Application of LES combined with a wave equation for the simulation of noise induced by a flow past a generic side mirror

Abstract

The paper presents validation results of a hybrid simulation method for aeroacoustics in turbulent flows at low Mach numbers. The hybrid method implemented in the Ansys Fluent® CFD package applies a scale-resolving turbulence model to compute the noise sources in an incompressible flow, while the noise propagation is modeled by a wave equation formulated for the acoustic potential. The selected test case deals with a flow and a sound field around a generic side view mirror of a car. The SBES model by Menter, which belongs to the class of the RANS-LES models, is used for the flow simulation. It switches to the Large Eddy Simulation (LES) mode in separated mixing layers and recirculation zone behind the mirror as well as in the following wake, where flow develops intensive turbulence and dominating noise sources. The acoustics wave equation is formulated in the model form of Kaltenbacher et al. and is applied in the time domain. The overall calculation is performed as a transient co-simulation on the same mesh using the finite-volume discretization method for both the flow and the acoustics parts. The wave equation is advanced in time using the HHT-α method. Obtained distribution of the mean wall pressure over the mirror surface closely matches the experimental one. Rich content of the resolved turbulent vortices in the separation zone and good agreement of the calculated and measured wall pressure spectra at sensor locations downstream the mirror evidence a proper LES resolution quality of noise sources. Comparison of the computed noise spectra at the remote microphones with the experimental data demonstrates the sound propagation accuracy and validates the overall aeroacoustics simulation method.

Keywords

Computational aeroacoustics hybrid simulation method wave equation generic side mirror low Mach number scale-resolving simulations

Introduction

The purpose of this work is to report on a validation study of a hybrid simulation method for aeroacoustics in low Mach number flows, which was recently implemented in Ansys Fluent®. Hybrid simulation approaches are widely used in the computational aeroacoustics. In the framework of these approaches, the solution variables are split to hydrodynamic and acoustic parts, which are then calculated by different methods. The hybrid aeroacoustics simulation methods are addressed by extensive existing literature, with few selected key publications referred later in this section. Application of hybrid methods becomes especially beneficial in simulations of low Mach number flows, where it helps to deal with the high disparity of hydrodynamic and acoustic scales.

Development and application of hybrid simulation methods for aeroacoustics of low Mach number flows has a long history originating from the classical works of Lighthill¹ and Curle,² published in 50s. Lighthill’s method of acoustic analogy was further developed by a number of authors (Powell, Phillips, Lilley, Möhring, and others), who suggested various forms of wave equations with different recipes for the sound sources and incorporation of the mean flow effects on the sound propagation. For an overview of acoustic analogies see, for example, Goldstein.³ Most hybrid methods, which are based on acoustic analogies, use them in a surface integral form, the most popular of them being the Ffowcs Williams and Hawkings (FW-H) generalization of the Lighthill’s analogy in the formulation of Farassat.⁴ Limitations of analytical surface integrals prevent their use in cases with acoustically non-compact sources, as well as in cases where reflection and refraction effects have significant influence on the sound propagation. This gave a rise to the development of methods, which use numerical integration of either the linearized Euler equations or the wave equation with volumetric source terms. Historically the first such method was the acoustic/viscous splitting method by Hardin and Pope.⁵ Most of such differential hybrid methods apply a finite-element discretization, see, for example, Oberai et al.⁶ Decades of application proved that hybrid methods based on acoustic analogies are appropriate tools for most practical simulations. However, all of them inherited a main uncertainty element of Lighthill’s model, namely, a subjectivity in splitting the wave equation to a sound source part and a sound transport part. Despite suggested physical interpretations of source terms in acoustic analogies (such as a consideration of the surface dipole term in Curle’s integral form as describing the sound scattering by a solid body), the uncertainty remains since it is caused by a necessary “arbitrary” splitting step in the wave equation derivation.

