The Role of Forebody Topology on Aerodynamics and Aeroacoustics Characteristics of Squareback Vehicles using Computational Aeroacoustics (CAA)

This study investigates the in�uence of forebody con�guration on aerodynamic noise generation and radiation in standard squareback vehicles, employing a hybrid computational aeroacoustics approach. Initially, a widely used standard squareback body is employed to establish grid-independent solutions and validate the applied methodology against previously published experimental data. Six distinct con�gurations are examined, consisting of three bodies with A-pillars and three without A-pillars. Throughout these con�gurations, the reference area, length, and height remain consistent, while systematic alterations to the forebody are implemented. The �ndings reveal that changes in the forebody design exert a substantial in�uence on both the overall aerodynamics and aeroacoustics performance of the vehicle. Notably, bodies without A-pillars exhibit a signi�cant reduction in downforce compared to their A-pillar counterparts. For all con�gurations, the �ow characteristics around the side-view mirror and the side window exhibit an asymmetrical horseshoe vortex with high-intensity pressure �uctuations, primarily within the con�nes of this vortex and the mirror wake. Side windows on bodies with A-pillars experience more pronounced pressure �uctuations, rendering these con�gurations distinctly impactful in terms of radiated noise. However, despite forebody-induced variations in pressure �uctuations impacting the side window and side-view mirror, the fundamental structure of the radiated noise remains relatively consistent. The noise pattern transitions from a cardioid-like shape to a monopole-like pattern as the probing distance from the vehicle increases.


