-the-art in vehicle design decouples flight feasible trajectory generation from the optimization process of an entry spacecraft shape. The disadvantage to this decoupled process is seen when a particular aeroshell does not meet in-flight requirements when integrated into Guidance, Navigation, and Control simulations. It is postulated that the integration of a guidance algorithm into the design process will provide a real-time, rapid trajectory generation technique to enhance the robustness of vehicle design solutions. The potential benefit of this integration is a reduction in design cycles (possible cost savings) and increased accuracy in the aerothermal environment (possible mass savings). This work examines two aspects: 1) the performance of a reference tracking guidance algorithm for five different geometries with the same reference trajectory and 2) the potential of mass savings from improved aerothermal predictions. An Apollo Derived Guidance (ADG) algorithm is used in this study. The baseline geometry and five test case geometries were flown using the same baseline trajectory. The guided trajectory results are compared to separate trajectories determined in a vehicle optimization study conducted for NASA's Mars Entry, Descent, and Landing System Analysis. This study revealed several aspects regarding the potential gains and required developments for integrating a guidance algorithm into the vehicle optimization environment. First, the generation of flight feasible trajectories is only as good as the robustness of the guidance algorithm. The set of dispersed geometries modelled aerodynamic dispersions that ranged from +/-1% to +/-17% and a single extreme case was modelled where the aerodynamics were approximately 80% less than the baseline geometry. The ADG, as expected, was able to guide the vehicle into the aeroshell separation box at the target location for dispersions up to 17%, but failed for the 80% dispersion cases. Finally, the results revealed that including flight feasible trajectories for a set of dispersed geometries has the potential to save mass up to 430 kg.

spacecraft guidance↗

An investigation of design optimization using a 2-D viscous flow code with multigrid

Computational fluid dynamics (CFD) codes have advanced to the point where they are effective analytical tools for solving flow fields around complex geometries. There is also a need for their use as a design tool to find optimum aerodynamic shapes. In the area of design, however, a difficulty arises due to the large amount of computer resources required by these codes. It is desired to streamline the design process so that a large number of design options and constraints can be investigated without overloading the system. There are several techniques which have been proposed to help streamline the design process. The feasibility of one of these techniques is investigated. The technique under consideration is the interaction of the geometry change with the flow calculation. The problem of finding the value of camber which maximizes the ratio of lift over drag for a particular airfoil is considered. In order to test out this technique, a particular optimization problem was tried. A NACA 0012 airfoil was considered at free stream Mach number of 0.5 with a zero angle of attack. Camber was added to the mean line of the airfoil. The goal was to find the value of camber for which the ratio of lift over drag is a maximum. The flow code used was FLOMGE which is a two dimensional viscous flow solver which uses multigrid to speed up convergence. A hyperbolic grid generation program was used to construct the grid for each value of camber.

Doria, Michael L.↗

Estimation of Supersonic Stage Separation Aerodynamics of Winged-Body Launch Vehicles Using Response Surface Methods

A collection of statistical and mathematical techniques referred to as response surface methodology was used to estimate the longitudinal stage separation aerodynamic characteristics of a generic, bimese, winged multi-stage launch vehicle configuration using data obtained on small-scale models at supersonic speeds in the NASA Langley Research Center Unitary Plan Wind Tunnel. The simulated Mach 3 staging was dominated by multiple shock wave interactions between the orbiter and booster vehicles throughout the relative spatial locations of interest. This motivated a partitioning of the overall inference space into several contiguous regions within which the separation aerodynamics were presumed to be well-behaved and estimable using cuboidal and spherical central composite designs capable of fitting full second-order response functions. The primary goal was to approximate the underlying overall aerodynamic response surfaces of the booster vehicle in belly-to-belly proximity to the orbiter vehicle using relatively simple, lower-order polynomial functions that were piecewise-continuous across the full independent variable ranges of interest. The quality of fit and prediction capabilities of the empirical models were assessed in detail, and the issue of subspace boundary discontinuities was addressed. The potential benefits of augmenting the central composite designs to full third order using computer-generated D-optimality criteria were also evaluated. The usefulness of central composite designs, the subspace sizing, and the practicality of fitting low-order response functions over a partitioned inference space dominated by highly nonlinear and possibly discontinuous shock-induced aerodynamics are discussed.