A new class of aeroacoustics models appeared in the last two decades, which rely on the mathematically strict asymptotic analysis of the gas dynamics equations, which is used to derive a system of equations for acoustic perturbations. We cite here the three original publications by Ewert and Schröder,⁷ by Seo and Moon,⁸ and by Munz et al.⁹ as the most relevant ones for the method used in our simulations. In these works, partial differential equations for sound propagation were derived from the linearized Euler equations by filtering out terms not related to acoustics (vortex and entropy terms). A concrete form of the resulting system of equations depends on the accepted expansion form for the full static pressure and other flow variables: expansion around the time-average field, expansion around the transient incompressible flow field, or others. Applying further simplifications, this system of transport equations can be reduced to a single wave equation with a corresponding sound source term. The wave equation model, which is used in a present work and available in Ansys Fluent®, can be derived from either the APE-2 model by Ewert and Schröder⁷ or from the LPCE model by Seo and Moon,⁸ both considering the transient incompressible flow field as an expansion basis. In accordance with this, the resulting wave equation can only be used in isothermal low Mach number flows, where density variations in the background fluid field may be neglected. Therefore, the constant density flow model is applied to the fluid dynamics part of the problem, which calculates the sound sources for the acoustics wave equation. This wave equation model was first derived, implemented into an FEM solver and extensively tested by Kaltenbacher et al.¹⁰

Typical target applications for this method are aeroacoustics simulations in the automotive industry, which are characterized by low to moderate Mach numbers. At a sufficiently high car speed, the aerodynamic noise becomes the dominant noise source outside as well inside the cabin, affecting the passengers comfort. This is particularly the case for electric vehicles. Among the various types of aerodynamic noise, the broadband and the tonal noise generated by additional devices at the vehicle body, like side mirrors, is probably the most noticeable. These phenomena were widely studied both experimentally and numerically. Real and simplified geometries of a side mirror were measured, for example, by Hartmann et al.,¹¹ Werner et al.,¹² and Siegert et al.¹³ Numerical simulations of these and other mirrors were done by Hartmann et al.,¹¹ Frank and Munz,¹⁴ Siegert et al.,¹³ and others.^15–24 In most of these works, authors applied hybrid approaches to aeroacoustics simulation. An exception is a paper by Frank and Munz,¹⁴ who directly computed the tonal whistling noise for a very special simplified mirror geometry, which was designed and experimentally studied by Werner et al.¹² The tonal noise in that flow was generated by a significant feedback of acoustics on a flow over a mirror with the non-optimized sharp edges. Obviously, the standard hybrid approach with its one-way coupling of flow and acoustics is not applicable to analyze this phenomenon, which explains the application of the direct noise simulation using the compressible flow equations. Papers by Hartmann et al.,¹¹ Yuan et al.,²⁰ Ambo et al.,¹⁹ and Chu et al.²¹ reported on numerical investigations of real mirror geometries by different car manufacturers, installed either on the real full-scale cars or on simplified bodies. Hartmann et al.¹¹ compared different flow simulation methods (finite-volume method vs. Lattice Boltzmann method). Yuan et al.²⁰ studied flow around mirror of Hartmann et al.¹¹ and analyzed the influence of installation environment on turbulence in separation zone, demonstrating the role of the A-pillar vortex. Ambo et al.¹⁹ focused on application of a high fidelity LES method to the numerical prediction of the boundary layer separation on a convex surface of the mirror at a super-critical Reynolds number. Chu et al.²¹ used a simplified method of estimating the broadband noise sources, based on the steady-state RANS simulation, to optimize the shape of their mirror. Snegirev et al.²² compared performance of unsteady RANS, DES, and LES turbulence models applied to the flow and noise prediction for the two bluff bodies, replicating car side mirrors. A number of papers^{13,15–18,23,24} analyzed generation and propagation of sound in a flow around a generic side view mirror, which was experimentally studied by Siegert et al.¹³ Simplicity of the geometry of this mirror, together with the availability of the measured data for the mean flow pressure, the spectra of the wall pressure fluctuations, and the sound spectra at the remote microphones made this particular flow very popular for validation of aeroacoustics simulation methods. Ask and Davidson,¹⁸ as well as Belamri et al.²⁴ calculated a transient flow using the LES and SAS turbulence models, respectively, whereas Rung et al.,¹⁷ Lokhande et al.,²³ and Wang et al.¹⁶ addressed the acoustics part of the problem as well. They all used the FW-H integral method, but Wang et al.¹⁶ additionally applied the boundary element method and compared it with FW-H. The generic side view mirror by Siegert et al.¹³ was also selected for the validation work reported in the current paper, which illustrates the capabilities of the considered hybrid approach based on the acoustics wave equation.

