Computational study on an Ahmed Body equipped with simplified underbody diffuser
Introduction
Among the standard automotive bluff bodies in literature, the most studied one is the Ahmed body, firstly proposed by Ahmed (Ahmed et al., 1984). It is based on the geometry designed by Morel (1978), with the main dimensions highlighted in Fig. 1. The proposed geometry of the Ahmed body aims to reproduce the main features of road vehicles, such as the frontal stagnation, ground effect and well-defined separation points.
The most emblematic characteristic of the Ahmed Body is a angled upper back section with fixed length, here referred as slant, on the upper rear portion, allowing the simulation of different automotive body styles. According to (Huminic and Huminic, 2010), it has been shown that the flow over the slanted surface back section is dependent on specific inclination angle. Two critical angles, at 12.5° and 30° have been observed, in which the flow structure changes significantly, and where a change of curvature of the drag coefficient is also evident. For angles below 12.5°, the airflow over the slant remains fully attached before separating from the model when it reaches the rear of the body. The flow from the angled section and the side walls produces a pair of counter rotating vortices, which then persist downstream.
For angles between 12.5° and 30°, the flow over the slant becomes highly complex. Two counter-rotating lateral vortices are shed from the sides of the angled section with increased size, which affects the flow over the whole back end, specially the previously existing three-dimensional wake. These vortices are also responsible for maintaining attached flow over the rest of the angled surface up to a slant angle of 30°, and it has been shown that they are extended up to half of the length of the model beyond the trailing edge, as discussed in (Strachan et al., 2007) and (Lienhart and Becker, 2003). Close to the second critical angle, a separation bubble is also formed over the inclined slant. The flow separates from the body, but re-attaches before reaching the vertical back section.
Above a 30° slant angle, the flow over the or slant is fully separated. However there is a weak tendency of the flow to turn around the side of the model, as a result of the relative separation positions of the flow over model top and those over the slant side edges. When the flow is in this state, a near constant pressure is found across that region. To characterize all three flow configurations here discussed, representative slant angles are commonly used in literature with 0° (or squared-backed), 25° and 35◦.
The first experimental study on Ahmed Body (Ahmed et al., 1984) was with static floor conditions, considering a Reynolds number Re = 4.29 × 106 based on its full length. In this study, results for the drag coefficient were obtained for different slant angles, ranging from 0° to 40°, in increments of 5° with an additional measurement at 12.5°. Due to limitations on the wind tunnel setup, only drag force measurements and a few flow visualization test were performed. In order to better understand the flow phenomena and turbulence structures around the model, a complementary study was performed by (Lienhart and Becker, 2003) using laser Doppler anemometry (LDA), hot-wire anemometry (HWA) and static pressure measurements.
Aiming to reproduce realistic road conditions and understand the phenomena associated to flow fields close to the ground, the authors of (Strachan et al., 2007) performed an Ahmed Body wind tunnel test using moving ground and acquired both the aerodynamic forces and the flow characteristics by employing time-averaged LDA. The flow conditions were also slightly different from the ones used on Ahmed’s first test, since it had a Reynolds number of Re = 1.7 × 106. Nevertheless, similar flow behaviour were observed on the slant, despite the quantitative results being slightly different. One of the most interesting features found in this flow visualization results is the lower vortex system, a pair of vortices that appears close to the ground interface, which were absent in the fixed-ground studies. According to (Strachan et al., 2007), this could be attributed to the interference caused by the four studs used to support the model on the floor. Fig. 2 illustrates this phenomenon on an Ahmed Body with a squared-back.
An important development in automotive industry directly associated with the flow near the ground is the introduction of underbody diffusers, initially for high performance race vehicles with relatively low ground clearance. By providing a smoother transition from the underbody flow to the base of the car body, the strength of the rear wake can be reduced, contributing to drag reduction. In addition, it was found that at slightly inclined angles, the underbody diffuser also increases the downforce generated, assisting the acceleration and handling.
To explore detailed features of the near-ground vortices, and to examine the potential benefits of implementing underbody diffusers, we propose a series of computational studies considering same simulation conditions as the experiment from (Strachan et al., 2007), with moving ground. The Ahmed bodies used in the study are the squared-back and the slant angle of 25°, representing respectively estate car/station-wagons (attached flow) and performance cars (vortex generation with flow detachment). The length of the underbody diffuser is set to be the same as the classic Ahmed body slant length, with angles ranging from 10° to 50°, in increments of 10°. An additional case also considers a diffuser angle of 5°, a setting commonly found in racing vehicles. This study focus essentially on the aerodynamic quantities on the Ahmed body, as well as, on the flow structures on its geometry, such as the vortices on the slant and diffuser.
CFD has become an underpinning technology for most automotive companies to reduce development times and costs. Since the Ahmed Body is a widely studied bluff body, it has become a test case to validate new CFD codes, specially for applications in the automotive industry. Lower vortices observed by (Strachan et al., 2007) were not present in CFD simulation studies with fixing studs modelled. They were first observed by (Krajnović and Davidson, 2004), where an Ahmed Body with slant angle of 25° was simulated without the fixing studs. Nevertheless, the location where these vortices are generated and possible interactions with underbody components were not highlighted.
