Accepted Manuscript

Static Computational Fluid Dynamics Simulations around a Specialised Delta

Wing

Christopher Pevitt, Firoz Alam

PII: S0045-7930(14)00175-3

DOI: http://dx.doi.org/10.1016/j.compfluid.2014.04.025

Reference: CAF 2537

To appear in: Computers & Fluids

Received Date: 6 October 2011

Revised Date: 4 April 2014

Accepted Date: 24 April 2014

Please cite this article as: Pevitt, C., Alam, F., Static Computational Fluid Dynamics Simulations around a

Specialised Delta Wing, Computers & Fluids (2014), doi: http://dx.doi.org/10.1016/j.compfluid.2014.04.025

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Static Computational Fluid Dynamics Simulations around a Specialised Delta Wing

Christopher Pevitt and Firoz Alam† School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Melbourne,

AUSTRALIA †Corresponding author: E-mail firoz.alam@rmit.edu.au, telephone +61 3 99256103, fax +61 3

99256108 ABSTRACT The primary aim of this paper is to determine a suitable and reliable model for the full static angle of attack range in Computational Fluid Dynamics (CFD) applications while determining associated model dependencies. This would allow CFD to be utilised as a more reliable tool in the development of aircraft, reducing dependency on wind tunnel investigations, with a consequent reduction in development costs. The model used in this study is based on a specialised delta wing configuration. The study has been undertaken by incorporating simulation parameters such as mesh resolution, discretisation schemes, turbulence and transition models, time step sizes and the order of the time integration operator. The modelling has been carried out using specialised meshing software, the flow simulation software (TAU) developed by the German Aerospace Agency (DLR), and the graphical interface Tecplot. Findings indicate that current CFD capabilities to model the flight envelope of a configuration are near-sufficient. The findings also show the difficulties in utilising one CFD model to represent the entire angle of attack range and the effect of model dependencies. Keywords: Computational Fluid Dynamics; Delta wing; TAU; Stability and control; Pitching moment.

1. Introduction There is no doubt that the determination of the aerodynamic characteristics of a new combat aircraft with highly swept delta wings is complex and time–consuming, because a lengthy iterative process combining semi-empirical, lower-order modelling, wind tunnel, and flight-test is required [1]. Since the 1960s, the period of all major fighter plane developments, the nonlinear aerodynamic and/or fluid-structure interaction issues were not well known until physical flight tests were undertaken, even when utilising the best available predictive tools [2-6]. Cummings and Schütte [1] provided some examples of such constraints found in the development of combat aircraft such as the F-15, the F/A-18, F/A-18A, the AV-8B, the F/A- 18C, the B-2 Bomber, and the AV-8B. Furthermore, the F-15, F/A-18A, and AV-8B exhibited significant aero-elastic flutter, the F/A-18C experienced tail buffet at high angles of attack due to leading-edge extension vortex breakdown, and the B-2 Bomber experienced a residual pitch oscillation [1-9]. With recent advances in the aerospace industry, the demand and commonality of Unmanned Aerial Vehicles (UAVs) have increased significantly. Among UAVs, Unmanned Combat Aerial Vehicles (UCAVs) are dominant. These UCAVs often lead to configuration with nonlinear aerodynamic behaviour, dominated by vortical flow across the upper surfaces due to their highly swept wing planform design. Despite the characteristics of flow phenomena associated with highly swept delta wings having been a subject of research for a long time, the flow behaviour around such geometry is still not fully understood. The financial costs for the development of aircraft with highly swept delta wings could have been significantly reduced if their static and dynamic flow characteristics had been identified in the design phase. Under such circumstances, as Cummings and Schütte [1] have said, a high-fidelity tool capable of predicting with confidence and/or identifying aircraft components vulnerable to handling quality instabilities prior to flight testing would be of great interest.

