REDUCED-ORDER WAKE INFLOW FOR MODELS FOR ROTORS IN GROUND-EFFECT

Abstract

This thesis deals with the identification of reduced-order wake inflow models for rotors operating in ground effect suitable for flight dynamics applica tions, flight simulator and control law design. The wake inflow is one of the most fundamental factors affecting the performance of rotorcraft systems, it is the induced influence of the main rotor wake on rotor air-loads and related performance. It is well known that the induced-flow field associated with a lifting rotor responds in a dynamic fashion to changes in either blade pitch (i.e., pilot inputs) or rotor flapping angles (i.e., rotor or body dynamics), thus severely influences the helicopter dynamic attitude and response. Figure 1: Helicopter comprehensive simulation tool main ingredients, sketch of the solution loop. In figure 1 a sketch of a widely used helicopter aerodynamic-structural dynamic loop is presented, the intrinsic coupling and complexity of the problem is clearly shown, as well as the importance of a correct simulation of the wake induced inflow dynamic for a realistic prediction of the helicopter response. The ability of a flight simulator to accurately predict the behavior of an helicopter using information only from its physical characteristics would be highly desirable as it would allow manufacturers to get an early feedback from pilots on any design decision (concerning, for instance, handling qualities, rotorcraft-pilot coupling proneness, etc.). However, despite the complexity and the accuracy reached by the modules in modern simulators, they are not yet able to provide a fully coherent representation of reality. Moreover, with the aim of correcting some sub-optimal behavior in specific flight conditions and to respect the tolerances needed for the validation of a flight model, a certain amount of artificial tuning is often applied on top of the physical model. These modifications are often not justified from an engineering or physical standpoint and, while improving simulations for particular operating conditions, they may have an adverse effect on other parts of the flight envelope. The need to tune the model can often be related to the deficiencies of the mathematical model describing the helicopter dynamics. The physics involved is indeed the result of the coupling of complex phenomena like the nonlinear structural dynamics of the slender main rotor blades, the complex rotor aerodynamic environment resulting from the combination of blade motion and inflow induced by wake vorticity remaining in close proximity of the rotor disk, the interaction of the air flow with the fuselage, the main and tail rotors mutual interactions, the interaction with ground and surrounding obstacles, the dynamics of engine and actuators, the effects of control systems. Obviously, real-time simulation of these phenomena requires a suitable trade-off between modeling accuracy and computational efficiency. In this context rotor wake modeling is clearly one of the most challenging tasks in rotor aerodynamic numerical applications, in particular for the simulation of ground effect. Due to the complexity of the problem, in order to well capture the wake deformation dynamics, a free-wake algorithm could be used to derive a coherent reduced-order dynamic model. Hence, focusing the attention on rotor configurations in ground effect (IGE), the objective of this thesis were twofold: development of an efficient high-fidelity aerodynamic solver, followed by the definition of a state-space dynamic inflow modelling technique that, based on the high-fidelity aerodynamic simulation tool, is capable of taking into account arbitrary rotor-ground relative kinematics. The ground effect problem is one of the most important wake-obstacle-interference problems in rotor aerodynamics, hence for the helicopter community. Under an engineering point of view the main effect of the phenomena related to this interaction are those regarding the increased thrust for a given (induced) power, conversely the reduced (induced) power for a specific thrust production. Recalling that the relationship between thrust and torque involves the axial induced velocity resulting from the momentum conservation law on the rotor disc, and that the viscous drag over the blade can not be influenced by ground presence, the effect of ground has to be due to a reduction in the averaged induced velocity, hence to a reduction in the inflow local angle. Nevertheless, a deep comprehension of the aerodynamics of the problem is not yet full-filled and numerical simulations are requested to well investigated the behaviour of the helicopter when operating in ground effect condition. In this work, firstly, the extension to the ground simulation of a Boundary Element Method potential-based aerodynamic solver is performed. From a numerical point of view, the principal issue to be solved is the imposition of the impermeability condition at the ground surface, two different techniques are implemented and compared. Of the two, the so called BEM-MIM (Mirror Image Method) has proven to be more suited for ground effect simulation, in that the boundary condition is automatically satisfied. Moreover, the computational efficiency of the algorithm is improved through the introduction of a novel wake structure allowing for a considerable reduction in the number of calculations required to evaluate the flow-field and, hence of the pressure-field, over the rotor blades. The proposed solutions for the aerodynamic simulations of the ground effect condition are then compared and validated with experimental data proving their accuracy, specifically the capability to exploit this solver to simulate the wake inflow due to arbitrary input perturbation is proven. A deep comparison between experimental data and numerical predictions of the performance and of the flow-field in the whole wake region of rotors operating in ground effect has been carried out. Furthermore, ground surface not parallel to rotor disc has been considered in the analysis characterizing also this extreme but common