The rest of the paper is organized as follows. In the Method section, a brief description of the applied hybrid approach is presented, including the wave equation formulation. The Sound Generated by the Flow Around a Side Mirror section provides the computational setup for the test case along with the discussion of the results. Finally, conclusions are outlined.

Method

As stated above, the hybrid approach based on the wave equation implies splitting of flow simulation and noise propagation simulation. The flow is modeled with the use of the incompressible flow assumption and a scale-resolving approach for turbulence, while the sound propagation is addressed by the differential wave equation. A transient co-simulation of the incompressible fluid flow and the acoustics field is performed using the same time step and on the same mesh.

The simulation was carried out using the software package Ansys Fluent®. Its cell-based finite-volume discretization scheme can work on unstructured meshes. The implicit time integration scheme applies an algebraic multigrid linear solver. Some details on the flow and sound modeling are presented in following subsections.

Flow modeling

Scale-resolving simulation of the turbulent flow was performed using the Stress-Blended Eddy Simulation method by Menter²⁵ (SBES), which is a global (non-zonal) hybrid RANS-LES turbulence model that uses a shielding function to switch from the underlying RANS model directly to the selected LES model. In this work, SBES was based on the SST RANS model²⁶ and on the algebraic WALE LES subgrid-scale model.²⁷ Unlike many other non-zonal hybrid approaches, SBES does not suffer from the delayed RANS-LES transition in separated shear layers.²⁵`

The following numerical settings were used:

The pressure-based SIMPLEC method with eight iterations at each time step.

The second-order implicit backward Euler scheme for time integration.

The bounded central differencing scheme similar to Ref. 28 for the approximation of convection terms in the momentum equations, and the second-order upwind scheme for the turbulence model equations of the SST model.

Wave equation

Acoustic propagation is described by the perturbed wave equation model suggested by Kaltenbacher et al.¹⁰

\frac{\partial^{2} ϕ}{\partial t^{2}} - c^{2} \nabla^{2} ϕ = \frac{1 \partial}{ρ \partial t} p_{f l o w}

(1)

Here, φ is the acoustic potential (∂φ/∂t = −p'/ρ), p' is the sound pressure, p_flow is the local instant static pressure, obtained from the flow solution, c and ρ are the speed of sound and the fluid density, both assumed to be constant.

This model has been derived by Kaltenbacher¹⁰ from the “acoustic perturbation equations (2)”⁷ under the assumption of constant density in the background flow to calculate the sound propagation in low Mach number flows. In our simulation, the effect of convection on the sound transport is neglected.

Several numerical tools are implemented in Ansys Fluent® to improve the robustness of the wave equation solver. The source in the right part of equation (1) can be masked out in space to ensure that the sound is generated only in the desired part of the turbulent flow region, where the solution is known to be well resolved. Filtering procedures in time and space are also applied to the sound source, in order to suppress the under-resolved high-frequency noise. Moreover, during the initial phase of the sound simulations, the source term is multiplied with a slow ramping factor to avoid start-up disturbances. Concrete parameters used in this work are outlined in the Sound Generated by the Flow Around a Side Mirror section.

