Effects of Installation Environment on Flow around Rear View Mirror.
External rear view mirror is one of the most important automobile adds-on. Its primary function is to permit clear vision for the driver to the rear of the vehicle. Conventional reflective mirrors will be the main method used for rear vision for several years to come, and none of the world's automobile laws permits using electro-optical systems instead of conventional reflective mirrors.
The flow field around external rear view mirror is highly three-dimensional, unsteady, separated and turbulent. The unsteady flow field in the wake of the external rear view mirror of a typical production car is known to be a significant source of aerodynamic noise ,  and a contributor to the total drag force on the vehicle . Studies show that unsteady flow field in the wake of the external rear view mirror also contributes to the vibration of the mirror glass which affects effective rear view vision from external mirrors .
Wake flow structure around external rear view mirror has been studied extensively. In early wake, an alternating vortex was found along the upper and the lower edge of the mirror housing, and in downstream, a vortex wrap like a tip vortex was also found . Studies showed that within the half distance of the mirror span the recirculation zone appeared and the intrinsic vortex was shed with the frequency of 19.6 Hz, also showed that a conical envelop of the vortex sheet was developed .
While among all the researches on the flow field around external rear view mirror, different installation environment were employed. Researchers experimentally investigated the wake flow structure around an external rear view mirror which is mounted on a production car . The experiments were performed in an open circuit wind tunnel, and the wake flow structure was captured by hot wire anemometry and two-dimensional laser Doppler velocimetry. This kind of installation environment is the most accurate one and also the most expensive one, and it needs a full-scale wind tunnel. In smaller wind tunnels, experiments were performed with a real external rear view mirror mounted on the ground, and researchers measured the pressure field around a full-scale side mirror mounted on the ground of a wind tunnel . GM performed experiments about characterization of the unsteady flow field behind two outside rear view mirrors mounted on the ground of a small wind tunnel and both PIV and dynamic pressure system were used . When side mirror is mounted on the ground, the boundary layer on the ground affects the flow field around the mirror. To avoid the significant flow boundary layer on the wind tunnel floor and to facilitate the installation of the flow and noise measuring instruments, the mirror was mounted on a specially designed table in an acoustic wind tunnel , . A real scale mirror and mounting jig which were mounted in the middle of a wind tunnel test section were used to demonstrate the body frame interaction which resulted in noise increase . A generic vehicle model based on the SAE Type 4 (fullback) was used for an investigation of wind noise caused by the A-pillar and the side mirror flow . The side mirror was mounted on a full-scale SAE model. The generic model is simple enough to exclude excess deviation keeping the interaction with the vehicle body.
Flow field around external rear view mirror has relationship with the installation environment. The purpose of the present paper is to investigate the effects of installation environment on flow field around the external rear view mirror.
In this paper, the external rear view mirror is mounted on production car model, SAE model, specially designed table and mirror-only model respectively. The hybrid RANS-LES method (DES) is employed to investigate both the time-averaged and unsteady flow field around the external rear view mirror.
A new generic DrivAer model is introduced to close the gap between the strongly simplified models and the highly complex production cars . It consists of three car configurations i.e. estate, fastback and notchback shown in Figure 1. Each configuration has several variants such as with and without mirrors and wheels, with smooth and detailed underbody. The CAD geometry is available for researchers and has been subject to experimental investigations. The present study focuses on the flow structure around the front side window. The notchback DrivAer model with side mirrors and wheels is chosen as the baseline model. A smooth underbody without detailed features and a stationary floor are used.
Three contrastive models are chosen in this study i.e. SAE model, a specially designed table and mirror-only shown in Figure 2. The mirror of DrivAer model is used in contrastive models. For SAE model the mirror is mounted on the SAE Type 4 (fullback) model and its position refers to previous study . For table model the mirror is vertically mounted on a specially designed table where the edges of the table need to be aerodynamically shaped to minimize or eliminate non-mirror related flow structure. The last contrastive model is a mirror-only model which is hanging in the air without any approach body. To simplify the model and save computational resources, all support components were removed.
