A Study of Non-linear Dynamic Aerodynamic Behaviour of a Specialised Delta Wing

The objective of this paper was to model the stability and control derivatives using Computational Fluid Dynamics (CFD). This would provide a more reliable tool in the development of aircraft. This process could reduce the reliance on wind tunnel results with a consequent reduction in development costs. The test model used for this paper was a specialised delta wing configuration. The study was undertaken by comparing simulation parameters and determining their effects on the flow characteristics. The simulation was undertaken using internal meshing software, the flow simulation software TAU and the graphical interface Tecplot. Results showed that a single CFD model could not be used for the prediction of aerodynamic behaviour under the full range of angle of attack (0° to 25°). However the surface mesh refinement and optimisation of simulation parameters allowed for a better prediction at lower angle of attack (0° to 15°). The dynamic simulation showed that flow characteristics were better captured for higher pitching frequencies. Overall the study will assist the progress of future studies.


Introduction
Computational Fluid Dynamics (CFD) modelling has been used to a significant extent in the development of aircraft.As capabilities and computing power, of CFD modelling, have increased over time, the importance of and reliance upon, CFD simulations has similarly increased.Simulation results, obtain over time have progressively become more accurate and reliable.However the data provided by CFD simulations has had limitations.As such, the results of CFD simulations have never been relied on, as the sole source of data.The results were always validated with additional data obtained, either via wind tunnel or flight tests, both of which are costly and time consuming.Also, these options are not always practical or suitable alternatives.Additionally, under certain flight characteristics the wind tunnel results do not entirely represent the true flow over an aircraft.
It is preferable if all flight characteristics are known before the full scale aircraft enters the flight testing.Once full scale flight testing commences, it is costly and time consuming to modify the design.Furthermore, unexpected aircraft handling during testing can be very dangerous.Therefore, it would be greatly beneficial to improve the reliability and accuracy of current CFD modelling, which would reduce the necessity for additional alternative testing.This would help to reduce costs, in addition to opening up possibilities for more detailed testing under the entire flight envelope of the aircraft.
With recent advances in the aerospace industry, the demand and commonality of Unmanned Aerial Vehicles (UAV) have also increased.The leading factor in this area is Unmanned Combat Aerial Vehicles (UCAV).These planforms often lead to configuration with nonlinear aerodynamic behaviour; this can be dominated by vortical flow across the upper surfaces.The cause of these more complicated flows is often linked to UCAV's highly swept wing planform design.Many of the characteristics of flow phenomena associated with highly swept delta wings have been well documented and well-studied (Gursul, Gordinier, & Visbal, 2005).These planforms often are associated with the sharp leading edge geometry.However, the flow is not entirely understood in less swept wings with rounded leading edges.It is these characteristics that need to be better understood in order to effectively enhance future development of aircraft.The mode reinforced of the extr more accu more than measurem behaviour., 2010).Additionally, it allows for the utilisation of the freedom and capabilities of the unstructured volume mesh.In this study, an unstructured grid was used that is developed with an in-house meshing program called "Mesher".