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Among all available tools (flight and wind-tunnel testing, semi-empirical lower-order modelling, and Computational Fluid Dynamics), physical flight tests provide better results. However, this is difficult to use in the early stages of aircraft development and this method is also expensive and time-consuming [1]. The second most accurate method is wind tunnel measurement, but this needs correct scaling and poses difficulties in investigating unsteady dynamic behaviour. The third method is semi-empirical lower-order modelling, which provides less accurate results compared to flight and wind tunnel measurements, due to its limitation in reliably predicting unsteady nonlinear aerodynamic behaviour [1]. Therefore Computational Fluid Dynamics (CFD) modelling remains a cheaper and relatively easier alternative. With the current capabilities of computers and CFD codes, CFD modelling can provide a reasonable compromise between flight and wind-tunnel testing and semi-empirical lower-order modelling [1]. To accurately and reliably predict the stability and control characteristics of an aircraft with highly swept delta wings prior to costly wind-tunnel and flight tests, CFD modelling should be attempted with predictive modelling of lower complexity. At present, several research projects (e.g., Computational Methods for Stability and Control (COMSAC) and Simulation of Aircraft Stability and Control Characteristics for Use in Conceptual Design (SimSAC)) have been undertaken to utilise all available tools, including CFD modelling, for the determination of various flight characteristics. The recently formed NATO Research and Technology Organization (RTO) Task Group AVT-161 is researching the enhancement of the ability of computational methods to predict better the static and dynamic stability characteristics of air and marine vehicles [1, 40-41]. The determination of static flow characteristics in combat aircraft development is an essential part of the development cycle in flight physics. When reviewing an unstable aircraft, knowledge of the flight characteristics is critical for design of the flight control systems, as many future unmanned aircraft with highly swept delta wing configurations exhibit aerodynamic stability and control issues in various regions of the flight envelope. Although several research papers have been reported in the public domain on the delta wing configuration and its effects in CFD simulations using static and dynamic modelling, a significant disagreement in angle of attack (AoA) over the linear range was reported. These deviations become even more noticeable and serious over the nonlinear range, where the leading edge vortex-breakdown begins to develop. Hence the objectives of this paper are to be able to model the flow phenomena around a highly swept delta wing configuration and be capable of understanding and visualising the key characteristics of the flow. These simulations are to be performed using the TAU flow simulation system, which was developed by the German Aerospace Center (DLR) [1]. These objectives include modelling a range of parameters and determining how each can influence the flow accuracy and characteristics around a specialised delta wing configuration under a range of AoA. In this study, individual parameters will be assessed. These include dependencies on configurations (with and without sting), mesh resolutions, discretisation schemes, turbulence and transition models, time step sizes and order of the time integration operations. The results will then be compared to the characteristics of both in-phase and out-of phase contributions to the aerodynamic forces and moments.

2. Delta wing configurations

As technology and demands on modern aircraft are advancing, the desire for additional speed and manoeuvrability capabilities is becoming more imperative. These factors should be considered in the design and developmental phase of modern aircraft. The configurations associated with both supersonic and subsonic aircraft vary greatly. The delta wing is not new technology: its initial concept was developed in 1867 [15]. It is one of the most efficient ways to achieve the desired high speed capabilities of a wing. Delta wings are a common feature of aircraft tailored for supersonic flight. The majority of modern aircraft have some aspects of swept wings to gain the beneficial effect of preventing the high speed shock effect [16]. There is a large number of delta wing types, including a) Standard, Ogival, b) Compound, c) Cropped, d) Tailless, e) Cranked Arrow, and f) Diamond/Lambda configurations [17]. These delta wing configurations are shown in Figs. 1 and 2.

