Identification of Coaxial-Rotors Dynamic Wake Inflow for Flight Dynamics and Aeroelastic Applications

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Identification of Coaxial-Rotors Dynamic Wake Inflow for Flight Dynamics and Aeroelastic Applications 42st European Rotorcraft Forum 2016 IDENTIFICATION OF COAXIAL-ROTORS DYNAMIC WAKE INFLOW FOR FLIGHT DYNAMICS AND AEROELASTIC APPLICATIONS Felice Cardito, Riccardo Gori, Giovanni Bernardini Jacopo Serafini, Massimo Gennaretti Department of Engineering, University Roma Tre, Rome, Italy Abstract This paper presents the development of a linear, finite-state, dynamic perturbation model for wake inflow of coaxial rotors in arbitrary steady flight, based on high-accuracy radial and azimuthal representations. It might conveniently applied in combination with blade element formulations for rotor aeroelastic mod- elling, where three-dimensional, unsteady multiharmonic and localized aerodynamic effects may play a crucial role. The proposed model is extracted from responses provided by an arbitrary high-fidelity CFD solver to perturbations of rotor degrees of freedom and controls. The transfer functions of the multihar- monic responses are then approximated through a rational-matrix approach, which returns a constant coefficient differential operator relating the inflow multiharmonic coefficients to the inputs. The accuracy of the model is tested both for hovering and forward flight by comparison with the wake inflow directly evaluated by the high-fidelity CFD tool for arbitrary inputs. 1. INTRODUCTION ing the need for a tail rotor and its associated shafting and gearboxes. Due to the improved performance they may provide, coaxial rotors are expected to become a common solu- While coaxial rotors have been investigated since the tion for next-generation rotorcraft. begin of aeronautics, for decades, the increased com- plexity of rotor hub suggested the manufacturers to use Indeed, as the forward flight speed increases, the differ- simpler main-tail rotor configurations. Nowadays, the ence of dynamic pressure between the advancing and difficulties in overcoming the limits of single rotor heli- retreating sides of a single rotor becomes greater, mak- copters resulted in a growing interest for coaxial rotor ing necessary higher values of the cyclic pitch to main- configurations as demonstrated by the Sikorsky X2 and tain the aircraft trimmed. In order to avoid blade stall on the Kamov Ka-92 projects, among the others. the retreating side of the rotor disk, the amount of col- lective pitch has to be correspondingly reduced, thus This fact motivates the development of dedicated com- negatively affecting the rotor thrust capability. [1] putational tools suited for their analysis. Dynamic wake inflow modeling is one of the main issues in ef- In coaxial, contra-rotating rotors the advancing blades ficient and reliable rotorcraft simulation tools concern- of each rotor may operate at higher pitch angles to ing aeroelasticity, flight mechanics, and handling qual- produce more lift without compromising roll trim. At ity assessment, as well as for flight control laws defini- the same time, the retreating blade may be kept far tion. [3–5] The most widely used dynamic inflow models from stall, with two major consequences: i) rotor RPM for single rotors (see for instance, Refs. [6,7]) cannot be may be reduced, increasing the speed at which tran- extended to coaxial rotors with satisfactory accuracy, sonic effects arise at the tip of advancing blades, and due to the importance of the aerodynamic interaction ii) the overall vibratory loads transmitted to the fuselage effects occurring. are strongly reduced, thus allowing the employment of stiffer blades that improve helicopter manoeuvrability. [2] This paper presents the development of a linear, finite- In addition, the maximum lift-to-drag ratio is improved: state, dynamic perturbation model for wake inflow of the coaxial rotors have proven to be intrinsically more coaxial rotors in arbitrary steady flight, based on high- efficient in hover, forward flight than single rotors of the accuracy radial and azimuthal representations. It is ex- same solidity and blade geometry. Furthermore, coax- tracted through a numerical process starting with the ial rotors provide torque cancellation, thereby eliminat- evaluation of wake inflow corresponding to perturba- 42st European Rotorcraft Forum 2016 tions of rotor degrees of freedom and controls by a a high-fidelity aerodynamic solver, it might be applica- high-fidelity CFD solver. Next the transfer functions of ble to arbitrary multi-body rotor configurations and flight the multiharmonic responses are identified, and then conditions. approximated through a rational-matrix approach. This returns constant coefficient differential operators relat- 2.1. Inflow Representation ing the inflow multiharmonic coefficients to the input perturbations (see later for details). Here the wake in- In order to