Experimental study and finite element analysis of wind-induced vibration of modal car based on fluid-structure interaction*

TAO Li-li

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

School of Automotive Engineering, Shandong Jiaotong University, Jinan 250023, China, E-mail: tlljinan@gmail.com

DU Guang-sheng, LIU Li-ping

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

LIU Yong-hui

School of Automotive Engineering, Shandong Jiaotong University, Jinan 250023, China

SHAO Zhu-feng

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

Experimental study and finite element analysis of wind-induced vibration of modal car based on fluid-structure interaction*

TAO Li-li

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

School of Automotive Engineering, Shandong Jiaotong University, Jinan 250023, China, E-mail: tlljinan@gmail.com

DU Guang-sheng, LIU Li-ping

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

LIU Yong-hui

School of Automotive Engineering, Shandong Jiaotong University, Jinan 250023, China

SHAO Zhu-feng

School of Energy and Power Engineering, Shandong University, Jinan 250061, China

(Received July 30, 2012, Revised October 15, 2012)

The wind-induced vibration of the front windshield concerns the traffic safety and the aerodynamic characteristics of cars. In this paper, the numerical simulation and the experiment are combined to study the wind-induced vibrations of the front windshield at different speeds of a van-body model bus. The Fluid-Structure Interaction (FSI) model is used for the finite element analysis of the vibration characteristics of the front windshield glass in the travelling process, and the wind-induced vibration response characteristics of the glass is obtained. A wind-tunnel experiment with an eddy current displacement sensor is carried out to study the deformation of the windshield at different wind speeds, and to verify the numerical simulation results. It is shown that the windshield of the model bus windshield undergoes a noticeable deformation as the speed changes, and from the deformation curve obtained, it is seen that in the accelerating process, the deformation of the glass increases as the speed increases, and with the speed being stablized, it also tends to a certain value. The results of this study can provide a scientific basis for the safety design of the windshield and the body.

Fluid-Structure Interaction (FSI), wind-induced vibration, numerical simulation

Introduction

It is well-known that cracks caused by suddenly bursts in the windscreen during the bus’s travelling would severely affect the passenger’s safety and the bus’s performance[1]. Now with more ergonomic considerations and improvements of the processing technology, the bus generally uses a large-area integral panorama windscreen, directly combined with the upper part and the body-side as a single entity, with its height close to or even larger than 2/3 of the total height of the bus, so that drivers may enjoy a wide vision, without blind spot, with an optimal degree of visibility and lighting, and a significantly improved security. Besides, the body surface is smoother and the flow-linearity is increased, more conducive to a further improvement of the aerodynamic characteristics. On the other hand, the design speed of the bus, especially, the high speed bus, reaches over 120 km/h due to the technological development. Under high speed conditions, the large-area windshield of the bus is under a large wind pressure and pressure pulsation, and the deformation increases, which would lead to windshield damages.

Many numerical simulations and experiments were carried out for the windshield. Aslk and Tezcan[2]analyzed and verified the deformation characteristicsunder loading and the effects of the temperature for the single tablet glass and the laminated glass under different boundary conditions of the point support and the full support, and pointed out that for the single tablet glass, under the conditions of either the point support or the full support, its deflections and stresses are in a linear relations, but for the laminated glass, under the point support boundary condition, the relation is linear, but under the full support condition, the relation is nonlinear, Scigliano et al.[3]used the finite element method to study the kinetic characteristics of a car windshield in a free state and the actual boundary conditions, and pointed out that the temperature variation has a significant effect on the kinetic characteristics of the windshield.

Timmel et al.[4]used an explicit finite element method to analyze the car collision effects on the windshield, Shen et al.[5]studied the mechanism of rupture of the windshield based on the fluid dynamics and the body dynamic characteristics, respectively. The analyses of the pressure and the speed distributions in a stable wind field show that the maximum stress obtained is far less than the yield limit of the windshield, and he pointed out that the effects of the steady-state air pressure on the strength of the windshield are small. However, this study did not consider the impact of the wind-induced vibration and the deformation of the glass bi-directional interaction. Chen[6]and Feng[7]applied the static pressure instead of the wind-induced pressure to obtain the relationship between the displacement at the point on the windshield and the wind-induced pressure. But this testing condition is quite different from the actual air pressure condition in the wind tunnel.