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A Lambda-type delta wing configuration with a 53º swept angle has been selected for this study. In addition to the delta configuration, the sweep angle of the wings characterises slender and non-slender delta wings [19]. A non-slender delta wing is defined as having a sweep angle equal to or less than 55º [16]. These are known as low sweep angle wings. Therefore the delta wing used in this study is a low sweep angle and non-slender Lambda delta wing. This wing possesses combined rounded and sharp leading edge geometry, and the Lambda wing model is a specifically designed UCAV delta wing configuration. It has been specifically designed in order to develop key aerodynamic characteristics such as flow separation and the development of vortices [20]. The exact configuration is not shown here, but a close representation of the configuration is shown in Fig. 1g and Fig. 2, and more details of such a configuration can be found in Cummings & Schütte [1]. As mentioned above, the model has a 53º swept leading edge, with the capability of interchanging a sharp or rounded leading edge. In this study, the rounded leading edge is considered. The rounded leading edge configuration is created with a sharp inboard leading edge, which transitions into a medium round leading edge on the outer panels of the wing. The outer panel has a parallel leading and trailing edge with a washout twist of 5º [21]. The model consists of three main sections: the fuselage, the wing section and wing tips. It is made of light weight reinforced plastics, with an overall mass of less than 10 kg [22]. The purpose of the extra-light model is to reduce the dynamic inertial loads [23]. This allows for a more accurate and sensitive balance that leads to better force and moment resolution. The model contains more than 200 pressure taps on its upper and lower sides to obtain the dynamic measurement of unsteady pressures. The model was designed to gather both static and dynamic pressures. For the scope of this study with the delta wing configuration, experimental data was made available to allow for detailed CFD simulations to be undertaken and compared.

3. The DLR TAU-code The CFD modelling was undertaken using the DLR TAU-Code package developed by the DLR Institute of Aerodynamics and Flow Technology. The DLR TAU-Code has been developed to undertake complex CFD simulations. The solver is based on compressible three-dimensional, steady, and unsteady Reynolds Averaged Navier-Stokes equations [24]. This has been achieved by using finite volume flow solutions. Because of the complexity and time constraint associated with each of three discretisation methods (Finite Volume, Finite Element and Finite Difference), only the Finite Volume method was chosen for this study, as its success has been reported in previous studies [1, 40]. With this in mind, and based on the capability of the software used, both the upwind and cell-centred finite volume methods were reviewed, and it was found that the cell-centred method led to more stable results and improved convergence. Although there are more accurate methods available, they are neither possible in the software utilised nor reviewed for their performance capability. The TAU-Code is established from a hybrid, unstructured grid approach, which allows implementing multiple forms of grids to enhance the capability of analysing complicated and detailed models [25]. The unstructured grid consists of hexahedral and prismatic grids, which offer good resolution within the viscous shear layers, in order to accurately represent near-wall conditions, through the use of a structured prismatic grid [24]. In this study, an unstructured grid has been used with an in-house meshing program called ‘Mesher’. The TAU-Code has the capabilities to utilise both the Cell-Vertex and the Cell-Centred schemes. The Cell-Centred scheme has been utilised here. In the Cell-Centred scheme the Navier-Stokes equations are solved on a dual background grid, which is determined directly from the primary grid [27]. This approach allows using a greater number of solution variables compared to other approaches in order to achieve higher accuracy in results. The TAU-Code is capable of performing multi-tasks. These multi-tasks can be sub grouped into five main modules [24,46]. These modules are:

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a) Pre-processor – this module takes information from the primary grid to develop a dual-grid or multi-grids which are based on fine and coarse grid level structures; b) Solver – it performs the flow calculations over the dual-grid; c) Adaption – it refines and de-refines the grid to the capture of all flow phenomena, including vortex structures and shear layers around viscous boundaries; d) Deformation – it propagates the deformation of surface-coordinates to the surround grid; e) Motion – this module defines the motion of the model and relates this motion to any control devices. All these modules are inbuilt within the TAU code. In this study, the Pre-processor and Solver modules have been examined in more detail, while other modules remain non-variable. The Pre-processor module is based on the meshed grid, which forms the primary grid. This then produces a dual-grid, allowing the TAU-Code to run over multiple grids and in a parallel cluster [27,41]. In this work, a system of five dual grids was used. The Solver module calculates the gradients in time, which are then discretised through the use of a multi-step Runge-Kutta scheme. The calculations are then executed using multi-grid techniques and local time steps that accelerate the ability to converge the results for steady state solutions. The Solver module is used to solve simulations with upwind and central schemes, which can be used for calculating the spatial discretisation. The flow gradient variables can then be determined through the use of the Gauss-Green formulas, whereby the viscous fluxes are discretised with the use of central differences [27, 41]. There are many different turbulence models available in TAU-Code. In this work, three different turbulence models (Spalart-Allmaras Edwards one-equation model, Wilcox k-ω TNT and Wilcox k-ω LEA two-equation models) were examined.