represent the complex wake inflow field over flow responses are evaluated through simulations pro- a rotor blade with a level of accuracy suitable for (high- vided by a Boundary Element Method (BEM) tool for frequency) aeroelastic applications, it is expressed in a potential-flow solutions, suited for rotors in arbitrary mo- non-rotating frame in terms of spanwise-varying multi- tion. [8] It is capable of taking into account free-wake blade variables. and aerodynamic interference effects in multi-body con- Indeed, introducing over the rotor disc the hub-fixed po- figurations, as well as the effects due to severe blade- lar coordinate system, (r; ), for (both upper and lower) vortex interactions. three-bladed rotors (typically considered in coaxial ro- The wake inflow modelling presented here may be con- tor configurations), the perturbation wake inflow, v, is sidered as a direct extension to coaxial rotors of the represented through the following extension of the form formulation introduced in Ref. [9] for isolated rotors applied in the Pitt-Peters model [6, 12] which, in turn, extended the LTI, finite-state wake inflow (1) v(r; i; t) = v0(r; t) + vc(r; t) cos i + vs(r; t) sin( i) modelling approach presented in Ref. [10] to include the multi-harmonic effects related to the intrinsic time- where i denotes the azimuth position of the i-th blade, periodic nature of advancing, rotor aerodynamics, as whereas v0; vc and vs are, respectively, the instan- well as the complex radial distributions induced by the taneous multiblade collective and cyclic inflow coeffi- wake-blade interactions. cients at a given radial position, r (see also Ref. [9] for higher number of rotor blades). Considering a coaxial rotor in hovering and advancing flight conditions, the numerical investigation presents For vi denoting the wake inflow perturbation evaluated the identified transfer functions and the assessment of by the high-fidelity aerodynamic tool on the i-th rotor the accuracy of the proposed dynamic inflow model by blade, applying the separation of variables technique, comparison with wake inflow directly calculated by the and choosing suitable sets of linearly independent ra- α time-marching BEM solver. Particular attention is fo- dial basis functions, φj (r), the multiblade wake inflow cused on the examination of the capability of captur- coefficients are expressed in the following form ing radial distributions and multi-harmonic components 0 N N arising in forward flight. 1 Xb Xr v (r; t) = v (r; t) = λ0(t) φ0(r) 0 N i j j b i=1 j=1 c 2. WAKE INFLOW MODELLING Nb Nr 2 X X c c The multi-harmonic wake inflow perturbation model (2) vc(r; t) = vi(r; t) cos i = λj(t) φj(r) Nb presented here is suited for coaxial rotors aeroelastic i=1 j=1 s applications, and is an extension of those proposed by Nb Nr [9–11] 2 X X s s the authors in Refs. vs(r; t) = vi(r; t) sin i = λj (t) φj (r) Nb The main steps of the process of wake inflow model ex- i=1 j=1 α traction from arbitrary high-fidelity aerodynamic solver where Nb denotes the number of rotor blades, Nr is the are: definition of a suited approximation form of the in- number of functions used to define the α-coefficient ra- α flow distributions; LTI representation of the model pa- dial distribution, with λj representing the corresponding α rameters identified from responses of the aerodynamic component onto the basis function φj . It is worth noting 0 c s 0 c s solver; finite-state approximation of the parameters dy- that, for Nr = Nr = Nr = 1, φ1 = 1, and φ1 = φ1 = r, namics, and hence of the inflow model. the proposed inflow distribution coincides with that of [6, 12] The model inputs are the rotor degrees of freedom and the Pitt-Peters model. controls (in this case including upper and lower rotor blade collective and cyclic pitches). Its accuracy de- 2.2. Model Parameters Extraction pends on that of the CFD solver used for the evalua- The extraction of the dynamic wake inflow model from tion of the aerodynamic responses. Since derived from high-fidelity aerodynamics starts with the identification 42st European Rotorcraft Forum 2016 of the transfer functions relating the perturbations of the 2.3. Finite-State Approximation system state variables (namely, rotor rigid and elastic The transfer functions between inputs and the (upper degrees of freedom) with the components of the inflow and lower rotor) inflow parameters introduced in Eq. (3) multiblade coefficients. represent LTI dynamics, thus allowing the description To this purpose, following an approach similar to that of a LTP operator through combination of outputs of LTI used in Refs. [9–11], first, a high-fidelity aerodynamic sub-operators. tool is applied to evaluate the blade wake-inflow pertur- Upper and lower wake inflow dynamics are described in bations, v (r; t), corresponding to harmonic small per- i finite-state form by representing the LTI dynamics of the turbations
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