INTRODUCTION
The automotive industry is continuously striving to revolutionise the aerodynamics and aeroacoustics environment of vehicles, aimed at alleviating discomfort, enhancing communication systems, reducing vehicular emission noise (such as the pass-by noise signature), in uencing sound barriers on urban roads, and improving overall safety [1][2][3][4].The sources of vehicle noise can primarily be classi ed into four categories: aerodynamic noise, ancillary system noise, and tire-road noise, with occasional secondary classi cations such as slosh noise, which may gain prominence [5][6][7].In the current era of vehicle electri cation, aerodynamic noise is of primary signi cance during cruising, as wind-induced noise increases with vehicle speed and supersedes tire noise at approximately 100 km/h [5].The reduction of aerodynamic drag is a crucial objective for Electric Vehicle (EV) manufacturers, as it directly in uences the driving range of electric vehicles.However, it is important to note that the signi cance of aerodynamics extends beyond mere energy e ciency.In the context of EVs, aeroacoustics also plays a critical role in enhancing the overall driving experience and passenger comfort.For example, eliminating exterior mirrors and replacing them with cameras and screens can further reduce wind noise and aerodynamic drag by up to 7%, regulatory obstacles currently hinder this approach, despite potential bene ts for EV manufacturers [8].Whilst reducing aerodynamic drag is crucial for EVs, it does not automatically ensure low wind noise.The primary factors causing aerodynamic drag and noise in a bluff body vehicle are attributed to ow separation around features such as A-pillar, exterior mirrors, and front side glass, which can lead to wind noise issues independent of drag.It is important to highlight that these features are situated in the forebody of the vehicle, where the interaction with the upstream ow can give rise to distinctive pressure uctuations and radiated noise in addition to the aerodynamic forces experienced by the vehicle.For instance, the interface between the A-pillar and mirror generates much of the high-frequency aeroacoustics energy radiated from the vehicle [9][10][11] in addition to altering the vehicle drag by ~ 13.3% [9].Therefore, alongside the emphasis on aerodynamic drag reduction, there is a growing recognition of the importance of addressing the overall aeroacoustics signature of the vehicle [12][13][14][15][16].
Many studies have employed a range of experimental and numerical techniques to examine the mechanisms underlying wind-induced noise radiation.These studies have covered a wide spectrum of scenarios, ranging from isolated features such as generic half-round side-view mirrors [17][18][19][20][21] to standard squareback SAE-T4 geometries that incorporate simpli ed side-view mirror representations with both generic and modi ed A-pillars [11,22,23].Investigations have also been conducted on SAE-T4 models without side-view mirrors but with an A-pillar [9,24], as well as with realistic mirrors [22,25,26].
These investigations have shed light on the interactions between separated ows resulting from different A-pillar topologies, thereby altering the mirror wake vortices and pressure recovery and subsequently enhancing the generation and propagation of noise radiated from vehicles.
Numerical approaches for aeroacoustics simulations can be broadly categorized as hybrid and direct methods.Hybrid methods commonly employ incompressible Computational Fluid Dynamics (CFD) coupled with aeroacoustics analogy techniques, such as Möhring, Ffowcs Williams-Hawkings (FW-H), and Kirchhoff aeroacoustics equations [22].The hybrid approach effectively decouples the ow and acoustic solvers, resulting in a less computationally demanding solution.While both hybrid and direct methods play pivotal roles in understanding the pressure uctuations and ow characteristics around automotive components, they are applied differently based on speci c objectives.Direct methods, which involve computationally demanding compressible CFD, are employed to capture induced convective and acoustic pressure uctuations, often utilising wavenumber ltering techniques.These methods have proven valuable in analysing near-eld ow around features such as side windows, mirrors, and A-pillars.
For instance, studies by Frank and Munz [52], Dawi and Akkerman [53], Beck and Munz [54], and Kabot et al. [55] have successfully utilised direct methods to identify tonal noise generation mechanisms on realistic side view mirrors.
On the other hand, hybrid methods are widely used for studying noise characteristics in the far eld, particularly focusing on the noise radiating away from the vehicle at much lower computational cost compared to Direct methods.Some of the works using hybrid method include Chode et al. [9] where they reported that the radiated pattern shows a transition from dipole-like structure to monopole-like when measuring distance is traversed away from the vehicle.While He et al. [56] demonstrated the capability of hybrid method for obtaining interior noise levels and observed that the contribution of acoustic pressure uctuations is dominant at frequencies ranges above coincidence frequency of the glass.
The distinct strengths of direct methods lie in comprehending noise transmission mechanisms to the vehicle's interior.Thus, the combined use of both hybrid and direct methods offers a comprehensive approach to gaining valuable insights into the intricate dynamics of automotive aerodynamics, providing a holistic understanding of both the near-eld and the far-eld noise signatures 11].In the realm of computational aerodynamics and aeroacoustics for automotive vehicles, RANS-LES methods have emerged as prominent approaches over the past two decades.Regardless of the chosen approach for investigating both vehicle aerodynamic performance and aeroacoustics (direct or hybrid), RANS-LES methods have gained recognition for their ability to deliver solutions with superior accuracy compared to the RANS approach [14,27,28] while remaining computationally more e cient than the full LES subjected to realistic ow conditions [9,29,30,31].To date, various RANS-LES variants, viz., DES, DDES, IDDES, and SBES approaches coupled with near-wall modelling using SST, SA, and k-ε approaches, have been extensively applied to generic and non-generic mirror geometries [52,53,54,55], SAE-T4 and DrivAer vehicle con gurations [10,11,22,32].RANS-LES-based numerical investigations on these geometries have not only shown excellent agreement with experiments but have also enhanced our understanding of ow physics.In particular, comparisons under different uid assumptions (compressible or incompressible) revealed insigni cant differences in all frequency bands for hydrodynamic pressure uctuations on the side window [11,22,32].The IDDES and the SBES-based predictions on the SAE-T4 [9,11,50] body have particularly revealed several insights, including i) the A-pillar serves as the primary noise source in the absence of a side mirror, while in the presence of a side-view mirror shifting the focus to the mirror as the major noise source; ii) the turbulent pressure uctuations predominantly excite the window below 800 Hz, while acoustic pressure uctuations dominate above 800 Hz; iii) for frequencies lower than 1 kHz, hydrodynamic pressure uctuations are primarily responsible for the window excitation; and iv) the noise radiated from the vehicle can exhibit dipole-monopole transitions at several stages based on the noise source in consideration.Despite such considerable efforts invested, several questions and unresolved aspects persist.
To the best of the authors' knowledge, existing studies on vehicle aeroacoustics have predominantly centred around SAE-T4 and DrivAer con gurations, both featuring distinct A-pillars.However, there is a noticeable gap in utilising the hybridized RANS-LES approaches coupled with far-eld approaches such as the Ffowcs Williams-Hawkings (FW-H) to predict noise signatures from various standardized vehicle con gurations.Additionally, the intricate vortex structures produced by standard bluff mirrors remain unexplored, prompting questions about potential alterations in uenced by different standard forebodies and their subsequent in uence on the overall base wake of the vehicle.The relationship between aerodynamic forces experienced by diverse forebody con gurations of squareback bodies and their potential in uence on radiated sound is of notable interest but has received relatively limited exploration.
These unexplored aspects represent a substantial knowledge gap in the current understanding of vehicle aeroacoustics and aerodynamics of different forebody squareback vehicles.The present work is primarily motivated by these critical gaps, aiming to bridge the gap in the literature by providing insights into the FW-H approach's application, the nature of vortex structures in standardized bluff mirrors, and the intricate interplay between aerodynamic forces and radiated sound across different squareback body con gurations.
The current study employs the SBES modelling approach coupled with the FW-H acoustic equation to describe the near-eld ow and far-eld noise, respectively.The key aims of the current study are threefold: i) to investigate the pattern of noise generated and radiated in six squareback vehicle con gurations, identifying in uential forebody designs, ii) to examine the role of A-pillars in modifying/interacting with the vortices generated by mirrors and their effects on noise, and iii) to explore the relationship between hydrodynamic pressure uctuations on the side window, radiated noise, and corresponding aerodynamic coe cients associated with different forebody vehicle con gurations.This paper is organised as follows: Section 2 focuses on "System Details and Forebody Design Con gurations", presenting the selection and details of the topologies of the forebody con gurations used in the study.In Section 3, "Numerical and Computational Details," the computational domain, grid details, boundary conditions, grid independence, and validation of the SBES-FWH method are discussed.Section 4, "Results and Discussions", offers an intricate analysis of surface pressure spectra, ow elds, and the generated and radiated noise, providing an in-depth exploration of acoustic signatures within diverse forebody squareback con gurations.Additionally, this section presents a comprehensive assessment of the aerodynamic coe cients and aerodynamics-aeroacoustics characteristics associated with the different forebody topologies employed.Finally, Section 5, "Conclusions" summarizes the crucial contributions and ndings derived from the study.

