Aeroelastic analysis of a single element composite wing in ground effect using Fluid Structure Interaction


 The present work focuses on an advanced coupling of computational fluid dynamics (CFD) and structural analysis (FEA) on the aeroelastic behaviour of a single element inverted composite wing with the novelty of including the ground effect. The front wing of the Formula One (F1) car can become flexible under the fluid loading due to elastic characteristics of composite materials, resulting in changing the flow field and eventually altering overall aerodynamics. The purpose of this study is to setup an accurate fluid-structure interaction (FSI) modelling framework and to assess the influence of elastic behaviour of the wing in ground effect on the aerodynamic and structural performance. Different turbulence models are studied to better capture the changes of the flow field and variation of ride heights are considered to investigate the influence of ground effect on aerodynamic phenomena. A steady-state two-way coupling method is exploited to run the FSI numerical simulations using ANSYS, which enables simultaneous calculation by coupling CFD with FEA. The effect of various composite structures on the wing performance is extensively studied concerning structure configuration, ply orientation and core materials. The numerical results generally represent good agreement with the experimental data, however, discrepancy, especially in the aerodynamic force, is presented. This may be consequence of less effective angle of attack due to the wing deflection and deterioration of vortex-induced effect. For the structural analysis, the woven structure gives rise to more stable structural deflection than the unidirectional structure despite the associated weight penalty.


INTRODUCTION
Among aerodynamic components to affect performance of Formula One (F1) racing cars, the front wing operated in ground proximity contributes approximately 30% of total downforce [1], which is used in line with mechanical grip to improve acceleration, braking, and cornering speed. In addition to the front wing's aero performance, the wing, as the first component directly interacting with fresh airflow, plays an important role in controlling the airflow which interacts with downstream features such as undertray or rear wing, thus ensuring they contain high-energy flow with low turbulence intensities. Figure 1 shows a typical Formula One car with an inverted front wing.

