Aerodynamic Performance of a Baja SAE Vehicle Using Hybrid RANS-LES Approach

Sergio A. Ardila Gomez; Jessica G. Maradey Lazaro; Jhon J. Quiñones; Deisy Y. Rodriguez Sarmiento

doi:10.12688/f1000research.171076.1

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Research Article

Aerodynamic Performance of a Baja SAE Vehicle Using Hybrid RANS-LES Approach

[version 1; peer review: 2 not approved]

Sergio A. Ardila Gomez¹, Jessica G. Maradey Lazaro¹, Jhon J. Quiñones², Deisy Y. Rodriguez Sarmiento ¹

PUBLISHED 03 Nov 2025

Author details Author details

¹ Universidad Autonoma de Bucaramanga, Bucaramanga, Santander, Colombia
² Purdue University, West Lafayette, Indiana, USA

Sergio A. Ardila Gomez
Roles: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Software, Validation, Writing – Original Draft Preparation

Jessica G. Maradey Lazaro
Roles: Conceptualization, Funding Acquisition, Project Administration, Resources, Validation, Writing – Original Draft Preparation

Jhon J. Quiñones
Roles: Formal Analysis, Investigation, Methodology, Software, Writing – Original Draft Preparation

Deisy Y. Rodriguez Sarmiento
Roles: Investigation, Supervision, Writing – Review & Editing

OPEN PEER REVIEW

REVIEWER STATUS

Abstract

This study presents a high-fidelity computational investigation of the aerodynamic performance of a Baja SAE off-road vehicle using a hybrid Reynolds-Averaged Navier–Stokes (RANS) and Large Eddy Simulation (LES) turbulence modeling approach. The methodology combines the Spalart–Allmaras RANS model for near-wall flow treatment with Detached Eddy Simulation (DES) for resolving large-scale unsteady turbulent structures in the vehicle’s wake. A detailed computational domain and refined meshing strategy were implemented using ANSYS Fluent, including mesh adaptation based on the LES filter size (Δ = 23.5 mm) and mesh independence validation.

Simulations were performed under steady (RANS) and unsteady (DES) conditions at 30 km/h, yielding a drag coefficient (Cd) of 1.290 for RANS and 1.249 for DES. While RANS provided stable results with low variance (σ = 0.005), the DES model captured transient phenomena such as vortex shedding and near-wake recirculation with higher accuracy (σ = 0.024), enhancing the prediction of flow separation zones and aerodynamic forces. Pressure and velocity field analyses revealed improved resolution of stagnation zones and vortex dynamics under the DES framework, particularly around the roof, rear, and underbody regions.

The Q-criterion visualization showed that DES allowed the identification of both large-scale and fine-scale vortex structures in the near and far wake, offering a comprehensive representation of turbulence intensity and flow instabilities. These findings confirm the suitability of hybrid RANS–LES methods for aerodynamic optimization of complex vehicle geometries, providing enhanced predictive capabilities compared to traditional steady-state models.

Keywords

Baja SAE vehicle aerodynamics, Hybrid RANS LES turbulence modeling, Computational Fluid Dynamics CFD, Drag and lift coefficients, Flow separation and wake dynamics

Corresponding author: Deisy Y. Rodriguez Sarmiento

Competing interests: No competing interests were disclosed.

Grant information: This research was funded by the research office of the Universidad Autónoma de Bucaramanga (UNAB), under code I-78041. Additional support was provided through institutional resources and access to computational infrastructure.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright: © 2025 Ardila Gomez SA et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite: Ardila Gomez SA, Maradey Lazaro JG, Quiñones JJ and Rodriguez Sarmiento DY. Aerodynamic Performance of a Baja SAE Vehicle Using Hybrid RANS-LES Approach [version 1; peer review: 2 not approved]. F1000Research 2025, 14:1199 (https://doi.org/10.12688/f1000research.171076.1) First published: 03 Nov 2025, 14:1199 (https://doi.org/10.12688/f1000research.171076.1) Latest published: 12 Jun 2026, 14:1199 (https://doi.org/10.12688/f1000research.171076.2)

1. Introduction

The Baja SAE competition is an international engineering challenge that promotes the design, analysis, and manufacturing of off-road vehicles by university students under real-world constraints. Participating teams must address key aspects such as safety, reliability, regulatory compliance, cost-efficiency, and overall performance.¹ Beyond technical development, the project fosters management and teamwork skills, aligning with educational objectives outlined by the Accreditation Board for Engineering and Technology (ABET).^2,3

The vehicle must meet critical requirements including robustness, ease of maintenance, driver accessibility, and the ability to traverse rough terrain—all within a limited budget of $2,500.⁴ To achieve optimal performance, technical efforts focus on chassis design, material selection, and the improvement of mechanical systems such as suspension and steering.¹ Structural integrity is assessed using Finite Element Analysis (FEA), which enables virtual evaluation of stress, deformation, and vibration modes under various loading scenarios typical in Baja SAE events, such as acceleration, endurance, and impact tests.^4,5 Static and dynamic analyses help prevent structural failure and enhance occupant safety, while software tools like ANSYS, COMSOL, or LS-DYNA are used for advanced simulations including frontal crashworthiness and torsional stiffness validation.^6,7

In addition to structural strength, aerodynamic performance plays a key role in reducing drag, improving stability, and optimizing fuel efficiency. Aerodynamic assessments can be conducted experimentally or numerically, with Computational Fluid Dynamics (CFD) emerging as a cost-effective alternative to wind tunnel or on-road testing.^8,9 CFD allows accurate prediction of flow behaviour including drag, lift, vortex shedding, and pressure distributions using only the vehicle’s 3D geometry. This methodology accelerates the design process and reveals flow inefficiencies that may be overlooked through conventional design approaches.^10,11 Drag force is a major contributor to fuel consumption at high speeds,⁸ while lift affects tire adherence and vehicle stability. Understanding these parameters is essential for performance optimisation. Table 1 summarise recent studies involving FEA and CFD in the design of Baja SAE vehicles.

Table 1. Overview of relevant studies involving Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) applied to structural and aerodynamic optimisation of Baja SAE vehicles.

Reference & year	Methods used	Key findings
Zhang et al., 2024¹²	Vehicle Dynamics Modeling, sensor instrumentation	Validated vehicle dynamics, improving prototype design
Franco-Camacho et al., 2020¹³	Multi-body dynamics, FEA for suspension & chassis	Optimized suspension and chassis, validated handling & strength
Zainal et al, 2018¹⁴	FEA structural & modal analysis with experimental validation	Optimized resonance modes, improving structural safety
Bhardwaj et al., 2023¹⁵	FEA design & optimization of steering assembly	47% weight reduction, enhanced handling
Vinod et al, 2017¹⁶	Modal Analysis of chassis with CAD and ANSYS	Identified natural frequencies, improved durability
Khan et al., 2023¹⁷	CAD and power transmission simulation for driveshaft	Optimized driveshaft design for off-road 4x4 system
Kumar et al., 2024¹⁸	CAD and FEA design of customized brake caliper	Created brake caliper supporting 315,645 Nm torque
Maradey et al., 2019¹	CFD Simulations (ANSYS Fluent) for aerodynamics analysis	Improved airflow understanding, drag, lift, pressure distribution
Silva et al., 2023¹⁹	Suspension design and MSC Adams Car© (with aerodynamic considerations)	Double-stage springs improved dynamic response and aerodynamics
Trinadh Raju et al.,2025²⁰	CFD (ANSYS) for aerodynamics; FEA for impact analysis	Drag force 185N at 60km/h; validated structural integrity
Abu Farjad & Predators Racing, 2025²¹	CFD (Ansys Fluent) and FEA for drag reduction & optimization	5% drag reduction and 6.5kg weight saving through simulation

Computational Fluid Dynamics (CFD) has become a vital resource in the aerodynamic development of Baja SAE vehicles, enabling accurate analysis of complex flow phenomena—such as drag, lift, vortex shedding, and pressure distribution—using only the vehicle’s 3D geometry. By eliminating the need for physical prototypes, CFD accelerates design iterations, reduces costs, and enhances precision in flow prediction. It supports the optimisation of key components like bodywork, intakes, and cooling systems, improving thermal performance, reducing aerodynamic drag, and increasing overall vehicle stability. Additionally, CFD visualisations of pressure and velocity fields provide critical insights during early development, making it a cost-effective and powerful alternative to experimental methods like wind tunnel or road testing^1,22–24 The general CFD workflow followed in this study is summarised in Figure S1 (see Supplementary Material 1).

To simulate these flow phenomena with sufficient accuracy and computational efficiency, particularly in regions with flow separation and vortex dynamics, the selection of an appropriate turbulence model is essential. Turbulent flows pose significant challenges due to their inherent unsteadiness and wide range of scales. While Direct Numerical Simulation (DNS) offers the most accurate solution, it is computationally prohibitive for full-vehicle analysis. Therefore, turbulence modeling strategies such as Reynolds-Averaged Navier–Stokes (RANS), Large Eddy Simulation (LES), and hybrid RANS–LES frameworks are widely used. RANS is commonly applied near walls for its efficiency, while LES resolves large-scale structures in regions such as wakes and shear layers.^25,26

Hybrid models combine both approaches, leveraging the strengths of RANS in boundary layers and LES in separated flow regions to balance accuracy and computational cost. A critical component of these models is the transition mechanism between RANS and LES zones, managed via zonal interfaces or dynamic blending functions based on local flow properties.²⁵ Among the most commonly used hybrid methods are Detached Eddy Simulation (DES), Delayed Detached Eddy Simulation (DDES), and Scale-Adaptive Simulation (SAS). DDES improves stability by preventing premature switching and reducing sensitivity to grid resolution,²⁷ while SAS dynamically adjusts turbulence length scales based on local conditions, eliminating the need for manual interface definitions.²⁶ A comparative overview of these turbulence models is provided in Figure S2 (see Supplementary Material 2).