4. Numerical results

4.1 Initial CFD findings

In order to determine the degree of accuracy of CFD simulations, and how different parameters can be improved for the quality of the results, initial simulations are required to be undertaken. With a view to checking these parameters accurately, it is important to generate a good quality grid density [26, 28]. The mesh created can significantly affect the results of the simulation. Hence, a mesh convergence study was undertaken first. From the mesh convergence study it was found that initial simulations with a low grid density have an order of magnitude of around 1. This was far from accurate enough for the required detailed simulations. With increased mesh density, the order of magnitude was greatly improved. The most consistent results saw an order of magnitude of 3. Better accuracy would be ideal, although with available computing power and grid densities this accuracy was deemed to be acceptable. As all models are different, the goal is to find a good quality mesh capable of capturing all key features of the flow. Originally three different meshes were created, ranging from 1.5 million to 10.5 million nodes, in the mesh generation process. Then, based on initial simulation results, a fourth model was developed. To explain the justification of the fourth model, and to compare the effect of mesh refinement, the force and moment results for all three of the initial meshes are shown in Figs. 3 and 5. The first three meshed configurations were used with 1.5, 9.6 and 10.5 million nodes. A total of 22 different mesh configurations and refinements were looked at in total. A range of refinement ratios that incorporated surface refinements, volume refinements and source refinements was used. The three mesh configurations chosen represented major changes in the flow phenomena. These were also compared to changes in the y+ values in the mesh. They were compared under different angles of attack in order to see how increased turbulence and complications in the flow altered the value. An average was then taken for each of the mesh densities. The exact results are not shown here due to some restrictions, though three major meshes looked at had y+ values ranging from 6 to 1.9. The final model

