AIAA-2008-309-758

Fluid-Structure Interaction of HALE Wing Configuration

with an Efficient Moving Grid Method

Greg Carniea and Ning Qinb

Department of Mechanical Engineering, University of Sheffield, Sheffield, S1 3JD, UK

This paper describes an automated process that runs a loosely coupled fluid-structure interaction simulation of a high-altitude, long-endurance (HALE) wing that encompasses Delaunay graph based grid deformation. A Tcl scripting language code has been written to couple two commercial CFD and CSD packages and our own moving mesh code for the interaction. The computational fluid dynamics flow solver used is the Fluent package and the coupled implicit method was used to solve the Reynolds-averaged Navier-stokes equations. The computational structural dynamics part was solved using finite element analysis in Ansys. A static linear aeroelastic analysis was carried out to determine the deforming profile of the high aspect ratio wing using data interchange between the two codes. A full internal structure of the wing was constructed to more accurately represent the high-altitude, long-endurance wing. The grid deformation was carried using the Delaunay graph based mesh deformation method, which maintains the mesh topology throughout the entire process.

I. Introduction

HE application and development of fluid structure interaction (FSI) has been rapidly growing in notoriety over the last decade, mainly due to the increased processing speed and memory of workstations and clusters required

to run such complex jobs. Industry has now realised the significant benefits associated with FSI in the design and testing of new products based on the actual interaction/deformation that occurs on a body due to the fluid dynamic loads generated as a results of the body’s geometric shape.

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NASA highlighted in the failure report [1] of its high altitude, long endurance Helios HP03 that, “The accident investigation board determined that the mishap resulted from the inability to predict, using available analysis methods, the aircraft's increased sensitivity to turbulence following modifications to allow long-duration flights.” This highlights the deficiency in modelling techniques used for flexible wing structures, which is necessary for light wing structures and, therefore, long endurance. Romeo and Frulla [2] have investigated the design and build of HALE wings, running separate test models for both the computational fluid dynamics (CFD) and the computational structural dynamics (CSD). In order to fully implement FSI successfully, the present study addresses the issues of coupling and data transfer between the CFD and CSD models and the updating of the CFD mesh. The implementation of dynamic grid techniques result from deformation generated from FSI.

A. Coupling methods

There are different methods available to achieve FSI. The main issue is one of data transfer between what are usually two different solution algorithms; this is classed as a fully coupled simulation. A decoupled simulation involves prescribed structural motion being applied, such as an indical response [3]. Alternatively two separate algorithms can be used with data transferred between the two.

a Research student b Professor of Aerodynamics, AIAA Associate Fellow

American Institute of Aeronautics and Astronautics

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46th AIAA Aerospace Sciences Meeting and Exhibit7 - 10 January 2008, Reno, Nevada

AIAA 2008-309

Copyright © 2008 by G Carnie amd N Qin. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

