Free-Wake Based Dynamic Inflow Model for Hover, Forward and Maneuvering Flight

In this paper, the potential flow equations are converted to ordinary differential equations through a Galerkin approach in which velocity and pressure potential functions are expanded in terms of closedform solutions to Laplace's equation. Because the method gives differential equations for the flow in terms of a relatively few generalized coordinates (that represent modes of the flow field) the resultant equations can be used effectively in preliminary design, real-time simulations, and dynamic eigenvalue analysis for aeroelasticity. This new theory is more general than the Peters-He dynamic wake model since it has a more rigorous derivation and includes inflow modes previously neglected in the Peters-He model. Results are presented in the frequency domain for simple harmonic motion. The axial velocity components are obtained by this new methodology on and off the disk, for axial and skewed flows, and for different pressure distributions and are compared with the Peters-He model and with an exact solution obtained by a convolution integral. INTRODUCTION Dynamic inflow models go back over 50 years in terms of their development and application. Sissingh first formulated a mathematical model that described how gradients in inflow could result from cyclic pitch changes or from fuselage pitch and roll rates. He further showed how these inflow gradients could create cyclic changes in blade angle of attack that significantly changed the actual rotor response. Curtiss and Shupe refined this idea into a lift deficiency function for rotor cyclic variations. Ormiston and Peters showed how the formulation could be generalized into an inflow model * AIAA Fellow Copyright © 2002 The American Institute of Aeronautics and Astronautics Inc. All rights reserved. for both uniform and side-to-side variations in inflow. Peters generalized these concepts to the unsteady case by including apparent mass terms to account for the time delay involved in the development of the rotor flow field. Comparisons with static data in hover and forward flight showed that the previous methodologies were inadequate in forward flight. Pitt and Peters used principles of potential flow theory to show that these concepts could be developed from first principles without ad hoc assumptions on time delay or on the effects of forward flight. They obtained an unsteady flow model from potential functions that gave spectacular correlation with wind tunnel response data throughout the frequency and advance ratio range. However, despite the unquestioned success of this inflow model, it still remained a theory with only three inflow degrees of freedom: 1) uniform, 2) fore-to-aft, and 3) side-to-side. Later, Peters and He showed how the Pitt-Peters ideas could be truly generalized to a theory with an arbitrary number of inflow harmonics and an arbitrary number of radial shape functions per harmonic. They showed how the general theory could reduce in special cases to the old Pitt-Peters model as well as to Loewy theory and Prandtl tip-loss theory. This new theory was used to correlate unsteady wind tunnel data from the NASA Langley wind tunnel for various planforms, thrust coefficients, and advance ratios. The match in both steady and unsteady distributions was excellent The Peters-He model represents a mature dynamic inflow model that is now used in many production codes, including 2GCHAS (Government code), FLIGHTLAB (Advanced Rotorcraft Technology), COPTER (Bell helicopter), ONERA-DFVLR (European Community) and many university applications. More recent extensions of the theorv include applications to the off-axis coupling problem, and to ground effect in flight simulation. 1 American Institute of Aeronautics and Astronautics (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. The inflow models described in the above paragraphs are formulated such that the states of the model represent induced flow distributions on the rotor disk (expanded radially as polynomials and azimuthally as Fourier coefficients). The first-order differential equations for these states depend on the free-stream impingement angle, flight speed, and thrust level. However, they are all in closed form in terms of a mass matrix and a damping matrix, such that they are easily assembled either into a comprehensive code, an eigenvalue analysis, or a flight simulator. This makes the model extremely efficient. However, in many of the applications, such as the ground effect work, it is necessary to find not just the normal flow at the disk, but all three components of flow off of the disk as well. Peters and Morillo presented a consistent methodology for computing all three components of the flow in axial flow, both on and off of the rotor disc within the context of a finite-state model. The model is formulated in a manner fairly similar to previous work (in that the potential functions in ellipsoidal coordinates are used). However, in contrast with the previous work, the states represent velocity potentials rather than individual flow components. In addition, all potential functions are considered (not just the ones that have a pressure discontinuity across the disk); and the derivation of the equation coefficients is done in a more consistent and rigorous manner than in the earlier derivations. The result is a simpler derivation and a more complete inflow theory for the velocity both off and on the disk. Previous dynamic inflow models in axial flow are shown to be special cases of the new model when offdisk coupling is neglected. This new methodology based on a Galerkin approach provides the exact solution on as well as off the disk for the axial velocity component in axial flow. In this paper, the concepts introduced by Peters and Morillo are extended to analyze skewed flow cases. FLUID DYNAMICS EQUATIONS The three-dimensional potential flow equations (momentum and continuity equations) for the pressure and velocity fields P and v , with a free-stream velocity V^are f;-Jp-^ (1) V • v = 0 (2) These equations have been non-dimensionalized by defining P as pressure divided by pVj, v as induced velocity divided by V^ and time as a reduced time T, (i.e., time multiplied by VJR.) The variable £ is the non-dimensional coordinate along the free-stream line, positive upstream. All lengths are divided by the rotor radius R. Figure 1 shows the coordinate system. Fig.l Coordinate system. From continuity, Eq. (2), it is observed that v can be expressed by a velocity potential that satisfies Laplace's equation. It can also be shown that P satisfies Laplace's equation. Therefore, P can be expressed as a summation of pressure potentials, 0; and v can be expressed as a summation of the gradient of velocity potentials, V. NEW FORMULATION Pressure Potentials* and Velocity Potentials To transform Eqs. (1) and (2) by a Galerkin method, it is required to expand the pressure potential, 4>, and the velocity potentials, *P, in terms of complete set of functions that satisfy Laplace's equation. In addition, they have to fulfill the boundary conditions for pressure in the case of <&, and for velocity in the case of V. The boundary conditions for pressure are given by a discontinuity across the rotor disk. The use of an ellipsoidal coordinate system, has the advantage that any odd function in v, will allow a representation of a discontinuity across the rotor disk. An additional advantage of using an ellipsoidal coordinate system is that an analytical solution of Laplace's equation is known and can be expressed as,