flight condition. According to the experimental results, the proposed aerodynamic solver is capable to well simulate the mean features of the flow-field. The inner part (close to the rotation axis) has a very low-velocity air extending from the ground upward to a point above the rotor depending on the distance between rotor and ground and the their relative inclination. Generally, the recirculation zone in the inner part, described above, causes the occurrence of an annular jet of high-velocity curved flow going outward from the rotation axis. These modifications in the wake shape change the relative vortex-blade position, hence the wake induced velocity (wake inflow), leading in particular to a reduction of the inflow as the rotor comes close to ground. Enlarging the analysis of this particular but common flight condition, characterized by the complex interaction between, rotor, rotor-wake and ground, the real nature of the problem clearly appears: a highly-unsteady, three-dimensional aerodynamic problem which affects not only the static or quasi-static performance of the machine but also its handling qualities. It is worth noting that the analysis of the radial distribution of the axial velocity induced on the rotor disk has shown differences between the experimental data and the simulations. In particular, the numerical evaluation of the velocity has shown a variation of the distribution on the disk consistent with what is expected from the analysis of the velocity maps and the streamlines. Specifically, the inflow has to decrease in the upstream area and to increase in the downstream one while increasing the ground angle. Experimental data, on the other hand, has not shown this trend clearly. This fact, which deserves a detailed study, could be due to phenomena related to the chaotic nature of the turbulent structures present in the wake, which are not captured by potential non-viscous solver, as well as the uncertainty inherent in the measure. Then, two different approaches to dynamic inflow modeling of rotor in ground effect conditions have been applied. In the first, inflow coefficients are directly related to the kinematic degrees of freedom and subsequently to rotor loads involving a complete aerodynamic simulation, whereas the second one considers the relation between inflow coefficients and rotor loads (as in the well known Pitt-Peters’ model) in terms of blade bound vorticity perturbations. The first approach is based over complete BEM-MIM solver simulation, both wake and body are discretized. Even if with a better approximation in loads evaluation, it is computationally inefficient for ground-effect simulation, indeed, due to the wake evolution complexity, the ground-effect simulation has been demonstrated to require a considerable computational effort.The complexity of the problem and the numerical instabilities those arise when part of the wake is re-ingested by rotor disk (due to the ground presence) have required the definition of a new identification technique. Very long-time perturbations and various test are necessary to make the identified transfer functions smoother and more coherent, thus a very efficient vortex-lattice-like solver is derived from the BEM one. This second methodology, applied for the identification of a state-space dynamic wake inflow model, is based on inflow responses to arbitrary perturbations of blade bound vortex circulation distribution. Which, in turn, can be easily connected through the Glauert theory to the blade and hence rotor air-loads. This approach requires only the simulation of the wake which, moreover, if treated as a vortex-lattice surface and exploiting the Biot-Savart law for the inflow evaluation, results in a very efficient computational tool for dynamic wake inflow model identification. Furthermore, the input/output coherence is higher than the kinematic-based model, thus allowing an easier identification of the wake inflow transfer function. The numerical investigation has concerned the application of the proposed methodologies for the wake inflow state-state model synthesis of rotors both out-of-ground-effect and in-ground-effect conditions, above parallel and inclined grounds. Considering the differences between the two dynamic inflow models presented in this work, a coherence could be seen regarding some main effects of the ground wake dynamic inflow, which are the following: - the presence of the ground noticeably affects the wake inflow dynamic response; - the ground presence affects remarkably the transfer functions dynamic inflow models identified from the high-fidelity BEM aerodynamic solver, depending on the distance from the rotor plane in a non-monotonic way; - the ground presence increases the cross-coupling effects described by the off-diagonal terms of the transfer functions matrices of the dynamic in flow models, in particular the inclined ground condition show a coupling analogous to the one characterizing the forward flight condition; - the proposed finite-state models predict with satisfactory accuracy dy namic wake inflow perturbations both in HOGE and HIGE conditions, as demonstrated by correlation with the simulations directly provided by the BEM solver for arbitrary perturbations system input; - these models are not capable of simulating the higher-frequency inflow content, but capture the main features of the ground influence on the dynamic inflow and are particularly suited for flight dynamics applications; - the validation tests show that the state-space model is capable of accurately reproduce the linear time invariant part of the low-frequency inflow content which is that significantly affecting flight dynamics. However, the wake inflow is also characterized by time-periodic phenomena, which cannot be reproduced by the proposed model, but would require the introduction of a time-periodic modeling approach; - the identification process of the transfer functions involving axisymmetric components has been significantly more difficult, requiring further regular ization of numerical free-wake algorithm to take into account the presence of the ground