The data transfer can either be classed as strong coupling or weak coupling. Strong coupling implies that both algorithms are effectively combined so that only one set of equations are solved, thus simultaneous data transfer occurs. Whereas weak coupling relies on the different algorithms being run one at a time before data transfer commences. This weak coupling can either be integrated or modular. If the weak coupling is integrated this implies that the source codes are altered to include the coupling algorithm, whereas the modular approach does not directly interact with the source codes. Therefore this method can be readily interchanged with different types CFD and CSD codes, whether they are actual source codes or commercial software. It should be noted that throughout the term loose coupling and weak coupling are indiscriminately interchanged. Liu et al. [4] performed an integrated simulation between CFD and CSD to determine flutter of a wing. The solution was achieved by employing strong coupling fully implicit method. The aeroelastic response was determined by the coupling of the CFD and CSD; however the unsteady moving grid algorithm was achieved in an uncoupled manner. The accuracy of the simulation in terms of time was maintained with a dual-time stepping algorithm. When comparing the coupled solution to that of a prescribed solution it was found that the coupled method provided a quicker and more accurate solution if the initial and boundary conditions were selected correctly. The coupled solution also compared favorably to the experiment results, except for cases at supersonic speeds. Lee-Rausch and Batina [5-7] developed a 3D method for the Euler and Navier-Stokes equations for predicting flutter on a 3D wing too for both a coupled CFD-CSD and indicial, however for Mach numbers greater than unity a premature rise in the flutter boundary condition was experienced in the computer model. Chen et al. [8] then further improved the methods of Lee-Rausch and Batina [5] by using a Gauss-Seidel iteration, which is unconditionally stable and permitted the use of a larger pseudo time than previous explicit method. Further to this, Chen et al. [8] implemented a Roe Scheme, details of which can be found in [9] which was advantageous over Liu et al. [4] central differencing scheme as it did not require artificial dissipation. Their results were more accurate than the previous case stated and their capture of the sonic dip compared favorably to that of the experimental data. However at the highest Mach number there was still some discrepancy which was noted in the other papers and was put down to the failings of the turbulence model when strong shock boundary interaction occurred. Guruswamy developed a code, ENSAERO [10] for calculating the modal response of an aeroelastic wing solved by a Navier-Stokes finite difference method, which was upgraded later to a parallel version by Byan and Guruswamy [11-12]. A linear acceleration method was used to solve the coupled aeroelastic equations. The results obtained in general compared favorably with the experimental data, however the computational shock wave predicted slightly downstream to that of the experimental measured one. In one of there previous papers Guruswamy and Byun [13] examined the use of a domain decomposition approach for a coupled FSI. They stated that fully coupled methods where better suited to solving large deformation due to aeroelastic response of aerospace vehicles. However at the end of each time step a new field grid was required to be generated to allow for the deformed surface. Garcia [14] also opted for a fully coupled procedure when investigating the nonlinear effects on flexible HALE wings at transonic speeds. He still carried out a static aeroelastic on the wing, but the structure deflection was solved using a non-linear finite element method (FEM). Both linear and nonlinear results were compared and it was found that the nonlinear method showed a reversal in tip twist that was not picked up by the linear model at transonic speeds. Guruswamy and Yang [15] had previously used a loose coupling scheme but instead of using the full Navier-Stokes equations the fluid equations were solved using a finite difference (FD) based transonic, small perturbation equations. Alonso and Jameson [16] performed a fully coupled implicit two-dimensional analysis of flutter based on Euler equations with the decomposition of the structural modal equations. The implicit scheme was based on Jameson’s multigrid method [17], which Chen et al. [8] also used. The paper was based on the analysis of the NACA 64A010, work which was initially carried out by Bendikson and Kousen [18]. They predicted the flutter boundary of a NACA 64A010 aerofoil based using an explicit coupled aerodynamic code. The aerodynamic loads were solved via the Euler equations. The aeroelastic results were accurate to that of experimental results up until the formation of a strong shock wave occurred.