Turbulence Modeling Approach
Computational Fluid Dynamics (CFD) is now one of the most important design tools for the automotive industry. Both computational resources and commercial software are now sophisticated enough to handle the often complex geometries that are common in automotive design. Generally, two types of flow separation can be distinguished in the flow field around a moving car . First, flow can separate on edges such as the front edge of the hood, the sides of the fenders, the front of the windshield and the rear of the vehicle. The second type of separation is three-dimensional by nature around the A- and C- pillars. Studies have shown that DES offers a clear advantage over RANS models in terms of the force coefficients, pressure coefficients distribution and capture of the three-dimensional flow feature , . The DES model has been chosen in the present study.
DES is a hybrid RANS-LES method which attempts to provide a compromise between accuracy and computational expense by only using LES in regions of flow which are challenging to RANS models (such as separated flow) but then use RANS models elsewhere. The time-dependent IDDES (based on SST model)  used in the present paper adds additional functionality to shield the attached RANS boundary layer from the incorrect activation of LES modes, as well as wall-modelled LES capability to allow some of the boundary layer to be resolved by LES together with a quicker transition to resolved turbulence , . All simulations in this paper used the same turbulence modeling approach.
Computational Grid and Boundary Conditions
The size of computational domain is 11L (L is the length of the car) x 11W (W is the width of the car) x 8H (H is the height of the car) and a schematic of the domain and a car are shown in Figure 3. A velocity inlet condition is imposed at the start of the domain (4L upstream of the car) with a freestream velocity U = 40m[s.sup.-1] (Re = 4.71 x [10.sup.6] based upon L = 1.85). The turbulence at the inlet boundary is specified by intensity and viscosity ratio which are 1% and 20 respectively A pressure outlet condition with 0 gauge pressure is imposed 6L downstream of the rear of the car. Slip wall condition is imposed on each side wall and top wall of the domain. The floor is set to a no-slip condition with non-rotating wheels to match the experimental non-ground simulation case. No-slip wall boundary condition is also used on the surface of the vehicle and mirrors.
The topology of the computational grid is trimmer, which contains prism layers at the wall boundaries and a perfect hexahedral grid in the rest of the domain, and the prism layers are connected to the hexahedral grids by trimming them. The resulting mesh is composed predominantly of hexahedral cells with trimmed cells next to the surface. Trimmed cells are polyhedral cells but can usually be recognized as hexahedral cells with one or more corners and/or edges that are cut off. The initial surface mesh is trilateral and the final is almost quadrilateral which is the projection of the volume cells. The prism layer is also hexahedral and its transition to core cells is controlled by the volume growth rate. Three grids are generated for DES calculations, which are summarized in Table 1 and illustrated in Figure 4. Each mesh is refined in the boundary layer to allow the integration of the transport equations to the wall and thus a non-dimensional wall-distance, [y.sup.+] < 1 was ensured over the car. Near-wall mesh has 20 prism layer cells to ensure that the boundary layer was well captured. The refinement regions are around front side window and rear portion of the car. Contrastive calculations used the same domain and boundary conditions. Trimmed mesh strategy was employed for all contractive cases with refinement in mirror region.
A segregated incompressible unstructured finite-volume solver was employed for DES simulation. To discretize the convective terms of the momentum equations, a hybrid numerical scheme  was used, which switches between a bounded Central Differencing Scheme (BCDS) in regions where LES is active to a second order upwind scheme where RANS modes are active. A second order upwind scheme was used for the turbulent quantities. The unsteady SIMPLE algorithm was used for the pressure-velocity coupling.
An Algebraic Multigrid (AMG) method was employed using a V cycle for the momentum equations and a flex cycle for the turbulence quantities. The solution was initialized using the steady RANS results.
The temporal discretization was done using second-order implicit scheme. The time step was 5 x [10.sup.-4] s. Time-averaged statistics were gathered for 20 convective flow units (convective flow unit = L/U) after 5 convective flow units. All contractive models were simulated by the same numerical approach.