SYSTEM DETAILS AND FOREBODY DESIGN CONFIGURATIONS A. Forebody Topologies
In this work, the study comprises two distinct categories of full-scale simple squareback representations: bodies without a distinctive A-pillar and bodies with such a characteristic, thereby addressing the fundamental objectives outlined previously.Regarding the former, this study considers the Generic Bluff Body (GB), a model proposed by Duell and George [33], which has been utilised with LES by Krajnović and Davidson [34], as well as the Ahmed body (AB) [35].As the primary focus of this research is the examination of the in uence of forebody topology, a novel amalgamation of GB and AB, termed the Fused Generic-Ahmed Body (FB), is devised.Within the FB con guration, the upper portion of the forebody is meticulously designed to mirror the dimensions of the Ahmed body's radii, whereas the lower portion retains an identical pro le to that of the GB's.The primary motivation behind this con guration change is to investigate the consequences of leading-edge separation bubbles that form around the different curvatures of forebody corners, the periodic interaction of the upper and lower partitions of the ring vortex in the near wake of the body (contributing to drag), and the resulting near-and far-eld noise signatures.
The latter category includes well-studied forebody topologies, such as the SAE T4 body (SB) [9,[23][24], extensively investigated for Aeroacoustics, and the Windsor body (WB) [36-38], which has recently gained attention as a test case geometry, particularly with broader research participation aimed at comprehending various numerical modelling approaches [39].Both SB and WB exhibited clearly de ned but slightly exaggerated A-pillars, as shown in Fig. 1.Modern square-back vehicles, such as but not restricted to the Mercedes T-Class and Citroën ë-Berlingo, inherit forebody features from the AB, SB, and WB, resulting in a detailed A-pillar structure arising from forebody curvature.To address this con guration more closely and effectively understand the aerodynamics and aeroacoustics effects of vehicles with curved A-pillars while retaining the features of standard research bodies, the Hybrid Body (HB) is introduced in this study which combines key forebody features of the geometries mentioned above.
B. Noise Sources: location and considerations Previous experimental investigations of aeroacoustics and aerodynamics on full-scale squareback SAE-T4 geometry have identi ed key contributors to the overall noise radiation from the vehicle [9,15,23,24].These entities include the side-view mirror, A-pillar, side window, and frame, all of which are present within the forebody of the vehicle, as illustrated in Fig. 2a.
To ensure robustness, the employed modelling methodology is extensively veri ed and validated against the available experimental results of Nusser et al. [23], speci cally concerning the full-scale squareback SB geometry (detailed in Section 3).However, for other squareback geometries examined in this study, no corresponding experimental data or numerical results are available for comparison.Therefore, to ensure consistency and enable meaningful comparisons, a meticulous approach is adopted in this study to preserve identical design characteristics for speci c entities across all geometries, that is, standardising the origin, height (H), length (L), and reference area of the vehicle including mirror and struts (A) to match the SB geometry is a crucial aspect of this work, as shown in Fig. 2a.The side view mirror (see Fig. 2b) is represented as a generic square cylinder of length (l c ) in all vehicle con gurations and the side window with the frame and its position remains identical from the point of origin throughout.All models are mounted on four identical stilts (ϕ) and the same ground clearance (g c ) dimension is also maintained across all model con gurations, as shown in Fig. 2a.This comprehensive standardisation ensures a fair and unbiased assessment, enabling us to isolate and investigate the distinctive aeroacoustics and aerodynamic characteristics associated with each vehicle con guration, while effectively comparing them.The hydrodynamic excitation path on the side window of each examined geometry was probed at 39 evenly spaced measuring positions in the simulations, as depicted in Fig. 2c, emulating the approach used in the corresponding experiments [23,24].In the far-eld, multiple locations were probed to capture a comprehensive representation of the noise radiated from various topologies, including those measured experimentally by Muller et al. [24].For the convenience of readers, the complete set of CAD geometries, along with their dimensions and probing locations, are available for download from the Supplementary Material.

