Computational aero-acoustic modelling of external rear-view mirrors on a mid-sized Sedan

Abstract

Ever-rising fuel costs necessitate design of fuel-efficient vehicles. Consequently, modern vehicle manufacturers are focused on designing low aerodynamic drag vehicles which would in-turn reduce the fuel consumption. This study analyses the contribution of external rear-view mirrors to the total drag force and the overall sound pressure level at the A, B and C pillars, while optimising the external rear-view mirror design accordingly. Solid Works renditions of external rear-view mirror models mounted on a reference luxury sedan were analysed using a commercially available computational fluid dynamic package ANSYS FLUENT. A different approach was followed to carry out the empirical flow visualisation and predict sound pressure levels. The aerodynamic characterisation of the vehicle was done utilising the widely used shear stress transport turbulence model, while the analysis of wind noise and the contributing vortices employed a large eddy simulation. This approach significantly reduced computational time without compromising on accuracy.

Keywords

Aero-acoustics computational fluid dynamics side-view mirrors optimisation

Introduction

Research through the last couple of decades has shown that the key to energy saving lies in aerodynamic drag reduction in the vehicle. The number flow separations on modern vehicles have gone down drastically as a result of the above-mentioned findings. However, flow control over a vehicle mounted with external rear-view mirrors (ERVMs), and present generation door handles (especially on top range cars), is becoming an uphill task. The vibration and sound caused by the outer rear-view mirrors have been studied,¹ using numerical simulation.² The unsteady patterns of the vortices causing wind noise and vibration are usually the result of variations in flow structure. However, the importance of drag reduction by varying the effect of drag and noise caused by an ERVM at different velocities has been paid very little attention. The turbulent structures of mirror wake regions have been measured by high-speed particle image velocimetry (PIV), and the multi-scale structures have been analysed by wavelet multi-resolution technique.³ It was found that the size of vortices and the vorticity concentration increase with Reynolds number. It is clear that a methodology to define the flow structures accurately is the first step towards an attempt to predict the causes of wind noise.⁴

Another method by which velocity vector field fluctuations in velocity in the mirror wake are calculated is hot wire anemometry and laser Doppler velocimetry, in a blown down wind tunnel,⁵ which showed that the frequencies of vortex shedding in the mirror wake were all under 50 Hz. These studies have provided a wide range of reasons as to how the drag is affected by the vortices behind the ERVMs but a way to reduce the same drag has not been discussed. The drag and wind noise caused can be considerably decreased by experimenting with various designs of ERVM casings, which motivates our study.

This article focuses on the drag contribution of external rear-view mirrors and how to optimise them by varying designs. Also, the sound pressure levels (SPLs) at A, B and C pillars of a typical mid-segment luxury sedan have been calculated. First, there was a considerable difference in drag coefficient values when the different models were mounted on the sedan and simulated using ANSYS FLUENT. This prompted measurement of noise levels at different points of the vehicle. The ERVM is a major hotspot for vortex formation on a vehicle at high velocities as there is no bigger protrusion than this obstructing the upstream flow of wind. There is another major factor contributing to the design-based problems and that is ergonomics. An ERVM should always be designed according to the needs and comfort of the driver.⁶

Basically, a two-step approach was followed in visualising the flow regions and to find the SPLs. First, the shear stress transport (SST) model was used to describe the flow around the chosen sedan, while a large eddy simulation (LES) model was adopted for finding the vortices leading to increased noise levels at the three pillars of the vehicle. This two-step approach was instrumental in decreasing the time spent on computation and did not reduce the accuracy.

Methodology

Modelling

To achieve the main objectives of this study, that is, assessing and minimising the contribution of ERVMs to the flow around the vehicle, four different models were rendered using the software Solid Works. The base model created to simulate a mid-sized luxury sedan was considered as case 1; the three other cases had three different ERVMs mounted on the base model. The models considered are depicted in Figures 1 –4.