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tested resulted in an average y+ of 1.05. The CFD results were compared with the experimental results obtained in wind tunnels. The wind tunnel measurements were performed across two wind tunnel facilities with a total of three full tests. The first two of these tests were conducted in the DNW-NWB and the final in the NASA Langley 14-by-22-Foot Subsonic Tunnel in Hampton, Virginia [22]. For experimental validation, the results found from the DNW-NWB were used. Both static and 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 obtained [24]. THE DNW-NWB is a closed, atmospheric test section, capable of operating under both open slotted and closed [1, 29]. 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 [22]. For the purpose of this work, the wind tunnel data at a speed of 50 m/s, corresponding to a Reynolds number of 1.57 million and a Mach number (Ma) of 0.147, were acquired [29]. 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 [22]. For the work being done, the static results and the pitch oscillation results are to be used under the angle of attack range of 0º to 25º. The force and moment data for each of the initial three meshes show that there are considerable differences in the results. When reviewing the CL and CD values shown in Figs. 3 and 4, it is noted that all of the meshes appear quite good at representing the experimental flow characteristics. However, in Fig. 5 for the pitching coefficient, it was observed that there are large variations between CFD simulation results and the experimental data. It was also noted that the variations increased for coarser models as the AoA of the model increases. As the variations in the results are less for the two higher meshes, this indicates that the model is moving towards a mesh converged model. To further understand why there is a difference in the results of each of the meshes, the surface contours were taken of the pressure coefficient over the configuration. These comparisons are shown for an AoA of 15º in Fig. 6. As shown in Fig. 6, it is clear that the flow is modelled very differently and has very different characteristics. For the 1.5 million node mesh it is observed that the distribution of forces over the wing is very uneven and unclear. This would mean little confidence could be placed in this model. As the mesh is refined, it can also be seen that the flow characteristics become more defined and accurate. In addition to this increase in accuracy as the mesh was refined, there was also a corresponding increase in the y+ values associated with each model. This results in a smoother and more accurate mesh, which is more capable of accurately modelling the flow characteristics over the configuration [30, 41]. Based on previously completed experimental flow visualisations, it was noted that even the most refined model did not capture all of the flow characteristics over the configuration. The visualisation also indicated that at 15º AoA there should be the beginning of a dual vortex formation occurring, but this was not found in the CFD simulations [31]. As a result, a further refined model was developed, with a concentration on refinements along the leading edge of the configuration. This model consisted of 22.5 million nodes capable of representing the dual vortex formation. The leading edge refinement is shown in Fig. 7 and the improved flow visualisation is illustrated in Fig. 8. It may be noted that the 22.5 million node mesh was developed with the main purpose of improving the accuracy of low AoA results. The mesh refinement was primarily based on leading edge and surface refinements. Based on the mesh refinement studies, it was noted that the 10.5 million node model did represent the flow accurately to some extent. It was able to capture the key flow characteristics for all AoA, and resulted in a more accurate set of results than in coarser models. It is valid to say that this model can be used with confidence for further testing in the knowledge that it will still represent the flow characteristics accurately. However, it is recommended that, for more accurate results or for any

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final conclusions, the more refined 22.5 million node model should be used. Additionally, it was noted that the pitching moment coefficient was a good representation of the quality of the CFD results.

4.2 Sensitivity of turbulence models When analysing the flow over the configuration, it is vital to determine the sensitivity of the results due to the turbulence models [32]. Each individual turbulence model is generally developed for different applications, despite having its own capabilities and drawbacks. If an incorrect model is chosen, the quality and accuracy of the flow results will be degraded. Therefore it is vital to select a range of turbulence models that are assumed to be appropriate and determine a sensitivity analysis in order to conclude which is most suitable for the particular configuration [33, 34]. There are also some more accurate models, such as the Detached Eddy Simulation. These turbulence models were not used in this study due to the limitation of computational time. Extensive studies were undertaken regarding the SAE and k-ω models. These two models were compared using the force and moment graphs, surface contour plots and pressure coefficient graphs [41]. All three methods of modelling were used to ensure a clear understanding between the accuracy and capabilities of the difference turbulence models. This process was then done again for the LEA and SST turbulence models. These simulations were undertaken at a range of AoA to ensure a consistent trend. A representation of these simulation results is shown in the pitching moment graphs in Figs. 9 and 10. The Figures show that the SAE model had provided good results. It was able to represent the flow phenomena better than other models. For example, using the k-ω model, the key flow phenomena such as the pitching moment dip at 17º AoA was not well represented. Also, the SAE is one equation model, while the others are two equation models. This is simple and allows the simulation to run much faster. Therefore, the rest of the simulations were based on the SAE turbulence model. Although the results are still not ideal, this model is the closest and easiest to improve with further refinements.