Two types of boundary conditions for the acoustic potential are used in our simulation: ideal reflection on hard walls and a non-reflective boundary condition at far-field boundaries. The latter condition effectively absorbs sound waves coming to the boundary at normal or near-normal incidence. In the case of an oblique incidence, however, a small reflection may still occur; therefore, a sponge layer is used in addition. Within the sponge layer, an additional viscous damping term is activated in the wave equation (1).²⁹

For the discretization of the Laplacian term in equation (1), the same second-order accurate finite-volume scheme is applied, which is used for the diffusion terms of the flow and the turbulence model equations.²⁹ Solution is advanced in time using the implicit second-order accurate Hilber–Hughes–Taylor alpha method.³⁰

Sound generated by the flow around a side mirror

As already mentioned in the Introduction, the present work reports on the simulation of noise generated by a flow around a generic side mirror, which was studied experimentally by Siegert et al.¹³ and Höld et al.¹⁵ in the acoustic wind tunnel at the University of Stuttgart. The model mirror geometry consists of a half of a cylinder with a diameter D = 0.2 m and the same height. The cylinder is blunted by a quarter of a sphere of the same diameter (see Figure 1). The mirror is mounted on a flat plate 0.9 m downstream from the leading edge at zero yaw angle. Aerodynamically covered struts were used to host the experimental equipment and to fix the plate (see the sketch of the setup in Figure 2). The incoming airflow speed U₀ is 140 km/h, corresponding to Reynolds and Mach numbers of 5·10⁵ and 0.11, respectively. This Mach number is low enough to consider the flow to be incompressible and use the hybrid approach based on the perturbed wave equation for the noise simulation.

The available experimental data include the mean pressure coefficient distribution along the mirror surface as well as the static pressure spectra at different sensor locations on the plate and on the mirror surface. The sound radiation in the experiment has been measured using an inflow microphone placed at several positions about 0.5 m from the mirror (see Figure 3), and the sound spectra at these positions are available for the comparison as well.

Computational setup

A computational domain with the size of 12D × 10D × 8D was used in the simulations (Figure 4). The length and the width of the domain correspond to the size of the flat plate in the experiments. The distance between the mirror and the inlet section was 4D, which corresponded to the distance between the mirror and the leading edge of the plate in the experiment.

The computational mesh was based on a structured-grid multi-block arrangement with a total of about 9m cells and was prepared using Ansys ICEM. The grid was refined to the plate and to the mirror surface with the height of the first near-wall cell Δ_w = 3·10⁻⁴m. This corresponds to the sizes in wall law units of y⁺∼20 on the plate, y⁺ ∼50–100 on the mirror surface. The mirror surface grid as well as the grid on the plate and on the central XY-plane are shown in Figure 5.

In the part of the domain where the major sources of the sound are located (recirculation bubble upstream of the mirror and the separation zone behind the mirror), grid cells are nearly cubical with the size of 3·10⁻³m (Δ_LES). Further away from the mirror the grid steps are growing, however they remain limited by 14·10⁻³m (Δ_acoustics) in the “acoustics region,” that is, the region where acoustic waves are propagating to the microphone positions. The maximum cell size in the acoustics region was estimated based on the requirements of having at least 12 cells per wavelength in the entire measured frequency range²⁹ (note that experimental spectra are valid up to 2 kHz which gives a smallest wavelengths of interest to be about 0.17 m). Test simulations of sound propagation from one-dimensional monopole source have shown that with even 10 cells per wavelength, the errors in the obtained wavelength and amplitude do not exceed 6% after the wave propagated for 10 wavelengths from the source.

The time step in the simulation was set to Δt = 2·10⁻⁵s. This corresponded to a convective Courant number not more than 1 in a major part of the domain and an acoustic Courant number of about 2 in the “LES” part of the domain and about 0.5 near the microphones. A zone of the intensive turbulent noise sources is an uncertain region for any hybrid method. Therefore, further reduction of the time step size to reach the acoustic Courant number of 1 was not considered as critical for the overall accuracy. The size of the fine mesh LES zone is not significantly relative to the wavelength range of interest, which limits possible dispersion errors.

Boundary conditions used for the flow simulations were as follows. At the inlet, a uniform constant velocity profile was set, and the pressure was extrapolated from the domain. On all walls, non-slip boundary conditions with wall functions were used. Finally, pressure outlet boundary conditions were applied for all other boundaries, which means that a constant pressure value was set at these boundaries while other variables were extrapolated from the domain. The boundary conditions for the wave equation were: the walls were considered acoustically hard, ideally reflecting sound, and the permeable boundaries (velocity inlet and pressure outlets) were handled using the non-reflective conditions.