Figure 1.

Base model (case 1).

Figure 2.

Mirror 1 (case 2).

Figure 3.

Mirror 2 (case 3).

Figure 4.

Mirror 3 (case 4).

Grid construction

The grid generated for the prototypes was unstructured, based on proximity and curvature. The mesh was made to be more refined near the wall region, in the immediacy of the vehicle body, with reducing mesh density on moving away from the body. Additionally, a body of influence was introduced, measuring approximately 1.5 times the prototype dimensions, to create a cuboidal region of fine equisized elements. A soft transition with a growth rate of 1.2 was employed, to ensure gradual increase in the cell size. Inflation layers were introduced to accurately capture the boundary layer, with initial Y-Plus values of less than 1, which the LES necessitates. The programme controlled inflation with five layers was introduced on the ground and vehicle body, using the first aspect ratio approach. The final mesh contained approximately 5 million elements in the computational domain, with slight variations due to the change in ERVM design in the considered cases. The grid was constructed taking the suggestions of Lanfrit,⁷ who has categorically explained the best practices to obtain good-quality meshes for automotive aerodynamic studies (Figure 5).

Figure 5.

Computational domain and grid structure of base model.

Case setup

The computational case was setup to simulate the test section of a wind tunnel with a vehicle secured on the floor of the section. A constant velocity of 144 km/hr, in the direction of vehicle motion corresponding to a Reynolds number of Re = 2.58 x 10⁶, was assigned to the velocity inlet at a turbulence intensity of 1%. The vehicle body being symmetric allowed the use of a symmetry boundary condition at the plane of symmetry, thereby requiring the modelling of only one half of the entire computational domain. The pressure outlet at 1 atm was assigned a turbulence intensity of 5%. All solid walls on the model were assigned with a no-slip boundary condition to facilitate the development of the boundary layer.

Governing equations

The analysis of the three-dimensional flow around the models necessitated the use of appropriate governing equations catering to the conservation of mass and momentum. With the study not requiring the investigation of heat transfer, it was not necessary to include the energy equation. The fundamental physical principle of mass conservation inside a given control volume is monitored by the continuity equation articulated below⁸

\frac{\partial ρ}{\partial t} + [\frac{\partial (ρ u)}{\partial x} + \frac{\partial (ρ v)}{\partial y} + \frac{\partial (ρ w)}{\partial z}] = 0

(1)

In equation (1), $ρ$ is the density of air, $t$ represents the time and $u, v and w$ denote the velocity in the $x, y and z$ directions, respectively.

The conservation of momentum in the three dimensions has been addressed by the Navier–Stokes equations⁸

ρ \frac{D u}{D t} = - \frac{\partial P}{\partial x} + \frac{\partial τ_{x x}}{\partial x} + \frac{\partial τ_{y x}}{\partial y} + \frac{\partial τ_{z x}}{\partial z} + ρ f_{x}

(2)

ρ \frac{D v}{D t} = - \frac{\partial P}{\partial y} + \frac{\partial τ_{x y}}{\partial x} + \frac{\partial τ_{y y}}{\partial y} + \frac{\partial τ_{z y}}{\partial z} + ρ f_{y}

(3)

ρ \frac{D w}{D t} = - \frac{\partial P}{\partial z} + \frac{\partial τ_{x z}}{\partial x} + \frac{\partial τ_{y z}}{\partial y} + \frac{\partial τ_{z z}}{\partial z} + ρ f_{z}

(4)

In equation (4), P is the pressure, while $u, v and w$ denote the velocity components in the $x, y and z$ directions, respectively, with $f_{x}, f_{y} and f_{z}$ being the body force per unit mass in the $x, y and z$ directions, respectively.

With the dipole wind noise generated being the prime focus, a high-Reynolds-number case was considered where the aural characteristics would be more prominent. Hence, the turbulent flow at these locations requires turbulence modelling to obtain closure to the Navier–Stokes’ equation.

