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Steady Aeroelastic Response Prediction and Validation for Automobile Hoods.


Automobile hood design is complicated by many weight reduction efforts and often competing factors such as: pedestrian/crash safety, weight, durability, styling, aerodynamics, manufacturability, and cost. One important design feature is hood compliance, which must be appropriately balanced to meet the above objectives. However, the impact of hood compliance is not easily handled in the early stages of design due to: (1) the potential for aeroelastic interactions; (2) tight margins on allowable hood deflection, (3) the high cost of prototyping and experimentation, and (4) the fact that sub-discipline modeling errors tend to aggregate in coupled systems. The second and fourth issues indicate that a high level of model detail may be needed, while the third issue indicates that computational capabilities are critical. Thus, the development and assessment of aeroelastic prediction tools, and considerations for their application and validation, are important areas of study.

Previous studies published on the general problem of automobile aeroelasticity are limited. One study focused on aeroelastic tailoring of an Indy car rear spoiler to reduce drag at high speeds and maximize downforce at low speeds [1]. The analysis was carried out by coupling the Computational Fluid Dynamics (CFD) software ANSYS Fluent and Finite Element Method (FEM) software MSC Nastran to solve the static structural response. The optimized spoiler obtained a 3% reduction in wing drag while maintaining the same downforce during cornering maneuvers. Consequently, the vehicle top speed was projected to improve by 1 kilometer per hour (kph). Another study investigated the increase in drag due to a deformed chin spoiler [2]. STAR-CCM+ was used to carry out the coupled analysis for both domains. The chin spoiler deflection was predicted to increase the drag coefficient by 0.004, corresponding to a 0.15 mile per gallon decrease at 80 kph. The simulation results showed reasonable agreement with test data. Gupta et al. [3] and Gaylard et al. [4] used an uncoupled approach to assess hood vibrations due to wake shedding of an upstream vehicle. Time-dependent pressure distributions on the trailing vehicle hood were predicted using the CFD software PowerFLOW. Subsequently, these pressure distributions were prescribed on an FEM model constructed with MSC Nastran. In some cases the wake shedding produced pressure fluctuations with frequency spectra near the free vibration modes of the hood structure, naturally leading to relatively large vibratory response. No validation effort was conducted in either study. In [5], the steady aeroelastic response of a Jaguar XK8 convertible car roof was predicted by coupling of the CFD software STAR-CD to a third-party FEM solver. The coupled results were within 20% of the uncoupled response. No comparison to test data was given. Ramsay et al. [6] predicted the static deflection of an automobile hood in an uncoupled manner using unspecified CFD and FEM solvers. The model did not include internal flow; however, pressure inlet/outlet boundary conditions were used on the front fascia openings to model the resistance provided by the engine compartment. Results indicated less than a 10% difference between the prediction and experimental results for displacement measured at two locations. Also, it was discovered that the externally mounted displacement measurement devices exhibited flow induced vibrations, leading to noisy data.

This study is motivated by the need for a better understanding on aeroelastic interactions of automobiles, and specifically aeroelastic simulation of the hood. The goal is to assess the degree of aeroelastic coupling in a typical automotive hood, the importance of engine compartment flow, and also model validation. This is carried out through systematic development of coupled CFD-FEM for simulation of the aeroelastic response of an automobile hood, and validated by comparison with experimental data for hood surface pressures and deflections. Successful understanding of the steady-state solution will also enable confidence in pursuing unsteady aeroelastic predictions of automobile hoods.

Experimental Setup

Experimental results for this study were obtained in a single return closed test section wind tunnel with a maximum wind speed of 320 kph. The dimensions of the test section are given in Table 1. The tunnel is equipped with floor blowing, a feature where a slot in the floor at the inlet of the test section inserts air at the equivalent dynamic pressure of the mean flow to eliminate the boundary layer. Floor blowing simulates an on-road aerodynamic environment and was used in the experiment.