This article outlines the aerodynamic analysis methodology for a Baja SAE vehicle. Section 2 describes the geometry, meshing strategy, RANS and DES turbulence models, and simulation setup. Section 3 presents results comparing both models in terms of drag prediction, flow fields, vorticity, and 3D vortex structures.

2. Methods

2.1 Geometry and computational domain

The 3D model of the Baja SAE vehicle used in this study is shown in Figure 1a. It was developed based on the geometric specifications listed in Table 2. To reduce computational cost, several geometric details—particularly in the engine bay, underfloor region, and driver compartment—were simplified. Additionally, aerodynamic refinements were implemented on the vehicle’s front and roof areas to improve flow behaviour and streamline continuity.

Figure 1. Vehicle geometry and computational domain.

Table 2. Vehicle and computational domain dimensions.

Baja SAE		Computational domain
Dimension	Value	Dimension	Value
Height	1530 mm	Model incident flow	1.3 x vehicle length
Width without wheels	856.8 mm	Model – outflow	3 x vehicle length
Total length	1883.71 mm	Total width	7 x vehicle width
Front area (half )	0.60033 m²	Model – roof	3 x vehicle height
Characteristic length (between axis)	1175.85 mm

The computational domain dimensions are shown in Figure 1b and summarized in Table 2, and were selected following established guidelines from previous aerodynamic simulations to avoid influence from far-field recirculation and ensure numerical accuracy.^28,29 A symmetry boundary condition was applied along the lateral plane, which effectively halves the simulation domain when the flow is symmetric, significantly reducing computation time without compromising fidelity³⁰

A) 3D CAD model of the Baja SAE vehicle; B) Schematic of the computational domain with dimensions in meters.

2.2 Meshing

Figure 2a shows the hybrid mesh generated in the ANSYS meshing module. This mesh consists of tetrahedral elements throughout the domain and prism layers near the vehicle surface, where the turbulent boundary layer is expected ( Figure 2b). The prism layer was configured with an initial height of 0.393 mm, a growth rate of 1.12, and five total layers, resulting in a non-dimensional wall distance (Y⁺) below 5. Prism elements were also applied to the tire surfaces.

Figure 2. A) Computational domain and vehicle mesh; B) Detail of the prism layer on the vehicle; C) Body of influence boxes.

To improve resolution around the vehicle and its wake, two box-shaped bodies of influence were added ( Figure 2c), using element sizes of 50 mm near the vehicle and 200 mm in the wake region. These refinements help capture vortical structures at multiple scales and ensure a smooth transition from near-field to far-field mesh densities.

A mesh independence study was conducted using six mesh configurations with total cell counts ranging from 800,000 to 10 million. The drag coefficient (Cd) was used as the convergence criterion, and mesh independence was achieved with approximately 1.16 × 10⁶ elements. Mesh quality was evaluated using the Jacobian determinant, with most elements scoring between 0.7 and 0.95, which is acceptable for accurately resolving boundary layer phenomena. Results of the mesh independence analysis are presented in Figure S3 (see Supplementary Material 3).

2.3 RANS Model implementation

In the implemented model, the airflow was assumed to be incompressible (isothermal), Newtonian, and three-dimensional. The working fluid was dry air under standard conditions (T = 25°C, 1 atm), corresponding to a Reynolds number of 6.7 × 10⁵, based on the vehicle’s wheelbase.

The boundary conditions were defined as follows: a uniform inlet velocity of 30 km/h (8.33 m/s) was imposed at the domain entrance ( Figure 1b), while the outlet was set to constant atmospheric pressure. The lateral, upper, and symmetry planes were treated as symmetry boundaries (zero-gradient) to avoid artificially enclosing the wake region and to ensure realistic flow development. The ground, vehicle chassis, and tyres were modelled as stationary no-slip walls.

Simulations were performed using ANSYS FLUENT v19.2³¹ under steady-state conditions. The one-equation Spalart–Allmaras turbulence model³² was employed for the RANS formulation due to its efficiency in external aerodynamic flows at high Reynolds numbers and its relatively low computational cost. The transport equation for the model is expressed as Eq 1:

\frac{\partial}{∂t} (ρ \tilde{v}) + \frac{\partial}{\partial x_{i}} (ρ \tilde{v} u_{i}) = G + \frac{1}{σ} {\frac{\partial}{\partial x_{j}} [(ρ \tilde{v} + μ) \frac{\partial \tilde{v}}{\partial x_{j}}] + C_{b} {(\frac{\partial \tilde{v}}{\partial x_{j}})}^{2}} - Y

Equation 1. Transport equation for the modified turbulent kinematic viscosity ν in the Spalart–Allmaras one-equation turbulence model.³²

where G represents the production of turbulent viscosity, Y is its destruction near the wall due to viscous damping and wall-blocking effects, σ and cb are empirical constants, and ν is the molecular viscosity. A second-order spatial discretisation scheme was used, and pressure–velocity coupling was achieved through the COUPLED algorithm. Convergence was considered achieved when the residuals dropped below 1 × 10⁻⁵ within 5000 iterations.

2.4 DES Model adaptation

The hybrid RANS-LES turbulence model DES was implemented in this study to obtain more accurate results and improve the visualization of the vorticity iso-surfaces in the near wake of the Baja SAE vehicle. In the DES model, the flow field can be divided into three regions: Euler Region, RANS Region and LES Region. The boundary layer regions are modelled with unsteady RANS (URANS) and the outer detached vortices are captured with LES.^33,34,35 The LES region and the called grey zones were calculated based on the guidelines reported on.³⁵ First, the LES filter was estimated to divide the characteristic length of the vehicle (distance between wheels) by 50. It results in a LES filter value of Δ = 23.517 mm, which is less than the smallest vortex diameter observed in the vorticity contours of the RANS model ∅_min = 33.6 mm. The smallest vortex diameter was measured in a vorticity contour located in the near wake of the vehicle using the MATLAB algorithm developed by Smith R.³⁰ Then, the volume of refinement of the cells (∆³ = 1.3006 × 10⁻⁵ m³) was calculated using the Filter LES value. Finally, the calculated volume of refinement was used to adapt the mesh in ANSYS FLUENT ( Figure 3). The total number of elements of the adapted mesh was 7 million as shown in Figure 3.

Figure 3. Mesh adaptation from RANS to DES.

The time step for the DES simulations is calculated according to⁹ as ∆t = ∆/Umax = ∆/U∞ = 2.822 × 10⁻³ s, where Umax, is the maximum velocity registered in the simulations, which in this case is the velocity of the incident fluid flow. The total time of analysis was determined as t = 4 Lcar/U∞ = 0.904s and 40 iterations per time step were used, where Lcar is the total length of car model.

3. Results

3.1 Drag coefficient

For the RANS model, the drag coefficient (Cd) was calculated by averaging the values from the final 100 iterations of the steady-state simulation. The resulting Cd was approximately 1.290, with a standard deviation of 0.005. This low deviation indicates good convergence stability of the RANS solution. In contrast, the hybrid RANS–LES model was implemented under unsteady-state conditions. The time-averaged Cd, computed from the instantaneous values at each timestep, was 1.249, with a standard deviation of 0.024, as shown in Figure S4 (See Supl. Mat. S4). As expected from unsteady simulations, the Cd fluctuates around a mean value.^25,36 This fluctuation reflects the model’s ability to capture a broader range of turbulence scales, particularly in the wake region. The DES model achieves this through its spatial filtering mechanism (Δ_LES), which dynamically resolves detached vortices in both near-wall and far-wake regions. Accurate prediction of these vortex structures significantly improves the precision of the drag coefficient estimation.

3.2 Pressure and velocity field

The aerodynamic behaviour of the Baja SAE vehicle model, as shown in Figure 4, reflects the unique characteristics of a competition-oriented off-road prototype rather than those of a conventional land vehicle. Due to the simplified bodywork and the absence of a front windshield, the flow does not exhibit well-defined aerodynamic features such as coherent recirculation bubbles, separation zones with distinct contours, or consistent vortex formation along roof pillars and between the hood and windshield. Figure 4A presents the velocity field on the symmetry plane using the RANS model. Although flow separation is evident in the near wake, the contours lack definition, revealing two distinct recirculation zones (labelled A and B in Figure 4B). Zone A is elongated in the streamwise direction due to the inertia of flow over the slanted roof, which has an inclination of approximately 5°.³⁷ In contrast, Zone B shows a more compact flow reattachment near the lower rear of the chassis, attributed to the sharp downward change in vehicle geometry. Additionally, the absence of a windshield creates internal recirculation near the driver’s chest and legs (labelled C).

Figure 4. Velocity field and streamlines in symmetry plane.

A) Velocity field contour on the symmetry plane using the RANS model; B) Detailed velocity distribution in the near wake region under RANS conditions; C) Velocity field contour on the symmetry plane using the DES model; D) Streamlines on the symmetry plane illustrating flow behaviour around the vehicle with the RANS model.