The numerical method is validated by reference to experiment results in published papers . The results for the drag coefficient are shown in Table 2 as well as the pressure coefficients in Figure 5, 6& 7. The mesh sensitivity study shows a constant trend of increasing Cd from the coarse mesh to the fine mesh and all average percentage differences from the experimental data are less than 3%. Pressure coefficient lines in Figure 5, 6& 7 for all three meshes are almost coincident and are close to the experiment data. The turbulent viscosity ratio, vt/v can be thought of as a measure of the contribution of the SGS (modeled turbulence) to the overall dissipation level. This value decreases with mesh refinement shown in Figure 8. The turbulent viscosity ratio in the middle mesh case is less than 20 in the front window region which is considered enough for this investigation . In this paper, the middle mesh scheme is employed for all simulations.
To describe the flow field around external rear view mirror and compare different cases, the coordinate system was established shown in Figure 9. The original point was set in the central of and behind the mirror. The post-processing was made by points, lines and planes in X-, Y- and Z-planes.
Time-Averaged Flow Field
As shown in Figure 10, the approach flow is deflected both in Z-plane and Y-plane. The u-velocity of the far away approach flow is larger than the freestream u-velocity, it decreases close to the mirror and is accelerated around the edge of the mirror shown in Figure 11&13. The approach flow far from the mirror yaws away from the vehicle body in the Z-plane and pitches down in the Y-plane shown in Figure 12&14. Both deflection and acceleration imply the existence of A-pillar vortex , . The flow field around front side window is mostly determined by A-pillar vortex and also by the external rear view mirror. The blockage effect of the mirror causes flow deflection and acceleration around the mirror body and a wake which can interact with the vehicle body .
The time-averaged wake flow structure is shown in Figure 15. The wake of the mirror is pretty like but not the same as the wake of a finite length circular cylinder  and its length is 1.5D (D is mirror's characteristic length defined as the length of the mirror in vertical direction). A pair of asymmetric rotating flow structure is captured in Y-plane and also two rotating flow structures exist in Z-plane. Compared with a finite length circular cylinder, mirror has a smaller angle with the approach flow and a streamline shape at the edge of the mirror, which results in a larger wake region and a delayed downwash flow.
Two counter-rotating flow structures form in the mean wake along x orientation shown in Figure 16. The anticlockwise rotating flow dominates in the downstream which is considered as the result by the A-pillar vortex and the downwash flow.
Instantaneous Flow Field
The instantaneous u-velocity was recorded at six points along three lines respectively shown in Figure 17. At each measurement point, 1850 velocity data were acquired at a 2 kHz sampling rate. The Fast Fourier Transform (FFT) algorithm was employed to calculate the power spectral density function, [E.sub.u] of u-velocity or the spectral phase [PHI] between two simultaneously captured velocity signals.
Characteristic dimensionless frequencies, approximately 0.2 are captured in the wake which are close to the Strouhal number of the measured vortex shedding for a two-dimensional cylinder and larger than that for finite length circular cylinder . The results shown in Figure 18&19 enhance that there exists alternate vortex shedding downstream in the wake. Details are shown in Figure 20 and there is a larger and relatively stable shear layer in the near wake of the mirror.
Figure 21 shows the turbulent viscosity ratio in external rear view mirror region for contrastive models. As mentioned above it can be considered enough for this investigation. Due to different installation environment, there are a few differences among mirror front areas shown in Table 3. While the drag and Cd of the external rear view mirror mounted on DrivAer model is largest followed by SAE model.
Time-Averaged Flow Field
Figure 22, 24, 25& 27 show that there is almost no approach flow deflection for table mounted model and mirror-only model both in Z- and Y-planes. SAE mounted model has the similar approach flow pattern as DrivAer model. The approach flow almost doesn't accelerate for table mounted model and mirror-only model shown in Figure 23& 26. Although the approach flow of SAE mounted model is approximate to that for DrivAer model, there still has differences in quantity of deflection and acceleration.
Similar to approach flow, DrivAer and SAE mounted models have the same time-averaged wake flow structure with a few differences in details shown in Figure 28& 29. Table mounted model has a totally different mean wake flow that enlarged wake region contains one dominating rotating flow in z=0 plane and y=0 plane respectively. Mirror-only model has a pair of asymmetric rotating flow in y=0 plane and in z=0 plane which are different from that of DrivAer mounted model.