Transverse hood displacement and surface pressure measurements were recorded on a full-scale vehicle at 100, 160, and 200 kph. Displacement was recorded at three locations specified in Figure 1. Externally mounted lasers were used to measure the hood displacement, with an accuracy to within 5 microns. The lasers at Points 1 and 2 were placed in an airfoil-type enclosure to mitigate disturbances in the flow, and mounted on the fenders of the vehicle as shown in Figure 2. The laser at Point 3 was suctioned to the windshield and held by a rigid fixture as shown in Figure 3.

Surface pressure was measured on five strips of probes as shown in Figure 4. Strips 2-5 consisted of 20 probes, while strip 1 consisted of 18. In addition, a pitot-static tube was affixed to the right mirror to record a reference pressure in the flow, as shown in Figure 5. The displacement and pressure data were taken separately so that the presence of the lasers would not affect the surface pressure measurements.

Modeling Description

Fluid Model

Vehicle Configurations Three separate configurations of a production vehicle were considered for the present study. The first configuration resembled an initial design model or "styling" model. This configuration, shown in Figure 6, neglected the internal flow through the front fascia and had a simplified underbody and wheels. This vehicle geometry is denoted as V1. The second configuration was a "complete" vehicle model, which included all under-hood and underbody components shown in Figure 7. The radiator and condenser were modeled as porous media. This vehicle geometry is denoted as V2. Because of an inability to obtain a coupled CFD-FEM solution using the V2 model, a third configuration was considered using a simplified engine compartment and underbody as shown in Figure 8. As highlighted in Figure 9, the only under-hood components retained were the radiator, condenser, front bumper support, chin spoiler and under-hood structure. Furthermore, the powertrain and exhaust systems were completely removed from the underbody exposing the vehicle floor. This vehicle geometry is denoted as V3.

As indicated, aeroelastic computations were not achievable with V2. This was due to relatively poor grid quality around the complex internal geometries that yielded negative volumes during grid morphing. However, V2 provided the most accurate internal flow modeling for estimating underhood pressure. To properly account for the effects of underhood flow in the simplified models, the V2 model was used to provide a distributed pressure loading condition during aeroelastic simulations of V1 and V3.

Fluid Domain and Boundary Conditions The fluid domain was modeled by solving the Reynolds Averaged Navier-Stokes Equations using STAR-CCM+. The realizable two-layer k-epsilon turbulence model was used assuming incompressible flow conditions. The boundary conditions and dimensions of the domain are shown in Figures 10 and 11. The inlet and outlet boundaries were specified as a velocity inlet and mass flow outlet, respectively. A mass flow outlet specifies the percentage of mass that flows through the boundary face, which for this setup was 100 percent. Using this boundary condition over the more traditional pressure outlet allowed the specification of a reference gauge pressure at a single (x, y, z) location to anchor the solution. This was set to the average pressure measured by the probe positioned off the passenger mirror in the experimental study shown in Figure 5. Note that this value need not be freestream pressure. The top, bottom, and side walls were specified as a slip wall boundary condition, while the vehicle surface boundaries were set to no-slip walls. The cross section of the fluid domain was set to match the size of the wind tunnel facility so that the blockage ratios were identical. The inlet and outlet were extended four and eight vehicle lengths from the vehicle, respectively, so that the presence of these boundaries did not affect the flow solution.

Mesh Generation A grid of the outer domain was created for each vehicle configuration (V1, V2, V3) by surface wrapping to create a watertight geometry. Body cutlines were modeled for configurations V2 and V3 and ignored for V1. This implies that V2 and V3 consist of several watertight geometries where V1 is a single watertight geometry. This was then followed by surface and volume meshing. Each boundary on the vehicle had a surface size ranging from 2.5-10 millimeters (mm) depending on the geometric complexity and location of the part. The volume mesh was composed of two types of cells: prism layers and trimmed cells. Prism layers are the first cells off the wall used to capture the boundary layer. The first cell height was calculated so that the wall y+ values fell within the log-law range (30 < y+ < 300). Three rectangular zones were created to locally refine the mesh around the vehicle. The cell sizes of the zones, as shown in Figure 12, were 10, 20 and 40 mm. A nearfield top view of the floor and a planar slice (y = 0) in the streamwise direction are provided in Figures 12 and 13, respectively. Planar slices of the computational domain through the engine compartment for each vehicle configuration are shown in Figure 14. The under-hood region was captured within the 10 mm refinement zone, and the grid size was reduced closer to the vehicle surface to capture the boundary layer. The total cell count for each configuration is presented in Table 2.

