The work in this thesis was partly developed within the SimSAC (Simulating Aircraft Stability and Control Characteristics for Use in Conceptual Design) project 1 funded by the European Commission 6th Framework Programme. The project consisted of a partnership of European academics and industrial contributors. The main driver of the project was the inadequacy of standard semi-empirical approaches currently used in conceptual design when confronted with more advanced aircraft configurations [80]. This may cause errors in the design process, which may prove expensive to rectify via additional design work, wind tunnel and flight testing, in addition to a delay in certification and performance degradation. To overcome these potential issues, it is worthwhile to introduce high-fidelity (physics-based) approaches early in the design process.
In this thesis, the exploitation of CFD is investigated for the generation of the aero- dynamic database. A framework for the automated generation of tabular aerodynamic models for studies of flight dynamics is discussed, allowing stability and control con- siderations to be developed early in the design process. For the representation of the aerodynamic loads, a model based on stability or aerodynamic derivatives is assumed because traditionally used by flight dynamicists. In the model formulation, dynamic derivatives are used to update the static predictions to account for the aircraft motion. Emphasis is on the evaluation of dynamic derivatives with various CFD methods. As the limitations of the aerodynamic model are exposed for several test cases, there is a need for models of more realism and fidelity to be used in flight dynamics. Advances in this direction are discussed.
Chapter 2 introduces the framework for the generation of aerodynamic tables using CFD as the source of the data. The framework has been developed at Liverpool by the author and a colleague. A method to efficiently reduce the number of high-fidelity anal- yses is accomplished by use of a kriging-based surrogate model. Low-fidelity estimates are augmented with higher fidelity data, and data fusion combines the two datasets
1
More details athttp://www.simsacdesign.euandhttp://www.ceasiom.com/[retrieved March 19, 2012]
into one single database. Once constructed, the look-up tables can be used in real-time to fly the aircraft through the database. Two methods for the evaluation of dynamic derivatives are also discussed.
Chapter 3 discusses the evaluation of dynamic derivatives computed using unsteady time-domain CFD simulations. Two configurations are considered: a generic fighter model and a transonic cruiser concept design. Numerical results are compared to experimental measurements, and a good agreement is noted in all cases. A systematic study to evaluate the dependencies of dynamic derivatives on aircraft motion and flow parameters, beyond the range of motions performed in dynamic testing facilities, is presented. It is recognized that in the presence of aerodynamic non-linearities, mainly due to three dimensional separated flow and concentrated vortices, dynamic derivatives exhibit a dependence on motion and flow parameters. These dependencies are not reconcilable with the model formulation, which is based on a Taylor series expansion. An approach to evaluate the sensitivity of the non-linear unsteady aerodynamic loads to variations in dynamic derivatives is introduced.
Chapter 4 introduces the use of reduced models, based on the manipulation of the full-order model, for the fast computation of dynamic derivatives. The underlying idea is to exploit the periodicity of the resulting aerodynamic system for oscillatory motions to decrease the cost of calculations. A linearized solution in the frequency domain and a harmonic balance technique are illustrated for two- and three-dimensional configurations. To stress the potential of the frequency-domain methods in conditions of practical interest for aircraft applications, flow conditions were in the transonic regime. For the formation of moving shock waves, the energy of aerodynamic modes redistribute at higher frequencies than the predescribed frequency of motion. While a time-domain calculation supports a continuum of frequencies up to the frequency limits given by the temporal and spatial resolution, the reduced models considered resolve only a small subset of frequencies typically restricted to include one Fourier mode at the frequency at which dynamic derivatives are desired. While providing good estimates of dynamic derivatives, the cost of the reduced models is a fraction of the cost for solving the original unsteady problem.