The following simulation strategy was used. First, the incompressible flow was simulated with the scale-resolving approach SBES, until the developed state of the flow was reached. After that, the wave equation was activated, and a co-simulation of flow and acoustics proceeded. The increase of computational time for flow and acoustic simulations compared to flow only simulations was about 15%.

The source term of the wave equation was activated gradually, using a smooth ramping in time (500 time-steps were used) in order to avoid start-up disturbances. The source term of wave equation was included only in a part of the domain close to the mirror where the sound sources are located and properly resolved, while in the outer part of the computational domain, the source term was masked out. The masking marker used in the present simulations is shown in Figure 6 (left).

To avoid spurious waves and reflections from the grid coarsening regions outside microphone locations, these regions were covered by a viscosity-based sponge layer to gradually damp acoustics (the sponge layer marker is shown in the right frame of Figure 6).

Results and discussion

Results of the flow simulation

The flow visualizations are shown in Figures 7 and 8. The figures demonstrate the complex structure of the flow: the “horseshoe” vortex upstream of the mirror model and a highly turbulent wake downstream of the mirror with a separation region are the major features of this flow. The fine resolution of turbulent structures in the separation zone behind the mirror as well as the rapid formation of resolved structures in the shear layer confirms the expected performance of SBES.

The mean pressure distribution (sensor positions are shown in Figure 9) over the mirror surface, plotted in Figure 10, agrees well with the measured data. In particular, the difference between computed mean pressure values and experimental ones is less than 2% at majority of sensor positions. At probe locations at the windward surface located near the mirror edge (especially at sensors 10–11 and 24–25), the agreement is worse and the difference is up to 30%. The reason for this is most likely that the present simulation does not capture the laminar to turbulent transition bubble observed in the experiment (fully turbulent flow is assumed in the present setup). Overall, however, these results along with the flow visualizations suggest a good accuracy in simulating the turbulent separation zone, which is the main source of the aeroacoustics noise in this flow.

A comparison of the calculated and the measured wall pressure spectra (sensor positions are shown in Figure 11) is presented in Figures 12–14. Computed spectra are obtained with the use of Hanning window function and are scaled to the experimental resolution of 10 Hz.¹⁸

The high-frequency part of experimental spectra above 1000 Hz does not match the simulation results. This was also observed in the other simulations for this experiment. A commonly accepted explanation, suggested in Ref. 17, is that most likely no window function was used in post-processing of the experimental signals.

Within the present setup, we do not resolve turbulence in the oncoming boundary layer on the plate. This is most likely the reason why the spectra (Figure 12) are underpredicted there and at the windward side of the mirror. An additional possible reason for the underpredicted spectra at the windward side is the laminar to turbulent transition bubble in the boundary layer of the mirror close to the edge observed in the experiments and not modeled here, as discussed above. It is expected, however, that this will not influence the sound predictions significantly as the main source of the sound is the massive separation region behind the mirror.

Downstream from the mirror, in the area where turbulent structures are resolved, the agreement with experimental data is better. Only at the center of the leeward surface of the mirror the spectrum is underpredicted by 10 dB (sensor 115, right frame of Figure 13), while closer to the mirror edges and on the plate in the recirculation region the difference is less than 5 dB. Overall, the agreement is consistent with the numerical setup and suggests sufficient resolution of the sound sources.

Results of acoustics simulation

A snapshot of the instantaneous sound pressure on the central XY-plane (Figure 15), as obtained from the wave equation, shows sound waves radiated by the mirror and the separation zone behind the mirror. There are, however, high-frequency waves radiating from the early shear layer, which experience artificial reflection. These are the waves with high frequencies over 2000 Hz, which we did not intend to resolve (the grid in the major part of the domain as well as the time step is not fine enough for these waves). No artificial reflection is observed in the frequency range of interest. This is supported by the frequency band-filtered sound pressure shown in Figure 16, as well as by the acoustics spectra in the mid field discussed next.

Both the sound pressure and the static pressure signals were collected at positions, corresponding to the experimental microphone positions shown in Figure 3.