The above studies mainly focus on the material characteristics, the static characteristics and the collision effects of the windshield, with little consideration of effects of the flow and the deformation interaction on the windshield glass. This paper applies the Fluid-Structure Interaction (FSI) model of a van-body model bus to simulate the wind-induced vibration of the windshield, and carries out the wind-induced vibration response test in the wind tunnel. The wind-induced vibration characteristics of the front windshield are obtained at different speeds.

1. Fluid-Structure Interaction numerical calculation

The impact of the FSI between the flow field and the glass plane induced by the wind is considered in this paper.

1.1 Fluid-structure interaction mathematical model

1.1.1 Calculation model for fluid

The Detached Eddy Simulation (DES) model is used in the numerical simulation of the fluid field for the calculation of the fluid region of the model bus. The DES model is a model between the RANS model and the Large Eddy Simulation (LES) model. To address issues of wide isolations and Reynolds numbers, the calculation via the LES is costly and the calculation via the RANS is not accurate enough. In recent years, the DES model finds applications in the numerical simulations of the automotive external flow field[8-10].

In this study, the Smagorinsky-Lilly Sub-Grid Scale (SGS) model in the LES is applied in the nearwall region with sufficiently dense grids as the DES model, and the Spalart-Allmaras model in the RANS method is used in other regions.

1.1.2 Structure finite element mathematical model

The finite element analysis method is used for the solid structure. The glass and steel are regarded as elastic materials, and the dynamic finite element equation of the elastic structure takes the form[11]

1.1.3 Fluid-structure interaction model

The Arbitrary Lagrangian-Eulerian (ALE) formulation is used in the FSI simulations. The structure model is based on the Lagrangian coordinate systems, with the displacement as the basic variable, the deformation occurs on the interface of the fluid model, so the ALE coordinate system is used.

The fundamental conditions applied to the fluidstructure interfaces are the kinematic condition (or the displacement compatibility)

and the dynamic condition (or the traction equilibrium)

where dfand dsare, respectively, the fluid and solid displacements and τfand τsare, respectively, the fluid and solid stresses. The underlining indicates that the values are defined on the fluid-structure interfaces only. The fluid velocity condition is determined by the kinematic condition v=ds, if a no-slip condition is applied, or ng v=ng ds, if a slip condition isapplied, wherev is the velocity of the flow.

The fluid nodal positions on the fluid-structure interfaces are determined by the kinematic conditions. The positions of the other fluid nodes are determined automatically by the program to preserve the initial mesh quality. The governing equations of the fluid flow in their ALE formulations are then solved. According to the dynamic conditions, on the other hand, the fluid traction is integrated into the fluid force along the fluid-structure interfaces, which acts on the structure node

where hdis the virtual solid displacement,dS is the element area.

Completely different elements and meshes can be used in the fluid and solid models within the availability of the solid and fluid models in the ADINA system. The nodal point positions of the two models are therefore generally not the same on the fluid-structure interface, but the time integrations for both fluid and solid equations must be consistent[12,13].

1.2 Physical model and meshing

In the process of the FSI, the fluid force is applied to the structure, and the deformation of the structure, in turn, affects the fluid region. In the calculation of the FSI, one must establish both the structure model and the fluid model in the structure module and the fluid module in the ADINA software, and then combine the two models for the FSI solver in the ADINA to obtain various results of the flow field and the structure field.

Table 1 The materials elastic constants of the model car

1.2.1 Structural model

The dimensions of the compartment of the vanbody model bus are 0.5 m×0.4 m×0.4 m (length× width×height), with four semicircular wheels below of 0.04 m in height. The material of the windward surface is the single layer glass, and that of other parts is the 20# low-carbon steel. Under the wind-induced load in a wind tunnel, the single layer glass is considered as an isotropic elastic material[2]. The parameters of the materials are shown in Table 1. As this analysis concerns the wind-induced vibration characteristics of the glass, and to reduce the influence of the vibration of the rest body on the glass, the thickness of the glass is selected as 0.002 m, and the thickness of the lowcarbon steel is selected as 0.0025 m.