Turbulence modelling

Several turbulence models have been utilised for car-body analysis, with their selection resting on the result of a trade-off between superiority, ease of convergence and computational resources. The two-equation Menter’s K-ω SST model has been widely preferred for its potency in modelling both near-field and far-field flows. Ramchandran et al.⁹ have extended the above model to the analysis of a bluff body with door handles.

The analysis of noise generated by the turbulent flow requires the solution of the flow field which is used to calculate the acoustic sources. This is possible through more expensive models like the LES which has been gaining popularity for challenging applications like vortex shedding and aero-acoustics. With different models being more efficient in different scenarios, a two-step computational process was adopted. From the works of Lokhande et al.,¹⁰ who have used the combination of K-ε and LES and Tsai et al.,¹¹ who have used a K-ε Re-Normalisation Group (RNG) model along with the LES, it is inferred that researchers have found a two-step process more viable, and computationally less expensive while providing desired results. This article highlights a similar process where the aerodynamic characteristics are ascertained by Menter’s K-ω SST model and the aero-acoustic qualities are determined by the LES model with the activated Ffowcs Williams–Hawkings (FW-H) acoustic model.

SST K-ω model

A two-equation eddy viscosity turbulence model and the SST K-ω model have become very popular. The SST model utilises model transport equations based on turbulent kinetic energy (K) and specific dissipation rate (ω) similar to the standard K-ω model. The SST model formulated by Menter and colleagues^12,13 blends the accuracy of the K-ω model in the near wall region up to the viscous sub-layer, with the free-stream independence of the K-ε model in the far-field region avoiding extreme sensitivity of the K-ω model to the inlet turbulence conditions. This has been accomplished with the introduction of a blending function which activates the required turbulence model according to the proximity to the surface. This makes the SST model adept and reliable for a wider class of flows especially in adverse pressure gradients and separating flows. The transport equations for the model are given by¹⁴

\frac{\partial}{\partial t} (ρ κ) + \frac{\partial}{\partial x_{i}} (ρ κ u_{i}) = \frac{\partial}{\partial x_{j}} (Γ_{κ} \frac{\partial κ}{\partial x_{j}}) + {\tilde{G}}_{κ} - Y_{κ} + S_{κ}

(5)

\begin{array}{l} \frac{\partial}{\partial t} (ρ ω) + \frac{\partial}{\partial x_{i}} (ρ ω u_{i}) = \frac{\partial}{\partial x_{j}} (Γ_{ω} \frac{\partial ω}{\partial x_{j}}) \\ + G_{ω} - Y_{ω} + S_{ω} + D_{ω} \end{array}

(6)

where ${\tilde{G}}_{κ} and G_{ω}$ represent the generation of turbulent kinetic energy and $ω$ , respectively; $Γ_{κ} and Γ_{ω}$ symbolise the effective diffusivity of $κ and ω,$ respectively; $Y_{κ} and Y_{ω}$ denote the turbulent dissipation of $κ and ω$ , respectively; and $S_{κ} and S_{ω}$ are user-defined source terms

Γ_{i} = μ + \frac{μ_{t}}{σ_{i}}, where i = ω, κ

(7)

The term $σ_{i}$ refers to turbulent Prandtl numbers of $κ and ω$ ; $μ_{t}$ is the turbulent viscosity given by

μ_{t} = \frac{ρ κ}{ω} \frac{1}{m a x [\frac{1}{α^{*}}, \frac{S F_{2}}{a_{1} ω}]}

(8)

σ_{i} = \frac{1}{F_{1} / σ_{i, 1} + (1 - F_{1}) / σ_{i, 2}}, where i = ω, κ

(9)

where $S$ is the strain rate magnitude and $F_{1} and F_{2}$ are the blending functions.