As evidenced by the SPL spectra comparison, presented in Figures 17–19, the method offers good accuracy of the aeroacoustics simulations. The biggest difference between present simulation and the experiment is observed for the microphones located upstream of the mirror (microphones 1 and 2), in the frequency range of 50–200 Hz (the difference is less than 10 dB), while at higher frequencies, the difference is less than 5 dB (see Figure 17).

At the microphones located at the sides of the mirror, the agreement is better: less than 5 dB in the frequency range of 50–200 Hz and about 1–2 dB at other frequencies (Figure 18). Finally, there is virtually no difference in the sound spectra for microphones located downstream of the mirror (Figure 19).

These results are consistent with wall static pressure spectra, which are underpredicted upstream from the mirror and on its windward side, and well predicted downstream. This suggests that both the turbulence resolution upstream from the mirror and the laminar to turbulent flow transition on the mirror could be rather important for noise predictions in this flow. In order to model it properly, however, more data on transition on the mirror and plate surfaces is needed. Nevertheless, overall a good agreement of simulation results with experimental data was obtained on noise predictions with the scale-resolving simulations combined with the wave equation.

Conclusions

Simulation of the low Mach number flow around a generic car side mirror and the noise generated by this flow was conducted with the use of a hybrid approach: the incompressible flow simulations with the SBES model and the sound propagation simulation with the wave equation model. Accuracy of the mean flow prediction is confirmed by the comparison of the calculated mean pressure on the mirror surface with the experimental data. The fast formation of turbulent structures in a shear layer behind the mirror and the fine resolution of vortices in the separated region demonstrate the high quality of the SBES simulation in computing the major sound sources. Sound spectra predicted by the wave equation are in a good agreement with the available experimental data, which proves the practical accuracy of the applied hybrid method for calculating acoustics in low Mach number flows.

Footnotes

Acknowledgments

Authors appreciate the valuable help provided by Dr Andreas Hüppe during the discussions of results of the current work. Computations were performed with the use of resources of the Supercomputer Center “Polytechnichesky”

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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research was funded by the Ministry of Science and Higher Education of the Russian Federation as part of World-class Research Center program: Advanced Digital Technologies (contract no. 075-15-2020-934 dated 17.11.2020).

ORCID iD

Ekaterina Guseva

References

Lighthill

. On sound generated aerodynamically II. turbulence as a source of sound. Proc R Soc Lond Ser A Math Phys Sci 1954; 222: 1–32.

Curle

. The influence of solid boundaries upon aerodynamic sound. Proc R Soc Lond Ser A Math Phys Sci 1955; 231: 505–514.

Goldstein

M∼E

. Aeroacoustics. New York: McGraw-Hill International Book Co, 1976.

Farassat

Succi

. A review of propeller discrete frequency noise prediction technology with emphasis on two current methods for time domain calculations. J Sound Vibration 1980; 71: 399–419.

Hardin

Pope

. An acoustic/viscous splitting technique for computational aeroacoustics. Theor Comput Fluid Dyn 1994; 6: 323–340.

Oberai

Roknaldin

Hughes

TJR

. Computational procedures for determining structural-acoustic response due to hydrodynamic sources. Computer Methods Appl Mech Eng 2000; 190: 345–361.

Ewert

Schröder

. Acoustic perturbation equations based on flow decomposition via source filtering. J Comput Phys 2003; 188: 365–398.

Seo

Moon

. Linearized perturbed compressible equations for low mach number aeroacoustics. J Comput Phys 2006; 218: 702–719.

Munz

C-D

Dumbser

Roller

. Linearized acoustic perturbation equations for low mach number flow with variable density and temperature. J Comput Phys 2007; 224: 352–364.

10.

Kaltenbacher

Hüppe

Reppenhagen

, et al. Computational aeroacoustics for HVAC systems utilizing a hybrid approach. SAE Int J Passenger Cars - Mech Syst 2016; 9: 1047–1052.

11.

Hartmann

Ocker

Lemke

, et al. Wind noise caused by the a-pillar and the side mirror flow of a generic vehicle model. In: 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), Colorado Springs, CO, 06 June 2012.