Figure 5A and 5B show the pressure field in the symmetry plane and on the vehicle’s surface under RANS conditions. Notable pressure gradients are observed beneath the chassis and at key stagnation points—on the nose of the fairing, the front of the wheels, and particularly on the flat canvas behind the driver’s seat. The latter acts as a normal surface to the flow, generating a large stagnation region that significantly contributes to drag.

Figure 5. A) Pressure contour in the symmetry plane and on the vehicle surface by the RANS model; B) Pressure distribution on the vehicle surface; C) Pressure contour in the symmetry plane by the DES model.

In contrast, the DES model provides a more detailed and realistic depiction of the flow, particularly in the velocity gradients and wake structure ( Figure 4C). This model captures small low-velocity regions near the lower chassis (Zone D), where the boundary layer develops complex flow behaviour not resolvable by RANS due to its time-averaging limitations. Figure 5C shows the corresponding pressure field obtained by the DES model, where enhanced detail is seen in the near wake. Notably, alternating high- and low-pressure zones are observed near the rear roof region, approximately 1 m downstream (Zone E), reminiscent of the von Kármán vortex street.³⁸

Streamline analysis based on the steady-state RANS model is presented in Figure 4D. Two prominent counter-rotating vortices (labelled X and Y) emerge in the near wake, in agreement with vehicle aerodynamics literature by Hucho³⁷ and Ahmed.³⁹ The upper rear flow conforms to the behaviour of a squareback vehicle with a slant angle α = 5°, as expected. The lower rear wake shows slight deviations due to the chassis’ upward inclination but still produces flow dynamics consistent with squareback-type wake structures, particularly in the formation of the Y-vortex that remains attached to the chassis.

It is important to note that streamline visualisation using the transient DES model is not included, as the temporal discretisation inherent to DES captures rapidly evolving multi-scale turbulence in the wake. These dynamic variations disrupt streamline continuity across time steps, making it impractical to depict a representative streamline field in the near wake using this model.

3.3 Vorticity field analysis in the near and far wake

As previously discussed, turbulence models provide a valuable approximation of the flow dynamics around complex geometries, such as a Baja SAE vehicle. Figure 6 presents the longitudinal vorticity contours on the symmetry plane for both the RANS ( Figure 6a) and DES ( Figure 6b) models. In both cases, the near and far wake exhibit similar vortex trajectories and lengths; however, the DES model offers a more detailed representation of vortex structures due to its hybrid formulation. It captures both large-scale and small-scale vortices with greater clarity and spatial resolution.

Figure 6. A) Vorticity field contour on the symmetry plane for the RANS model; B) Vorticity field contour on the symmetry plane for the DES model; C) Detailed vorticity field contour in the near wake of the vehicle for the RANS model; D) Detailed vorticity field contour in the near wake of the vehicle for the DES model.

The RANS model succeeds in identifying the principal vortex structures formed behind the vehicle ( Figure 6C), but it lacks accuracy in resolving their intensity, propagation, and dissipation downstream. This is attributed to the nature of the RANS approach, which models all turbulent scales via statistical averaging, limiting its ability to depict transient or fluctuating phenomena. In contrast, the DES model by blending RANS near walls with LES in detached regions captures a broader spectrum of turbulent scales ( Figure 6D). As a result, the DES simulation reveals a denser and more realistic distribution of vortical structures throughout the wake, particularly in the rotor and downstream zones.

Moreover, the application of the DES model clearly enhances the capture of both micro- and macro-scale vortices along the entire wake region. This improved resolution directly contributes to more accurate predictions of flow field variables, including the vehicle’s drag coefficient and streamline behaviour. The key differences in performance between these turbulence models arise from two fundamental features. First, the RANS model employs a statistical averaging method, decomposing flow variables into mean and fluctuating components, and is applied in a zonal fashion i.e., across the entire computational domain as predefined by the user. Second, the DES model operates as a wall-distance-based method. It dynamically transitions from RANS to LES depending on the distance of the mesh element from the wall and the local grid size, using a spatial filtering mechanism (∆_LES) and requiring mesh adaptation to function effectively.

3.4 Theoretical framework of vorticity dynamics

Figures 6a and 6b show the vortex structures in the near wake, revealing stretching and diffusion behaviour consistent with classical vorticity dynamics. In the RANS approach, small and medium turbulence scales are entirely modelled, so the analysis is limited to averaged large-scale vorticity structures. According to Bernard and Wallace,⁴⁰ the steady-state, averaged vorticity transport equation is expressed as:

\frac{D {\bar{ω}}_{i}}{Dt} = {\bar{ω}}_{j} \frac{\partial {\bar{u}}_{i}}{\partial x_{j}} + \bar{ω'_{j} \frac{∂u'_{i}}{\partial x_{j}}} + υ \frac{\partial^{2} {\bar{ω}}_{i}}{\partial x_{j}^{2}}

Equation 2. Averaged vorticity transport equation.

Here, the left-hand side represents the convection of mean vorticity. The first term on the right-hand side corresponds to stretching due to the mean velocity field, the second term to stretching from turbulent fluctuations, and the third term to viscous diffusion. In RANS models using eddy-viscosity closures (such as Spalart–Allmaras), the fluctuating term is not directly resolved. Instead, the averaged vorticity field is derived from the velocity field obtained via the RANS equations.

This leads to a simplified form of the vorticity transport equation:

\frac{D {\bar{ω}}_{i}}{Dt} = {\bar{ω}}_{j} \frac{\partial {\bar{u}}_{i}}{\partial x_{j}} + \nabla \times (\nabla v_{t} \times \nabla \bar{u})

Equation 3. Vorticity transport equation.

In this form, the two main physical mechanisms that influence the development of the mean vorticity field are stretching and eddy-viscosity-based $\bar{ω}$ diffusion. The stretching term governs the rotation and amplification of vortical structures as they evolve downstream, while the diffusion term governs their spatial dispersion. This theoretical framework explains observed phenomena such as reconnection and cancellation of averaged vortical structures in the near wake.

3.5 3D Visualization of vortex structures

The generation and transport of vortex structures in the near and far wake of a vehicle can significantly affect its aerodynamic performance. These vortices, resulting from the interaction between the airflow and solid surfaces, are inherently three-dimensional phenomena. Therefore, visualising their evolution and intensity in 3D during post-processing is essential to identify optimisation strategies for vehicle components such as the chassis, fairing, or other elements influencing aerodynamic efficiency.

One widely used method for vortex visualisation is the Q-criterion, which is derived from the second invariant of the velocity gradient tensor, defined as:

Q = \frac{1}{2} ({‖ Ω ‖}^{2} - {‖ S ‖}^{2})

Equation 4. Mathematical definition of the Q-criterion for vortex visualization.

Where S is the symmetric part of the velocity gradient tensor (the rate of strain), and Ω is the antisymmetric part (the vorticity tensor). A region where Q>0 indicates that the local vorticity magnitude dominates over the strain rate, and therefore represents the presence of a vortex.⁴¹ Compared to planar vorticity iso-contours, the Q-criterion allows for a more detailed and three-dimensional visualisation of flow dynamics.

Figure 7 presents a comparison of vortex structures obtained using the Q-criterion with both RANS (a) and DES (b) turbulence models. In both cases, the main large-scale vortex structures in the near and far wake of the vehicle are consistent with the aerodynamic principles proposed by Hucho.³⁷ These include counter-rotating vortices originating from the vertical uprights that extend from the roof towards the far wake, paired vortices resulting from the interaction between lateral and underbody flows, and small-scale vortices formed around the vehicle’s tires.

Figure 7. Isocontours of Q-criterion showing vortex structures around the vehicle and in the near wake region.

A) RANS model colored by turbulence intensity; B) DES model colored by turbulence intensity.

The key distinction between the two models lies in their ability to resolve the evolution of these vortex structures. While the RANS model captures the origin of large-scale vortices and propagates them through a spatial averaging process, the DES model introduces both spatial and temporal discretisation. This enables more accurate resolution of both the location and evolution of vortical structures in the near wake, and allows for the capture of smaller, secondary vortices that RANS tends to neglect.

Figure 7 further illustrates these phenomena, showing isocontours of the Q-criterion colored by turbulence intensity. High-intensity vortices are observed at the front fairing, the struts, and the frontal areas of the front wheels regions where vortex formation initiates (RANS model in Figure 7A and DES model in Figure 7B). This behaviour is attributed to specific design characteristics of the Baja SAE vehicle: flat metal panels in the front fairing, uncovered structural struts formed from a single pipe frame integrated into the chassis, and wheels that extend beyond the width of the chassis, which is common in high performance of all-terrain vehicles (ATVs).

4. Discussion

The comparative analysis of turbulence models in this study reveals critical insights into the aerodynamic behaviour of the Baja SAE vehicle. The drag coefficient (Cd) computed using the RANS model yielded a value of 1.290 ± 0.005, demonstrating numerical stability through its low standard deviation. However, when using the hybrid RANS-LES (DES) model, the Cd decreased to 1.249 ± 0.024, indicating a more accurate estimation of aerodynamic drag due to the DES model’s capability to resolve a broader range of turbulence scales. This improvement aligns with theoretical expectations for unsteady turbulence modelling⁴² and validates the utility of DES in external vehicle aerodynamics.