$D_{ω}$ is the cross-diffusion term defined as

D_{ω} = 2 (1 - F_{1}) ρ σ_{ω, 2} \frac{1}{ω} \frac{\partial κ}{\partial x_{j}} \frac{\partial ω}{\partial x_{j}}

(10)

A few constants used in the model are given by $σ_{κ, 1} = 1.176$ , $σ_{ω, 1} = 2.0$ , $σ_{κ, 2} = 1.0$ , $σ_{ω, 2} = 1.168$ and $a_{1} = 0.31$ .

LES

The LES model is a combination of a direct numerical recreation and a more conventional turbulence modelling. With the large eddies being dependant on the geometry and flow conditions, while small eddies are more universal, the LES resolves the time and space dependence of the fluid flow to a certain filter length. Numerically, the velocity field can be divided into resolved and unresolved parts. The large-scale eddies are resolved completely, while the unresolved part includes sub-grid scales (small eddies). The resulting appearance of unknown Reynolds sub-grid-scale stresses requires further modelling using a sub-grid-scale turbulence model. Thereby in terms of usage of computational resources, LES can be placed in between the direct numerical simulation (DNS) approach, where all scales are resolved and the Reynolds-averaged Navier–Stokes (RANS) approach, in which all the eddies are modelled regardless of the scale. This technique is very efficient for a flow where the transportation of scalars like momentum and mass is done predominantly by large eddies and not by small (filtered) eddies. The formulation of the LES turbulence model in Einstein notations is as follows¹⁴

\frac{\partial {\bar{u}}_{i}}{\partial t} + \bar{u_{j}} \frac{\partial {\bar{u}}_{i}}{\partial x_{j}} = - \frac{1}{ρ} \frac{\partial \bar{p}}{\partial x_{i}} + ν \frac{\partial^{2} {\bar{u}}_{i}}{\partial x_{j} \partial x_{j}} - \frac{\partial τ_{i j}}{\partial x_{j}}

(11)

where the sub-grid-scale stress $τ_{i j}$ is given by

τ_{i j} = \bar{u_{i} u_{j}} - {\bar{u}}_{i} {\bar{u}}_{j}

(12)

The sub-grid-scale turbulence model uses the Boussinesq hypothesis, where the deviatoric part of Sub-Grid-Scale(SGS) stresses are calculated using

τ_{i j} - \frac{1}{3} τ_{k k} δ_{i j} = - 2 μ_{t} {\bar{S}}_{i j}

(13)

In equation (13), $μ_{t}$ is the sub-grid-scale turbulent viscosity. The Smagorinsky–Lilly model, first proposed by Smagorinsky,¹⁵ is used to model the eddy viscosity

μ_{t} = ρ L_{S}^{2} | \bar{S} |

(14)

The mixing length scale $L_{S}$ is defined as

L_{S} = m i n (κ d, C_{S} Δ)

(15)

where $κ$ is the Von Karman constant; $d$ is the distance from closest wall; $C_{S}$ is the Smagorinsky constant, which for this study takes on the value of 0.1; and $Δ$ is the local grid scale.

The variables are defined as

| \bar{S} | = \sqrt{2 {\bar{S}}_{i j} {\bar{S}}_{i j}}

(16)

where ${\bar{S}}_{i j} = \frac{1}{2} (\frac{\partial {\bar{u}}_{i}}{\partial x_{j}} + \frac{\partial {\bar{u}}_{j}}{\partial x_{i}})$

Δ = V^{1 / 3}

where $V$ is the volume of the computational cell.