Mesh convergence was analyzed at a freestream velocity of 200 kph. V2 was used to confirm mesh convergence since it contained the most complexity. The integrated lift force of the hood was used to determine convergence where percent error was measured against the finest grid. Results of the study are summarized in Table 3. The medium grid is considered converged with a percent error of 1.26% and was selected as the best balance between accuracy and modeling resources.

Structural Model

The structural model was solved using the commercial FEM software Abaqus Standard. The model consists of an assembly of several structural components and accounted for geometric nonlinearity Each component, material, mesh size and element type is listed in Table 4. The mesh size for each component was 4 mm. All materials were linear and modeled using shell elements. The structural assembly is shown in Figure 15. The frame is the load-bearing component of the hood structure and is attached to the skin by a mastic material; the latch and hinges are bolted to the frame and attach to the surrounding vehicle structure. In the structural model, the mastic interaction with the skin and the frame was solved as a contact problem using the penalty method. A depiction of the boundary conditions for the latch and hinges is shown in Figure 16; both were constrained in translation, but were free to rotate about any axis.

Coupling Procedure

STAR-CCM+ and Abaqus use a native co-simulation engine (CSE) to couple the domains. The CSE uses a loosely coupled partitioned approach where the fluid and structure are solved on separate solvers and coupled through an exchange of boundary conditions at the interface of the domains. The partitioned fluid-structure interaction (FSI) workflow is depicted in Figure 17. The fluid equations are initially solved to determine the static pressure. The resulting fluid load is then mapped onto the FEM mesh. The structural equations are solved, and the resulting displacement field is mapped to the CFD mesh. The CFD mesh is morphed according to the computed displacement field, and the process is repeated. In this study, the process was iterated until the steady aeroelastic response was achieved, where convergence was defined by a change of less than 0.001 mm between successive time steps of the displacement at the measurement locations. Despite the fact that the problem considered is steady-state in nature, the CSE is implemented by STAR-CCM+ in time-accurate mode. Thus the steady-state aeroelastic response was computed using a time step of 0.1 s. Convergence to the steady-state solution was accelerated by implementing critical Rayleigh damping. The steady-state flow solution of the rigid vehicle was used as the initial condition to the coupled simulation.

As noted earlier, one of the challenging aspects of aeroelastic simulation is morphing the CFD grid to accommodate structural deformation. This is a challenge for complex topologies with associated poor cell quality, as well as two structures in close proximity to each other, both of which are susceptible to the appearance of negative volumes during mesh deformation. For this work, the engine compartment mesh for configuration V2 experienced negative volumes during aeroelastic simulation. Furthermore, the hood skin and frame were close in proximity, and morphing these boundaries simultaneously lead to the appearance of negative volumes. The mesh resolution required to morph both components simultaneously was impractical for simulation within the confines of the study duration; as a result, the coupling procedure described herein was only applied to configurations V1 and V3 with the hood skin as the lone boundary deformed.


Comparison between Numerical and Experimental Results

Experimental and numerical results were obtained for operating speeds of 100, 160, and 200 kph. Fluid properties in the simulation were specified to be consistent with that of the experiment. Configuration V3 was used to compute the FSI baseline prediction. The steady-state internal pressure distribution of V2 was mapped to the underside of the hood skin, and the top and bottom of the hood frame. The static pressure contours are shown in Figure 18, and indicate that the skin bottom and frame top essentially have constant, low-magnitude negative pressure distributions. The frame bottom is predominately negative, excluding positive pressure regions near the cowl top and engine cooling aperture (flow stagnation zones).