Figure 1 A Formula One car with an inverted front wing [2]
During the 2011 Australian Grand Prix it was apparent that, Red Bull RB6's flexi-wing design enabled the tips of the front wing to bend far closer to the ground compared to those of their rivals [3]. Observation showed that the wing was deflected under fluid loading with the resultant of aerodynamic benefits. Although the relevant technical regulation stipulated that aerodynamic components, including the front wing, should be regarded as rigid bodies and must comply with the load and deflection test, F1 engineers exploited the phenomenon of 'Aero Elasticity' to improve the aerodynamic performance. In essence they circumvented the regulation governing the bodywork of the F1 car, mainly its wings, to facilitate flexing, which alters the flow characteristics and the shape of vortex structure, lowering the ground clearance.
Many studies have been conducted to investigate the inverted wing aerodynamics in ground effect by means of experimentation and computation. The first computational investigation into this was started by Katz [4][5][6] in which a single-element wing in ground effect was modelled and investigated using a panel method. As a consequence of a lack of viscous effect in his study, downforce reduction was not represented at low ride height. A single element GA(W)-1 wing was investigated at various ride heights from out of the ground effect up to ground proximity experimentally and computationally [7]. It was observed that the downforce increased as the ground was approached. However, when comparing this with numerical results gained using a twodimensional panel method, there was a huge discrepancy of force measurement at lower heights. Ranzenbach and Barlow [8][9][10][11] presented experimental results of twodimensional aerofoils in ground effect in a fixed ground wind tunnel in comparison with computation results using a Reynolds-Averaged Navier-Stokes (RANS) solver. A single element aerofoil was tested at different ride heights with a fixed angle of attack. It was found that the downforce sharply dropped below ground clearance of 0.1c. This was defined as the force reduction phenomenon due to merging of the wing and ground boundary layers. The computational solution presented this phenomenon as well.
However, the results obtained from a moving ground wind tunnel produced a greater magnitude of downforce and higher ride height at which the force reduction phenomenon occurs. An extensive investigation into wing in ground effect was performed in a moving ground wind tunnel by Zerihan and Zhang [12][13][14][15]. This faciliteated further investigation of the ground effect. Their experiments showed the results of surface pressure, overall forces and wake flow using laser Doppler anemometry (LDA) and particle image velocimetry (PIV) methods. The computation results were produced using a RANS solver modelled by the Spalart-Allmaras model [16] and the k-ω SST model [17], and showed good qualitive trends for the aerodynamic performance regarding surface pressures and wake thickness when compared with the experimental data [15]. In another study, Lawson et al. [18] carried out a computational study of a GA(W)-1 aerofoil in ground effect using RANS equations modelled by the Spalart-Allmaras model [16]. Comparing the numerical results with the experimental data obtained by PIV method, significant discrepancy was observed due to the application of different freestream velocities in each study. The pressure and wake of an inverted cambered aerofoil in ground effect was numerically investigated by Mahon and Zhang [19] by solving RANS equations. The simulations were found to offer reasonable trends of flow field regarding surface pressure distribution, sectional forces, and wake profile at various ride heights in comparison with the experimental data. Recently, numerical studies on the wing performance were carried out. Arrondeau and Rana [20] performed computational analysis on a multi-element wing with implementation of the humpback whale flipper to improve the aerodynamic efficiency. Castro and Rana [21] also investigated the multi-element wing performance in terms of structural configuration modelled with different materials. In both studies, the wing was considered as a rigid body and elasticity was not taken into account. Although the inverted wing in ground effect has been thoroughly investigated experimentally and computationally. These studies are restricted to the flow characteristics such as forces, surface pressure and wake flow. Additionally, to the best of our knowledge, the numerical simulations are performed assuming the wing to be a rigid body. This is problematic as it is not how the wing works in reality.
Due to the fact that the aero-structural interaction is too complicated to obtain, analytical equations and experiments are limited in scope owing to its strong nonlinearity and multidisciplinary nature, a numerical approach known as fluid-structure interaction (FSI) may be employed. In addition, with recent advances in computer technology, an efficient numerical algorithm can be exploited to resolve sophisticated FSI engineering problems. The computational solution using FSI analysis plays an important role in many scientific and engineering sectors such as aerospace, wind engineering, automotive, and hydrodynamics. In aerospace engineering, aeroelasticity is one of the key factors to be considered in design process to avoid aeroelastic problems such as divergence or flutter [22][23][24]. Accurate FSI modelling of wind turbine blades is crucial in the development of large wind turbines which are more susceptible to aeroelastic response [25][26][27]. Large blades under aerodynamic loading can cause additional vibration that could result in unbalanced load alteration and instability problems so that ultimately it could have a significant impact on the whole wind turbine system.
In the automotive sector, research has been undertaken related to aeroelastic behaviour of car components. Gayland et al. [28] simulated the interaction of transient flow fields with the structure of a vehicle hood using a one-way coupling, continuing the development of a methodology that can be utilised early in the design phase of a vehicle to capture and resolve potential panel vibration issues. Ratzel and Dias [29] studied a generic car model with a flexible/deformable flap at the rear end using a coupled transient FSI simulation. Several shape variations of the flap causing reduction in the maximum deflection are identified and used in an optimisation loop to determine a flap design with minimum displacement. Similarly, Patil et al. [30] used a two-way weakly coupled method to simulate an FSI model of a chin spoiler around the airflow. The local and global flow field changes due to the interaction between them and its effect on vehicle drag was discussed. The numerical results were validated by experiments carried out in a wind tunnel. Andreassi et al. [31] presented an example of FSI approach in the study of a Formula One car front wing with different speed and angle of attack.
However, the ground effect was not applied as the bottom was stationary. One of the recent works published regarding FSI analysis in automotive application is to investigate hydroplaning phenomenon between a tyre and water road surfaces by incorporating finite element methods and Navier-Stokes equations [32]. It was found that a FSI model combined with two commercial packages shows better agreement with empirical model despite more computational resources.
Several studies used the FSI approach to investigate performance of a hydrofoil used for hydraulic machinery system [33,34]. It was demonstrated that the FSI model connected with two-way coupling method is proved to be appropriate for accurately predicting the effect of added mass and hydrodynamic damping ratio on its performance. Furthermore, Smith et al [35] studied the cavitation behaviour of the flow field caused by the effect of FSI and Dincer et al [36] suggested a new FSI monolithic approach to solve fluid-structure coupled problems simultaneously.
Evidence suggests that in racing application, investigation into the inverted wing in ground effect has been extensively studied experimentally and computationally due to its substantial benefit to performance. However, it seems that there have been few comparative studies carried out to predict accurate inverted wing performance considering aeroelastic response using advanced computational methodology. This work aims to investigate the influence of aeroelastic behaviour of a single element inverted wing including the ground effect on the aerodynamic performance using a two-way coupled FSI method by joining of CFD with FEA solutions. Computational analysis on the FSI inverted wing is performed to indicate the flow characteristics in terms of surface pressure distribution, aerodynamic forces, and wake profile. A number of ride heights are studied describing variation of the force regions. In addition to the aerodynamic performance analysis, the effect of structural characteristics with various combination of composite structure on the performance is also studied.