For incompressible flows, $τ_{k k}$ can be neglected and thereby the Smagorinsky–Lilly model relates to the SGS turbulent stresses to the fluid strains through the equation

τ_{i j} = - 2 ρ {[m i n (κ d, C_{S} Δ)]}^{2} | \bar{S} | {\bar{S}}_{i j}

(17)

FW-H acoustic analogy

The analysis of the flow-induced noise is carried out using an integration method based on Lighthill’s acoustic analogy – explained thoroughly for low Mach number flows by Layton and Novotný,¹⁶ which is a rearrangement of the Navier–Stokes equations and the continuity equation into an inhomogeneous wave equation. The solution to the FW-H acoustic model, which is achieved through the use of a free-space Green function, contains volume integrals which represent the contribution of quadrapole sources and surface integrals which predominantly denote the contribution of monopole and dipole sources to the aerodynamic noise. In a case where the Mach number of the flow is low (subsonic regimes), similar to the one in this study, the quadrapole contribution is minimal. As such, the volumetric integrals are dropped by the employed solver. The FW-H analogy requires the receivers to be placed outside the source which is defined by the control surface (FW-H surface), also the receivers need to be placed away from wakes and separated flows, in mid- or far-field regions. Yang et al.¹⁷ have successfully demonstrated the usage of the FW-H analogy in their work. The FW-H equation can be written as¹⁸

\begin{array}{l} \frac{1}{a_{0}^{2}} \frac{\partial^{2} p^{'}}{\partial t^{2}} - Δ^{2} p^{'} = \frac{\partial^{2}}{\partial x_{i} \partial x_{j}} {T_{i j} H (f)} \\ - \frac{\partial}{\partial x_{i}} {[P_{i j} n_{j} + ρ u_{i} (u_{n} - v_{n})] δ (f)} \\ + \frac{\partial}{\partial t} {[ρ_{0} v_{n} + ρ (u_{n} - v_{n})] δ (f)} \end{array}

(18)

In equation (18), $u_{i}$ = fluid velocity component in the x_i direction, $u_{n}$ = fluid velocity component normal to surface f = 0, $v_{i} = surface velocity component in the x_{i} direction,$ $v_{n} = surface velocity component normal to the surface,$ δ (f) = Dirac delta function $δ (f)$ , $H (f) = Heaviside function$ , $a_{0}$ = speed of sound in the far-field, $p^{'}$ = far-field sound pressure and $f = 0$ refers to the FW-H surface which is used to embed the external flow problem $(f > 0)$ and facilitates the use of the free-space Green function to obtain the solution. The FW-H corresponds to the emission surface and is made to be coincident to the body surface.

$T_{i j}$ is the Lighthill stress tensor given by

T_{i j} = ρ u_{i} u_{j} + P_{i j} - a_{0}^{2} (ρ - ρ_{0}) δ_{i j}

(19)

where $δ_{i j}$ is Kroenecker’s delta, and $P_{i j}$ is the compressive stress tensor and for a Stokesian fluid is given by

P_{i j} = p δ_{i j} - μ [\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}} - \frac{2}{3} \frac{\partial u_{k}}{\partial x_{k}} δ_{i j}]

(20)

The transient pressure fluctuation on the surface of the vehicle body and ERVM (acoustic sources) is computed by the transient flow analysis using LES, which is necessary to obtain the solution to the FW-H equation. The sources in this study can be categorised as dipole sources, where the aerodynamic noise is generated due to the interaction of the fluid with a solid surface. The static pressure for every cell is evaluated and recorded. The FW-H model permits the use of multiple sources and receivers. The pressure signals obtained are post-processed using a fast Fourier transform (FFT) routine to compute the SPL and power spectra, converting the time histories of the signals to frequency-based results. The maximum frequency is dependent on the size of the time step being used, with it being inversely proportional to twice the value of the employed time step; in this study, with a time step of 5 x 10^–6, the maximum frequency is 100 kHz, and it reduces to 50 kHz as source data write frequency is 2. SPLs, which are logarithmic measures of relative sound pressure value, were converted to dB units using the formulation

L_{P} = 20 \log_{10} (\frac{p}{p_{0}}) d B

(21)

where $p$ is the recorded pressure and $p_{0}$ is the reference pressure which is 20 µPa. For multiple sources, the SPL is computed as

L_{P, E q} = 10 \log_{10} \sum_{i = 1}^{n} {(\frac{p_{i}}{p_{0}})}^{2}

(22)

Validation studies

Validation through an Ahmed body

With the focus of this study on the aerodynamic drag of mid-sized sedans, a validation has been carried out on the methodology being employed against experimental and computational results obtained on the Ahmed body (Figures 6 and 7).