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Bhardwaj et al. [19] opted to go down a different path from previous research. They went along the lines of not having the source code of either the CFD or CSD solvers. Hence they were looking at coupling the codes via an external interface which did not have to be integrated into the source codes. Their results compared well to that of experimental results. They were within three percent of error when using FE equations and highlighted the advantage over modal analysis as this method produced a twenty five percent error. The actual displacements were relatively small though relative to the overall dimensions of either the wing or stabilator. For some reason they did not construct a new FE model after each iteration, although they did point out that such a feature could have implemented. The paper also cited the efforts of Guruswamy and Yang [15] loosely coupled approach and that the two-dimensional method has been extended to encompass three-dimensional models such as XTRAN3S [20] and ATRAN3S [21]. A collaborative project to enhance the understanding of flutter on highly flexible wings [22], particular that of large transport aircraft by five major companies could not resolve the issue on which coupling scheme was more accurate and requires further investigation. Work by Schoor and Von Flotow [23] used a combination of modal solutions to simulate the characteristic of a highly flexible wing. They stated that the angle of attack of the aircraft could be as high as ten degrees. They concluded that the aeroelastic response of the aircraft had to be incorporated into the flight control. The aeroelastic solution itself required the use of complex frequencies Patil and Hodges investigated the aeroelastic behaviour of high-aspect-ratio wings [24]. The wing itself was a 16:1 high aspect ratio. Patil and Hodges cited the importance of being able to model consistently the exchange of information between the structure and aerodynamic model. Continuing on from this Patil and Hodge studied the flight dynamics of flexible flying wing [25]. Their work accounted for a complete analysis of a complete aircraft. A Newton-Raphson method was used to solve the aeroelastic equations. This resulted in a steady-state trim solution. The effect of the payload had drastic effects on the stability of the aircraft. As the payload increased the aircraft headed towards an unsteady phugoid mode. Recent work by Su and Cesnik also utilised beam theory for their coupled simulations [26] of a highly flexible wing. The aerodynamics is accounted by a finite-state unsteady subsonic aerodynamic load. The overall model is that of a low-order simulation. The effects of gust and skin wrinkling of the wing were investigated. As is the case their results could not be validated against any experimental results due to the lack of published data from the private sector. The trim had a significant effect on the overall deformed shape of the wing. In particular a light (0kg) and heavy (227kg) payload case changed the trim body AOA from 3.1o to 4.86o. The resulting flap angle also decreased from 5.68o to 0.47o. B. Data Transfer between CFD and CSD Meshes This is a critical part of the process as any misinterpolation of the acquired solution data could inadvertently cause the wrong deformation characteristics to be passed onto the subsequent mesh, whether that is the CFD or the CSD mesh. Similarly the extrapolation of data can also lead to a degradation of the solution accuracy [27]. There are two methods available, both the CFD and CSD share the exact same mesh topology, in which data transfer can be linked via nodal positions. This of course relies on topology remaining intact and thus grid adaptation could result in a slight mismatch. Subsequently the data can be interpolated between mismatched grids. This allows for a reduced mesh for the CSD model as the surfaces mesh does not have to be as fine as the CFD inviscid/viscous mesh. Bendikson and Hwang [28] developed a finite element algorithm that allowed data to be exchanged across the CFD and CSD girds based on similar surface meshes. The program MSC/NASTRAN [29] uses a combination of spline methods, thin plate spline and infinite plate spline, and can perform static analysis right through to dynamic aeroelastic response [30]. This method was ultilised by Liu et al. [4]; however it was pointed out in the paper that much higher flutter velocities were determined for the supersonic region.


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A spline is a mathematical algorithm for interpolating a function of two variables based upon small deflection of an infinite plate, hence an infinite plate spline (IPS). This method was first investigated and applied to aeroelasticity by Harder and Desmarais [31]. The thin plate spline (TPS) method by Duchon [32] is a smooth function that interpolates a fixed surface about a specific location. Mathematically it is a two-dimensional analog of the cubic spline in one-dimension. The above two spline methods are ideally suited to aeroelastic analysis involving thin plate or shell elements. For beam elements in this context one should refer to the work by Done [33]. Indeed Smith et al. investigate six different algorithms to act as the interface between the CFD and CSD, the detail of which can be found in Ref. [34]. They conclude that the (TPS) and multiquadric-biharmonic (MQ) were overall the method of choice in terms of interpolation schemes. The TPS and MQ methods along with the others were then implemented and evaluated by Smith et al. [35] the limiting factor for MQ and TPS was that three data points were required to define a plane in order to achieve an accurate solution. They concluded that no one method can be exclusively used and the TPS and MQ methods where within five percent of the intended target value. Byun and Guruswamy [13] maintained the accuracy of their solution by ensuring domain decomposition. Here they matched the two meshes of the CFD and CSD at the surface interface of the aerospace vehicle to ensure full data transfer between the algorithms. They employed a virtual surface approach to accommodate the data transfer based on a mapping matrix developed by Appa [36]. This method was similar to that of Bhardwaj et al. [19] where the data transfer between the codes in order to obtain a static aeroelastic solution relied on the passing of information through an interface map. This map was generated by matching nodes from the two different grids. However they experienced some computational problems which meant the mapping of the structure did not extend to the root of the wing, which could account for some of the error in their results. C. Dynamic meshing Liu et al. [4] employed a spline matrix method to interpolate the data between the CFD and CSD meshes. However the grid topology of each block was changed via grid adaptation and recalculated after each time step. The moving grid algorithm was developed by Wong et al. [37]. The algorithm was based on arc-length transfinite interpolation with the motion of the blocks based on a spring network. Robison et al. [38] also used a continuously moving mesh algorithm to account for the changes in the flow field as a result of the deformation of the wing. This algorithm was spring based and thus limited to relatively small deflections which is adequate for flutter predication. Robinson et al. adapted Batina [39] original algorithm to encompass both tetrahedral and hexahedral cells. Guruswamy [10,13] used a time accurate configurative adaptive dynamic grid when applying the deformed profiles at each time step. Chen et al. [8] method seemed robust enough and obtained some excellent results from their computer model. However they relied on grid remeshing at each updation time step. Bhardwaj et al. [19] acknowledged the limiting factor of their CFD mesh deformation, which could not cope with relatively large deflections. This was due to the spring based approach for deforming the CFD mesh which was controlled with a cosine spacing function. Garcia’s [14] approach was to deform the mesh after every CFD iteration. The FEM values had to however, be interpolated onto the CFD grid using a cubic spline. This was due to the vast differences in mesh topologies between the CFD and FEM meshes. The whole CFD mesh including the pressure far-field nodes moved as a result of each displacement. This differs from the conventional way when it is usually just the interior mesh that deforms. A paper by Liu et al. [40] explains, and introduces an alternative dynamic grid method based on the Delaunay graph; that in comparison to spring analogy is computational a lot more efficient. Delaunay graph mapping involves the generation of Delaunay triangles (2D) and tetrahedrons (3D) between the geometrical points and the fixed outer boundary points. The method uses the Bowyer-Watson algorithm [41, 42]. Only the Delaunay graph and not the Delaunay grid is used for this dynamic mesh technique so the problems as highlighted by the authors are not apparent in the process. The code for the complete Delaunay generation process (Quickhull algorithm) was developed by Barber et al. [43].