Visualisations of the velocity field and pressure distribution further highlight the enhanced resolution offered by the DES model. The RANS results reveal two distinct recirculation zones in the near wake—Zone A, influenced by the inertia of the upper flow, and Zone B, formed by abrupt geometric changes in the rear lower chassis. However, the DES model resolves finer details of low-velocity regions near the underbody ( Figure 4D), as well as alternating pressure zones at the rear roofline indicative of von Kármán vortex shedding, a phenomenon not captured by RANS. These results confirm that DES enables a richer description of flow structures around the vehicle, especially in wake regions critical for drag generation.

Additionally, streamline analysis of the RANS solution identified two counter-rotating vortices (X and Y) in the near wake ( Figure 4D), consistent with known behaviour in squareback vehicle geometries.^37,39 The Baja SAE vehicle exhibits a slant angle of ~5°, resembling Ahmed-type body configurations. Despite geometric differences in the underbody, a similar vortex formation pattern is observed, although the recirculation region remains more closely attached to the chassis.

Overall, the results demonstrate that while the RANS model provides a reasonable first-order approximation of aerodynamic characteristics, the DES model offers superior fidelity in capturing transient vortex structures, wake turbulence, and drag prediction. These findings are essential for future design improvements aimed at optimising the aerodynamic performance of non-commercial, competition grade vehicles like the Baja SAE.

5. Conclusion

This study presents a comparative aerodynamic analysis of a Baja SAE vehicle using RANS and hybrid RANS-LES (DES) turbulence models. While RANS provided stable and computationally efficient results, it underestimated vortex dynamics and turbulent fluctuations in the wake. DES, by contrast, captured a richer spectrum of vortex structures particularly in the near and far wake resulting in a more accurate prediction of aerodynamic forces. DES predicted a lower drag coefficient (1.249 ± 0.024) than RANS (1.290 ± 0.005) and delivered higher spatial detail in velocity, pressure, and vortex fields. Q-criterion and streamline visualizations confirmed its ability to resolve a broader range of turbulent scales, offering deeper insights for aerodynamic optimization. Future work will focus on coupling DES with shape optimization techniques and wind tunnel validation to further enhance the aerodynamic performance of competitive off-road vehicles.

Use of artificial intelligence

We acknowledge that artificial intelligence tools (ChatGPT, OpenAI) were employed exclusively to assist with the revision of the English language and to improve the clarity of the writing. All scientific content, analyses, and conclusions are entirely the work of the authors.

Data availability statement

The materials supporting the findings of this study are available in the Zenodo repository: https://doi.org/10.5281/zenodo.17295975.⁴³

These materials include the ANSYS simulation files used to generate the computational results presented in the paper (geometry, mesh, boundary conditions, and solver configuration). No external datasets were used in this study, as all results derive from numerical simulations developed by the authors.

The files are shared under a Creative Commons Attribution 4.0 International (CC BY 4.0) license, allowing reuse and adaptation with proper citation. Due to file size limitations, the complete raw simulation output can be provided upon reasonable request to the corresponding author.

Extended data

Additional materials supporting this study are available in the Zenodo repository: DOI: https://doi.org/10.5281/zenodo.17295975.⁴³

This record includes the ANSYS project files used in the numerical simulations described in the manuscript, comprising the 3D geometry model of the vehicle, computational mesh file, boundary condition setup, solver configuration, and post-processing parameters.

All files are shared under a Creative Commons Attribution 4.0 International (CC BY 4.0) license.

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Version 2

VERSION 2 PUBLISHED 03 Nov 2025

Author details Author details

¹ Universidad Autonoma de Bucaramanga, Bucaramanga, Santander, Colombia
² Purdue University, West Lafayette, Indiana, USA

Sergio A. Ardila Gomez
Roles: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Software, Validation, Writing – Original Draft Preparation

Jessica G. Maradey Lazaro
Roles: Conceptualization, Funding Acquisition, Project Administration, Resources, Validation, Writing – Original Draft Preparation

Jhon J. Quiñones
Roles: Formal Analysis, Investigation, Methodology, Software, Writing – Original Draft Preparation

Deisy Y. Rodriguez Sarmiento
Roles: Investigation, Supervision, Writing – Review & Editing

Competing interests

No competing interests were disclosed.

Grant information

This research was funded by the research office of the Universidad Autónoma de Bucaramanga (UNAB), under code I-78041. Additional support was provided through institutional resources and access to computational infrastructure.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Article Versions (2)

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Published: 12 Jun 2026, 14:1199

https://doi.org/10.12688/f1000research.171076.2

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Published: 03 Nov 2025, 14:1199

https://doi.org/10.12688/f1000research.171076.1

© 2025 Ardila Gomez SA et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ardila Gomez SA, Maradey Lazaro JG, Quiñones JJ and Rodriguez Sarmiento DY. Aerodynamic Performance of a Baja SAE Vehicle Using Hybrid RANS-LES Approach [version 1; peer review: 2 not approved]. F1000Research 2025, 14:1199 (https://doi.org/10.12688/f1000research.171076.1)

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Reviewer Report 10 Apr 2026

Luis Fernando Rodriguez, Mechanical and Aerospace Engineering, Clarkson University, Potsdam, New York, USA

Not Approved

https://doi.org/10.5256/f1000research.188621.r469214

General Assessment

The manuscript presents an interesting computational study of the aerodynamic performance of a Baja SAE vehicle using both RANS and hybrid RANS–LES (DES) turbulence models. The authors demonstrate strong technical effort and familiarity with advanced CFD tools. The work has clear educational value and provides useful insight into the application of hybrid turbulence modeling for vehicle aerodynamics.

Strengths

The study includes a well-developed CFD methodology, a detailed meshing strategy, and a thoughtful comparison between RANS and DES approaches. The use of post-processing techniques such as vorticity contours and Q-criterion visualization is appropriate and helps illustrate key flow features. The manuscript is also well motivated within the context of Baja SAE design.

Points for Improvement

1. Validation: The manuscript would benefit significantly from validation against experimental data, simplified benchmarks, or published results. Including such comparisons would strengthen the credibility of the conclusions.

2. Aerodynamic Metrics: Expanding the analysis beyond drag coefficient to include lift, side forces, or moments would provide a more complete characterization of vehicle performance.

3. Turbulence Model Justification: Additional discussion on why DES is necessary for this flow regime, including comparisons with simpler models, would improve the methodological clarity.

4. Boundary Conditions: The assumption of stationary ground and non-rotating wheels should be discussed in more detail, including its potential impact on results.

5. Quantitative Analysis: Complementing visualizations with quantitative metrics (e.g., frequency analysis or additional flow parameters) would strengthen the analysis.

6. Scope: Exploring additional cases (such as different speeds or geometric variations) could enhance the practical impact of the work.

Minor Comments

The introduction could more clearly define the research gap. Some figures would benefit from additional quantitative annotations. The organization of the methods section could also be improved for clarity.

Recommendation

The manuscript has solid potential but would benefit from revisions addressing the points above. With additional validation, expanded analysis, and clearer justification of modeling choices, the work could make a valuable contribution to the field.

Final Comment

Overall, this is a promising study that demonstrates strong technical effort. With further refinement and strengthening of the scientific rigor, it could be suitable for indexing.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Mechanical Engineering: Structural Analysis and Fluid Mechanics (Turbulent Analysis).

I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above.

CITE

Report a concern

Author Response 12 Jun 2026

Deisy Yurley Rodriguez Sarmiento, Universidad Autonoma de Bucaramanga, Bucaramanga, Colombia

12 Jun 2026

Author Response
Points for Improvement
1. Validation: The manuscript would benefit significantly from validation against experimental data, simplified benchmarks, or published results. Including such comparisons would strengthen the credibility of
... Continue reading
Points for Improvement

Validation: The manuscript would benefit significantly from validation against experimental data, simplified benchmarks, or published results. Including such comparisons would strengthen the credibility of the conclusions.

Response: We thank the reviewer for this valuable suggestion. The importance of validation is fully acknowledged and was also raised by Reviewer 1. In response, we have revised the manuscript to clarify that the present work is a comparative numerical study of turbulence modeling approaches rather than a fully validated aerodynamic prediction.
Additionally, we have included a benchmarking discussion showing that the predicted drag coefficient values fall within ranges reported in the literature for similar bluff-body and off-road vehicle configurations, supporting the physical plausibility of the results.
The absence of experimental validation is now explicitly acknowledged as a limitation, and future work will address this through experimental and parametric studies.

Aerodynamic Metrics: Expanding the analysis beyond drag coefficient to include lift, side forces, or moments would provide a more complete characterization of vehicle performance.

Response: We thank the reviewer for this valuable suggestion. This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that a complete aerodynamic characterization would include additional force components such as lift, side force, and aerodynamic moments. However, the objective of the present study is to provide a comparative assessment of turbulence modeling approaches, focusing on wake dynamics and drag as a representative parameter of wake-induced aerodynamic losses. This scope has now been clearly stated in the revised manuscript. Additionally, we have included a statement highlighting that future work will incorporate a more comprehensive set of aerodynamic metrics to enable a complete evaluation of vehicle performance.

Turbulence Model Justification: Additional discussion on why DES is necessary for this flow regime, including comparisons with simpler models, would improve the methodological clarity.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that, although the Reynolds number considered falls within a range where steady RANS approaches can provide reasonable predictions of global aerodynamic quantities, the use of DES is motivated by its ability to better represent unsteady flow structures, particularly in the wake region. The manuscript has been revised to explicitly state that the use of DES is intended to enhance the representation of wake dynamics rather than to serve as a strictly necessary modeling approach for this flow regime. Also, the scope of the study has been clarified as a comparative evaluation of turbulence modeling approaches, rather than a fully optimized or validated aerodynamic prediction.