Figure 6.

Dimensions of Ahmed body.

Figure 7.

Grid structure for Ahmed body.

The Ahmed body was modelled with the dimensions depicted in the above figure with a back rake angle of 25°. An enclosure was then created to have an inlet at five times the car length from the Ahmed body and the outlet at seven times the car length. The height of the enclosure was taken as four car lengths. The solution converges after approximately 6000 iterations.

A grid independence study has been done with the coefficient of drag obtained at five different grid sizes, varying from about 400,000 elements to 12.2 million elements. The computed value of C_D has been calculated to be 0.2857 compared with the experimental value of 0.299 (Figure 8).¹⁹

Figure 8.

Velocity of flow over Ahmed body.

Validation through a two-dimensional cylinder case

Acoustic pressure or local pressure deviations at various probe points were recorded on a transient frame to ascertain the SPLs. The overall sound pressure level (OASPL) is what is required to distinguish between the acoustic characteristics of different models. A two-dimensional (2D) cylinder was utilised to study the pressure variations, with a probe placed inside the domain under consideration to validate the computational model being engaged. The 2D cylinder model is of radius R = 0.01 m and the probe point is placed at a distance of 1.3 m from the centre above the horizontal axis and subtending an angle of 45° with it, creating a record point at an r/R = 130. The model has been depicted in Figure 9.

Figure 9.

Grid for the 2D cylinder.

The computational domain extends 10R upstream and 40R downstream. The boundaries of the enclosing block were assigned certain conditions, the top and bottom boundaries acting as symmetric walls so as to avoid boundary layer formation on the walls. The boundary on the left was assigned as the inlet with air flowing at a velocity of υ = 40 m/s in the horizontal direction with a $Re = 2.75 \times 10^{4}$ , leaving the right boundary to act as an outlet at a pressure of 1 atm. The grid for the numerical study was created using the ANSYS ICEM computational fluid dynamic (CFD) code available commercially. An unstructured mesh with quadrilateral cells was created with 83,116 nodes defining the entirety of the enclosed model. The simulation was done at courant numbers of the order 1. The SST model was used to obtain the aerodynamic characteristics, while the LES model along with the FW-H acoustic model was solved to obtain the acoustic results. The solver settings used for the simulation are specified in Table 1.

Table 1.

2D cylinder simulation solver settings.

Function	Setting
Fluid	Air
Transient formulation	Second-order implicit
Pressure–velocity coupling	Fractional step
Gradient discretisation	Least squares cell based
Pressure discretisation	PRESTO!
Momentum discretisation	Bounded central differencing

A plot of the acoustic spectra obtained in Figure 2 has been compared with experimental and computational results from a previous study.¹¹ The validation study of the 2D cylinder shows a very high degree of accordance with existing results, with acceptable deviance from the cited results. The SPL has been observed to peak at a Strouhal number of 0.27 amounting to 82 dB with a divergence of 4 dB from experimental data and no significant difference with the computational results, consequently verifying the ability of the currently employed two-step computational process (Figure 10).

Figure 10.

Sound pressure level at receiver 1 (r/R = 130).