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The work presented here encompasses a loosely coupled modular static aeroelastic FSI simulation of a HALE wing. The HALE wing is based on NASA’s Helios HP03. The exact specifications where not publicly published, however a representative model based on NASA’s report [1] and images enabled a model to be constructed. With a HALE wing being the subject of investigation, initially at a cruise condition of 22Km, with an equivalent airspeed of Mach 0.11. A further test at sea level was also performed. Subsequently the mesh for both the CFD and CSD match exactly at the boundary interface. This allows for complete data exchange between the models. The dynamic meshing approach encapsulates the Delaunay mapping which maintains the existing topology, even under high deflection. The commercial codes Fluent 6.1.22 and Ansys10.0 were used for the aerodynamic and structural simulation. The interfacing program used a nodal mapping method to ensure complete data transfer back and forth between the codes. The overall simulation was controlled through a scripting language Tcl that automated the process. This coupled with moving mesh capability to maintain the topological map of the deformed CFD mesh allows the updated CFD step to start from the previously saved data point. The CFD solution is not required to be converged after every FSI interaction step [19] however as the wing reaches its equilibrium positions the CFD model did reach full convergence.

II. Aeroelastic Equations: The finite element discrete aeroelasticity element equation for a structural system can be defined as,

.. .[ ]{ } [ ]{ } [ ]{ } { ( )}M q C q K q F t+ + = (2.1)

Where [M] is the system mass matrix, [C] is damping matrix and [K] is the stiffness matrix which corresponds to the overall time dependent force vector, {F(t)}. For a static analysis, with gravity effects, equation 2.1 would reduce to

..[ ]{ } [ ]{ } { }M q K q F+ = (2.2)

In an ideal world aeroelasticity problems for the aviation industry would not exist if the aircraft was completely rigid [44]. This however is not the case as the airframe has to be lightweight in order to maximise the thrust to weight ratio. With the processing speed of computers nearly doubling every year more and more complex studies were able to be performed. Initially predetermined modal responses were applied. This has now advanced to fully coupled FSI involving data exchange based on the structural deformation of the body due to the aerodynamic loads. Nowadays it is common to have a computer cluster that can run in parallel in order to solve a relatively complex FSI problem.