Boundary Conditions: The assumption of stationary ground and non-rotating wheels should be discussed in more detail, including its potential impact on results.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We have included a more detailed discussion of the assumption of stationary ground and non-rotating wheels, highlighting its potential impact on near-ground flow development, wake structure, and the absolute values of aerodynamic forces. This modeling choice has been clarified as a simplification adopted to maintain computational feasibility and ensure consistency in the comparative analysis between turbulence models.
The corresponding limitations are now explicitly stated in both the Methods and Discussion sections, and future work will incorporate moving ground conditions and rotating wheels to improve the physical realism of the simulations.

Quantitative Analysis: Complementing visualizations with quantitative metrics (e.g., frequency analysis or additional flow parameters) would strengthen the analysis.

Response: This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that the flow visualizations presented in this study are intended for qualitative analysis of flow structures rather than for quantitative characterization of unsteady phenomena. Accordingly, we have revised the manuscript to avoid overinterpretation and to explicitly state the limitations of the visual analysis. We also acknowledge that a more rigorous quantitative characterization such as frequency analysis, Strouhal number estimation, or additional flow metrics would further strengthen the analysis, but is beyond the scope of the present study. Future work will incorporate these approaches to provide a more comprehensive assessment of unsteady wake dynamics.

Scope: Exploring additional cases (such as different speeds or geometric variations) could enhance the practical impact of the work.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that the present study is limited to a single geometry and operating condition, and therefore does not capture the influence of parameters such as velocity or geometric variations.
The scope of the work has been clarified as a comparative evaluation of turbulence modeling approaches rather than a parametric or optimization study. Additionally, we have included a discussion highlighting how the identified flow features can inform future design improvements. Future work will extend the analysis to include parametric variations, such as different speeds and geometric configurations, in order to enhance the practical applicability of the results.

Minor Comments

The introduction could more clearly define the research gap. Some figures would benefit from additional quantitative annotations. The organization of the methods section could also be improved for clarity.
Response: We thank the reviewer for these helpful suggestions.
These aspects were also raised by Reviewer 1 and have been addressed in the revised manuscript. Specifically, the Introduction has been refined to more clearly define the research gap and the scope of the study as a comparative evaluation of turbulence modeling approaches.
The Methods section has been reorganized to improve clarity and reproducibility, with a clearer distinction between model description and methodological justification.
In addition, figure descriptions have been revised to enhance clarity, and where appropriate, annotations and explanations have been improved to better support interpretation. The qualitative nature of the visualizations has also been explicitly stated.

Recommendation

The manuscript has solid potential but would benefit from revisions addressing the points above. With additional validation, expanded analysis, and clearer justification of modeling choices, the work could make a valuable contribution to the field.
Response: We sincerely thank the reviewer for the positive evaluation and constructive feedback. All the points raised have been carefully addressed in the revised manuscript. In particular, we have clarified the scope of the study, strengthened the methodological justification, and incorporated additional discussion regarding validation through literature benchmarking and the limitations of the modeling approach. These revisions aim to improve the clarity, rigor, and overall contribution of the work. We appreciate the reviewer’s comments, which have significantly helped to enhance the quality of the manuscript.
Points for Improvement

Validation: The manuscript would benefit significantly from validation against experimental data, simplified benchmarks, or published results. Including such comparisons would strengthen the credibility of the conclusions.

Response: We thank the reviewer for this valuable suggestion. The importance of validation is fully acknowledged and was also raised by Reviewer 1. In response, we have revised the manuscript to clarify that the present work is a comparative numerical study of turbulence modeling approaches rather than a fully validated aerodynamic prediction.
Additionally, we have included a benchmarking discussion showing that the predicted drag coefficient values fall within ranges reported in the literature for similar bluff-body and off-road vehicle configurations, supporting the physical plausibility of the results.
The absence of experimental validation is now explicitly acknowledged as a limitation, and future work will address this through experimental and parametric studies.

Aerodynamic Metrics: Expanding the analysis beyond drag coefficient to include lift, side forces, or moments would provide a more complete characterization of vehicle performance.

Response: We thank the reviewer for this valuable suggestion. This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that a complete aerodynamic characterization would include additional force components such as lift, side force, and aerodynamic moments. However, the objective of the present study is to provide a comparative assessment of turbulence modeling approaches, focusing on wake dynamics and drag as a representative parameter of wake-induced aerodynamic losses. This scope has now been clearly stated in the revised manuscript. Additionally, we have included a statement highlighting that future work will incorporate a more comprehensive set of aerodynamic metrics to enable a complete evaluation of vehicle performance.

Turbulence Model Justification: Additional discussion on why DES is necessary for this flow regime, including comparisons with simpler models, would improve the methodological clarity.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that, although the Reynolds number considered falls within a range where steady RANS approaches can provide reasonable predictions of global aerodynamic quantities, the use of DES is motivated by its ability to better represent unsteady flow structures, particularly in the wake region. The manuscript has been revised to explicitly state that the use of DES is intended to enhance the representation of wake dynamics rather than to serve as a strictly necessary modeling approach for this flow regime. Also, the scope of the study has been clarified as a comparative evaluation of turbulence modeling approaches, rather than a fully optimized or validated aerodynamic prediction.

Boundary Conditions: The assumption of stationary ground and non-rotating wheels should be discussed in more detail, including its potential impact on results.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We have included a more detailed discussion of the assumption of stationary ground and non-rotating wheels, highlighting its potential impact on near-ground flow development, wake structure, and the absolute values of aerodynamic forces. This modeling choice has been clarified as a simplification adopted to maintain computational feasibility and ensure consistency in the comparative analysis between turbulence models.
The corresponding limitations are now explicitly stated in both the Methods and Discussion sections, and future work will incorporate moving ground conditions and rotating wheels to improve the physical realism of the simulations.

Quantitative Analysis: Complementing visualizations with quantitative metrics (e.g., frequency analysis or additional flow parameters) would strengthen the analysis.

Response: This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that the flow visualizations presented in this study are intended for qualitative analysis of flow structures rather than for quantitative characterization of unsteady phenomena. Accordingly, we have revised the manuscript to avoid overinterpretation and to explicitly state the limitations of the visual analysis. We also acknowledge that a more rigorous quantitative characterization such as frequency analysis, Strouhal number estimation, or additional flow metrics would further strengthen the analysis, but is beyond the scope of the present study. Future work will incorporate these approaches to provide a more comprehensive assessment of unsteady wake dynamics.

Scope: Exploring additional cases (such as different speeds or geometric variations) could enhance the practical impact of the work.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that the present study is limited to a single geometry and operating condition, and therefore does not capture the influence of parameters such as velocity or geometric variations.
The scope of the work has been clarified as a comparative evaluation of turbulence modeling approaches rather than a parametric or optimization study. Additionally, we have included a discussion highlighting how the identified flow features can inform future design improvements. Future work will extend the analysis to include parametric variations, such as different speeds and geometric configurations, in order to enhance the practical applicability of the results.

Minor Comments

The introduction could more clearly define the research gap. Some figures would benefit from additional quantitative annotations. The organization of the methods section could also be improved for clarity.
Response: We thank the reviewer for these helpful suggestions.
These aspects were also raised by Reviewer 1 and have been addressed in the revised manuscript. Specifically, the Introduction has been refined to more clearly define the research gap and the scope of the study as a comparative evaluation of turbulence modeling approaches.
The Methods section has been reorganized to improve clarity and reproducibility, with a clearer distinction between model description and methodological justification.
In addition, figure descriptions have been revised to enhance clarity, and where appropriate, annotations and explanations have been improved to better support interpretation. The qualitative nature of the visualizations has also been explicitly stated.

Recommendation

The manuscript has solid potential but would benefit from revisions addressing the points above. With additional validation, expanded analysis, and clearer justification of modeling choices, the work could make a valuable contribution to the field.
Response: We sincerely thank the reviewer for the positive evaluation and constructive feedback. All the points raised have been carefully addressed in the revised manuscript. In particular, we have clarified the scope of the study, strengthened the methodological justification, and incorporated additional discussion regarding validation through literature benchmarking and the limitations of the modeling approach. These revisions aim to improve the clarity, rigor, and overall contribution of the work. We appreciate the reviewer’s comments, which have significantly helped to enhance the quality of the manuscript.
Competing Interests: The authors declare that they have no competing interests. Close
Report a concern
Respond or Comment

COMMENTS ON THIS REPORT

Author Response 12 Jun 2026

Deisy Yurley Rodriguez Sarmiento, Universidad Autonoma de Bucaramanga, Bucaramanga, Colombia

12 Jun 2026

Author Response
Points for Improvement
1. Validation: The manuscript would benefit significantly from validation against experimental data, simplified benchmarks, or published results. Including such comparisons would strengthen the credibility of
... Continue reading
Points for Improvement

Validation: The manuscript would benefit significantly from validation against experimental data, simplified benchmarks, or published results. Including such comparisons would strengthen the credibility of the conclusions.