The DL
The TAU-Code has the capabilities to utilise both the Cell-Vertex and the Cell-Centered schemes, both with their own advantages and disadvantages (Liu & Chen, 2011).Here the Cell-Centered scheme was used.In the Cell-Centered approach, the Navier-Stokes equations are solved on a dual background grid, which is determined directly from the primary grid (Hübner, 2007).This approach was used as it consists of a larger number of solution variables than other approaches, which would in turn lead to greater accuracy.
The TAU-Code is capable of performing many different tasks splitting into five main modules.These modules are (Shütte, 2010): a) Preprocessor -Takes information from the Primary grid to develop a dual-grid or multi-grids.b) Solver -Performs the flow calculations over the dual-grid.c) Adaption -Refines and de-refines the grid to allow for the capture of all flow phenomena.This includes a large range of categories, including the representation of vortex structures and shear layers around viscous boundaries.d) Deformation -Propagates the deformation of surface-coordinates to the surround grid.e) Motion -Defines the motion of the model and relates this motion to any control devices.Many of these modules are inbuilt within the code and for this study; they would not be altered from their default values.As a result, the Preprocessor and Solver modules would be examined in more details while the other modules would be taken as non-variable.
The Preprocessor module is based on the meshed grid forming the primary grid.Here, a system of five dual grids was used.This introduction of multiple grids greatly improves the computational time and power required to run any simulation.
The Solver module calculates the gradients in time, which are then discretised through the use of a multi-step Runge-Kutta scheme.These calculations are then calculated using multigrid techniques and local time stepping which accelerates the ability to find converged results for steady state solutions (Hübner, 2007).Three different turbulence models were examined: a) one one-equation model, b) two two-equation models.These were the Spalart-Allmaras Edwards one-equation model, and the Wilcox k-ω TNT and Wilcox k-ω LEA two-equation models

Findings of Initial CFD Modelling
In order to determine the possible accuracy of CFD simulations and how different parameters can be improved, the quality of the initial simulations results are needed.To be able to check these parameters accurately it is important to ensure a good quality grid density (Liu & Chen, 2011).The mesh can greatly affect the results of the simulation.As a consequence it is vital to ensure that any simulations being used have reached a mesh converged state (Ismadi, 2011).For this work a large array of simulations was developed with meshed densities ranging from 1.5 to 22.5 million nodes.These simulation results were compared to wind tunnel findings to determine the accuracy of each model.A detailed look at this mesh convergence study was undertaken in a previous study by Pevitt & Alam (2011).
The wind tunnel investigations were undertaken across two wind tunnel facilities with a total of three full scale investigations.The first two of these tests were conducted in DNW-NWB wind tunnel and the final test in NASA Langley 14-by-22-Foot Subsonic Tunnel in Hampton, Virginia (Vicroy, 2010).For this work the results obtained from the DNW-NWB wind tunnel will be used.Dynamic measurements of integral forces and moments, the pressure distribution over the wing surface, transition measurements and field measurements (both static and dynamic) using Particle Image Velocimetry (PIV) were taken (Shütte, 2010) .
The DNW-NWB wind tunnel is a closed loop, with an atmospheric test section, capable of operating under both open slotted or closed configuration (Cummings et al., 2010).The wind tunnel is 3.25 m by 2.8 m and has a maximum free stream velocity of 80 m/s for the closed test section and 70 m/s for the open test section (Vicroy, 2010).The wind tunnel data collected at a speed of 50 m/s will be used for this study, corresponding to a Reynolds number of 1.57 million and a Mach number of 0.147 (Cummings, 2010).The model was tested statically at an angle of attack range of -15º to 30º and dynamically under pitch and yaw with oscillation of ±5º amplitude (Vicroy, 2010).For the work being done the pitch oscillation results will be used for angles of attack between 0º and 25º.
The previous mesh convergence study found that there were considerable differences in changing meshes.to ensure an accurate representation of the results.In previous studies it has been suggested that the lack of a sting on the model can affect the pitching moment results (Frink, 2010).
Detailed analysis was completed previously both on full and half model simulations and with and without sting attachments.These simulations were run over a large range of AoA to gain a detailed overview of their effects.
Based on these results it was seen that all of the features of the flow were the same for both the full and half model, allowing for further testing to be completed on half models (Pevitt & Alam, 2011).When testing the effects of sting attachment it was seen that in general the sting caused the pitching moment results to translate upwards.As the results for pitching moment coefficients were generally under predicted, in previous finding, the upwards shift was a beneficial translation (Pevitt & Alam, 2011).