Comparisons of the hood surface pressure are shown in Figures 19-24. Pressure data along strips 1 and 4 are shown in each figure for the experimental values, FSI predicted values, and rigid hood prediction, at each speed. The CFD derived pressures from the FSI prediction and rigid hood cases are nearly identical, indicating that the pressure at the measured locations is not strongly sensitive to fluid-structural coupling. The simulation captures the overall trend of the experimental data, but consistently overshoots the pressure on the trailing edge. [L.sub.1] (mean absolute error) and [L.sub.[infinity]] norms for each velocity are provided in Table 5 using the data from all probe locations. The agreement between predictions and experiment decreases with increasing wind speed. Overall, the results indicate reasonable agreement between the experiment and prediction.

A potential source of error in the static pressure prediction is the shape of the fluid domain. The fluid model neglects the wind tunnel contraction and diffusion in which the effect on the hood pressures is unknown. Since the simulation successfully captures the overall trend, it appears the contraction and diffusion of the tunnel is insignificant. Another potential source of discrepancy is the pressure sensor strips, which are not modeled in the CAD representation. The sensors may cause turbulence particularly on the aft side of the hood where the turbulence model is unable to fully capture adverse gradient effects. The sensors were not modeled due to grid refinement requirements that would exceed available resources for the simulation. Another potential issue is the presence of flow separation and recirculation between the hood and windshield, which is not adequately captured with the current turbulence model with wall functions.

The hood deflection results of Points 1, 2, and 3 are provided in Figures 25-27. Post-analysis of the experimental results indicated deflection of the laser measurement devices at Points 1 and 2 due to aerodynamic force. Subsequently, bench testing of the laser assembly was used to correlate the aerodynamic loading at each tested wind speed to the laser deflection. The uncertainty bars on the experimental values, shown in Figures 25-27, account for the induced deflection of the laser assemblies. This was not observed to be an issue at Point 3, thus no error bars are included since the measurement uncertainty of the laser itself is smaller than the symbols in each figure. In general, the predicted displacements are reasonably close to within experimental uncertainty of the measured displacements. Furthermore, the maximum displacements are O (1 mm) or less, which is consistent with the pressure comparisons, suggesting that the chosen hood structure does not exhibit strong steady aeroelastic coupling.

A potential cause of discrepancy between the predictions and experimental measurements is the alteration of the local surface pressure due to the presence of the laser devices. This effect was examined by adding the laser devices to the CFD domain, as shown in Figure 28, and repeating the coupled analysis using V3 at 160 kph. As indicated in Figure 29, there are significant local changes in surface pressure near the measurement locations. However, as indicated by the results listed in Table 6, these local pressure changes have a negligible effect on the predicted displacement at Points 1 and 2, and a modest improvement on the predicted displacement at Point 3. This is likely due to the relative stiffness of the considered hood. Aeroelastic analysis of more flexible configurations may exhibit stronger sensitivity to these local pressure variations, making this an important consideration for future study.

The degree of fluid-structural coupling was further assessed by comparing the uncoupled and coupled structural response at 160 kph. V3 was used for the uncoupled analysis, and compared to the baseline coupled prediction discussed in Figures 19-27. The results of the comparison are shown in Figure 30 and Table 7. Consistent with the previous examination of hood pressure values, the difference between the coupled and uncoupled predictions is relatively small. This is indicative of a relatively stiff hood construction for the chosen vehicle. Furthermore, these results indicate an uncoupled analysis is adequate when predicted hood deflections are 1 mm or less.