Because the thickness of two kinds of materials of the model bus are much smaller than the length and the width, the shell element is selected as the cell type to discretize the structure, and the minimum mesh grid is 0.005 m. The number of the solid grid nodes is 7 679. The transient implicit method is applied in the simulation analysis. The finite element mesh of the structure is shown in Fig.1.

Fig.1 Finite element analysis model of model car

Fig.2 The results with different mesh numbers

1.2.2 Fluid model

Set the wheel bottom surface of the model bus as in the full constraint stationary boundary condition. This is consistent with the test conditions for the wind-tunnel testing. The domain size of the fluid model is 1.7 m×9 m×3 m. The hybrid tetrahedral grids are used in meshing. Figure 2 shows the numerical simulation results with different mesh number. The mesh numbers of Mesh-1 and Mesh-2 are 299 300 and 171 700, respectively. It can be seen that the two kinds of meshes give nearly the same results. Therefore, Mesh-2 is adopted in this paper. The flow field mesh is shown in Fig.3.

The PISO algorithm is used in the pressure speed interaction calculations, and a speed load is imposed at the entry, which takes the value of 20 m/s, 25 m/s, 30 m/s and 35 m/s in turns; the free flow condition is used at the exit border; the normal speeds on both sides and the upper border of the calculated field are set to 0 m/s, and the ground boundary condition is setas in a wall condition. For the model bus in the flow field, the upwind side glass and the rest of the body are set as the FSI interface. The pressure interpolation is done by the Standard method, the time item is treated by the composite time integration method, with the time step Δt=0.001 s, and with the gradual stabilizats ieosn[14o,1f5]t.h e calculation, the time step gradually increa-

Fig.3 Grid of central symmetric planar of flow field

Fig.4 Vibration response of the front glass

2. Analyses of the numerical simulation results

2.1 The vibration response of the front bus windscreen at different wind speeds

Figure 4 shows the vibration response of the front bus windscreen in the longitudinal section when the wind speed is 35 m/s, at the time t =1.48 s. As shown in the Fig.4, the vibration of the windscreen is clearly seen under the wind flow. The vibration curve is in the parabolic form, and the maximum vibration amplitude is at the center of the windscreen. Therefore, the central vibration amplitude is used as the index for the windscreen in this paper.

Fig.5 Vibration response at the center point on the front glass surface at different wind speeds

The vibration curves of the front windscreen at different wind speeds are obtained by the method of the FSI in the numerical simulation. As shown in Fig.5, the displacements at the center of windscreen, Δs, at the wind speed of 20 m/s, 25 m/s, 30 m/s, and 35 m/s are obtained, with theY -axis as the displacement, and theX -axis as the time t.

Compared with the displacement at the different wind speeds, the deformation of the windscreen is clearly seen followed by the change of the wind speed, and it increases as the wind speed increases. The maximum displacement is 0.000673 m at the time of 0.96 s at the maximum wind speed of 35 m/s. The form of the displacement curves are similar at the different wind speeds. The displacement increases with the time until the end of the acceleration stage, when a maximum value is reached and then the displacement keeps unchanged. It is shown that there is a maximum displacement at the varied wind speeds, mainly due to the influence of the fluid-structure interaction. The inertial force is another factor that leads to that the fact that the pressure increases with the time. The change of the pressure causes the change of the stress in the windscreen, as shown in Fig.6 by the curve of the stress at the windscreen central point against the time. It is obvious that the changing trends of the stress and the displacement at the central point are similar.

Fig.6 The curve of the stress at the central point at the different wind speeds

2.2 The pressure distribution of the windscreen

The pressure distribution of the flow field is shown in Fig.7.

The surface of the windscreen is located in the positive pressure area, and the tail of the car is locatedin the negative pressure area. A deformation of the windscreen can be clearly seen because of the action of the positive pressure, and the maximum pressure is located at the central point of the windscreen. Figure 8 shows the curve of the pressure at the windscreen central point against the time. It is shown that the form of the curve of the pressure is similar to that of the displacement at the central point. Table 2 shows the difference between the pressures with and without the FSI. It is shown that the pressure with the FSI is higher than the pressure without the FSI.