12.

Werner

Würz

Krämer

. Experimental Investigations of Tonal Noise on a Vehicle Side Mirror. In: Dillmann

Heller

Krämer

Wagner

Breitsamter

(eds). New Results in Numerical and Experimental Fluid Mechanics X, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 132. Springer, Cham, 2016, Vol. 32. https://doi.org/10.1007/978-3-319-27279-5_68

13.

Siegert

Schwarz

Reichenberger

. Numerical simulation of aeroacoustic sound generated by generic bodies placed on a plate: Part II - Prediction of radiated sound pressure. In: 5th AIAA/CEAS Aeroacoustics Conference and Exhibit, 10–12 May 1999, Bellevue,WA. AIAA 99-1895.

14.

Frank

Munz

. Large eddy simulation of tonal noise at a simplified side-view mirror using a high order discontinuous Galerkin method. In: 22nd AIAA/CEAS Aeroacoustics Conference, Lyon, France, 1 June 2016. AIAA 2016-2847.

15.

Höld

Brenneis

Eberle

, et al. Numerical simulation of aeroacoustic sound generated by generic bodies placed on a plate: part I - prediction of aeroacoustic sources. In: 5th AIAA/CEAS Aeroacoustics Conference and Exhibit, Bellevue,WA, 12 May 1999. AIAA 99-1896.

16.

Wang

, et al. Evaluation of aerodynamic noise generation by a generic side mirror. World Acad Sci Eng Technol 2010; 37: 1288–1295.

17.

Rung

Eschricht

Yan

, et al. Sound radiation of the vortex flow past a generic side mirror. In: 8th AIAA/CEAS Aeroacoustics Conference and Exhibit, Breckenridge, Colorado, 17–19 June 2002. AIAA 2002-2549.

18.

Ask

Davidson

. A numerical investigation of the flow past a generic side mirror and its impact on sound generation. J Fluids Eng Trans ASME 2009; 131: 061102.

19.

Ambo

Yoshino

Kawamura

, et al. Comparison between wall-modeled and wall-resolved large eddy simulations for the prediction of boundary-layer separation around the side mirror of a full-scale vehicle. In: AIAA SciTech Forum - 55th AIAA Aerospace Sciences Meeting, Grapevine, Texas, 9–13 January 2017. AIAA 2017-1661.

20.

Yuan

Yang

. Effects of installation environment on flow around rear view mirror. SAE Int J Passenger Cars - Mech Syst 2017; 10: 580–590.

21.

Chu

Y-J

Shin

Y-S

Lee

S-Y

. Aerodynamic analysis and noise-reducing design of an outside rear view mirror. Appl Sci 2018; 8: 519.

22.

Snegirev

Lupulyak

Grigoriev

, et al. Use of high performance computing for simulations of aerodynamically generated noise in turbulent separated flows. In: West-East High Speed Flow Field Conference, Moscow, 19–22 November 2007.

23.

Lokhande

Sovani

. Computational aeroacoustic analysis of a generic side view mirror. In: SAE Technical Papers; 2003: 01–1698.

24.

Belamri

Egorov

Menter

. CFD simulation of the aeroacoustic noise generated by a generic side view car mirror. In: 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference), Rome, Italy, 23 May 2007; . AIAA 2007-3568.

25.

Menter

. Stress-blended eddy simulation (SBES)-a new paradigm in hybrid RANS-LES modeling. Prog Hybrid RANS-LES Model 2018; 137: 27–37.

26.

Menter

. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 1994; 32: 1598–1605.

27.

Nicoud

Ducros

. Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow, Turbulence and Combustion 1999; 62: 183–200.

28.

Jasak

Weller

Gosman

. High resolution NVD differencing scheme for arbitrarily unstructured meshes. Int J Numer Methods Fluids 1999; 31: 431–449.

29.

Ansys® Ansys Fluent . Release 19.2, Help System, Ansys Fluent Theory Guide. ANSYS, Inc.

30.

Hilber

Hughes

TJR

Taylor

. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Eng Struct Dyn 1977; 5: 283–292.