Numerical modelling framework
Fluid-structure interaction (FSI) is defined as the mutual interaction between a deformable structure and an internal or surrounding fluid flow [37]. The fundamental consideration when developing a numerical simulation algorithm is the choice of appropriate governing equations of the continuum, which determines relationship between the deforming structure and fluid domain and ability of numerical method to deal with large distortions [38]. Based on the design type of scientific and engineering systems where fluid-structure interaction is concerned, different approaches of numerical procedure may be employed. One of possible methods to solve these multiphysics problems may be categorized into two approaches: the monolithic approach and the partitioned approach. The monolithic approach containing governing equations for the fluid and structure dynamics within a single mathematical framework is solved simultaneously with a solitary solver [39,40]. This approach can produce better accuracy for multidisciplinary problems; however, it may require significant effort to develop a code for a particular combination of such problems. On the contrary, the partitioned approach including governing equations of the fluid and structure dynamics is solved separately with two individual solvers [41]. This approach enables to reduce time for code development by integrating existing available codes or numerical algorithms, which have been proved and used for sophisticated FSI problems. The focus, however, should lie in correlating the fluid and structure algorithms in order to achieve stability of the coupling method. As shown in [38], the coupled FSI model can be represented by Eq. The fluid exerts pressure loads on the structure, causing it to deform, at the same time, the fluid geometric domain is updated considering the structural deformations. In the partitioned approach, the information gained from each numerical algorithm is shared at the boundary between them, the fluid structure interface, which is dependent on one-way or two-way coupling methods as shown in Figure 2. In one-way coupling, the calculated fluid forces from CFD analysis is transferred to the structure analysis as the boundary condition and the structure side is calculated until the convergence is reached as shown in Figure 2 (a). After that, the FEA analysis is performed to calculate the structural responses of the wing such as deformation and stress distributions subjected to aerodynamic loads, followed by it will be interpolated to the fluid mesh accordingly. This is regarded as one inner loop of the simulation and these steps are repeated until the changes in the flow forces and the structural displacements fall below a prescribed level of tolerance as shown in Figure 2 (b). In this study, the FSI problem of the inverted wing in ground effect is solved with a two-way coupling partitioned method provided by the ANSYS software as the workflow described in Figure 3, which presents a single iteration of the fluid-structure coupled process. The iterative procedure is repeated for several time step until the desired simulation time is reached.

Geometry and mesh generation
The single element inverted wing used in this study is extracted from Zerihan's experiment [12]. A span and a chord are 1100mm and 223.4mm respectively. The cross section of the wing is a derivative of type LS (1)-0413 MOD shown in Figure 4 (a) and the details can be found in his study. The incidence of the wing is set at 3.45° and the height is defined by the vertical distance from the ground to the lowest point on the suction surface of the wing. To save computational resources, the half of the wing model is used for this study.
The computational grid is generated using ICEM CFD in ANSYS as presented in Figure 4 (b). A multiblock hybrid mesh is implemented containing both structured and unstructured grids and the relative grid topology and structure is maintained at various  (2) and set as y+ ≈ 1. (2) Where y is the distance to the wall, is friction velocity, and is the kinematic Naiver-Stokes equations. Upwind discretisation scheme is used for all cases, which are satisfied with second-order accuracy. The coupled pressure-velocity coupling algorithm is applied, which is considered compatible with coupling application including the structural analysis. Six turbulence models investigated with appropriate wall treatments and corresponding variants. The six turbulence models were used; the one equation Spalart-Allmaras model [16], the standard k-ε model [42], the standard k-ω model [43], the k-ω SST model [17], the k-ε RNG model [44], and the Realizable k-ε model [45].
Enhanced Wall Treatments are applied on all k-ε model variants.

