Analyses of Aircraft Responses to Atmospheric Turbulence

Abstract

The response of aircraft to stochastic atmospheric turbulence plays an important role in aircraft-design (load calculations), Flight Control System (FCS) design and flight-simulation (handling qualities research and pilot training). In order to simulate these aircraft responses, an accurate mathematical model is required. Two classical models will be discussed in this thesis, that is the Delft University of Technology (DUT) model and the Four Point Aircraft (FPA) model. Although they are well estabilished, their fidelity remains obscure. The cause lies in one of the requirements for system identification; it has always been necessary to relate inputs to outputs to determine, or identify, system dynamic characteristics. From experiments, using both the measured input and the measured output, a mathematical model of any system can be obtained. When considering an input-output system such as an aircraft subjected to stochastic atmospheric turbulence, a major problem emerges. During flighttests, no practical difficulty arises measuring the aircraft motion (the output), such as the angle-of-attack, the pitch-angle, the roll-angle, etc.. However, a huge problem arises when the input to the aircraft-system is considered; this input is stochastic atmospheric turbulence in this thesis. Currently, during flighttests it still remains extremely difficult to identify the entire flowfield around an aircraft geometry subjected to a turbulent field of flow; an infinite amount of sensors would be required to identify the atmospheric turbulence velocity component's distribution (the input) over the vehicle geometry. In an attempt to shed some more light on solving the problem of the response of aircraft to atmospheric turbulence, the subject of this thesis, it depends on the formulation of two distinct models: one of the atmospheric turbulence itself (the atmospheric turbulence model), and the other of the aircraft response to it (the mathematical aircraft model). As concerns atmospheric turbulence, stochastic, stationary, homogeneous, isotropic atmospheric turbulence is considered in this thesis as input to the aircraft model. Models of atmospheric turbulence are well established. As for mathematical aircraft models, many of them have been proposed before. However, verifying these models has always been extremely difficult due to the identification problem indicated above. As part of the mathematical aircraft model, (parametric) aerodynamic models often make use of (quasi-) steady aerodynamic results, that is all steady aerodynamic parameters are estimated using either results obtained from windtunnel experiments, handbook methods, Computational Aerodynamics (CA) which comprises Linearized Potential Flow (LPF) methods, or Computational Fluid Dynamics (CFD) which comprises Full-Potential, Euler and Navier-Stokes methods. In this thesis the simplest form of fluid-flow modeling is used to calculate the time-dependent aerodynamic forces and moments acting on a vehicle: that is unsteady Linearized Potential Flow (LPF). The fluid-flow model will result in a so called "unsteady panel-method" which will be used as a virtual windtunnel (or virtual flighttest facility) for the example discretized aircraft geometry, also referred to as the "aircraft grid". The application of the method ultimately results in the vehicle's steady and unsteady stability derivatives using harmonic analysis. Similarly, both the steady and unsteady gust derivatives for isolated atmospheric turbulence fields will be calculated. The gust fields will be limited to one-dimensional (1D) longitudinal, lateral and vertical gust fields, as well as two-dimensional (2D) longitudinal and vertical gust fields. The harmonic analysis results in frequency-dependent stability- and gust derivatives which will later be used to obtain an aerodynamic model in terms of constant stability- and gust derivatives. This newly introduced model, the Parametric Computational Aerodynamics (PCA) model, will be compared to the two classical models mentioned earlier, that is the Delft University of Technology (DUT) model and the Four-Point-Aircraft (FPA) model. These three parametric aircraft models are used to calculate both the time- and frequency-domain aerodynamic model and aircraft motion responses to the atmospheric turbulence fields indicated earlier. Also, using the unsteady panel-method the aircraft grid will be flown through spatial-domain 2D stochastic gust fields, resulting in Linearized Potential Flow solutions. Results will be compared to the ones obtained for the parametric models, i.e. the PCA-, DUT- and FPA-model. From the results presented, it is concluded that the introduced PCA-model is the most accurate for all considered gust fields. Compared to the Linearized Potential Flow solution (which is assumed to be the benchmark, or the model that approximates reality closest) the new parametric model shows increased accuracy over the classical parametric models (the DUT- and FPA-model), especially for the aircraft responses to 2D gust fields. Furthermore, it shows more accuracy in the aircraft responses to 1D longitudinal gust fields. Although results will be presented for a Cessna Ce550 Citation II aircraft only, the theory and methods are applicable to a wide variety of fixed-wing aircraft, that is from the smallest UAV to the largest aircraft (such as the Boeing B747 and the Airbus A380).