III. HALE Structure

The wing was based on NASA’s Helios HP03 configuration. Initially a reduced sized model was tested. The model size was reduced from an original aspect ratio of approximately 31:1, divided into six sections, to a smaller 21:1, divided into four sections. It was only the span length that changed so the overall configuration still resembled that of Helios HP03. Only two sections were modelled due to the symmetry of the wing. The ten degree dihedral angle was maintained and modelled. Each section consisted of three main ribs and twenty two internal support ribs. A fibreglass skin was wrapped around the whole structure. To maintain the profile of the aerofoil between the ribs Styrofoam nose pieces were used. This can be seen in Fig 1. The structure model used for Ansys is shown in Fig 2. The entire structure was represented by SOLID45 elements due to their ability to model creep, plasticity, stress stiffening and large deflections. Each element has three-degrees of freedom defined by eight nodes which is suitable for a linear calculation. The homogenous material used for the individual components are shown in Table 1. The structural part was only solved as a serial case; this was due to the educational license restriction of the software only.


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Density (kg/m3) Young' Modulus (GPa) Poisson's ratio ApplicationsCarbon fibre 1600 145 0.25 Tubular spar and ribsfoam 1050 3.28 0.33 Styrofoam nose pieces Glass fibre 2100 45 0.19 Skin

Table 1. Material properties used

Figure 1. 3D cut away view showing the layout of a section of the wing

Figure 2. Fully loaded and constrained partial view of wing in Ansys

A. Fluid-Structure Interaction Process

The process relies on information exchange at each FSI iteration. With a matching mesh interface all the data transferred between the CFD and CSD is assured. The steps below outline the current procedure.

1. Partial run of CFD solution 2. Surface pressures are converted to nodal pressure forces 3. Nodal pressure forces are mapped and formatted ready to be applied to CSD 4. CSD code run with nodal pressure forces and after 1st FSI loop stress history profile added 5. Displaced exterior nodes written to file 6. Fortran code to map new nodes to existing CFD grid 7. Delaunay grid mapping applied to deform existing CFD grid to fit new shape and update file 8. New CFD grid checked as is convergence 9. If CFD grid ok and convergence not reached return to step 1 and continue

For completion sake it should be noted that an FSI iteration refers to one complete loop of the process that entails steps 1-9. A new case file is written at step 7, since the topology and connective remains unchanged the previous CFD data file is used when the flow calculation resumes at step 1. Since this simulation is for a static aeroelastic problem one must ensure that the previous stress history is used in order for the structure to represent a continuous


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loaded body, as the loop is after all a continuation from the previous step. The above process is shown in a flow chart in Fig 3.

Start

FSI looping iteration, FSI = 1

Figure 3. FSI flowchart B. Coupling Loose coupling occurs between the two different codes with the update occurring at the end of the previously run. The process continues until the deflection of the wing is small enough as compared to the overall major dimension

Solve CFD mesh for n iterations Write out boundary nodes required by Delaunay mapping criterion and

surface pressure forces

Apply loads to CSD mesh and solve, writing out displaced nodal

data Convert CFD data to CSD data

Convert CSD node files to CFD node files

YES

Update CFD mesh using Delaunay mapping, solve for n iterations

Write surface pressure forces

Apply loads and stresses to CSD model and solve

Write out displaced nodal data

Nodal Displacement < tolerance? End

FSI = FSI + 1

NO


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of the wing. This represents the convergence criteria, which is a tolerance of the deflection the overall wing span in this case.

When this occurs and if the CFD is not already fully converged a further FSI iteration is initiated in order to achieve a fully converge CFD solution, this can be seen in Fig 9. If the further effects of these aerodynamic pressure forces change on the deflection are negligible the process ends, as was the case here. If not, further FSI iterations are run till full converge of both the CFD and CSD are achieved to the specified tolerances, so achieving a fully converged FSI model. For the CFD part the new displaced model is restarted from the previous time step as the topology of the mesh is maintained by the Delaunay mapping (which is explained below). C. Data Transfer between the Packages This is carried out on the basis that the meshes matched at node locations. Therefore the CFD mesh node points along the span of the wing correspond to that of a node on the FEA model. The number of points along the span of the CFD was kept to a minimum by running a grid sensitivity test. The CFD mesh used was based on a C-H topology of size 189x40x56, as shown in Fig 4. A test case with a 50% finer mesh was ran and converged to the same tolerance, the lift and drag coefficients differed by 0.4% and 1.63% respectively. The pressure far-field was extended to 17 chord lengths in the x and y direction and 15 in the z-direction. The model was run at altitude to represent the final cruse condition of a HALE wing. The CFD model was run in parallel to shorten computation time.