NUMERICAL AND COMPUTATIONAL DETAILS
The geometries studied are enclosed within a computational domain, aligned with dimensions speci ed in terms of vehicle length (L), width (W), and height (H), as shown in Fig. 3.The domain con guration is intentionally scaled up in overall size to be tailored for ground vehicle aeroacoustics, facilitating vehicle aeroacoustics simulations in strict accordance with the ERCOFTAC guidelines.This strategic adaptation is substantiated by the outcomes of previous numerical studies [9,22,23].The origin of the coordinate system, is located in the front of the geometry, as shown in Fig. 3.The inlet is located 3L from the origin, and the outlet is located at 9L.The cross-section of the domain is set at 11.1 H x 8.32 W, which results in a blockage ratio of ~ 1.5%, consistent with the previous setup [9].For all cases, a uniform in ow velocity (U ∞ ) of 27.78 m/s is assigned to the inlet which corresponds to a Reynolds Number Re L = 7 × 10 6 based on the length of the body.The inlet turbulent intensity is set to 0.1%, which is identical to the in ow conditions used in the experimental studies conducted by Müller et al. [24] and Nusser [23].The ratio of the 99% boundary layer thickness (δ 99 ) and ground clearance (g c ) is set to 1, which ensures that the effect of the ground boundary layer on the vehicle ow characteristics is minimal [40].A zero pressure is de ned for the outlet, and the surrounding walls are de ned as symmetry as shown in Fig. 3.The no-slip condition is assigned to the ground and vehicle body.
The simulations conducted in this study were carried out using ANSYS Fluent 2020 R2.Considering that the in ow velocity, corresponding to a Mach number (M) less than 0.1, the effect of compressibility is negligible, therefore, the ow is treated as incompressible which is in consistent with previous studies [9,18,22,23,41].A stress-blended Eddy Simulation (SBES) turbulence model was employed to capture the ow eld around the vehicle body.SBES has shown promising accuracy in predicting ow characteristics and resolving ow structures compared with other widely used turbulence models [9,18,41].The unique advantage of SBES is its ability to rapidly switch from RANS to LES modes in shear-separated layers and provide asymptotic shielding to RANS layers under heavy grid re nement [42,43].Following the approach described in [9], the same methodology and setup conditions were applied in this study.Regarding the numerical schemes, a bounded central difference scheme was employed for spatial discretisation and a bounded second-order implicit scheme was used for time advancement.
For unsteady SBES calculations, a fully converged solution obtained from the steady-state k-w shear stress transport (SST) turbulence model was used as the initial solution.To achieve a statistically converged solution, a time step of 1 x 10 − 4 s was employed, and the simulations were conducted for a physical time of 0.3s.Subsequently, the time step was reduced to 2.3 x 10 − 5 s, and the simulations were extended for an additional physical time of 0.35s.To mitigate potential instabilities resulting from the timestep change, the initial 0.05s is omitted from the time-averaging process.For further details on the numerical setup, readers are directed to the work of Chode et al. [9].For acoustic calculations, the surface pressure uctuations exerted on the side window, side-view mirror, frame, and A-pillar are obtained through out the time-averaging period.Approximately 13,000 samples were collected and utilised as inputs for the FW-H acoustic analogy to predict far-eld radiated noise.Microphone positions around the vehicle body were strategically chosen for investigation.Acoustic pressure data obtained at each probe position in time-domain were transformed into frequency domain using Fast Fourier Transform (FFT) after preprocessing the time input with windowing functions for enhanced accuracy.

A. Grid Assessment
An unstructured Poly-hex core grid generated using a built-in meshing tool in Fluent was utilised in this study, with a speci c focus on the forebody of the vehicle geometry.To achieve an accurate resolution of the wide range of turbulence structures responsible for exerting pressure uctuations on solid surfaces, local grid re nements were generated to obtain a uniform distribution of cells.The surface grid sizes were determined based on wall-normalised units, whereas the free-stream sizes were estimated using characteristic length scales.The Taylor microscale (λ T ) is used as the reference eddy size to determine the eddies which are in uenced by viscosity.Taylor microscale is de ned as where Re H is the Reynolds number based on the height of the vehicle [31,45,46,51].
For the grid evaluation and validation of the methodology, an SAE reference body with a squareback con guration (SB, see Fig. 1) was selected.The choice is based on the availability of reproducible and comparable experimental data from the published works of Nusser [23].To conduct the grid evaluation study, three poly hex core grids (Coarse, Medium, and Fine) are generated for the SB geometry.In the generation of all three grids, careful attention has been given to maintaining a Δy + < 1 on the SAE T4 body.The surface grid sizes were set as follows: for the coarse grid, Δx + = 140-1200 and Δz + = 140-1200; for the medium grid, Δx + = 70-980 and Δz + = 70-980 are used and for the ne grid, Δx + = 70-600 and Δz + = 70-600.Signi cant re nements have been made to the grid in the regions surrounding the wake of the vehicle and forebody.In the wake, the cell size of the grid has been reduced from 4λ T (coarse) to λ T ( ne) and for the forebody, the grid size has been varied from 2λ T (coarse) to 0.5λ T ( ne).An overview of the medium grid generated around the reference geometry is shown in Fig. 4. The total cell count of the medium grid for the geometries used in this study is approximately 25.2 x10 6 .
Comparing the coarse and medium grids, the overall drag coe cient (Cd vehicle ) shows a difference of 6.5%, whereas the difference between the medium and ne grids is 0.1%.The drag coe cient of the mirror ( , where F s is Force component in streamwise direction and S represents Reference area of the mirror) exhibits similar differences, with a 4.62% difference between the coarse and medium grids and yielding a mere 0.5% difference between the medium and ne grids.A comparison was made between the time-averaged streamwise velocity predictions for the vehicle and wake, as illustrated in Fig. 5.The qualitative differences between the medium and ne grids were minimal, but a considerable difference was observed in the velocity pro les predicted by the coarse grid in the wake.From a quantitative standpoint, the maximum differences in the three grids are observed at y/H = 1.21, here, the difference between the medium and coarse grid amounts to 3.78%, while the disparity between the medium and ne grid is 1.22% at y/H = 1.31.
In addition, a comparison of the mesh cutoff frequencies for the sensor located on the side window was conducted.The mesh cut-off frequency, denoted as f mc , is de ned as , where is the time-averaged kinetic energy, and represents the length of the cell [21].Both the medium and ne grids included a local re nement closer to the side window of 0.5λ T .This re nement corresponds to approximately 22 points per wave ( , where c is the speed of sound) for a frequency of ~ 4 kHz.The mesh cutoff frequencies obtained for the ve probe positions were compared and are presented in Table 1.The difference between the f mc values obtained for both the ne and medium grids was less than 8 Hz on average.Interestingly, despite using smaller grid sizes in the ne-grid case, the difference between the ne and medium predictions was minimal.

