The performance and stability characteristics of a regional jet design are presented. The baseline configuration is studied with different aerodynamic models. DATCOM results are very close to computational fluid dynamics and wind tunnel experimental data, underlining the effectiveness of the empirical method DATCOM for a traditional configuration. Some differences were found between the vortex lattice method Tornado because of linear assumptions. The CFD method Edge is the only one to capture the nonlinearity observed during the wind tunnel tests. The stall angles of attack predicted by Edge and measured in the wind tunnel are very similar but the CFD computation obtained a smaller effect from the nonlinear aerodynamics. The Kriging and data fusion methods are used to fill the aerodynamic tables with a reduced computational cost. The generated aerodynamic models are then compared and performance and stability characteristics computed. Among the computed models, Tornado is the only one to predict a positive elevator deflection to trim the aircraft during cruise and an unstable behaviour for the spiral mode. The impact of geometry changes on the aircraft dynamic characteristics is then investigated. The wing sweep angle is found to have a larger influence than the wing aspect ratio on the performance and stability characteristics. Increasing the wing sweep leads to a higher angle of attack and a less negative elevator deflection to trim the aircraft. Furthermore a more damped short period mode is obtained for higher sweep angle of the wing. The short period mode is influenced by the horizontal tail size and position. A higher tail volume coefficient causes a more damped short period.
Chapter 5
Alternative aerodynamic models
for flight dynamics
The traditional aircraft aerodynamic model formulation is based on aerodynamic table or aerodynamic derivatives. The table presents the external aerodynamic forces and moments for every entry of a discrete flight envelope domain. The derivatives instead linearize the external actions close to the steady flight cruise conditions.
A schematic example of the aerodynamic table is given in Table C.1. Static and dynamic states are combined with control variables to generate a model that cover the full aircraft flight envelope. For every point the aerodynamic model is then exploited to compute the external forces and moments. This model has a few limitations since the flight envelope is presented in a non–continuous form, and so any middle point has to be approximated via interpolation. Furthermore, for physics based models, all the entries with non–zero dynamic state variables have to be computed with a time accurate solution, approximating the time history as a pure harmonic. This is a strong hypothesis since the state variables during the flight can change following any generic time history. The intrinsic nonlinear nature of the fluid dynamics governing equations lead to potentially big errors caused by this approximation. For example, different approximated position of eddies, shocks or boundary layer separation may lead to very different pressure distribution over the body surface.
Bryan’s method approximation traditionally used to write the motion equation and to compute the static and dynamic aircraft properties, is based on the linearization of the aerodynamic response respect to the states and control variables, starting from a planar steady flight state in cruise conditions. Such approximation is valid only under small perturbations hypothesis, and consider a linear dependence between aerodynamic actions and parameters [38].
Both the formulations are based on very restrictive hypothesis, and so their validity in enclose in a small portion of the flight envelope. In case of time history involving fast and complex manoeuvres, the linear assumptions lead to important errors for the
evaluation of the aerodynamic forces and moments of the aircraft. The existing flight simulators are usually based on a tabular aerodynamic model. The use of inaccurate aerodynamic forces and moments for deriving the motion may cause misleading results that, time integrated, generate very different states. Let suppose, for example, the landing mission phase starting from the exact same condition: the real aircraft may land if a certain (non unique) elevator deflection and throttle time history is executed, but if the same commands time history is imposed in a flight simulator with a too strictly aerodynamic model, the simulation might lead to very different results, in the worst case leading to aircraft stall or crash. In this way an inaccurate flight simulator used for training might require the wrong command sequences.
The traditional methods can be accurate and well representative models, only for standard flight conditions, with not too fast and complex manoeuvres. A more pre- cise and not restricted method is presented in this Chapter. FlexFlight is a Python programme that implements time accurate models. The programme architecture is disclosed in the next Section, however the concept is based on a time accurate solver of a flexible flying aircraft. The structure deformation, the equation of motion and the CFD solver interact between each other at every time step to obtain a time accurate result. This model is no more based on the assumptions for a priori aerodynamic table generation and the simulation results are only dependent on the type of adopted models (e.g. VLM, Euler, RANS, etc. for the aerodynamic model and beam, half–shell, etc. for the structure).
5.1
Architecture
FlexFlight is a Python script that aims to intermediate between different blocks. A module represents one of the disciplines for the study of a flexible moving object in a fluid medium: CFD, motion equation integrator and structure. Any programme solving one of the involved disciplines may be inserted in the corresponding block, allowing the user to make it communicate with the others blocks. The modules interfaces are created in a way that each discipline can either be used as standalone for single discipline analysis or be imported as a module by a higher level class or script that performs a multi-disciplinary analyses.
Figure 5.1 shows the Flex Flight modular architecture. In the presented case the aerodynamic model block is filled with the C written parallel meshless (PML) CFD solver [39] developed at the University of Liverpool and both the flight dynamics and structures blocks with a Fortran written code [40].
This architecture allows the user to add any new required block, e.g. an auto–pilot as controller, making it able to communicate with any other block. Furthermore the open source python programming language does not impose any bounds about the
Figure 5.1: FlexFlight architecture scheme
programming language of the blocks functions, allowing to exploit any new or already developed scripts.
In order to perform coupled fluid/structure/flight analyses, a mesh deformation tool is needed to transfer information between the structural and fluid solver. The transfer of information between non-matching fluid and structural grids is here implemented with a linear fluid/structure interface. The scheme is exploited to transfer aerodynamic loads from the aerodynamic to the structural model, and map structural deformations from the structural to the aerodynamic model at no additional cost. For time accurate coupled solutions, a fully implicit partitioned approach is used. The solution sequencing between the fluid, flight and structural models is achieved within the pseudo-time stepping iterations. For every real time steps, inner sub–iterations are run calling all the modules, until convergence is reached.
For further information about the used blocks formulations the reader is referred to [39, 40].