Figure 4. HALE wing with 10o dihedral angle CFD mesh

A mapping program was used to find the corresponding nodes from both the CFD and CSD code, when established the same order of the output file could be used for the next FSI loop as an old version was temporarily kept that had the previous nodal coordinates. Therefore when the new coordinates were written a previous link still existed so that the new coordinates could be updated more efficiently. D. Dynamic Meshing Procedure Initial tests were carried out to determine which method of dynamic meshing, spring analogy or Delaunay mapping was more efficient. The tests indicate that the Delaunay mapping method is a far more efficient and robust method for updating the mesh. A test was carried out for the first displacement of 0.64m. The spring analogy algorithm with Fluent took 3hrs to update the mesh and used over 300Mb of memory. In comparison the Delaunay mapping method took, including writing the new case file 27mins and a maximum memory commitment of 67Mb.


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Delaunay graph mapping involves the generation of Delaunay triangles (2D) and tetrahedrons (3D) between the fixed outer boundary points, in this case a pressure far-field and the surface of the wing that will deform. Fig 5 shows the 3D Delaunay map for this particular simulation.

Figure 5. 3D Delaunay tetrahedron map

E. Scripting methodology Tcl scripting was used to run the FSI testcase. This allowed for the process to be automated. The process relied on the monitoring of the output files generated from running the CFD and CSD codes or making and formatting the additional files required to run the process. Such files included the boundary files required for the Delaunay mapping moving mesh and the formatting of the nodal pressure force file that was made with the aerodynamic pressure forces into a file that Ansys could read. These processes were checked and the FSI script only continued if no errors were found. Tcl as a scripting language has the advantage that it allows for common UNIX commands to be interpreted directly. This is essential as the CFD therefore can be run as a batch parallel computing job submitted to a cluster of computer nodes for processing. Each node consists of two processors, each being a 2.4GHz Xeon processor using a Linux Red Hat 9 operating system, and had up to 1.0Gb RAM available per processor.

IV. Initial Results The wall function is used in the CFD simulation due to that (1) the boundary layer is fully attached on the wing surface for the cruise condition here; (2) the grid density requirement near the wall is much lower than the case where resolution of the turbulence down to the wall is needed. For the initial simulation, the angle of attack was set to 2 deg. The pressure coefficient contours are shown in Fig 6(a) and 7(a). The structural solution shown in part (b) shows the Von Mises stress plot across the skin of the wing. The structures in this case were run as homogeneous properties of the equivalent composites before the construction of a laminate occurred. A section of the internal skeleton structure of the wing as previous explained is shown in part (c) with the stress contours from the structural solution. The majority of the stress loading is taken by the tubular spars that run throughout the wing. The ribs are primarily there to maintain the aerofoil profile over the span of the wing. However stresses are distributed from the beam to the ribs. The resulting stresses on the ribs are also transferred to the Styrofoam nose pieces which themselves are already under compression due to the bending of the wing.


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Figure 6(a) Pressure coefficient contours for first FSI loop (b) Resulting structural deflection

Figure 6(c) Part view of internal skeleton of wing showing constrained area

Figure 7 (a) Pressure coefficient contours for last FSI loop (b) Resulting structural deflection


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Figure 7(c) Part view of internal skeleton of wing showing constrained area

The position of the wing for each of the FSI iterations is shown in Fig 8. It shows the position of the wing in relation to its initial position. Fig 9 shows the residual of the flow solution for each of the FSI iterations. The solution was run till convergence.