Chapter 5 addresses the demand for alternative model formulations of more realism to be used in the representation of non-linear unsteady aerodynamic loads. The conven- tional model based on aerodynamic derivatives is recognized to be adequate in benign flow conditions. There is, however, the consideration that any model in principle is applicable to linear cases, and the generality realized in a CFD solver is therefore not needed. The point of the discussion here is that conditions of practical interest feature aerodynamic non-linearities. Various reduced models, based on system-identification methods, are evaluated in presence of aerodynamic non-linearities. While retaining complex flow features due to shock-induced phenomena, a two-dimensional test case is considered. For the flow conditions considered, the predictions obtained using the
conventional model are misleading and not representative of the unsteady time-domain solution. While providing good approximations for the non-linear unsteady aerody- namic loads, reduced models investigated were generated with no more computational resources than that required for the conventional model.
Chapter 6 concludes the thesis and offers an outlook and suggestions for future work.
The framework for creating CFD-derived stability and control databases described in Chapter 2 was exercised for several aircraft configurations. The application to six test cases is presented in Appendix A. The point of the work is to show the range of applications that this framework has opened up, illustrating the aerodynamic model generation for each case in the form of a review. Through the range of examples which have actually been computed, the review shows the progress achieved because of the adoption of the framework. The work presented in the appendix is the result of a collaborative effort, and the author contributed directly to the creation of the aerodynamic database in each case. In addition, the author has led the review article in [81].
Appendix B illustrates the use of the indicial theory applied to unsteady aerody- namic problems. The indicial theory can also be used to predict the unsteady aerody- namic loads in response to a gust perturbation, which is of interest for aircraft loads calculation and certification. The CFD-based simulation of the interaction between a gust and a rigid or flexible airframe poses few practical questions. The author has im- plemented a new functionality in the CFD solver of the University of Liverpool based on the field velocity approach. Validation studies demonstrate the readiness of the approach for cases featuring linear and weakly non-linear aerodynamics.
Finally, Appendix C formulates a multi-linear interpolation, which is implemented in the computational framework described in Chapter 2 as an alternative approach to kriging interpolation.
Chapter 2
Formulation
2.1
Introduction
Modeling the aircraft aerodynamics raises the fundamental question of what the math- ematical structure of the model should be. The functional dependencies of the force and moment coefficients are in general complex, as they depend in a non-linear fashion on present and past values of several quantities, such as airspeed, angles of incidence, etc. Reasonable simplifications are that fluid properties change slowly and the airplane mass and inertia are significantly larger than the surrounding fluid mass and inertia. The flow is often considered quasi-steady, which presumes that the flow reaches a steady state instantaneously and the dependence on the history of the motion variables can be neglected. One exception to this assumption is the retention of the reduced frequency effects. With these underlying hypotheses [47], the characterization of the functional dependencies is broken down as
Ci =f1(α, β, M, δ) +f2(Re) +f3 Ωc 2U∞ +f4 ω c 2U∞ (2.1) for i=L, D, m, Y, l and n
which is the common practice from wind tunnel testing. The first term on the right hand side is obtained in static wind-tunnel tests, the second term represents Reynolds number corrections and the last two terms are measured performing, respectively, ro- tary balance and forced oscillation tests. The above decomposition is valid when the effects are separable and the superposition principle can be used, that is, under the hypothesis of linear and uncoupled functional dependencies. The effects of rotary and forced oscillation are typically modeled as a function of the body axis angular rates, an- gles of incidence and their first time derivatives [82]. These derivatives were introduced to obtain a closer correlation between predicted and observed aircraft longitudinal mo- tion [83], and for a conventional aircraft they represent the finite time that aerodynamic loads at the tail lag the changes in downwash convected downstream from the wing.
The aircraft symmetry with respect to the vertical plane motivates the neglection of the dependence of symmetric (longitudinal) forces and moments on asymmetric (lat- eral) variables, and vice versa. While the dependence on ˙β is typically neglected for a quasi-state flow, the inclusion of the ˙αterm leads to an identifiability problem when es- timating the ˙αandq derivatives [84]. To avoid this problem, the two terms are lumped together and an equivalent derivative is defined as ¯Ciq =Ciα˙ +Ciq fori=L, D and m.