Based on CFD method and FW-Hpds equations, a numerical method for predicting aeroacoustic characteristics of coaxial rotor is established. In order to accurately simulate the flowfield of coaxial rotor, several techniques including moving-embedded grids, implicit LU-SGS scheme, ROE-MUSCL scheme and Spalart-Allmaras turbulence model are adopted to solve the RANS equations. The aeroacoustic characteristics of coaxial rotor in forward flight are calculated and analyzed by using FW-Hpds equations. The calculated acoustic characteristics of the AH-1/OLS model in forward flight for validation are in good agreements with the experimental data. The acoustic characteristics of coaxial-rotor in forward flight including the sound pressure time history and directivity patterns are investigated in detail. Some meaningful conclusions are obtained from the calculated results. The counter-rotation of upper and lower rotors has significant effects on the sound pressure time history and leads to different phases of peak value at different observation points. The noise radiation intensity of coaxial rotor in forward flight exhibits an approximately symmetrical distribution on both sides of the forward flight direction, which is one of the important differences between the coaxial rotor and the single rotor.

In this work, optimization methodologies of the kinematics of flapping wings in forward and hover flights are considered. Particularly, local and global optimization algorithms are combined with the unsteady vortex lattice method (UVLM) to determine the most efficient kinematics. In the first problem, the kinematic optimization of a three-dimensional flapping wing in forward flight with active shape morphing is aimed at maximizing the propulsive efficiency under lift and thrust constraints. Results show that due to the quasi-concavity of the objective function associated with the flapping kinematics employed in forward flight, local gradient-based optimizers perform very well in terms of accuracy and computational cost. In the second problem, the objective is to identify the optimized kinematics of a twodimensional hovering wing that minimize the aerodynamic power under lift constraint. The results show that using a hybrid optimization algorithm (combination of local and global schemes) accelerates the convergence to optimal points and avoids being trapped at local minimum points. While the efficiency of using a local optimizer, a global optimizer, or a hybrid of the two depends on the nature of the problem and associated design space, it is determined that hybrid optimization is best suited for determining local minima.

This study examines hexacopter performance in hover and forward flight with single rotor failure. A classical configuration (adjacent rotors spinning in opposite directions) and an alternate configuration are considered. The simulation model uses calculates rotor forces and moments by using blade element theory coupled with a finite-state dynamic inflow model. For the alternate hexacopter, if one of four rotors (out of six) fails, trim is possible in hover and forward flight, and the aircraft remains fully controllable. Recovery from the failure of one of the other two rotors is impossible. For the classical hexacopter, if any of the forward-facing rotors fail, the aircraft can be trimmed in forward flight and is fully controllable. If an aft rotor fails, trim is not possible but the aircraft could be turned around to orient the failed rotor forward. Although the classical hexacopter can be trimmed in hover by turning off the rotor diametrically opposite to the failed rotor, the aircraft is not independently controllable about all axes. In the event of a rotor failure, the classical hexacopter could cruise and land, but it cannot maintain a sustained hover. Power penalties of up to 23% are observed in the event of failure due to increased drag on the operational rotors.