Response: We thank the reviewer for this valuable suggestion. The importance of validation is fully acknowledged and was also raised by Reviewer 1. In response, we have revised the manuscript to clarify that the present work is a comparative numerical study of turbulence modeling approaches rather than a fully validated aerodynamic prediction.
Additionally, we have included a benchmarking discussion showing that the predicted drag coefficient values fall within ranges reported in the literature for similar bluff-body and off-road vehicle configurations, supporting the physical plausibility of the results.
The absence of experimental validation is now explicitly acknowledged as a limitation, and future work will address this through experimental and parametric studies.

Aerodynamic Metrics: Expanding the analysis beyond drag coefficient to include lift, side forces, or moments would provide a more complete characterization of vehicle performance.

Response: We thank the reviewer for this valuable suggestion. This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that a complete aerodynamic characterization would include additional force components such as lift, side force, and aerodynamic moments. However, the objective of the present study is to provide a comparative assessment of turbulence modeling approaches, focusing on wake dynamics and drag as a representative parameter of wake-induced aerodynamic losses. This scope has now been clearly stated in the revised manuscript. Additionally, we have included a statement highlighting that future work will incorporate a more comprehensive set of aerodynamic metrics to enable a complete evaluation of vehicle performance.

Turbulence Model Justification: Additional discussion on why DES is necessary for this flow regime, including comparisons with simpler models, would improve the methodological clarity.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that, although the Reynolds number considered falls within a range where steady RANS approaches can provide reasonable predictions of global aerodynamic quantities, the use of DES is motivated by its ability to better represent unsteady flow structures, particularly in the wake region. The manuscript has been revised to explicitly state that the use of DES is intended to enhance the representation of wake dynamics rather than to serve as a strictly necessary modeling approach for this flow regime. Also, the scope of the study has been clarified as a comparative evaluation of turbulence modeling approaches, rather than a fully optimized or validated aerodynamic prediction.

Boundary Conditions: The assumption of stationary ground and non-rotating wheels should be discussed in more detail, including its potential impact on results.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We have included a more detailed discussion of the assumption of stationary ground and non-rotating wheels, highlighting its potential impact on near-ground flow development, wake structure, and the absolute values of aerodynamic forces. This modeling choice has been clarified as a simplification adopted to maintain computational feasibility and ensure consistency in the comparative analysis between turbulence models.
The corresponding limitations are now explicitly stated in both the Methods and Discussion sections, and future work will incorporate moving ground conditions and rotating wheels to improve the physical realism of the simulations.

Quantitative Analysis: Complementing visualizations with quantitative metrics (e.g., frequency analysis or additional flow parameters) would strengthen the analysis.

Response: This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that the flow visualizations presented in this study are intended for qualitative analysis of flow structures rather than for quantitative characterization of unsteady phenomena. Accordingly, we have revised the manuscript to avoid overinterpretation and to explicitly state the limitations of the visual analysis. We also acknowledge that a more rigorous quantitative characterization such as frequency analysis, Strouhal number estimation, or additional flow metrics would further strengthen the analysis, but is beyond the scope of the present study. Future work will incorporate these approaches to provide a more comprehensive assessment of unsteady wake dynamics.

Scope: Exploring additional cases (such as different speeds or geometric variations) could enhance the practical impact of the work.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that the present study is limited to a single geometry and operating condition, and therefore does not capture the influence of parameters such as velocity or geometric variations.
The scope of the work has been clarified as a comparative evaluation of turbulence modeling approaches rather than a parametric or optimization study. Additionally, we have included a discussion highlighting how the identified flow features can inform future design improvements. Future work will extend the analysis to include parametric variations, such as different speeds and geometric configurations, in order to enhance the practical applicability of the results.

Minor Comments

The introduction could more clearly define the research gap. Some figures would benefit from additional quantitative annotations. The organization of the methods section could also be improved for clarity.
Response: We thank the reviewer for these helpful suggestions.
These aspects were also raised by Reviewer 1 and have been addressed in the revised manuscript. Specifically, the Introduction has been refined to more clearly define the research gap and the scope of the study as a comparative evaluation of turbulence modeling approaches.
The Methods section has been reorganized to improve clarity and reproducibility, with a clearer distinction between model description and methodological justification.
In addition, figure descriptions have been revised to enhance clarity, and where appropriate, annotations and explanations have been improved to better support interpretation. The qualitative nature of the visualizations has also been explicitly stated.

Recommendation

The manuscript has solid potential but would benefit from revisions addressing the points above. With additional validation, expanded analysis, and clearer justification of modeling choices, the work could make a valuable contribution to the field.
Response: We sincerely thank the reviewer for the positive evaluation and constructive feedback. All the points raised have been carefully addressed in the revised manuscript. In particular, we have clarified the scope of the study, strengthened the methodological justification, and incorporated additional discussion regarding validation through literature benchmarking and the limitations of the modeling approach. These revisions aim to improve the clarity, rigor, and overall contribution of the work. We appreciate the reviewer’s comments, which have significantly helped to enhance the quality of the manuscript.
Points for Improvement

Validation: The manuscript would benefit significantly from validation against experimental data, simplified benchmarks, or published results. Including such comparisons would strengthen the credibility of the conclusions.

Response: We thank the reviewer for this valuable suggestion. The importance of validation is fully acknowledged and was also raised by Reviewer 1. In response, we have revised the manuscript to clarify that the present work is a comparative numerical study of turbulence modeling approaches rather than a fully validated aerodynamic prediction.
Additionally, we have included a benchmarking discussion showing that the predicted drag coefficient values fall within ranges reported in the literature for similar bluff-body and off-road vehicle configurations, supporting the physical plausibility of the results.
The absence of experimental validation is now explicitly acknowledged as a limitation, and future work will address this through experimental and parametric studies.

Aerodynamic Metrics: Expanding the analysis beyond drag coefficient to include lift, side forces, or moments would provide a more complete characterization of vehicle performance.

Response: We thank the reviewer for this valuable suggestion. This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that a complete aerodynamic characterization would include additional force components such as lift, side force, and aerodynamic moments. However, the objective of the present study is to provide a comparative assessment of turbulence modeling approaches, focusing on wake dynamics and drag as a representative parameter of wake-induced aerodynamic losses. This scope has now been clearly stated in the revised manuscript. Additionally, we have included a statement highlighting that future work will incorporate a more comprehensive set of aerodynamic metrics to enable a complete evaluation of vehicle performance.

Turbulence Model Justification: Additional discussion on why DES is necessary for this flow regime, including comparisons with simpler models, would improve the methodological clarity.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that, although the Reynolds number considered falls within a range where steady RANS approaches can provide reasonable predictions of global aerodynamic quantities, the use of DES is motivated by its ability to better represent unsteady flow structures, particularly in the wake region. The manuscript has been revised to explicitly state that the use of DES is intended to enhance the representation of wake dynamics rather than to serve as a strictly necessary modeling approach for this flow regime. Also, the scope of the study has been clarified as a comparative evaluation of turbulence modeling approaches, rather than a fully optimized or validated aerodynamic prediction.

Boundary Conditions: The assumption of stationary ground and non-rotating wheels should be discussed in more detail, including its potential impact on results.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We have included a more detailed discussion of the assumption of stationary ground and non-rotating wheels, highlighting its potential impact on near-ground flow development, wake structure, and the absolute values of aerodynamic forces. This modeling choice has been clarified as a simplification adopted to maintain computational feasibility and ensure consistency in the comparative analysis between turbulence models.
The corresponding limitations are now explicitly stated in both the Methods and Discussion sections, and future work will incorporate moving ground conditions and rotating wheels to improve the physical realism of the simulations.

Quantitative Analysis: Complementing visualizations with quantitative metrics (e.g., frequency analysis or additional flow parameters) would strengthen the analysis.

Response: This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that the flow visualizations presented in this study are intended for qualitative analysis of flow structures rather than for quantitative characterization of unsteady phenomena. Accordingly, we have revised the manuscript to avoid overinterpretation and to explicitly state the limitations of the visual analysis. We also acknowledge that a more rigorous quantitative characterization such as frequency analysis, Strouhal number estimation, or additional flow metrics would further strengthen the analysis, but is beyond the scope of the present study. Future work will incorporate these approaches to provide a more comprehensive assessment of unsteady wake dynamics.

Scope: Exploring additional cases (such as different speeds or geometric variations) could enhance the practical impact of the work.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that the present study is limited to a single geometry and operating condition, and therefore does not capture the influence of parameters such as velocity or geometric variations.
The scope of the work has been clarified as a comparative evaluation of turbulence modeling approaches rather than a parametric or optimization study. Additionally, we have included a discussion highlighting how the identified flow features can inform future design improvements. Future work will extend the analysis to include parametric variations, such as different speeds and geometric configurations, in order to enhance the practical applicability of the results.

Minor Comments

The introduction could more clearly define the research gap. Some figures would benefit from additional quantitative annotations. The organization of the methods section could also be improved for clarity.
Response: We thank the reviewer for these helpful suggestions.
These aspects were also raised by Reviewer 1 and have been addressed in the revised manuscript. Specifically, the Introduction has been refined to more clearly define the research gap and the scope of the study as a comparative evaluation of turbulence modeling approaches.
The Methods section has been reorganized to improve clarity and reproducibility, with a clearer distinction between model description and methodological justification.
In addition, figure descriptions have been revised to enhance clarity, and where appropriate, annotations and explanations have been improved to better support interpretation. The qualitative nature of the visualizations has also been explicitly stated.