B. Validation and Veri cation
The methodology used in this study is validated using the experimental data presented by Nusser [23].
The pressure uctuations obtained is processed using a sample frequency of 3 Hz with Hanning window and 50% overlap which is consistent with the methodology used in previous study [9,18].The hydrodynamic pressure uctuations (HPF) obtained at Pos 1, situated on the side window (See Fig. 2c for identifying the sensor position on the side window), show that both the medium and ne grids predicted the presence of two aeolian tones at 40 Hz and 80 Hz which agrees well with the experimental data (See Fig. 6).The peak observed in the experimental data and the predicted data correspond to a Strouhal number ( ) of 0.116, which corresponds to the St of the square cylinder at a Strouhal frequency of 40 Hz.Despite the accurate prediction of aeolian tones at peak frequencies corresponding to 40 and 80 Hz, a difference of 3.19% and 4.01% is observed in the amplitude predicted by the medium and 2.8% and 3.6% the ne grid respectively compared to the experimental data.Additionally, while the coarse grid con guration successfully predicts intensity levels comparable to those of the medium and ne grids, there are disparities of 6.6 Hz and 4.4 Hz in the frequencies at which peak intensities are projected, as compared to both the medium and ne grid con gurations.Given the marginal differences observed between the medium and ne grids across a range of predictions, encompassing the pressure spectra, cut-off frequencies, HPF data, and velocity wake pro les, it becomes apparent that opting for the medium grid con guration is a notably prudent decision for this study.This choice is underpinned by its good agreement with the experimental results and reduced computational demand.

RESULTS AND DISCUSSION
This section provides an in-depth analysis of the outcomes derived from numerical simulations, conducted on two fundamental aspects.Firstly, it delves into the prominent ow characteristics and aerodynamic forces arising from distinct forebody con gurations.Subsequently, it explores the generation and emission of noise by these forebodies.

A. Distinctive Flow Features of Various Forebody Squareback Con gurations
The analysis of overall drag (Cd vehicle as de ned in Eq. 1) across all con gurations revealed a remarkable degree of uniformity, with variations of merely 1%, as presented in Table 2. Similarly, the predicted wake lengths for all cases as represented in Fig. 7 shows a high degree of similarity amongst all con gurations examined in this study.In terms of lift characteristics, all con gurations under scrutiny exhibited negative lift (downforce) obtained from Cl vehicle in Eq. 1.The (SB) con guration displayed the least downforce, while the (AB) design yielded the highest downforce.Notably, con gurations featuring an A-pillar experienced signi cantly reduced downforce in comparison to their no A-pillar counterparts, emphasizing the in uential role of the forebody in affecting the overall lift.This result was corroborated through the evaluation of forebody drag coe cient, denoted as Cd f in Table 2 that elucidates that those con guration with A-pillars encountered lessened stagnation pressure on the front, in a marked contrast to those con gurations without A-pillars examined in this study.
Furthermore, in Fig. 7 it is observed that all the bodies under examination exhibit a characteristic pattern of two distinct recirculation regions in their wake, upper and lower trapped vortices and the strength of the upper vortices is more compared to the lower vortices which is typical for a squareback con guration [48].The strength of the upper vortices increases with change in complex curvature of the forebody.In the case of bodies with A-pillars and rounded edges, namely the SB and HB, the focal point (denoted as f u (upper) and f d (lower)) f u1 appears closer to the base of the body.However, for the WB, which has a sharp edge at the base, the focal points diminish in number and appear further away from the base, indicating that the ow is less separated.
Here, Cd vehicle , and Cl vehicle represent the coe cient of drag and lift respectively, while F d and F l indicate the predicted drag and lift force while A, is the reference area of the vehicle including the mirror and struts (Frontal Area).