4.3 Influence of configuration changes When analysing the flow over the configuration it is noted that more than one layout for the model can be used. The two main alternatives were investigated for the possibility of using a half model configuration, and the effects of the wind tunnel sting attachment. The purpose of modelling a half model is to prove that the results for the full and half model are the same. If this is true, then it is possible to make a flow analysis with greater mesh refinements over the half model [35]. The advantage of the half model is that it is faster to solve and allows for additional refinements. The aim of modelling the effects of the sting attachment is to see if the sting is a cause of errors in the flow. In previous studies it has been suggested that the lack of a sting on the model can affect the pitching moment results [41]. Hence, by comparing this, it can be determined if a sting needs be used for further studies in order to achieve accurate results. To compare the full and half models, simulations were run at two AoA (15º and 25º). At these angles the force and moment graphs, as well as the surface contour plots, were reviewed. The results showed that all features of the flow were the same for both the full and half models. This is shown in the pitching moment graph in Fig. 11. The next modelling in configuration changes was undertaken to determine the effects of the sting attachment on the flow phenomena. The simulations were performed on a range of AoA between 10º and 20º. In general, the effect of the sting attachment was to translate the pitching moment results upwards. As the results for pitching moment coefficients were generally under predicting, the upwards shift is beneficial to the results. Thus it is useful for final simulations for the sting attachment to be included in the model configuration. The pitching moment coefficient graph with and without stings is shown in Fig. 12.

4.4 Influence of discretisation parameters

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Two parameters reviewed here are Preconditioning and Dissipation, since they can affect the simulation results. Preconditioning affects the assumptions made in the calculation process [36]. The simulations work through the use of the governing equations. The governing equations assume that the flow is compressible. As the flow in this work, over the configuration, is only 0.147 Mach, the assumptions of compressible flow are not completely valid [37, 41]. 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. It is expected that the implementation of Preconditioning should improve the convergence results [38]. Preconditioning was added to the standard 10.5 million node model with a correction factor of 1.5. The simulations were run at a range of AoA from 5º to 25º. The force and moment graphs generated from the simulation results are shown in Fig. 13, which clearly indicate that there is a notable effect on the flow, with Preconditioning in place. The results did not change consistently, however, so that, in order to further explain the effect of the Preconditioning, it became necessary to review the surface pressure contours. From the surface pressure contours, it is noted that the Preconditioning addition has both positive and negative effects for all AoA based on the pitching moment coefficient value. Overall, it was observed that using Preconditioning alone would be beneficial for the pitching moment coefficient results with a greater emphasis for lower AoA. With negative effects on lift and drag coefficients, the use of Preconditioning should be dependent on the results desired. Dissipation also affects the assumptions made in the calculation process. Dissipation refers to the degradation of the intensity in vortical flow [36]. The parameters associated with this value generally 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 larger vortices over the aircraft than expected, and their merging or separation will be delayed until higher angles of attack [36]. 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 [39]. The Dissipation parameters are based on the 2nd order and 4th order Dissipation coefficients [39]. The Dissipation tests were performed on the 10.5 million node model. A range of tests were undertaken, changing the 2nd and 4th order Dissipation values separately in order to determine their separate and joint effects. Three different combinations were run at two separate AoA. These results were then represented with force and moment graphs. The results for the pitching moment graphs are shown in Fig. 14. As the configuration being used here is undergoing a flow of 0.147 Mach, there will be no shock waves, so it is expected that a reduction in the 2nd order Dissipation would be beneficial. The 4th order Dissipation values represent the dispersion rate of the vortices. A higher number will lead to the flow dispersing at a quicker rate. The pitching moment graph indicates that under a low AoA, the changes in the pitching moment coefficients were negligible. Then, when reviewing the results at higher AoA, it was seen that two of the tests had an effect in the results, while for one set of parameters there was a noticeable effect. This occurred when the 2nd order Dissipation coefficient was reduced from 1 to 0 and the inverse 4th order Dissipation coefficient was increased from 64 to 84. With these inputs it was noted that the pitching moment values over predict the experimental data and translate back down onto the experimental results.