Figure 5 A schematic of computational domain
As shown in Figure

Structural model
In order to investigate the deflection of the inverted wing under aerodynamic loading, the wing is modelled with layered composite structure in ANSYS Composite PrepPost (ACP). The material used is Epoxy Carbon UD (230GPa) Prepreg provided by ANSYS Engineering Data Library, characterised by the mechanical properties shown in Table 1.
ANSYS Mechanical is used to carry out the structural analysis using the finite element technique.

Grid sensitivity analysis
First of all, the grid convergence study is conducted in order to make sure that the numerical uncertainty generated by computation solution is within asymptotic range of convergence. The Grid Convergence Index (GCI) suggested by Roache [46][47][48] is used to provide consistent and reliable results of the grid convergence. The Table 2 indicates the grid information with three different mesh grids and the resulting drag coefficients computed from the solutions. Each solution is properly converged with respect to iterations. Using 16 cores of the high computing system power, the computational time for each mesh is as follows: 1.44 hours for the coarse mesh, 3.68 hours for the medium mesh and 8.56 hours for the fine mesh.
Effective grid refinement ratio is calculated using total number of grid points (N) and dimension of the fluid domain. The order of grid convergence, P, is 1.64. The GCI values for the drag coefficient are 0.27% and 0.85% for the coarse-medium and medium-fine grid respectively. The GCI ratio is 1.005 which means that the solutions are in the asymptotic range of convergence. Therefore, based on the GCI study, it can be shown that discretisation error is improved with the grid refinement. In addition to the GCI study, the effect of grid sensitivity on the surface pressure distribution and wake survey at x/c = 1.2 is shown in Figure 6. There is little difference in the surface pressure distribution, but the coarse grid does not capture enough velocity deficit in the wake survey. In this study, as efficiency of computational resources is taken into consideration, the medium grid is eventually selected for all cases. Moreover, as the grid convergence of the fluid domain is investigated, mesh sensitivity study for structural analysis is also carried out. However, it is realised that the number of cells composed of surface mesh is too small to have an influence on performance of the wing compared to that of fluid domain in case of interaction between fluid and structure dynamics. Therefore, coarse mesh is selected for the structure modelling.  The maximum suction appears at a point called suction peak. Table 3 presents detailed information about the pressure coefficient at suction peak and its location gained by each turbulence model and compares FSI results with experimental data and 2D aerofoil numerical data. The suction peak and its location are better predicted by the CFD-FEA coupled model as large discrepancy is observed with the 2D CFD results due to lack of dimensionality.   Figure 7 (d), however there is no experimental wake data at this height. It is speculated that the trend between the turbulence models is analogous to those at higher ride height.

Chordwise Surface pressures
The effect of various ride heights concerning the surface pressure distribution is investigated in comparison with the experimental pressures [12]. The chordwise surface pressures at the centre of the wing are presented in Figure 8 for It is expected that a greater suction peak would be gained by the FSI computational simulation compared to the experimental data. It is caused by the fact that this numerical approach is capable of describing dynamics of the wing characteristics in terms of deflection, enhancing the pressure difference due to greater flow acceleration caused by the ground effect when the wing is approached to the ground. However, at the same time, the wing is twisted when deformed, so that the increase in suction pressure loading could be cancelled out by decrease in the effective incidence due to the wing being backed off. Therefore, it is speculated that the FSI analysis show similar level of suction peak compared to the experiments.