Systematic design methodology for development and flight testing of a variable pitch quadrotor biplane VTOL UAV for payload delivery

The design of new helicopter rotor blades is a challenging task. The individual blade sections undergo very different flow conditions during the various flight regimes of the helicopter. In forward flight, the advancing side operates in a transonic regime where potentially shock waves can occur, while on the retreating side little flow velocities at high angle of attacks are seen up to reverse flow. In hover, the oncoming tip vortex of the previous blade drastically influences the inflow on the rotor. This paper joins the classical blade shape design with numerical optimization techniques. Opposing to the direct solution process of directly modifying the blade shape, the rotor blade is conventionally considered as a set of airfoils, a planform and a twist distribution. First, rotor airfoils are found through numerical optimization and then placed on the reference rotor. The planform and twist of this rotor are then also numerical optimized. The obtained trade-off blade for hover and forward flight drastically improved the performance over the reference HART-II blade (11% in forward flight, 5% in hover flight). In order to arrive at industrial relevant blades, further work including more disciplines becomes necessary.

In this paper, an optimal controller is investigate d based on the Linear Quadratic Control method. The controller simulation is execut ed based on a small-scale autonomous model helicopter, Yamaha R-50. Genetic algorithms are employed to generate weighting matrices by optimizing the performance index of the control system. As a result, this method produces optimal weighting matrices which further improve the Linear Quadratic Controller. A full state feedback approach is used in the control design process. A Kalman observer is integrated into the controller to predi ct full state variables, since only a limited number of state variables are measured. Finally, th e performance of the controller is evaluated in the time domain with and without disturbances when the model helicopter is in hovering flight and forward flight. I. Introduction utonomous helicopters offer special advantages for major operations in both civilian and military sect ors, particularly in cases that are considered either in accessible or dangerous for human beings, due to th eir vertical take-off and landing (VTOL) capabilities. The contr ol system of autonomous helicopters plays a key rol e in its ability to carry out the assigned task effectively. This has lead to a growing interest in the design and analysis of the control system of autonomous helicopters. In 1990s, classic control theory was widely used for autonom ous helicopter control systems, which is mainly a succe ssive loop closure approach. The control gains are selected separately using tools such as Root locus, Bode and Nyquist plots. The controller parameters are usual ly tuned based on the controller performance measured either in ti me domain or in frequency domain. This design procedure becomes increasingly difficult as more and more loo ps are added, specifically, when the dynamics invol ve multiple inputs, multiple outputs, or multiple feedback loop s with complex performance criteria. To control an autonomous helicopter modeled as a complex Multiple Input Multiple Output (MIMO) system, the performance criteria can not be easily met by the approach based on classis cont rol theory. Several researchers have developed a number of diff erent ways for the control system design of autonom ous helicopters in the literature. Shim et al 1 presented three different control methods using li near robust, fuzzy logic, and nonlinear tracking controls, for an autonomous helicopter in hover and low speed flight. Johnson a nd Kannan 2

Dynamic characteristics of active twist rotor (ATR) blades during forward flight is investigated analytically in this paper. An aeroelastic model for an active rotor system is developed to identify dynamic characteristics of ATR blades with integral strain actuators embedded in their composite construction. More specifically, a time domain integration scheme for the geometrically exact formulation of passive beams is extended with the active materials constitutive relations for the forward flight analysis of the ATR system. In parallel, forward flight wind-tunnel tests are conducted at NASA Langley to collect control sensitivity functions experimentally using dynamically-scaled four-active-bladed rotor system. Preliminary results from the present analytical model are presented and compare well with experimental observations. The theoretical model will be used as a design and evaluation tool for closed-loop controller for twist actuation of the ATR system.

This paper deals with some recent developments of a boundary element methodology for the unified aerodynamic/aeroacoustic analysis of subsonic and transonic potential flows past helicopter rotors in hover and forward flight. In this methodology, first the potential solution is derived on the rotor-blade surfaces. Then, the boundary integral representation gives the potential everywhere in the field, and the Bernoulli theorem yields the acoustic pressure. Numerical results are presented for helicopter rotors in hover and forward flight at both subsonic and transonic rotor speeds. Comparisons with existing numerical results and experimental data are included.