Fig.7 Pressure distribution on the centro-symmetric surface of the model car

Fig.8 The curve of the pressure at the central point at the different wind speeds

Table 2 The pressure with and without FSI

Table 3 Aerodynamic drag coefficients of the model car

2.3 The influence on the aerodynamic characteristics

Table 3 gives the aerodynamic drag coefficients of the model at different wind speeds obtained by the numerical simulation, with and without the consideration of the influence of the FSI.

Comparing the different cases in Table 3, the aerodynamic drag coefficients without the FSI are smaller than those with the FSI. There is an error (negative in sign) for the aerodynamic drag coefficient without consideration of the influence of FSI.

3. The experimental research on the vibration characteristics of the windscreen

3.1 The equipment of the experiment

The experiment is carried out in the wind tunnel of Shandong University. The test section is 1 m×1.2 m, and the stabilized wind velocity is in the range of 10 m/s-45 m/s.

Fig.9 Model car

Fig.10 OD9000 eddy current displacement sensor

The experimental model scale is 1:1, as shown in Fig.9. The sensor used in the experiment is the eddy current displacement sensor of the type OD9000 and of the sensitivity of 10.41 mV/μm. The sheet metal is fixed at the central point of the windscreen, and the detector of the sensor is located at the center of the windscreen with a vertical distance of 0.0015 m, as shown in Fig.10. The flow field is obtained by the wind tunnel experiments.

The velocity of the wind takes the value of 20 m/s, 25 m/s, 30 m/s and 35 m/s, as obtained by the wind tunnel experiments. The signal of the windscreen displacement of the model car is obtained by the eddy current displacement sensor of the type OD9000. Then the signal is transmitted to the computer via ∑-ΔA/ Dtransducer, and the data is analyzed by the system of DH5923.

3.2 The analyses of the experimental results

The experimental results are shown in Fig.11.

Fig.11 The displacement at the central point on the front glass of the model car and the displacement on the base at different wind speeds

The results of the measurement of the dynamic condition fluctuate because of the turbulence of the flow, and from the curve, it is shown that they fluctuate around a time-average value. The fluctuation increases when the wind speed increases because the turbulence is more intense when the wind speed is higher. Therefore, the time-average value is adopted as an index for the experimental results. The results of the experiments and the numerical simulations are shown in Table 4.

Table 4 Comparison of calculation and experiment values of the center point’s vibration response

Fig.12 The curve of the experimental and calculation results

The curves of the experimental and numerical simulation results are shown in Fig.12, with theX -axis as the wind speed, and theY -axis as the displacement at the centre of the windscreen. It is shown that the results of the experiments agree with those of the numerical simulations. The displacement increases when the wind speed increases, especially in the high wind speed region, the error is getting smaller. Because of the large elastic modulus of the glass and the small area of the windscreen, the displacement of the windscreen is small, which leads to a larger relative error between the experiment and calculation results. When the wind speed is high, the displacement is large, and the results of the experiment and the calculation are in good agreement, which verifies the fluid-structure interaction model.

4. Conclusions

In this paper, the vibration characteristics of the front windscreen at different speeds are studied by the method of the FSI. And the results of the calculation are verified by the experiment.

(1) There is a significant deformation of the front windscreen when the car is in movement, and the displacement is shown to be in a parabolic distribution. The maximum displacement is at the center of the windscreen, and the displacement increases with the wind speed.

(2) The displacement of the windscreen has a maximum value at the point of the stabilization because of the FSI.

(3) The influence on the aerodynamic drag coefficients of the model is different with and without the consideration of the FSI. There is an error (of negative sign) for the aerodynamic drag coefficient when the influence of the FSI is ignored.

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10.1016/S1001-6058(13)60345-5

* Project supported by the National Natural Science Foundation of China (Grant Nos. 10972123, 10802042), the Natural Science Foundation of Shandong Province (Grant No. Y2007A04).

Biography: TAO Li-li (1972-), Female, Ph. D. Candidate, Associate Professor

DU Guang-sheng, E-mail: du@sdu.edu.cn