Position of wing relative to initial static position of zero metres

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0.6

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0 2 4 6 8 10 12 14 16 18 20

FSI loop number

Ove

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lace

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)

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Figure 8. Global displacement of the wing Figure 9. Convergence history of the FSI simulation

V. Discussion of Two Section Model

These results so far have shown a new and robust method for FSI simulation benefiting from the introduction of dynamic grid deformation based upon the Delaunay mapping. The topology of the mesh was maintained throughout the FSI iterations. This also makes the data transfer between the CFD and CSD more straightforward. The automated process will allow for future simulations involving composites wing structures to be run efficiently. Compared with the spring analogy approach, the Delaunay mapping moving mesh method shows about one order reduction in CPU time, which is similar to the improvement reported in Liu et al. [40]. However the memory commitment for Delaunay mapping for the current case was found to be also less than that of the spring analogy (about 5 times less). This contradicts the previous research that shows the Delaunay mapping method requires more memory. The discrepancy could be down to the algorithm for the internal smoothing iterations required by Fluent so as not to generate a negative mesh, which in itself is a limitation.

VI. Results for Full Three Section Span

The initial results showed that the method itself worked. However the displacement of the actual wing was not as great as expected. This was based on the observed deflection of Helios wing in photographs on NASA’s website [45]. Therefore the CSD model was reassessed. It was discovered that the CSD model was too heavy when


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compared to the data provided by NASA. Thus the material property of the skin was changed and structured was slimmed down. For the new material properties see Table 2. Also the model was extended to the full three section original aspect ratio of approximately 31:1, see Fig 10. The CFD mesh was 174x28x89, which means that the overall number of nodes was the same for both cases. Therefore the time to run the Delaunay map and write the new mesh file is nearly the same as for the two section model. The test condition is altered to sea level to match that of Patil and Hodges [25] and Su and Cesnik [26], who ran their cases at 12.2m/s. Also a pod weight of 22.7kg was applied as point load on the wing. The load CSD model with the point load can be seen in Fig 11.

Figure 10. Three section HALE wing with 10o dihedral angle CFD mesh

Figure 11. CSD model of three section HALE wing with point load

Density (kg/m3) Young's Modulus 0o (Gpa) Poisson's ratio Applications

Carbon fibre (Kevlar UD) 1600 135 0.3 Beam section 1Carbon fibre (std CF UD) 1400 75 0.34 Beam sections 2&3, support sparwhite styrofoam 36 0.00532 0.28 Styrofoam nose piecesMylar 1390 4.89 0.3 Skin

Table 2. Revised material properties

The overall mass of the wing, with a pod load is now 329kg. The number of DOF for the model had been reduced to 305861. One CSD calculation took around 7minutes to solve. The angle of attack required to generate enough lift force for this test is 4 degrees.


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Initially the wing was nearly 50kg lighter. However the wing experienced too much deformation due to the structure not being rigid enough. The wing was going to a near vertical position. Therefore the wing was strengthened and extra inner spar support was inserted into the tubular spars on section 1 and 2. The extra spar support at the root of the wing, 1.6m in length can be seen in Fig 12(a). With this support in place the location of the maximum stress was offset from the root of the wing. A spar support is located at 46% along beam 1, and is also 1.6m long. The final support is between sections 1 and 2 and is 1.16m in length. Extra tubing had also been used to strengthen the connection between the wing sections as described in [1]. Also the material used for the beam in section 1 was changed as per described in Table 2. All of the ribs now were all of the same design. The placement of the extra tubing was determined from the peak stresses occurring in the beam. One point that should be emphasised here from this initial test was the performance of the Delaunay graph. During one of the FSI loops the wing displaced by over 15m, and yet a good quality deformed mesh was still generated. This meant that a single Delaunay graph could be used for very large displacements. This in turn could reduce the amount of total computation time by around 6.5%.

Support spar

Figure 12. (a) Support spar at root of wing (b) Support spar and beam 1 at root of wing

With the new structure in place the FSI process was rerun. This time around the deflection was considerably larger than the initial test. The deflection of wing was just over 9m as compared to just under 0.7m from the initial test. See Fig 13. When the change in displacement was less than the convergence criteria the simulation exited. The wing was assumed to be in equilibrium when the change differed by less than 0.15% of the total span. When the simulation exited a manual check was performed to ensure the wing was in equilibrium. This involved running the CFD simulation to convergence and applying those aerodynamic pressure forces to the CSD model. See Fig 14. If the change in the CSD model deflection was, after this test, greater than the convergence criteria the FSI simulation was restarted.

