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While driving a car at high speed cruising, the mirror surface of side-view mirrors happens to vibrate. The vibration often leads to image blurs of objects reflected in the mirror. Once the phenomena happen, drivers cannot clearly identify the approaching vehicles from the rear. The paper aims to clarify the vibration modes of side-view mirror experimentally and to capture forces on the mirror surface induced by separating vortices around the mirror numerically. Experimental study clarified two findings. One is that the mirror has the primary natural frequencies of 25, 30 and 33 Hz. The other is that vibrations of the mirror increase in proportion to flow velocity and their frequencies have peak values at 120 and 140 km/h. The frequencies of the mirror vibration coincide completely with the primary natural frequencies. In order to capture the external forces vibrating the mirror surface, numerical study was performed by unsteady air-flow analyses. Relationships between flow velocity fluctuations close to the mirror surface and pressure fluctuations on the mirror surface were investigated. It was found that the two power spectra have peak values at the same frequency of 24.4 Hz at 120 km/h. This shows that flow velocity fluctuations with the frequency of 24.4 Hz affect directly pressure fluctuations on the mirror surface. Numerical analyses clarify that the frequencies of shedding vortices are 24.4 Hz at 120 km/h and 28.3 Hz at 140 km/h. The frequencies of mirror vibration are very close to those of flow fluctuations. This shows that the frequencies of the mirror vibration have much to do with the frequencies of the forces induced aerodynamically by vortex shedding. Therefore it follows that image blurs at high speed cruising are caused by resonance phenomena that the mirror surface resonates with the frequencies of shedding vortices around the mirror.

While driving a car, the mirror surface of side-view mirrors happens to vibrate. This vibration disturbs the driver to identify the approaching vehicles clearly, which has a great effect on the safety driving. The mirror vibration is defined as the image blurs induced by the vibration of the mirror surface. Once the phenomena happen, the driver look at the image blur of the object reflected in the mirror. This situation is very dangerous for the driver since the driver cannot understand clearly the approaching vehicles from the rear.

Regarding the mirror vibrations during high-speed cruising, only a few papers [

The present paper has the purpose of clarifying the aerodynamically induced forces on the mirror surface, and finally proposing the countermeasures for the vibration at an early stage of development in terms of the reduction of cost and weight. As a first step, the paper aims to identify dependence of the vibration modes of side- view mirror on the cruising speeds experimentally and to clarify forces on the mirror surface induced by separating vortices around the mirror numerically.

The experiment was conducted in the wind tunnel.

Provided that the vibration is considered as a simple harmonic motion, the shake amounts

The acceleration a on the mirror surface is given by second derivatives of

Therefore, the shake amounts

where ω is angular velocity, f the vibration frequency. From this equation it is found that shake amounts are proportional to the acceleration but inversely proportional to the square of the frequency of the acceleration. It, therefore, follows that to suppress the mirror vibration it is efficient to shift the vibration frequency from lower to higher frequencies.

The vibration measurements were conducted at the wind tunnel. The mirror attached to a fixing device was placed in the test section of the wind tunnel.

An ideal impact to a structure is a perfect impulse, which has an infinitely small duration, causing constant amplitude in the frequency domain; this would result in all modes of vibration being excited with equal energy. The impact hammer test is designed to replicate this. Natural frequencies of the mirror were measured by the impact hammer test.

The mirror attached to the testing apparatus, which was set in the same testing situation where the natural frequencies were measured, was immersed in the wind tunnel test section to measure how vibration frequencies of the mirror surface vary depending on the flow velocities. Figures 7-9 indicate frequency spectra of mirror surface

vibrations in X, Y and Z direction, respectively. The frequency spectra were measured for the flow velocities from 60 km/h to 160 km/h at every 20 km/h steps. The results show that all the vibration accelerations have the peaks at (25, 33 Hz), (25, 30 Hz), and (25, 30 Hz) in the X, Y and Z direction respectively. These vibration accelerations coincide completely with the primary natural frequencies shown in Figures 4-6. Therefore it follows that the surface of the mirror is resonating with the same frequencies as the primary natural frequencies.

The study uses the software STAR-CCM+ with software V9.04.009 (for Windows 64).

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The present study was performed by unsteady airflow analysis. Reynolds Averaged Navier-Stokes (RANS) Simulation was employed as the turbulence model for the steady-state analysis. K-ω model was used as eddy viscosity model. Flow data obtained by steady-state analysis were employed as initial values for unsteady analysis for reduction of the calculation time and for higher accuracy. Detached Eddy Simulation (DES) was used as turbulence model for the unsteady analysis and SST (Menter) K-ω model for eddy viscosity model.

The side-view mirror model is no gap between the mirror and the casing, and the mirror surface is regarded as a rigid body. For the steady state analysis, the maximum step number is 3000. For the unsteady calculation, the internal iteration number is 10, and maximum step number is 1024, and time step is Δ = 0.001 s. The airflow velocity is set to 120 km/h (33.3 m/s). Reynolds number is defined in Equation (2), and results in Re = 3.74 × 10^{5}, using U = 33.3 m/s, L = 0.17 m, and ν = 1.512 × 10^{−}^{5} m^{2}/s.

Flow field around the mirror was investigated.