We utilise a high fidelity spectral/hp element method simulation using under-resolved direct numerical simulation (uDNS) also known as implicit large eddy simulation (iLES) ((Grinstein et al., 2007)). The spectral/hp elemental method combines the advantages of higher accuracy and rapid convergence from the spectral (p) methods, while maintaining the flexibility of the classical finite element (h) complex meshes, allowing unsteady vortical flows around geometries to be effectively captured. We present the validation of the proposed numerical methodology on the classical Ahmed body with 25° slant angle, as in the study of (Buscariolo et al., 2020). The Ahmed body with 25° slant angle, although in the pre-critical regime, still poses a challenge for most CFD codes due to the complex flow physics, however, it is a well-established test configuration, as performed by (Lienhart and Becker, 2003) and (Strachan et al., 2007).
Most computational studies on the Ahmed Body employ simplified Reynolds Averaged Navier-Stokes (RANS) solution. This approach is very reliable for simple stable flow problems, however it is not suitable to correctly predict unstable phenomena around complex geometries. In the study by (Krajnović and Davidson, 2004), for the first time for an Ahmed Body, a LES methodology was used yielding solutions of higher flow details, especially for the critical slant angle of 25°. A major limitation of running LES or detached eddy simulation (DES) for this kind of geometry is the requirement of high mesh resolution, with considerably higher simulation cost and time.
The latest achievements in the high-fidelity turbulence models around an Ahmed body are found mainly for the slant angle of 25° and are summarized in the compilation work of (Serre et al., 2013) in which a comparative analysis of recent simulations, conducted in the framework of a French-German collaboration on LES of Complex Flows at Reynolds number of 768,000. The study offers a comparison between results obtained with different eddy-resolving modelling approaches: three classical h-type method (LES with Smagorinsky model and wall function (LES-NWM), Wall-resolving LES with dynamic Smagorinsky model (LES-NWR), and DES with shear stress tensor (DES-SST) and one spectral element method implicit LES with spectral vanishing viscosity (iLES-SVV). The iLES-SVV simulation in (Serre et al., 2013) work was conducted in various two-dimensional planes along the span-wise direction, and subsequently constructed into three-dimensional flow fields (commonly known as 2.5D simulation). Considering the drag coefficient, both LES-NWR and DES-SST overestimated the value in around 16%; the LES-NWM presented a difference around 6%, which presented the best agreement. The iLES-SVV model better modelled the flow behaviour compared to previous models, however the drag difference was around 44%
A new Improved Delayed DES (IDDES) methodology, an enhancement of the Delayed DES (DDES), is proposed by (Guilmineau et al., 2018) to solve the flow around the Ahmed body. The study presents a comparison between quantitative and qualitative results obtained with different methodologies previously presented with this newly proposed methodology. The IDDES case is the one that most closely correlates the flow behaviour and structures with experimental reference. However, results of the aerodynamic quantities are different, such as the drag coefficient with approximately 27% difference from same experimental reference.
Section snippets
Ahmed body equipped with rear underbody diffuser
Bluff bodies equipped with rear underbody diffusers are being studied by several researchers, especially from the automotive industry, to maximise the performance of the vehicle. The study of (Cooper et al., 1998) identified three important characteristics on a body underbody diffuser. The first is a diffuser pumping effect, which occurs once the outlet of the diffuser is set as the base pressure of the body, as identified by (Jowsey, 2013). The diffuser recovers pressure along its length,
uDNS/iLES simulations using spectral/hp element method
For both Ahmed body styles with diffuser, we performed implicit LES simulations based on a spectral/hp element approach. Classical h-type method is based on dividing the domain into non-overlapping elements of the same type, similar as in the Finite Element Method (FEM), offering geometric flexibility, a key factor for many complex industrial cases. To improve the accuracy of the solution, the mesh characteristic length (h) is reduced in order to capture smaller flow features, generating a
Numerical methodology validation on the classical Ahmed body geometry
In this simulation study, we use a coordinate system with X as the streamwise direction, Y as the vertical direction and Z as the spanwise direction. The Ahmed body model is positioned with its back end on the coordinate X = 0 and at a distance h of 50 mm from the ground (Y = 0). The wind tunnel test section size is defined with same dimensions as the experiment from (Strachan et al., 2007) 1660 mm × 2740 mm, keeping the same blockage ratio. Air flow inlet is positioned at X = −2L
Simulation of the Ahmed body with diffuser
With the numerical methodology validated on the classical Ahmed body, the following step is the application on a new variant of the Ahmed body equipped with underbody diffuser. Diffuser length DL is set to be at a fixed value, which is the same as the upper slant length SL of 222 mm, regardless of the inclination angle changes. The influence of the diffuser is evaluated in two variants of the classical Ahmed body: 0° slant (or squared-back) and 25° slant angle, as illustrated in Fig. 11,
Conclusions
A parametric study on the effect of diffusers is conducted on the Ahmed body at two slant cases: squared-back and 25° angle. The diffuser length is fixed with the same dimension of the slant and cases are evaluated at a Reynolds number of Re = 1.7 × 106 with moving ground condition. Diffuser angles considered range from 10° to 50° in increments of 10°, including one additional angle of 5° for both cases. The numerical methodology employed in this study was validated on the classical Ahmed
CRediT authorship contribution statement
Filipe F. Buscariolo: Methodology, development, simulation setup, Data curation, data processing, correlation study, Formal analysis, analysis, Writing – original draft, Writing – review & editing. Gustavo R.S. Assi: Supervision, Writing – review & editing. Spencer J. Sherwin: Conceptualization, Supervision, concept development, Software, implementation, Writing – original draft, Writing – review & editing, sponsor.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
We acknowledge the HPC facilities at Imperial College Research Computing Service, https://doi.org/10.14469/hpc/2232 and also under the UK Turbulence Consortium. CNPq for the sponsorship 202578/2015-1.
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