Spanwise surface pressures
Spanwise surface pressures at the quarter-chord location are investigated with regard to various ride heights using different turbulence models and compared between experimental and computational results shown in Figure 10, which highlights the threedimensionality of the flow. Little variation of the pressure value on the pressure surface is observed as the ground height is reduced, whereas the suction loading on the suction surface increases as the ground is approached. It is found that greater amount of pressures is generated across the wingspan by the FSI simulation at h/c = 0.313 for all turbulence models, which means increase in downforce. It can be due to the stronger ground effect as the wing is temporarily deflected with increase in ground proximity. On the other hand, when the wing is lowered closer to the ground, h/c = 0.134, the computational pressures are underpredicted than the experimental pressures over the whole range of the wingspan for both turbulence models. In addition, the magnitude of this discrepancy is observed larger for the k-ω SST model. Flow separation phenomena appeared with constant pressure region near the trailing edge is not captured at the quarter-chord location as contrasted with the one shown in Figure 9 (b). It is caused by the fact that the separation point does not move this far forwards.
In this section, it can be discussed that lack of the surface pressures on the suction side across the wingspan at the lower ride height is observed with the FSI modelling.
First, the effect of force reduction in ground effect becomes stronger. According to Zerihan and Zhang [12], as the ground height is decreased, the downforce is increased accordingly due to the ground effect. However, below a certain height, the slope of the downforce starts to be levelled off and then falls off after reaching the maximum value, which is called force reduction region. Then, as the ground proximity between the wing and the ground is increased further, the loss of downforce becomes greater. With the wing deformed in accordance with elastic characteristic of composite structure, the influence of the force reduction region on wing performance becomes severe, resulting in more loss of loadings as we can see less surface pressure in Figure 10 (a). Secondly, it can be attributed to the reduction of effective incidence at the wing tip due to the wing tip vortex. The airflow around the wing tip is operated at a relatively lower effective incidence due to the upwash caused by the tip vortex effect. The wing is deflected and twisted on account of structural elasticity of the composite materials, which results in amplifying the effect. Figure 11 shows the effect of non-dimensional ground heights on the downforce is quantified. The calculated downforce with different turbulence models is compared with the values measured experimentally [12]. In general, in accordance with the experimental results, as the wing is approached closer to the ground across large and moderate heights, the gradient of downforce is increased. As the ride height is further Similarly, the influence of various ride heights on the aerodynamic drag is shown in Figure 12. As the distance between the wing and ground is reduced, the downforce increases until the maximum value is achieved. This causes the induced drag of the wing and as a result the drag increases with decreasing the ride heights for moderate and large heights. However, at a range of ground heights, the drag continues to increase until it reaches a maximum whereas the downforce decreases after the peak point. It is speculated that the drag increase at small ride heights can be attributed to other reasons as the induced drag caused by the downforce is not enhanced within the force reduction region. The numerical analysis using the different turbulence models observes a similar trend of the increase in drag force as the experimentation does. However, the discrepancy between experimental and computational results is also presented and the magnitude of the gap is decreased with increased ground proximity.