2
where, and are the static pressure in the freestream and at the point where the pressure coe cient is evaluated respectively and is the density of the uid in the freestream.Figure 8 shows the pressure coe cient (Cp), de ned as indicated in Eq. 2. The Cp pro les extracted from the midplane of the mirrors across all con gurations reveal a consistent pattern that includes a stagnation point on the frontal surface peaking at x/l c = 2.5, with ow separation occurring and not reattaching at the top and bottom surfaces of the mirror at x/l c = 1 to 2 and 3 to 4. This behaviour is in line with previous studies on cubes and square cylinders, as demonstrated by Castro and Robbins [49] and Wang et al. [47].On the top surface of the mirror at x/l c = 3 to 4, the Cp pro les for various forebody con gurations exhibit similar curvatures, with the exception that mirrors mounted on bodies without Apillar experience reduced ow separation compared to those with A-pillars.However, a notable observation lies in the x/l c = 0 to 1 region, which corresponds to the rear side of the mirror.Here, it is intriguing to note that the GB and WB con gurations demonstrate less ow separation compared to the other con gurations, which is corroborated by the lower Cd m values in GB and WB compared to the con gurations SB and HB, where the highest mirror drag values are predicted, as shown in Table 2.
For all con gurations examined, the ow separation from the mirror results in the formation of two distinct counter-rotating vortices, V 1 and V 2 , originating from the top and bottom faces of the mirror, respectively as shown in Fig. 9.Although the changes in forebody con gurations had a negligible impact on the generation of these mirror-induced vortices.However, it's worth highlighting that there are variations within the structures of V 1 and V 2 themselves, in uenced by the speci c forebody con guration.In all cases, both V 1 and V 2 strengthen as they progress towards the vehicle's wake, as detailed in Table 3, with V 1 being stronger than V 2 .Importantly, this behaviour is not in uenced by the variations in the forebody con guration.However, the angle at which these vortices traverse in relation to the mirror's central axis (α' and α) is asymmetrical in nature, and α' is in uenced by the presence of the Apillar, as shown in Fig. 9.For the SB con guration, α' is the most pronounced among those examined, due to the interaction of ow from the A-pillar with the horseshoe vortex around the mirror.Conversely, in cases such as WB, the A-pillar's angle aids in aligning V 1 and V 2 more closely with the mirror's central axis in the streamwise direction.The effect of mirror-induced vortices on the vehicle's wake is depicted in Fig. 10, where ow separation is more prominent on the mirror side (CDw m ) than the no-mirror side (CDw' m ).The pressure imbalance between CDw m and CDw' m indicates that bodies with inherent sharp edges at the base, such as the GB, tend to experience less imbalance compared to those with rounded edges, as presented in the last column of Table 2.All the investigated squareback con gurations exhibit the emergence of a toroidal vortex ring in the near wake of the body [48,49].Flow separation from the roof, underbody, and side walls of the vehicle creates shear layers, which ultimately converge at the rear edges of the vehicle's base.
These converging shear layers give rise to a circular vortex ring, a characteristic feature of squareback vehicle wakes.Conditions such as nearly equal strength of upper and lower horseshoe vortices in the separation bubble can lead to their merging and the subsequent development of such a ring vortex, as shown in Fig. 7.For con gurations with sharp corners at the base, such as the GB, FB, WB, and AB, the toroidal vortex ring shows a high degree of similarity.In the case of bodies with curved corners on the base, such as SB and HB, it indicates a low-pressure region closer to the w m side covering the curved corners.This indicates that the ow is more separated compared to the sharp-edged bodies, owing to the mirror-induced vortex (V 1 ) traversing along the rounded edges, as shown in Fig. 9, and evidenced by the larger angle α' associated with V 1 for both SB and HB.
To gain insight into the interaction of the A-pillar with the sideview mirror, the instantaneous ow structures for different forebody cases are compared, as shown in Fig. 11.At the upstream of the mirror, the presence of a horseshoe vortex is evident for all cases, with highly unsteady smaller eddies generated downstream that interact with the A-pillar vortices, particularly in the case of SB than compared to the WB and HB.Interestingly, for cases without the A-pillar, a distinct vortex roll-up of the roof vortex was observed in FB (See Fig. 11b, marked by V r ) from the leading edge of the roof which is less prominent with the other cases such as the GB and AB.This roll-up is due to the presence of a sharp edge connecting the front curvature of the body and roof, which is unique to this con guration.Examining the ow behaviour closer to the mirror and side window, the time-averaged wall shear stresses of the ow on the forebody proximal to the side-view mirror and the side window are assessed, as shown in Fig. 12.The ow characteristics around the side-view mirror can be characterised based on the characteristics length as presented in previous studies of the standard cube cases by Wang et.al [17,47].The wake of the mirror is indicated by L ws , the smallest wake length is observed for the WB for all the cases investigated, whereas for the no A-pillar con gurations, the smallest wake is reported for the AB.It is observed that the horseshoe vortex that is formed around the mirror, is asymmetric in the normal direction for all cases examined.In most instances, L hy+ is dominant, as presented in Table 4, except in the case of SB, where L hy− prevails due to the A-pillar's proximity to the side-view mirror.In the SB case, the ow emanating from the A-pillar interacts with the horseshoe vortex in the L hy+ direction, consequently pushing the horseshoe vortex downwards of the mirror, which is also evidenced in Fig. 11d.Considering that the side-view mirror is the major source of noise generation in vehicles, the interaction of the ow from the mirror emanating from various forebody con gurations with other surfaces causes noise generation on the side window, and eventually gets radiated from the vehicle.In the following section, the generation of this aerodynamic noise and its directivity patterns representing the angular distribution of the radiated sound eld is discussed.