Figure 30 shows the mean wake flow structure in X-plane for SAE model. Compared with Figure 16, SAE model has a dominating anticlockwise rotating flow in the downstream wake flow similar to that of DrivAer model. The wake flow structure for table model has a pair of symmetry counter-rotating flow structures which is approximate to the wake of a finite circular cylinder  as shown in Figure 31. The wake flow of mirror-only model has a much complex flow pattern with more than three rotating flow, which is considered as results of irregular shape of the mirror and the strut.
Instantaneous Flow Field
Figure 33, 34, 35&36 show that dimensionless characteristic frequencies exist in the instantaneous wake of the external rear view mirror for all contrastive models. All dimensionless characteristic frequencies are close to 0.2 except that of SAE model which is 0.176. In Figure 36, the spectral phase [PHI] between u-velocity of point P6 and Q6 for mirror-only model is less than [pi], which implies that the vortexes shed not the same as the other three models. Figure 37 visually shows the instantaneous wake flow where the approximate flow structure for DrivAer model and SAE model, an enlarged shear layer and vortex shedding in the downstream wake for table model and complex and irregular flow structure for mirror-only model.
The hybrid RANS-LES method (DES) is employed to predict flow field around automobile. Aerodynamic drag and pressure coefficient consist well with experimental data. Flow field around rear view mirror is analyzed in details. Results show that the DES method can lead to good aerodynamic and aeroacoustics results.
Then, effects of installation environment on flow around rear view mirror are investigated. It shows that the flow field around external rear view mirror on DrivAer model is different from all other three contrastive models: SAE model, table model and mirror-only model. Under production car condition (DrivAer model), the approach flow of the mirror deflects and accelerates, which is considered to be affected by the A-pillar vortex. Vortex shedding whose Strouhal number equals to that of two-dimensional circular cylinder exists in the wake of the mirror. Among all contrastive models, the flow field around the external rear view mirror on SAE model is most similar to that on DrivAer model with a smaller vortex shedding frequency in the wake. For table model and mirror-only model, the flow field around external rear view mirror is totally different from that of a production car. Research suggestions are made by this study: investigations on the flow field around external rear view mirror should put the mirror on a production car (or a model similar to a production car) and SAE model can be an alternative solution.
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Please send any requests for further information to Haidong Yuan at firstname.lastname@example.org
This work was supported by the International Exchange Program for Graduate Students, Tongji University, State Education Ministry and Science and Technology Commission of Shanghai Municipality (Grant No. 11DZ2260400) and Professional and Technical Service Platform of Shanghai Automotive Wind Tunnel Center (Grant No.l6DZ2290400). Authors want to thank all colleagues in the research group of automotive body and aerodynamics who had gave much help on the simulation.
DES - Detached-Eddy Simulation
RANS - Reynolds Averaged Navier-Stokes
LES - Large-Eddy Simulation
BCDS - Bounded Central Differencing Scheme
AMG - An Algebraic Multigrid method
SGS - Sub-Grid Scale model
FFT - The Fast Fourier Transform algorithm
Haidong Yuan, Zhigang Yang, and Qiliang Li
Table 1. Mesh type and resolution Mesh Name Mesh type [y.sup.+] Cell Count Coarse Hexahedral + prism <1 28 x [10.sup.6] Middle Hexahedral + prism <1 35 x [10.sup.6] Fine Hexahedral + prism <1 51 x [10.sup.6] Table 2. Drag Coefficient for each mesh together with average percentage differences from the experimental data. Model Cd Percentage difference Exp. 0.258 Coarse 0.261 1.2% Middle 0.263 1.9% Fine 0.264 2.3% Table 3. Drag, front area and Cd of rear-view mirrors for contrastive models Drag/N A/[m.sup.2] Cd DrivAer 2.096 0.00468 0.473 SAE 1.878 0.00442 0.448 Table 1.563 0.00475 0.347 Mirror 1.669 0.00475 0.371
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|Author:||Yuan, Haidong; Yang, Zhigang; Li, Qiliang|
|Publication:||SAE International Journal of Passenger Cars - Mechanical Systems|
|Article Type:||Technical report|
|Date:||Jul 1, 2017|
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