4.5 Finalised simulation and results Discretisation parameters were investigated separately and found to affect the flow differently. Therefore, simulations with both the Preconditioning and Dissipation values decided previously were used together. In addition to these parameters, to try and improve the overall quality of the results, factors that were noted to be beneficial to the results discussed previously were also implemented. A mesh of 22.5 million nodes was used on the half model configuration. Additionally, the sting attachment was also used. The goal of this was to gain the most accurate results possible. To see the

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effect of these concepts being assembled, the force and moment graphs were combined in order to compare the changes. The pitching moment coefficient values are illustrated in Fig 15. From the pitching moment coefficients, it was observed that, for low AoA, the value translated up greatly, much closer to the experimental results. As the AoA increases, the values of the pitching moment coefficient dip further below the experimental results. To determine the reasons for this, additional AoA simulations were run. With these results it became clear that the pitching moment dip is now occurring earlier. This concept appears constant for the rest of the AoA. The mesh refinement, half model and sting attachment together translate the entire pitching moment graph to the left. The simulation is predicting the flow phenomena before it should have occurred. To further explain the changes in flow characteristics of the model, surface pressure contour plots and contour plots with stream lines were created. However, when reviewing the contour plots, it became apparent there was little difference between the improved model and the slandered model configuration. To understand and explain the flow better, results for the pressure coefficient graphs were developed. These were done at the pressure tap locations that lie on the 62% span line, running perpendicular to the leading edge, the 45% and 70% chord lines and the 26% span line along the length of the configuration. The graphs lie in this order respectively grouped by their corresponding AoA. Through the use of pressure contour plots, a greater representation of the flow phenomena can be observed. These graphs clearly represent the formation and dispersion of the vortices over the configuration. It may be noted that the experimental pressure distribution plots are not shown here. However, details about experimental pressure data can be found in [42-45]. In general, the half model with sting, preconditioning and dissipation is capable of more accurately representing the flow characteristics. Despite some deviations of the results at higher AoA, the improvements for lower AoA are more noticeable and improve the overall quality of the results. The flow characteristics can also be seen visually in the surface contour plots, which are shown in Fig. 16 for the final configuration choice.

5. Conclusions Based on the findings of CFD modellings, a final simulation model was created utilising all of the beneficial simulation factors. The final simulation model is based on a 22.5 million node half model, with the sting attachment, preconditioning and dissipation parameters.

The 22.5 million nodes, in the sting, preconditioning and dissipation parameter model, are quite capable of providing reasonably accurate results. In order to use the results with good confidence, only the low level angle of attack (between 0º and 15º) range should be used. The simulation model appears to predict results earlier than the experimental data. Between 0º and 15º angles of attack, the simulation results occur around 1º earlier than the experimental data. The model struggles to predict the results with confidence over a 17º angle of attack. Overall, it is vital to ensure an adequate mesh refinement with a definite focus on leading edge refinement. Without this, simulation results can deviate significantly from experimental results. The addition of sting, preconditioning parameters and increased dissipation parameters can lead to a more accurately refined model. With appropriate mesh refinements and flow parameters, the TAU-Code is capable of representing the force and moment coefficient results to an appropriate level of accuracy. However, in order to truly represent the overall flight envelope, two separate meshes would be required, one focusing on low angle of attack results and other focusing on high angle of attack results. The TAU computational model is capable of predicting the complex unsteady flow fields, incorporating the ability of grids, turbulence models, and time integration approaches for aircraft stability and control parameters.

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Overall, the present model is an addition to the wide range of code to code comparisons which have recently been published in the final report of the AVT-161 Task Group dealing with the present configuration [1, 40]. Acknowledgements The authors are highly grateful to Dr. Stephan Hitzel and Dr Herbert Rieger, from CASSIDIAN – Air Systems for their assistance and support with the organisation and preparation of this work, as well as for their time and effort spent in ensuring that it was produced to a high standard. Nomenclature AoA = Angle of Attack CD = Coefficient of Drag CFD = Computational Fluid Dynamics CL = Coefficient of Lift Cmy = Coefficient of Pitching Moment DLR = German Aerospace Centre DNW- NWB = German Dutch Wind Tunnel – Low Speed Wind Tunnel Braunschweig TAU = DLR Flow Simulation Software UCAV = Unmanned Combat Air Vehicle NASA = National Aeronautics and Space Administration References [1] Cummings RM, Schütte A. Integrated Computational/Experimental Approach to Unmanned