B. Analysis of the Aerodynamic Noise Generated and Radiated Figure 13 illustrates the overall distribution of hydrodynamic pressure uctuations (p') on the side window, represented by the root-mean-square of (p'), given by p' rms .The numerical predictions suggest that high-intensity pressure uctuations affecting the side window are primarily located within the horseshoe vortex and L ws .The intensity levels predicted for SB con guration are in agreement with the experimental data [23].Notably, the side window of the SB con guration experiences higher overall intensity levels, while the GB exhibits lower intensity levels.The high-intensity zones situated behind the side-view mirror exhibit asymmetrical behaviour, a result of the nature of the horseshoe vortex development, as indicated by the values presented for L hy+ and L hy− in Table 4.In cases with A-pillars, the interaction of upstream ow with the horseshoe vortex is more pronounced, leading to pressure uctuations extending up to the trailing edges of the side window.In contrast, for bodies without A-pillars, the pressure uctuations diminish after the midsection of the side window, as shown in Fig. 13.
Hydrodynamic pressure uctuations (HPF) extracted at positions 18 and 25, closer to the edges of the side window, indicate a reduction in intensity levels for bodies without A-pillars, as depicted in Fig. 14.Notably, experimental data reveals the presence of an aeolian tone at 40 Hz for SB (as shown in Fig. 6 at Pos1), while HB also reports peak intensity at 40 Hz.Conversely, other bodies display a slight shift in peak intensity by approximately ~ 3-4 Hz, consistent across locations where HPF is extracted (Pos 3, 7, 12, 18, and 25).This shift can be attributed to the presence of the A-pillar, which alters the horseshoe vortex and delays vortex shedding from the mirror, as illustrated in Fig. 11    Based on the analysis of uctuating pressure distributions derived from the SBES simulations discussed earlier, the FW-H method is employed to predict far-eld noise at various receiver locations.The evaluation of noise propagation from the bodies are evaluated at distances of 0.9m, 1.35m, and 1.8m in spanwise direction away from the vehicles' origin reveals that SB reports the highest overall sound pressure level (OASPL), while GB reports the lowest, as detailed in Table 5.In this study, the OASPL is de ned the logarithmic ratio between root mean square of sound pressure uctuations obtained at fareld microphone location ( ) to the reference pressure ( ) which is taken as 2x10 − 5 pa, and mathematical from is shown in Eq. 3. The pattern of the radiated noise, obtained through a circular array of 36 microphones placed at three different locations, demonstrates that when measured in close proximity (z = 0.9m) to all the key sources within the forebody of each vehicle con guration, including the side window, side-view mirror, frame, and, where applicable, the A-pillar, the pattern resembles a cardioidlike shape characterized by clearly de ned lobes.The minimum point, at 270º, represents the direction of oncoming ow where the dB value is the lowest in this location.Notably, the SB predicts signi cantly higher dB values closer to 0º-60º, indicating a strong asymmetry, perhaps in uenced by the A-pillar.In contrast, the other models demonstrate symmetric trends, particularly the GB, which exhibits symmetric lobes but at reduced dB levels.This indicates a strong in uence of multiple high-intensity sources on the radiation pattern, demonstrated by the visible contribution of the A-pillar in SB, as depicted in Fig. 15a.
As the probing distance from the vehicle increases (z = 1.35m), the directivity pattern transitions into a sub-cardioid-like (Fig. 15b) structure where there is no clearly de ned minimum point in this location, except for WB that still exhibits some features at 270º, where the dB value is at its minimum within this probed location.In contrast, GB shows the least evidence of the presence of a minimum point within the radiated sound pattern.At this stage, the radiated patterns from all cases become more oblique but tend to be symmetrical.The diminishing minimum point of sound radiated, and less pronounced lobes indicate a reduction in the directivity of noise sources.The symmetry of the sub-cardioid-like pattern at this stage suggests that the directional bias of noise generation decreases with distance.By z = 1.8m, all con gurations tend to resemble a monopole-like pattern, indicating that no speci c noise source p ′ nrms p ref dominates the radiation direction.GB consistently maintains lower dB levels compared to the others, as seen in Fig. 15c.While the forebody con guration differences in bodies without A-pillars do not signi cantly alter the pattern of radiated noise, the transition from a cardioid-like to a sub-cardioid-like to eventually a monopole-like pattern illustrates the signi cant in uence of speci c forebody components on the radiated noise.