It is found that much stronger vortices are generated especially at the top and the bottom of the side-view mirror, and in vicinity of the mirror surface. There exists a pair of vortices whose rotational directions are opposite. It is also recognized that vortices with stronger vorticity exist in the vicinity of the point A on the mirror surface. The point A is selected as the place where there exist the largest accelerations on the mirror surface. Since higher vorticity is located close to the mirror surface, unsteady motions of the vortices seem to have a greater effect on the mirror surface.

In order to evaluate quantitatively the magnitude of the pressure operating on the mirror surface, pressure coefficients defined in Equation (7) is introduced as an indicator of pressure.

where P_{m} is pressure of measurement points on the mirror surface, P_{∞} pressure in the uniform flow, ρ density of airflows, U_{∞} flow velocity in the uniform flow.

_{m} is pressure on the mirror surface, negative C_{p} means that the pressure of the entire mirror surface is lower than that of uniform airflows. It, therefore, follows that the mirror surface is always being dragged towards the vortices over

the mirror surface. It is found that there is much higher negative pressure in the dark blue-colored region where the point A is located.

As mentioned above, it was found that separation vortices cause the widely different forces on the mirror surface. The characteristics of separation vortices, therefore, will be clarified in terms of frequency analysis by FFT analyses. The separation vortices will be related to the pressure fluctuation on the mirror surface.

to the velocity fluctuations obtained at the point P, they reflect the existence of vortices. This is because the flow velocity in the X axis direction at the point P has negative values, and maximum amplitude of the flow velocity is fluctuating up to about 11 m/s, which account for one third of uniform flow velocity 120 km/h (33.3 m/s). Pressure fluctuations at the point A occurred at certain retarded time, compared with flow velocity fluctuations.

Generally speaking, the frequency f of shedding vortices from a bluff body is proportional to flow velocity U and inversely proportional to representative length of the body L, using Strouhal number St. For a cylinder, St is known as 0.2. The relationship is described as follows.

In case of the mirror body, the highest power spectra were numerically obtained for 80,100 km/h which are 16.6 Hz and 20.5 Hz, respectively.

spectra and flow velocity. Since St is calculated as 0.12 based on the graph, the frequencies of 140, 160 km/h are extrapolated as 28.3 Hz and 32.2 Hz, respectively.

Experimental measurements reveal that the mirror has primary natural frequencies of 25 and 33 Hz in the X direction whereas 25 and 30 Hz both in the Y and Z direction. The accelerations of the mirror vibrations coincide with these primary natural frequencies. Therefore, image blurs are caused by vibration phenomena, which can be interpreted as resonance phenomena that the mirror surface resonates with the frequencies of shedding vortices. Since numerical analyses clarify that the frequencies of shedding vortices are 24.4 Hz at 120 km/h and 28.3 Hz at 140 km/h, it follows that the shedding vortices exert aerodynamic loads on the mirror surface periodically with frequencies of 24.4 Hz and 28.3 Hz. One of the ways to reduce vibration amounts is to shift frequencies of the external forces induced periodically by shedding vortices to as higher frequency range as possible because vibration amounts decrease which are inversely proportional to the square of the resonance frequency according to Equation (1).

The paper clarifies relationships between causes and effects of side-view mirror vibration by means of the experimental method and Computational Fluid Dynamics. Both natural frequencies and vibrations of the mirror were measured in the wind tunnel under the same condition. Natural frequencies of the mirror were measured by the impact hammer test with coherence function for reliability of the data. In the measurement of vibrations, a vibration pickup set on the center point of the mirror surface measured accelerations in three directions for X, Y, and Z ranging from 60 to 160 km/h at every 20 km/h steps. As a result, it was found that the frequencies of the mirror vibration coincided completely with its primary natural frequencies. On the other hand, unsteady air-flow analyses clarified relationships between flow velocity fluctuations close to the mirror surface and pressure fluctuations on the mirror surface. It was also found that the two power spectra had peak values at the same frequency. This shows that flow velocity fluctuations affect directly pressure fluctuations on the mirror surface. Shedding vortices are, therefore, considered to be direct input sources to the mirror surface. As a result, the following findings are clarified. One is that frequencies of the side-view mirror vibration coincide with its natural frequencies even if any aerodynamic inputs are applied on the mirror. The other is that mirror vibration modes shift from the lower to the higher order vibration mode, responding aerodynamic inputs increasing in proportion to flow velocity around the mirror. Therefore it follows that image blurs at high speed cruising are caused by resonance phenomena that the mirror surface resonates with the frequencies of shedding vortices around the mirror.

ShigeruOgawa,TaikiKawate,JumpeiTakeda,IttetsuOmori, (2016) Side-View Mirror Vibrations Induced Aerodynamically by Separating Vortices. Open Journal of Fluid Dynamics,06,42-56. doi: 10.4236/ojfd.2016.61004

δ: Shake Amount (m)

a: Acceleration of Mirror Vibration (m/s^{2})

f: Frequency of Mirror Vibration (Hz)

Re: Reynolds Number

U: Flow Velocity (m/s)

L: Representative Length (m)

ν: Kinematic Viscosity (m^{2}/s)

P_{m}: Pressure of Measuring Points on Mirror Surface (Pa)

P_{∞}: Pressure in the Uniform Flow (Pa)

ρ: Density of Fluid (kg/m^{3})

U_{∞}: Flow Velocity in the Uniform Flow (m/s)

ω: Vorticity (1/s)

St: Strouhal Number