Erickson, Gary E.↗

Optimal Control Allocation for Distributed Electric Propulsion in a Series/Parallel Partial Hybrid Powertrain

The SUbsonic Single Aft eNgine (SUSAN) Electrofan is a NASA concept jet transport aircraft with a 2040 entry-into-service date. It utilizes electrified aircraft propulsion (EAP) to enable propulsive and aerodynamic benefits to reduce fuel usage, emissions, and cost. The powertrain consists of a single thrust producing, boundary layer-ingesting (BLI) turbofan gas turbine engine (GTE) with generators driving a series/parallel partial hybrid EAP system. The architecture includes 16 underwing contrarotating BLI fans, eight on each side, in a mailslot configuration. The 16 fans run on power extracted from the GTE through four 5 MW motor/generators connected to the Low-Pressure Spool, and a single 1 MW motor/generator on the High-Pressure Spool. The distributed fans can be used by the flight control to augment or replace the rudder function. At top of climb, the power extracted from the GTE for the fans is boosted by batteries. The design provides redundancy, and the capacity for boost means that the fans are designed to be able to provide additional thrust when necessary. These features can be leveraged in case of a fan or generator failure. This paper sets up the optimal control problem of setpoint determination for individual fans in the distributed propulsion system, accounting for electrical string efficiencies, saturations, and failures. The solution minimizes power consumption while maintaining thrust and torque on the airframe for maneuvering. Additionally, thrust that would have been lost due to temporary fan speed or power saturation is optimally redistributed to maintain overall desired thrust and torque on the aircraft. The power extraction range constraints derive from the gas turbine engine design and the small amount of variation allowed for the engine to maintain operability. The problem formulation allows the number and location of fan failures for which the thrust and torque can be maintained to be investigated, which has implications for certification. Simulations of a coordinated turn utilizing the distributed electric propulsion for yaw rate control under different failure scenarios demonstrate the robustness of the powertrain design to failures and help define its limitations.

Distributed Electric Propulsion↗

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun. Y.↗

Analysis and Optimization of Baseline Single Aisle Aircraft for Future Electrified Powertrain Flight Demonstrator Comparisons

The purpose of this study is to provide baseline single-aisle vehicles for future comparisons with NASA’s Electrified Powertrain Flight Demonstration (EPFD) turbofan-powered Vision Systems. State-of-the-art single-aisle transports with varying design capacities of 100 to 150 passengers are modeled using NASA Ames Research Center’s General Aviation Synthesis Program (GASP) as well as GASPy. GASPy is a modernized Python-based version of GASP built on the OpenMDAO framework to allow for future, efficient gradient-based optimization and coupled airframe-propulsion design. In order to meet projected NASA Aeronautics goals for 2035, advanced aircraft technologies must be incorporated into these vehicle systems. Methodology to parametrically infuse baseline aircraft models with advanced technologies simulating improvements in aerodynamics, structures, and propulsion systems is detailed, along with the results of technology sensitivity studies. Comparison of the baseline and advanced configurations will allow for future analysis of the benefits of future hybrid and fully electric aircraft concepts in the EPFD project, where fuel consumption and emissions will be modeled and assessed. This study has been conducted under the EPFD project to establish benchmark turbofan models and demonstrate System Analysis capabilities in multi-disciplinary aircraft design, analysis, and optimization for advanced turbofan concepts.

Carl J. Recine↗

Fully integrated aerodynamic/dynamic optimization of helicopter rotor blades

A fully integrated aerodynamic/dynamic optimization procedure is described for helicopter rotor blades. The procedure combines performance and dynamic analyses with a general purpose optimizer. The procedure minimizes a linear combination of power required (in hover, forward flight, and maneuver) and vibratory hub shear. The design variables include pretwist, taper initiation, taper ratio, root chord, blade stiffnesses, tuning masses, and tuning mass locations. Aerodynamic constraints consist of limits on power required in hover, forward flight and maneuvers; airfoil section stall; drag divergence Mach number; minimum tip chord; and trim. Dynamic constraints are on frequencies, minimum autorotational inertia, and maximum blade weight. The procedure is demonstrated for two cases. In the first case, the objective function involves power required (in hover, forward flight and maneuver) and dynamics. The second case involves only hover power and dynamics. The designs from the integrated procedure are compared with designs from a sequential optimization approach in which the blade is first optimized for performance and then for dynamics. In both cases, the integrated approach is superior.

Walsh, Joanne L.↗