CONCLUSIONS
In this paper, the Stress-Blended Eddy Simulation (SBES), a Scale-Resolving Simulation, in conjunction with the Ffowcs Williams-Hawkings (FW-H) method, was employed to gain insights into the near-eld ow and far-eld noise characteristics of two distinct classes of standard vehicle con gurations: those with A-pillars, namely the Generic Body (GB) and the Ahmed Body (AB), and those without A-pillars, namely the Windsor Body (WB) and the SAE-T4 Body (SB).To expand the scope of this work, two additional con gurations were introduced, namely the Fused Body (FB) and the Hybrid Body (HB), by combining design features from bodies without A-pillars and those with A-pillars, whilst preserving consistent design parameters and features across all con gurations.The numerical predictions have been rigorously validated and demonstrate good agreement with the available experimental data for the (SB) model, as reported by Nusser et al. [23], thus serving as a benchmark for the evaluation of our numerical predictions.
• One of the primary emphases of this study details the ow separation and the formation of mirrorinduced vortices (V 1 and V 2 ) on the upper and lower regions of the mirror.The formation of these vortices, while relatively insensitive to variations in forebody design, signi cantly affects the overall vehicle wake.Notably, the vortices' angles of incidence (α' and α) are subject to the presence of A-pillars, revealing an interaction between the nature of the forebody design and mirror-induced vortices, affecting both the aerodynamics and aeroacoustics performance of the vehicle.It is noted that the sharp-edged base vehicle con gurations exhibit similar toroidal vortex patterns, while vehicles with rounded base edges yield distinct wake behaviours due to the modulating in uence of mirror-induced vortices.Overall, con gurations lacking A-pillars consistently generate increased negative lift (downforce) in contrast to those with A-pillars.While a direct relationship remains elusive, an apparent trend emerges, suggesting a potential association between higher downforce and reduced radiated noise levels for both class of vehicle con gurations.
• In con gurations featuring A-pillars, a signi cant interaction, particularly for the SB model, occurs between the upstream ow and the horseshoe vortex, resulting in the extension of pressure uctuations towards the trailing edges of the side window.Conversely, con gurations without A-pillars display reduced pressure uctuations beyond the midsection of the side window.The numerical predictions detect a 40 Hz aeolian tone in SB in agreement with experimental data and HB, while other con gurations exhibit a ~ 3-4 Hz shift in peak intensity in (dB) at various locations probed.This shift can be ascribed to the A-pillars' impact on the horseshoe vortex, causing a delay in vortex shedding from the mirror.
• Investigating the radiated sound, closer to the vehicle, all models exhibit a cardioid-like pattern, which gradually transitions into a sub-cardioid-like shape before ultimately resembling a monopole-like pattern as the distance from the vehicle increases.However, the SB model demonstrates an intriguing asymmetry.While most models show balanced dB levels between the two lobes indicating the 0º and the 180º directions, the SB model exhibits higher dB levels closer to 0º (towards the A-pillar direction) compared to the 180º side (towards the ground).This indicates that the SB model's noise source, likely in uenced by the A-pillar and speci c vehicle features, had a directional bias towards the front of the vehicle, resulting in a unique noise pattern.The outcome of this study revealed that the Generic Body (GB) consistently exhibited the lowest radiated OASPL levels at all probed locations, while the Squareback (SB) model exhibited the highest levels.
Despite the limited availability of the experimental data for validation for all con gurations examined, the strong agreement with the validated SB model highlights the reliability of the numerical predictions in understanding the impact of forebody design on aerodynamics and aeroacoustics.However, by expanding the experimental comparisons for a broader set of forebody con gurations can further enhance the scope of this study.
Abbreviations NOMENCLATURE Squareback geometries with distinct forebody con gurations are used in this study.The gure illustrates the locations of key entities, including the side-view mirror, frame, and side window, for two categories of vehicles: those without the A-pillar and those with the A-pillar.
using dotted ovals.3 Where, p' n sound pressure uctuation obtained at far-eld microphone, p' nrms represents the root mean square of the sound pressure uctuations obtained at far-eld microphone and p ref indicate reference pressure (p ref = 2x10 − 5 pa).

Figure 2 a
Figure 2

Figure 4 a
Figure 4

Figure 5 Time
Figure 5

Figure 7 Comparison
Figure 7

Figure 9 Time
Figure 9

Figure 10 Comparison
Figure 10

Figure 11 Comparison
Figure 11

Figure 12 Comparison
Figure 12

Figure 13 Comparison
Figure 13

Table 1
Comparison of mesh cut-off frequencies for grids used in the study at various probe positions

Table 2
Comparison of force coe cients and pressure drag coe cients of mirror (Cdm), base (Cdb), front slant (Cdf), no mirror side (Cdw'm) and mirror side (Cdwm)

Table 3
Comparison of mirror induced vortices and its strength for all the models used in the study

Table 5
Comparison of Overall Sound Pressure Level (OASPL) emanating from the different vehicle bodies investigated.The microphone locations are given from the origin of the vehicle.