Recommendation

The manuscript has solid potential but would benefit from revisions addressing the points above. With additional validation, expanded analysis, and clearer justification of modeling choices, the work could make a valuable contribution to the field.
Response: We sincerely thank the reviewer for the positive evaluation and constructive feedback. All the points raised have been carefully addressed in the revised manuscript. In particular, we have clarified the scope of the study, strengthened the methodological justification, and incorporated additional discussion regarding validation through literature benchmarking and the limitations of the modeling approach. These revisions aim to improve the clarity, rigor, and overall contribution of the work. We appreciate the reviewer’s comments, which have significantly helped to enhance the quality of the manuscript.
Competing Interests: The authors declare that they have no competing interests. Close
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Reviewer Report 02 Jan 2026

Adit S Misar, University of North Carolina at Charlotte, Charlotte, North Carolina, USA

Not Approved

https://doi.org/10.5256/f1000research.188621.r434652

General Assessment
The reviewer would like to first acknowledge the substantial effort invested by the authors. The scope of this work goes well beyond what is typically required for a Baja SAE design exercise, particularly in the use of hybrid RANS–LES modeling, mesh adaptation, vorticity analysis, and 3D post-processing. These efforts demonstrate strong technical ambition and genuine curiosity about advanced CFD methods.
However, while the work is commendable from an educational and exploratory standpoint, the manuscript falls short of the technical, methodological, and validation standards required for archival journal indexing. Importantly, many of these shortcomings are not superficial or editorial in nature, but structural and foundational. As such, the reviewer does not believe that the manuscript is suitable for indexing through major revision alone.
The comments below are offered in a constructive and mentoring spirit, with the hope that the authors may successfully develop this work into a future indexing contribution after addressing the underlying gaps.
Major Technical Concerns
1. Scope and Framing of the Study
Abstract and Introduction, Pages 1 to 3
The abstract (Page 1) positions the study as a high-fidelity aerodynamic investigation using hybrid RANS–LES. While the numerical tools employed are indeed advanced, the scientific scope remains narrow. The manuscript focuses almost exclusively on drag coefficient, with no discussion of side force, lift, or aerodynamic moments.
For a ground vehicle, and especially for a racing or off-road competition vehicle, drag alone is an incomplete descriptor of aerodynamic performance. At minimum, a complete aerodynamic characterization should consider three forces (Cd, Cl, Cs) and three moments (rolling, pitching, yawing). Even if all quantities are not ultimately presented, the absence of discussion or justification for excluding them is a major omission.
Similarly, metrics such as L over D and front-to-rear balance percentage are central to racing vehicle aerodynamics, yet are not meaningfully addressed. This limits both the scientific value and the practical relevance of the results.
2. Absence of Validation and Physical Benchmarking
Section 3, Pages 7–12
A critical limitation of this study is the complete absence of experimental validation, high-fidelity reference data, or benchmark comparison.

The manuscript presents drag coefficients from RANS and DES simulations at a single velocity of 30 km/h (Section 3.1, Page 7), but provides no comparison to wind tunnel data, coast-down tests, published Baja SAE measurements, or even simplified analytical estimates.
The claim that DES provides “more accurate” predictions (Abstract; Sections 3.1, 4, and 5) is not substantiated. The manuscript reports only a numerical difference between RANS and DES, not accuracy relative to a reference truth.
The standard deviation of Cd in DES is interpreted as improved physical realism (Page 7), yet temporal variability alone does not imply improved accuracy.

Without validation, the work remains a numerical comparison study, not a demonstrable advancement in aerodynamic prediction.
3. Questionable Appropriateness of DES for the Problem Scale
Section 2.4, Pages 6–7
The choice and justification of DES for this application is insufficiently supported.

The vehicle operates at 30 km/h, corresponding to a Reynolds number of approximately 6.7 × 10⁵ (Page 6). This places the flow in a regime where steady or URANS models are often sufficient, especially given the simplified geometry.
The DES formulation relies on a mesh-dependent transition between RANS and LES regions, yet the manuscript provides no grid sensitivity analysis specific to DES behavior, only a drag-based mesh independence study using RANS (Section 2.2, Page 6).
The DES mesh adaptation is derived from vortex diameters observed in RANS results (Page 6), which introduces circular reasoning. If RANS does not resolve unsteady structures accurately, it cannot reliably inform LES filter sizing.

As presented, the DES implementation appears methodologically fragile and not robustly justified for this flow regime.
4. Overinterpretation of Flow Visualizations
Sections 3.2–3.5, Pages 7–11
The manuscript places strong interpretive weight on contour plots, streamlines, and Q-criterion visualizations, but these are not supported by quantitative flow metrics.

Claims regarding vortex shedding, von Kármán-like behavior, and improved wake resolution (Pages 7–9) are made without supporting evidence such as Strouhal number analysis, spectral decomposition, or force coefficient frequency content.
Streamlines from steady RANS are used to infer vortex topology and persistence (Page 8), which is not physically rigorous for inherently unsteady wake flows.
Q-criterion plots (Section 3.5, Pages 10–11) are presented qualitatively, without sensitivity to threshold selection or comparison across consistent isovalues.

Overall, the visual analysis is descriptive rather than diagnostic, and conclusions drawn from it exceed what the presented data can support.
5. Insufficient Treatment of Ground and Wheel Effects
Section 2.3, Page 6
All solid boundaries, including the ground and wheels, are modeled as stationary no-slip walls.

For a ground vehicle application, this modeling choice is known to significantly alter wake structure and drag prediction.
The manuscript does not discuss the implications of neglecting moving ground and rotating wheels, nor does it attempt a sensitivity study or justify the simplification.
Given the focus on wake dynamics and drag accuracy, this omission materially affects the credibility of the results.

6. Limited Parametric Scope and Practical Insight
Sections 3–5, Pages 7–12
The study evaluates a single geometry at a single velocity with no parametric variation.

There is no assessment of ride height, yaw angle, surface modifications, or speed dependence.
No aerodynamic optimization or design guidance emerges beyond the general statement that DES resolves more structures than RANS.
As a result, the manuscript does not provide actionable insight for Baja SAE design practice or aerodynamic decision-making.

Presentation and Structure Concerns
While secondary to the technical issues above, the following further limit the manuscript’s readiness:

The Introduction (Pages 3–4) devotes extensive space to general Baja SAE context but insufficiently narrows the scientific gap being addressed.
The Methods section intermixes modeling description and justification, making reproducibility difficult.
Several figures rely on qualitative interpretation without clear scaling rationale or quantitative annotation.

Recommendation
While the reviewer acknowledges the authors’ effort and the educational value of exploring hybrid turbulence models, the manuscript suffers from fundamental methodological and scientific limitations that cannot be resolved through incremental revision.
The absence of validation, the overextension of qualitative visualization, and the insufficient justification for DES usage collectively prevent the work from meeting indexing standards.
Recommendation: Not Approved.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

No
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Motorsports, CFD, Turbulence, Aerodynamics, Vehicle Dynamics.

CITE

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Author Response 12 Jun 2026

Deisy Yurley Rodriguez Sarmiento, Universidad Autonoma de Bucaramanga, Bucaramanga, Colombia

12 Jun 2026

Author Response
1. Scope and Framing of the Study
Abstract and Introduction, Pages 1 to 3
The abstract (Page 1) positions the study as a high-fidelity aerodynamic investigation using hybrid RANS–LES. While ... Continue reading
1. Scope and Framing of the Study
Abstract and Introduction, Pages 1 to 3
The abstract (Page 1) positions the study as a high-fidelity aerodynamic investigation using hybrid RANS–LES. While the numerical tools employed are indeed advanced, the scientific scope remains narrow. The manuscript focuses almost exclusively on drag coefficient, with no discussion of side force, lift, or aerodynamic moments.
For a ground vehicle, and especially for a racing or off-road competition vehicle, drag alone is an incomplete descriptor of aerodynamic performance. At minimum, a complete aerodynamic characterization should consider three forces (Cd, Cl, Cs) and three moments (rolling, pitching, yawing). Even if all quantities are not ultimately presented, the absence of discussion or justification for excluding them is a major omission.
Similarly, metrics such as L over D and front-to-rear balance percentage are central to racing vehicle aerodynamics, yet are not meaningfully addressed. This limits both the scientific value and the practical relevance of the results.

Response: We sincerely thank the reviewer for this insightful and valuable comment. We agree that a complete aerodynamic characterization of ground vehicles may include additional force components (lift and side force) and aerodynamic moments (rolling, pitching, and yawing), as well as derived performance indicators such as L/D ratio and aerodynamic balance. However, the primary objective of this study is not to provide a full aerodynamic characterization of the Baja SAE vehicle, but rather to evaluate the capability of hybrid RANS–LES (DES) modeling to capture wake dynamics and improve drag prediction compared to steady RANS approaches.

In this context, the drag coefficient (Cd) was selected as the primary metric because it is directly influenced by wake structures, flow separation, and vortex dynamics, which are the main phenomena investigated in this work. The focus on Cd is consistent with prior CFD studies aimed at assessing turbulence modeling strategies in external aerodynamics. We acknowledge that additional aerodynamic quantities such as lift (Cl), side force (Cs), and moments are highly relevant for vehicle stability and performance, particularly in racing applications. However, these quantities are more sensitive to detailed geometry, transient crosswind conditions, and suspension–ground interaction effects, which fall beyond the scope of the present study.