Influence of Discretisation Parameters
Two of the discretisation parameters reviewed here are Preconditioning and the Dissipation, as these can greatly affect the simulation results.Preconditioning affects the assumptions made in the calculation process (Blazek, 2001).The simulations work through the use of the governing equations, assuming that the flow is incompressible.As the flow over the configuration is only 0.17 Mach the assumptions of incompressible flow is not completely valid (Eidgenössische Technishe Hochschule Zürich [ETH], 2010).The goal of preconditioning is to implement a correction factor to account for these assumptions and to improve the convergence of the numerical schemes at low Mach numbers.Based on this it is expected that its implementation should improve the results discussed previously (Lomax, Pulliam, & Zingg, 1999).
The addition of preconditioning to the simulations was reviewed in detail (see Pevitt & Alam, 2011).The addition of preconditioning has both positive and negative effects for all AoA when looking at the pitching moment coefficient values.It was noted that using preconditioning causes beneficial effects on the accuracy of the results, with a greater emphasis for lower AoA values.Though it was important to note that it also had negative effects for the lift and drag coefficient results, indicating its use would be highly dependent on the desired results.
Dissipation also effects the assumptions made in the calculation process.Dissipation refers to the degradation of the intensity in vortical flow (Blazek, 2001).The parameters associated with this value will affect how the turbulence model calculates the unsteady turbulent flow over the configuration.If the flow does not dissipate fast enough the results will indicate much large vortices over the aircraft than expected and there merging or separation will be delayed until higher angles of attack (Blazek, 2001).If the flow dissipates too fast then the vortices will disperse too early and the flow will merge and become separated at AoA much lower than what would be expected from experimental data (Celik, 2004).The Dissipation parameters are based on the 2nd order and 4th order dissipation coefficients.
A range of simulations was undertaken changing the 2nd and 4th order dissipation values to determine their separate and joint effects by Pevitt & Alam (2011).Three different combinations were run at two separate AoA.These results were then represented with force and moment graphs.The results indicated that at low AoA, the changes in the pitching moment coefficients were negligible despite any changes in the dissipation values.When reviewing the results at higher AoA, a more noticeable effect was evident.With these inputs it was observed that the pitching moment values that were previously over predicting the experimental data were translated back down onto the experimental results, helping to improve the accuracy (Pevitt & Alam, 2011).

Finalised Static Simulation
Based on previous studies, a final static flow simulation model was developed to form the basis for further dynamic testing.The final flow simulations were run on a half model with 22.5 million nodes.This model also incorporated the sting attachment and the preconditioning and dissipation values, previously seen to help improve the simulation accuracy (Pevitt & Alam, 2011).This model implemented the lessons seen previously together to gain the most accurate results possible with the available resources.This model was then used as a reference guide for further testing where possible.
Detailed explanations of the complexities in the static flow over the delta wing were made by Pevitt & Alam (2011).The Study indicated that the key flow characteristics over this model were difficult to determine and predict.This means it will be difficult to directly represent the dynamic data as well.Additionally studies to consider a more detailed look at the flow characteristics were made through the use of surface pressure plots and pressure taps along the wing of the model.(Schütte, Hummel, & Hitzel, 2010;Pevitt & Alam, 2011).These graphs were able to clearly represent the formation and dispersion of the vortices over the configuration.These finding also indicated that though the static model struggled to represent the flow characteristics at higher AoA,    The numerical results and the flow characteristics improved for the mesh refined models.These improvements indicated notable beneficial changes in the flow characteristics at all AoA used in this study.
Based on the current accuracy of the dynamic models, the additional model refinement is needed.As the dynamic results follow the static findings, improvements made in the static results would greatly improve the dynamic results.It can be suggested that at current accuracy levels, it was not be possible to model the 1 Hz data in good confidence.However, the 3 Hz results can be modelled in quite good confidence, despite slight deviances were found in the C my results at 10º to 17º AoA.It is also believed that with further computational simulations with a more accurate model further improvement can be achieved in high dynamic modelling.
both in numerical results and flow characteristics, especially in the region of flow separation.