Design and experimental study of a new flapping wing rotor micro aerial vehicle

In the present study, the parametric study was performed to analyze the effect of the tab on the aerodynamic performance and characteristics of rotor blades. Also, the tab shape was designed to improve the aerodynamic performance of rotor blades. A computational fluid dynamics solver based on three-dimensional Reynolds averaged Navier–Stokes equation using an unstructured mesh was used for the parametric study and the tab design. For airfoils, the effect of length and angle of a tab was studied on the aerodynamic characteristics of airfoils. In addition, including those parameters, the effect of a span of a tab was studied for rotor blades in hovering flight. The results of the parametric study were analyzed in terms of change of the aerodynamic performance and characteristics to understand the effect of a tab. Considering the analysis, the design of tab shape was conducted to improve the aerodynamic performance of rotor blades. The simply attached tab to trailing edge of the rotor blades increases the thrust of the rotor blades without significant changing of aerodynamic characteristics of the rotor blades in hovering and forward flight.

Frequency domain system identification of higher order models for the Bell 412 helicopter was performed. First, a frequency response database was derived from flight-test data. For hover, a combination of sweep and 2311-multistep maneuvers had to be used to achieve good results. In addition to the classical six-DoF (degrees of freedom) rigid body states, the identified hover model includes dynamic inflow, rotor coning dynamics, and uses a Padé approximation for the influence of engine dynamics, to improve the response in the vertical axis. The forward flight (60 kn) model includes as extension first-order flapping dynamics, mainly to improve the roll and pitch response. Besides the simple Padé approach used in the hover model, two different engine model structures were investigated but they provided no significant improvement compared to the Padé solution when coupled to the rigid-body model. Finally, a method derived from feedforward principles of model following control is shown, to use the identified hover model to analytically derive an "input filter" correction that improves the fidelity of a linearized FLIGHTLAB simulation model.

Results from a neural network validation study with full-scale XV-15 tilt-rotor experimental hover and forward flight data are presented. Two test data bases, acquired during separate tests conducted at NASA Ames, were used. These two isolated XV-15 rotor test data bases were: the 80by 120-Foot Wind Tunnel hover and forward flight test data base, and secondly, an outdoor hover test data base. For this neural-network-based data validation study, the objective associated with the wind tunnel test data was: obtain neural network representations, conduct data quality checks, and demonstrate sensitivity to test conditions. Neural networks were successfully used to represent and assess the quality of full-scale tilt-rotor hover and forward flight performance test data. The neural networks accurately captured tilt-rotor performance at steady operating conditions and it was shown that the wind tunnel forward flight performance test data were generally of very high quality. The second objective, using outdoor hover test data, was to formulate and implement a neural-network-based wind correction procedure. Compared to existing, momentum-theorymethod based wiad corrections to outdoor hover performance, the present neural-network-procedure-based corrections were better. The present wind corrections procedure, based on a well-trained neural network, captured physical trends present in the outdoor hover test data that had been missed by the existing, momentum-theory-based method. Copyright © 1998 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental Purposes. All other rights are reserved by the copyright owner. A a

State-space representation of the dynamic inflow is an essential element in rotorcraft flight mechanics modeling and simulation. Identification of a reliable low-order model which is able to predict the transient response of the inflow as well as the steady part, becomes even more important during the maneuvering flights. The objective of this paper is to exploit an experimental setup, consists of a helicopter model and a simplified ship geometry, to investigate the possible effect of the wake interactions with environmental elements such as ground effect or airwake of the ship, on the time constants associated with the buildup of the inflow states. A series of wind tunnel tests were performed, simulating various flight conditions, including hover and forward flight, inside and outside of the ground effect, and the rotor over the deck of the SFS1 at two different positions with respect to the ship super-structure, with the wind coming from two different directions. After trimming the rotor at each flight condition, a sequence of pitch excitation commands were applied to the collective, lateral and longitudinal cyclic in order to excite the induced flow of the rotor. The frequency analysis of the measured aerodynamic loads shows the variation of the time lag, while rotor is operating in the same trim condition, but different positions with respect to the ground or the flight deck.

This paper describes the development and flight testing of an autonomous flight control system that allows for different levels of pilot interaction in both hover and forward flight. Three modes of operations are described, fully coupled autonomy, additive control, and piloted decoupled attitude-command. These modes are demonstrated on the Rotorcraft Aircrew Systems Concepts Airborne Laboratory (RASCAL) JUH-60A Black Hawk integrated with Obstacle Field Navigation (OFN) and Safe Landing Area Determination (SLAD) algorithms that both use a line scanning LADAR as their primary sensor. The paper will describe the control system, its performance, and demonstrate how it was used to transition into these modes while flying mission scenarios through mountainous terrain at speeds from hover to 100 kts.