Aerodynamic forces
The drag gained from the numerical simulation increases for all ride heights in a similar manner to the experiments. However, the gap between experimental and computational results is observed and its magnitude is decreased as the ride height is lowered. At large and moderate ground heights, larger drag is generated by the computational solution due to greater amount of induced drag caused by enhancing the downforce due to the wing deflection. At the small heights, it is speculated that the increase in drag is not much affected by the wing deformation due to weakened vortex strength but caused by the separation at the trailing edge and vortex dilution in a similar manner to the experiment. is also changed with the ground height variation. As the distance between the wing and the ground is reduced, the downforce is increased due to the flow acceleration.
Accordingly, the adverse pressure gradient is increased, which results in increasing the boundary layer thickness. When observing the wake profile at the h/c = 0.448 and at h/c = 0.09, the size of the velocity deficit is considerably increased as the ground height is lowered. In comparison with the experimental result, computational analysis presents velocity profile with slightly higher speed between the wing and the ground, which can be attributed to increasing flow acceleration caused by the wing deflection. The larger size of the velocity deficit region is observed with the FSI simulation It is believed that it may be wing deformation to deteriorate the vortex-induced effect and to develop the effect of adverse pressure gradient, which could cause larger separation.   [51] and the structure of the composite wing is created by the ANSYS Composite Prepreg. Table 6 presents a variety of composite structures in terms of different manufacturing structure (uni-directional and woven), ply orientation, and different core materials. The effects of the composite structure characteristics on the wing deflection and maximum stress are presented in the Figure 15 and additionally aerodynamic performance and weight results are shown in Table 6. The conclusion can be drawn as follows.
Comparing the UD cases with woven fabric cases, for example case 1 and 2, the wing constructed with UD structure shows more deflection of 19.2 mm and twice larger max stress shown in Figure 15, which means that the woven laminate structure has higher stiffness leading to less aeroelastic effect. Table 7 presents that the woven structured wing generates higher downforce and drag compared with the UD composite; however, difference of aerodynamic efficiency between two structures is marginal. It is concluded that, despite weight penalty, the woven structure can achieve better aerodynamic performance to avoid greater disturbance of flow field around the wing caused by larger deformation, maintaining good structural stability.
The composites structures are composed of changing ply orientations to evaluate its influence on the aerodynamic and structural performance, for example case 2 and 3 shown in Table 5. The results show that little increase in max deflection and max stress is achieved using the set [0/45] for the pile orientation shown in Figure 15 and it is speculated that the cross-ply orientation has little influence on the structural performance when most of the aerodynamic force applied on the wing is perpendicularly exerted. Along the same line, Table 6 presents that no significant changes are observed for the aerodynamic forces and efficiency by changing a sequential cross-ply orientation.
For designing the composite wing, core material can be often utilised in order to take structural advantages such as total weight reduction and strengthened mechanical characteristics. In this study, two core materials widely used in motorsport industry are evaluated, which are nomex honeycomb and aluminum honeycomb. First, by comparing cases between nomex and aluminum, decrease in max deflection and max stress is observed using the wing with aluminum honeycomb (case 7,8 and 9). However, the results describe that there is slight increase in total wing weight for the aluminum cases, followed by analogous level of aerodynamic performance. In comparison with the no core wing situation (cases 1, 2 and 3), significant weight reduction by 15% for UD and 22 % for woven fabric is achieved for utilising the aluminum structure replacing a couple of layer of CFRP, despite no substantial changes in aerodynamic performance and max stress. Likewise, it is shown that the nomex core results in similar consequences as the aluminum cases, obtaining substantial reductions in weight by 20% for UD and 24% for woven fabric. In summary, it is concluded that the core material could provide structural advantages of mechanical characteristics under the same amount of fluid loading as the no core structure, keeping the equivalent level of aerodynamic performance and weight benefit.   FSI numerical solution generated greater amount of suction pressure on the suction surface at the moderate height due to enhanced ground effect compared to the experiment. Conversely, the computational pressures were underpredicted at the lower height. It was speculated due to significant effect of force reduction region caused by the wing deflection and reduction of effective incidence at the wing tip.
Aerodynamic forces with a range of various ground heights were studied using FSI model. It was observed that the numerical method generated less downforce compared to the experiment, which may be caused by reduced effective angle of attack due to the wing deflection and deterioration of vortex-induced effect. In addition, greater increase  Chordwise surface pressures at wing centre and wing tip in ground effect generated by k-ω SST model (a) h/c=0.313 (b) h/c=0.134 Fig. 10 Spanwise surface pressures in ground effect for different ride heights (a) k-ω SST (b) Realizable k-ε Fig. 11 Downforce of single element wing in ground effect with various heights  Result of deflection and mas stress of single element composite wing with various composite structure Table Caption List   Table 1 Mechanical properties Table 2 Summary of GCI study Table 3 Surface pressure information for various turbulence models, h/c = 0.224 Table 4 Wake information for various turbulence models at x/c = 1.2 for h/c = 0.224 Table 5 Wake information for various ride heights at x/c = 1.2 Table 6 Variation of composite structure for single element wing Table 7 Results of aerodynamic performance and weights with various composite structure