Overall Displacement of 3 Section HALE Wing at Sea Level for an AOA of 4o with pod load

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0 1 2 3 4 5 6 7 8 9 10FSI Loop Number

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Figure 13. Global displacement of the wing Figure 14. Convergence history of the FSI simulation

In this case after the CFD solution had been run to convergence the wing displaced was still less than the convergence criteria. Hence an equilibrium position was assumed. The peak stresses of the wing were taken by the main beams and support spars. The peak stresses in the skin also had to remain lower than the yield stress; as if the skin was to rib the aerodynamics of the wing would be compromised. These peak stresses on the beams and skin can be seen in Fig 15. Just to reiterate the ribs and nose shaped foam were there predominately to maintain the profile of the aerofoil.


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Peak Stresses on Key Parts of the 3 section HALE Wing

5.00E+06

5.50E+07

1.05E+08

1.55E+08

2.05E+08

1 2 3 4 5 6 7 8 9 10FSI Loop Number

Von

Mis

es S

tres

s (P

a)

maximum stress on beam

maximum stress on skin

Figure 15. Maximum stresses on the beam and skin The stresses acting on the beam and skin from the converged solution can be viewed in Fig 16(a) and (b). The pressure coefficient from the converged solution can be viewed in Fig 16(c). The pressure coefficients for the complete FSI process can be viewed in Fig 16(d).

Figure 16 (a) Maximum stress on beam and supports (b) Maximum stress on skin

Figure 16 (c) Cp contours from converged solution (d) Cp contours for deforming wing


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Figure 17 Wing tip twist The final wing position experienced a tip twist of 2.3 degrees. The tip also bends backwards in the positive x direction by 0.306m. This can be seen in Fig 17, where the y-displacement (due to upward bending) is removed to compare. The overall time to do one complete FSI loop took around 1hour 40mins to complete. The final lift and drag force from the converged solution of the HALE wing are 3645N and 133N respectively, giving a lift drag ratio of 27.4. This lift provides the support to the total flying wing weight including the wing structure.

VII. Discussion of Three Section Model Without the exact structural detailed data of the wing, and flight data the comparison here was always going to be qualitative. Good visual comparison of the final displaced wing and that of the Helios HP03 in flight [45] does look encouraging though. The final wing position experienced a rotation at the tip of 2.3 degrees and was offset in the positive x-direction by 0.306m. Figure 16(a) and (b) show the stress acting on the key parts of the wing. The main beams and support spars have to be able to withstand the large stresses generated as a result of the large deflections. In this simulation the beams structural integrity was maintained. The performance of the skin is also equally important. As any failure with in it would drastically alter the airflow around the wing that could lead to a degraded performance of the wing. This ultimately could cause the wing to stall and crash. As can be seen from Fig 16(a) and (b) the peak stresses occur at different locations. For the beam the maximum stress occurs at the root of the beam where the first support spar ends, see Fig 12(a). However as can be seen from Fig 16(d) the wing deforms more rapidly about section 2. This is reflected in the maximum stress on the skin in Fig 16(b).

VIII. Conclusion A methodology for coupling commercial CFD and CSD packages and a moving mesh method using Tcl scripting has been developed for fluid structure interaction problems. Fully converged FSI simulations have been achieved for a HALE wing resembling the Helios HP03 wing. Whilst it is not known if the displacement and forces generated represent the actual flight condition well, the method used to obtain the results has been shown to be robust. What has been shown is the ability of the Delaunay mapping method to cope with large deflections. This method also has the advantage of maintaining the mesh topology, which in turn allows for the recommencement of the CFD solution from the previously saved data set. The deflection obtained is affected by the applied structural materials. Altering these will of course alter the deflection of the wing. By combining a high-order CSD model allows for the examination of, what could be an actual large displacement structure in flight. This would be a qualitative comparison with those shown for the real aircraft in flight. Quantitative comparison is desirable but requires further detailed data on wing structural layout, flight conditions, and wing deformation.


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