Sensitivity to Internal Flow

The sensitivity of the aeroelastic response to the flow through the front fascia, as well as the resulting under-hood pressure, was examined numerically through the comparison of the V1, V2, and V3 simulations. The impact of flow through the front fascia on the aeroelastic prediction was assessed at 160 kph by comparing the V1 prediction, which had a closed front fascia, to that of the V3 model. In both cases, the internal engine compartment pressure computed using V2 was applied onto the FEM model as a distributed load. The effect of closing the front fascia on the exterior hood skin pressure is shown in Figure 31. The largest differences in pressure occur at regions near the front and trailing edges of the hood. A larger suction (higher magnitude negative pressure) is observed on the central front and fender regions of the hood in the V1 model. This is due to the closed apertures on the front fascia accelerating the flow over the hood. Conversely, the positive static pressure on the trailing edge of the V1 hood exceeds that seen in the V3 model. This is due to the presence of flow through the more detailed cowl region in the V3 model compared to the simplified representation used in the V1 model. These modeling differences are highlighted in Figure 32. The impact on the structural response is provided in Figure 33 and Table 8. There is a small difference at Points 1 and 2, while the displacement for Point 3 of V1 is nearly five times that of V3. However, the magnitude of displacement at Point 3 remains relatively small compared to the other locations.

The impact of neglecting under-hood pressure on the aeroelastic predictions was assessed using the V1 model by eliminating the mapped V2 engine compartment pressure within the FEM model. The resulting comparison is considered in Figure 34 and listed in Table 9. For the analyzed hood, removing the effect of under-hood pressure tends to increase the displacement overall. This is due to the suction force induced by the negative engine compartment pressure, which tends to resist positive hood displacement. Compared to the minor effects of front fascia openings and instrumentation flow disturbances, the inclusion of under-hood pressure has a significantly larger impact on hood displacement at the measured points, suggesting its importance in obtaining accurate predictions of hood deflection.


Aeroelastic simulation in automobile development and design is an important consideration as manufacturers vary component compliance to meet increasingly challenging, and sometimes conflicting, objectives. Critical to this challenge are the development of computational tools, as well as validation of these tools. This article examines this task in the context of the aeroelastic response of a representative automobile hood using both a coupled CFD-FEM fluid-structure interaction framework and experimental measurement. Overall agreement between the experiment and aeroelastic predictions is reasonable. Furthermore, compliance and flow modification from the displacement measurement devices are observed to complicate the validation process. Results also indicate that hood displacements predicted at or below 1 mm from an uncoupled analysis do not exhibit strong aeroelastic interactions. Finally, sensitivity studies indicate that internal flow through forward and rear boundaries, as well as engine compartment pressure, can have a modest impact on hood deflections. For the configuration studied, the neglect of under-hood pressure was observed to be more significant than neglect of flow through the forward and rear boundaries. These findings provide important insight toward the use of aeroelastic prediction tools in the design of automotive components.

In this study, comparison to experimental data has only been done with one vehicle. Further validation on other vehicle models should be considered to gain insight to the fidelity of the FSI framework. In addition, this work should be carried out on a vehicle with more substantial hood compliance to further assess the importance of aeroelastic interactions on hood deflection. Last, current understanding of the steady-state aeroelastic problem enables confidence in progressing to unsteady aeroelastic study of automobile hoods.

Contact Information

Jack McNamara

The Ohio State University


The authors gratefully acknowledge support for this work by Honda R&D Americas, Inc.


(1.) Massegur, D., Quaranta, G., and Cavagna, L., "An Indy Car Rear Wing Is Designed for Aeroelastic Response Using Multidisciplinary Optimization," ANSYS Advantage 1(1):9-11, 2007.

(2.) Patil, S., Lietz, R., Woodiga, S. et al., "Fluid Structure Interaction Simulations Applied to Automotive Aerodynamics," SAE Technical Paper 2015-01-1544, 2015, doi: 10.4271/2015-01-1544.

(3.) Gupta, A., Gargoloff, J., and Duncan, B., "Response of a Prototype Truck Hood to Transient Aerodynamic Loading," SAE Technical Paper 2009-01-1156, 2009, doi: 10.4271/2009-01-1156.