Results and discussions

The analysis for the prototypes was done using the same computational settings as that of the validation models. Pressure distribution curves for all cases have been plotted in figures 14, 15, 17 and 19, while the pressure distribution around the different ERVMs have been plotted in figures 16, 18, and 20. It is evident that for all cases, the contour follows a similar path, with the pressure plot for the baseline prototype being marginally different from the other models. This is attributable to the absence of ERVMs on the first model. The coefficient of drag for typical mid-sized sedans range around 0.25.²⁰ The drag coefficient for case 1 was computed to be 0.235, which is in accordance with the referenced literature. The accuracy of the computation was determined based on the scaled residuals and the mass flow rate. Obtained results were accepted as satisfactory only if each residual and the difference of mass flow rate at inlet and outlet converged to 10⁻⁶ or below (Figure 11).

Figure 11.

Flow characteristics at the ERVM.

The drag coefficients for all the models are depicted in Figure 12. Case 1 has been found to have the least drag, which is acceptable as it does not include an ERVM, while case 2 has been found to have the highest drag. Cases 3 and 4 show significant improvements in this regard as their design included a blunted edge of a small radius with the rest of the casing shaped to facilitate a more gradual change in pressure rather than the abrupt one observed in case 2. The pressure contour for the base model is depicted in Figure 13.

Figure 12.

Values of coefficient of drag obtained for different cases.

Figure 13.

Pressure contour for base model (case 1).

Figures 14 –20 depict the variations in pressure of all the considered cases at a section coincident with their plane of symmetry. A general trend observed is that the coefficients of pressure are found to be positive near the front bumper, front windshield (where the flow stagnates) and rear windshield (where the flow separates).

Figure 14.

Pressure variation in case 1.

Figure 15.

Pressure variation in case 2 (only body).

Figure 16.

Pressure variation in case 2 (mirror 1).

Figure 17.

Pressure variation in case 3 (only body).

Figure 18.

Pressure variation in case 3 (mirror 2).

Figure 19.

Pressure variation in case 4 (only body).

Figure 20.

Pressure variation in case 4 (mirror 3).

The acoustic characteristics near the ABC pillar regions were investigated by the placement of receivers at a distance, perpendicular to the flow, from the aforementioned pillars away from the wake of the mirrors. The SPLs varied in a similar pattern for the mirror-mounted models – with the amplitude of sound peaking at A pillar, slightly lessened at B pillar and significantly lowered at C pillar (Table 2).

Table 2.

Distances of receivers at ABC pillars from point of reference.

Receiver location	X (m)	Y (m)	Z (m)
A pillar	−2.5	0.85	1.0
B pillar	−2	0.85	1.0
C pillar	−1.5	0.85	1.0

The baseline model showcases an even distribution with the SPLs being very similar at all receiver locations and having considerably lower amplitudes. These observations, in accordance with expectation, reveal the significance of ERVMs to turbulent noise. The maximum SPLs for the prototypes have been charted in Figure 21.

Figure 21.

Maximum sound pressure levels in different cases.

Conclusion

The contribution of shape factor towards the turbulent noise has been depicted in this study. It can be inferred from the obtained results that case 3 with mirror 2 has the most favourable characteristics. Significantly reduced vortex shedding due to the aerodynamic shape of the mirror resulted in SPLs significantly lower than case 2 – with a generic mirror mounted on it (a maximum deviation of 9.3% was observed) and slightly lower amplitudes than case 1 (with a maximum deviation of 2.7%) which was without a mirror mounted on it. A possible reason could be that the placement of the mirror broke up the vortices near pillar A region – thereby reducing OASPL and drag, while its addition caused a smaller increase in the amplitude than the decrease which could be attributed to its design and positioning.

The observed trend for mirror-mounted models reveal that the amplitude of sound reduces marginally from A to B pillar regions, but has a steeper descent at C pillar region, whereas the baseline model has similar SPLs at all three regions – with minute deviations. This presents a strong case, suggesting that the mirrors do indeed have a significant effect on wind noise at AB pillar regions, while only slightly adding to the acoustic characteristics near C pillar region.

Footnotes

Acknowledgements

The authors wish to acknowledge the management of VIT University, Vellore, for their kind support to the study in the means of providing high-performance systems and required software.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

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