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a) Tailless delta b) Tailed delta c) Cropped delta d) Compound delta e) Cranked arrow f) Ogival delta g) Lambda delta

Fig.1. Delta wing configurations, adapted from [15, 17]

Point of Rotation

Cref - Reference length for Reynolds number (Re) estimationCr - Inner root chord

a) Planform & geometric parameters of a SACCON UCAV configuration

Wind Direction

b) A SACCON UCAV low-speed wind tunnel model in DNW-NWB Wind Tunnel

Cref = 0.479 m

Cr = 1.0601 m

0.6 m

0.8554 m

S =

0.76

9 m

53º

Model Positioning Mechanism (MPM)

Moment Reference Point (MRP)

Fig.2. A SACCON UCAV delta wing configuration, adapted from [1]

Fig. 3. Test VN 1406, SAE – 1.5, 9.6, 10.5 results, CL vs. AoA

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Fig. 4. Test VN 1406, SAE – 1.5, 9.6, 10.5 results, CD vs. AoA

Fig. 5. Test VN 1406, SAE – 1.5, 9.6, 10.5 results, Cmy vs. AoA

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SACCON SAE 1.5 Million Ma=0.147 Re=1.93E06 AoA=15.0°

SACCON SAE 9.6 Million Ma=0.147 Re=1.93E06 AoA=15.0°

SACCON SAE 10.5 Million Ma=0.147 Re=1.93E06 AoA=15.0°

SACCON SAE_Sting 22.5 Million Ma=0.147 Re=1.93E06 AoA=15.0°

Fig. 6. Surface contour plots at 15º AoA, comparing mesh refinement

Fig. 7. Comparison of leading edge refinement between 10.5 and 22.5 million node meshes

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SACCON SAE_Sting 10.5 Million Ma=0.147 Re=1.93E06 AoA=15.0°

SACCON SAE_Sting 22.5 Million Ma=0.147 Re=1.93E06 AoA=15.0°

Fig. 8. Surface contour plot comparison between 10.5 and 22.5 million node meshes

Fig. 9. Test VN 1406, SAE and k-ω results, Cmy vs. AoA

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Fig. 10. Test VN 1406, SAE, k-ω, LEA and SST results, Cmy vs. AoA

Fig. 11. Test VN 1406, SAE, Full and Half, Cmy vs. AoA

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Fig.12. Test VN 1406, SAE, with and without sting, Cmy vs. AoA

Fig. 13. Test VN 1406, SAE, standard and preconditioning, Cmy vs. AoA

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Fig. 14. Test VN 1406, SAE, standard and dissipation, Cmy vs. AoA

Fig. 15. Test VN 1406, SAE, standard, sting and dissipation, preconditioning, Cmy vs. AoA

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SACCON SAE Preconditioning Cutoff=1.5 10.5 Million Ma=0.147 Re=1.93E06 AoA=20.0°

SACCON SAE 10.5 Million Ma=0.147 Re=1.93E06 AoA=17.0°

SACCON SAE Preconditioning Cutoff=1.5 10.5 Million Ma=0.147 Re=1.93E06 AoA=10.0°

SACCON SAE 10.5 Million Ma=0.147 Re=1.93E06 AoA=10.0°

SACCON SAE Preconditioning Cutoff=1.5 10.5 Million Ma=0.147 Re=1.93E06 AoA=17.0°

SACCON SAE 10.5 Million Ma=0.147 Re=1.93E06 AoA=20.0°

Fig.16. Surface contour plots of model with precondition, dissipation and sting

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• Determination of feasibility of CFD static simulations

• Changing model dependencies to improve flow characteristics

• Moving a step forward for CFD being a more reliable tool

• Improved reliability to reduce aircraft development cost

• Indications of difficulties in CFD simulations