(4.) Gaylard, A., Beckett, M., Gargoloff, J. et al., "CFD-Based Modelling of Flow Conditions Capable of Inducing Hood Flutter," SAE Technical Paper 2010-01-1011, 2010, doi: 10.4271/2010-01-1011.

(5.) Knight, J., Lucey, A. Shaw, C., "Fluid-Structure Interaction of the Jaguar XK8 Convertible Car Roof," 18th World IMACS/MODSIM Congress, Cairns, Australia, 2009.

(6.) Ramsay, T., Fredelake, A., and Stevens, K., "Correlation of a CAE Hood Deflection Prediction Method," SAE Technical Paper 2008-01-0098, 2008, doi:10.4271/2008-01-0098.

Justin Pesich and Jack McNamara, Ohio State University

Austin Kimbrell and Peter Kang, Honda R&D Americas, Inc.


Received: 02 Feb 2018

Accepted: 25 Feb 2018

e-Available: 10 Jul 2018


Hood, Aeroelasticity, Fluid-structure interaction, Computational fluid dynamics, Wind tunnel testing


Pesich, J., McNamara, J., Kimbrell, A., and Kang, P., "Steady Aeroelastic Response Prediction and Validation for Automobile Hoods," SAE Int. J. Passeng. Cars - Mech. Syst. 11(4):251-261, 2018, doi:10.4271/06-11-04-0021.
TABLE 1 Dimensions of wind tunnel test section.

Dimension  Value (m)

Height      4.95
Width       7.0 9
Length     13.1

TABLE 2 Cell count for each vehicle configuration.

Vehicle configuration  Cell count

V1                     35 million
V2                     86 million
V3                     59 million

TABLE 3 Summary of grid convergence study.

Grid    Cell count  Hood lift (Newtons)  % Error

Coarse   60M        248.3                4.87
Medium   86M        257.7                1.26
Fine    105M        261                  -

TABLE 4 Hood structural components.

Component  Material  Mesh size (mm)  Element type

Skin       Aluminum  4               Shell
Frame      Aluminum  4               Shell
Hinge      Steel     4               Shell
Latch      Steel     4               Shell

TABLE 5 [L.sub.1] and [L.sub.[infinity]] error norms of hood surface
pressure data using FSI prediction pressures.

Velocity (kph)  [L.sub.[infinity]] (Pa)  [L.sub.1] (Pa)

100              30.8                     9.97
160              70.9                    23.70
200             123.9                    36.13

TABLE 6 Coupled displacement results of V3 with and without lasers.

          Transverse displacement (mm)
Location  With lasers  Baseline prediction  % Difference

Point 1    0.46         0.47                 2.2
Point 2    0.44         0.44                 0.0
Point 3   -0.025       -0.012               52.0

TABLE 7 Comparison of uncoupled and coupled response.

          Transverse displacement (mm)
Location  Uncoupled  Baseline  % Difference

Point 1    0.45       0.47      4.26
Point 2    0.43       0.44      2.27
Point 3   -0.0098    -0.012    18.3

TABLE 8 Coupled displacement results of V1 and V3.

          Transverse displacement (mm)
Location  V1      V3      % Difference

Point 1    0.45    0.47     4.26
Point 2    0.43    0.44     2.27
Point 3   -0.054  -0.012  350

TABLE 9 Coupled displacement results of V1 with and without internal
pressure loading.

          Transverse displacement (mm)
          With internal  Without internal
Location  pressure       pressure          % Difference

Point 1    0.45           0.51             11.8
Point 2    0.43           0.52             17.3
Point 3   -0.054         -0.16             66.3
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Author:Pesich, Justin; McNamara, Jack; Kimbrell, Austin; Kang, Peter
Publication:SAE International Journal of Passenger Cars - Mechanical Systems
Article Type:Technical report
Date:Oct 1, 2018
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