To address the reviewer’s concern, we have clarified the scope and limitations of the study in the revised manuscript, explicitly stating:
(i) the rationale for focusing on drag coefficient,
(ii) the intended methodological contribution of the work, and
(iii) the need for future studies to include a more comprehensive aerodynamic characterization.

2. Absence of Validation and Physical Benchmarking
Section 3, Pages 7–12
A critical limitation of this study is the complete absence of experimental validation, high-fidelity reference data, or benchmark comparison.
The manuscript presents drag coefficients from RANS and DES simulations at a single velocity of 30 km/h (Section 3.1, Page 7), but provides no comparison to wind tunnel data, coast-down tests, published Baja SAE measurements, or even simplified analytical estimates.
The claim that DES provides “more accurate” predictions (Abstract; Sections 3.1, 4, and 5) is not substantiated. The manuscript reports only a numerical difference between RANS and DES, not accuracy relative to a reference truth.
The standard deviation of Cd in DES is interpreted as improved physical realism (Page 7), yet temporal variability alone does not imply improved accuracy.
Without validation, the work remains a numerical comparison study, not a demonstrable advancement in aerodynamic prediction.

Response: We sincerely thank the reviewer for this important and insightful comment.
We fully agree that the absence of experimental validation or high-fidelity reference data limits the ability to assess the absolute accuracy of the numerical predictions. The primary objective of this study, however, is not to provide a fully validated aerodynamic characterization of the vehicle, but rather to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) in capturing wake dynamics and flow structures.
Following the reviewer’s suggestion, we have revised the manuscript to avoid statements implying absolute accuracy. Instead, we now emphasize that the DES approach provides enhanced physical fidelity and improved resolution of unsteady flow phenomena, particularly in the wake region. We also acknowledge that experimental validation (e.g., wind tunnel testing or full-scale measurements) is a critical component in aerodynamic studies. However, such experimental campaigns require specialized infrastructure and significant financial resources that were not available within the scope of the present work. In this context, and consistent with common practice in computational aerodynamics studies under similar constraints, we have incorporated a benchmarking discussion based on published literature. Specifically, the predicted drag coefficient values (Cd ≈ 1.25–1.29) fall within the expected range reported for bluff-body and off-road vehicle configurations, which typically exhibit relatively high drag due to exposed structural elements and flow separation. This comparison supports the physical plausibility of the results, although it does not replace direct experimental validation.
Additionally, we have clarified that the temporal variability observed in DES results reflects the inherently unsteady nature of the simulation, rather than being a direct indicator of improved accuracy. Finally, we explicitly state in the revised manuscript that the present study should be interpreted as a comparative numerical analysis, and that future work will include experimental validation to enable quantitative assessment of predictive accuracy.

3. Questionable Appropriateness of DES for the Problem Scale
Section 2.4, Pages 6–7
The choice and justification of DES for this application is insufficiently supported.
The vehicle operates at 30 km/h, corresponding to a Reynolds number of approximately 6.7 × 10⁵ (Page 6). This places the flow in a regime where steady or URANS models are often sufficient, especially given the simplified geometry.
The DES formulation relies on a mesh-dependent transition between RANS and LES regions, yet the manuscript provides no grid sensitivity analysis specific to DES behavior, only a drag-based mesh independence study using RANS (Section 2.2, Page 6).
The DES mesh adaptation is derived from vortex diameters observed in RANS results (Page 6), which introduces circular reasoning. If RANS does not resolve unsteady structures accurately, it cannot reliably inform LES filter sizing.
As presented, the DES implementation appears methodologically fragile and not robustly justified for this flow regime.
Response: We sincerely thank the reviewer for this detailed and technically insightful comment. We acknowledge that the Reynolds number of the present study (Re ≈ 6.7 × 10⁵) lies within a regime where steady RANS or URANS approaches are often considered sufficient for predicting global aerodynamic quantities such as drag. However, the objective of this work is not limited to the prediction of integral forces, but rather to investigate the capability of hybrid RANS–LES methods to resolve unsteady flow features, particularly in the wake region. Even at moderate Reynolds numbers, bluff-body flows such as those around Baja SAE vehicles are characterized by flow separation, vortex shedding, and complex wake dynamics. These phenomena are inherently unsteady and may not be fully captured by steady RANS models. In this context, DES was employed as a tool to enhance the physical representation of these flow structures, rather than as a strictly necessary modeling approach.

Regarding mesh sensitivity, we agree that the mesh independence study was primarily conducted using RANS. In the revised manuscript, we clarify that the DES mesh was designed to ensure adequate resolution of the wake region based on characteristic length scales and refinement zones, although a full DES-specific grid convergence study was beyond the scope of this work. This limitation is now explicitly acknowledged. Concerning the estimation of the LES filter size (ΔLES), We agree that deriving the LES filter size (ΔLES) directly from vortex structures observed in RANS results may introduce circular reasoning, since RANS does not fully resolve unsteady flow features. In the revised manuscript, this aspect has been clarified and corrected. Specifically, the estimation of ΔLES is now defined based on established DES/DDES formulations, where the characteristic length scale is determined by the local grid size rather than flow features extracted from RANS simulations. Following standard practice in hybrid RANS–LES modeling, Δ is defined as a representative cell dimension, typically related to the cubic root of the cell volume or the equivalent cell diameter (e.g., Δ ≈ cell size / √3), as described in previous studies [A. Travin, P. Spalart et al., 1999; Lopez and Moser, 2008]. Within the DES framework, the grid spacing governs the transition between RANS and LES regions and determines the range of resolved turbulent scales. Therefore, ΔLES should be interpreted as a mesh-based parameter rather than a flow-derived quantity. The manuscript has been revised accordingly to remove any dependence on RANS-derived vortex scales and to clearly state that the LES filter size is defined as a grid-based approximation consistent with DES methodology. Finally, we have strengthened the discussion to clarify that the present study should be interpreted as a comparative numerical analysis aimed at evaluating modeling capabilities, rather than as a definitive or fully validated application of DES for this flow regime.

4. Overinterpretation of Flow Visualizations
Sections 3.2–3.5, Pages 7–11
The manuscript places strong interpretive weight on contour plots, streamlines, and Q-criterion visualizations, but these are not supported by quantitative flow metrics.
Claims regarding vortex shedding, von Kármán-like behavior, and improved wake resolution (Pages 7–9) are made without supporting evidence such as Strouhal number analysis, spectral decomposition, or force coefficient frequency content.
Streamlines from steady RANS are used to infer vortex topology and persistence (Page 8), which is not physically rigorous for inherently unsteady wake flows.
Q-criterion plots (Section 3.5, Pages 10–11) are presented qualitatively, without sensitivity to threshold selection or comparison across consistent isovalues.
Overall, the visual analysis is descriptive rather than diagnostic, and conclusions drawn from it exceed what the presented data can support.

Response: We sincerely thank the reviewer for this detailed and valuable comment.
We agree that the flow visualizations presented in this study (velocity contours, streamlines, and Q-criterion) are primarily qualitative and should be interpreted as such. The objective of these visualizations is to provide physical insight into the flow structures captured by each turbulence model, rather than to perform a fully quantitative characterization of unsteady flow phenomena.
Following the reviewer’s suggestion, we have revised the manuscript to avoid overinterpretation of these results. Specifically:

Statements suggesting confirmed vortex shedding or von Kármán vortex street formation have been softened to indicate qualitative resemblance rather than definitive identification.

The discussion of streamlines from steady RANS simulations has been clarified to reflect their limitations in representing inherently unsteady flow structures.

Q-criterion visualizations are now explicitly described as qualitative tools for illustrating vortex structures, without implying quantitative comparison or sensitivity to threshold selection.

We also acknowledge that a rigorous characterization of unsteady wake phenomena would require additional analyses such as Strouhal number estimation, spectral analysis, or force coefficient frequency decomposition, which were beyond the scope of the present study The manuscript has been revised accordingly to ensure that all interpretations remain consistent with the level of analysis performed.

5. Insufficient Treatment of Ground and Wheel Effects
Section 2.3, Page 6
All solid boundaries, including the ground and wheels, are modeled as stationary no-slip walls.
For a ground vehicle application, this modeling choice is known to significantly alter wake structure and drag prediction.
The manuscript does not discuss the implications of neglecting moving ground and rotating wheels, nor does it attempt a sensitivity study or justify the simplification.
Given the focus on wake dynamics and drag accuracy, this omission materially affects the credibility of the results.
Response: We sincerely thank the reviewer for this important observation.
We agree that the use of a stationary ground and non-rotating wheels is a simplification that can influence the development of the boundary layer, wake structure, and aerodynamic force prediction in ground vehicle simulations. Modeling moving ground conditions and rotating wheels would provide a more realistic representation of vehicle–road interaction.
In the present study, these effects were neglected to reduce computational complexity and to maintain a consistent modeling framework for the comparative evaluation of turbulence models (RANS vs DES). The primary objective was to assess the relative capability of each model to resolve flow structures and wake dynamics, rather than to provide a fully realistic aerodynamic prediction.
We acknowledge that this simplification may affect the absolute values of the drag coefficient and the detailed structure of the near-ground flow. However, since both RANS and DES simulations were performed under identical boundary conditions, the comparative analysis remains valid.
Following the reviewer’s suggestion, we have revised the manuscript to explicitly discuss this limitation and its potential impact. Future work will include moving ground conditions and rotating wheels to improve the physical realism and enable more accurate aerodynamic characterization.

6. Limited Parametric Scope and Practical Insight
Sections 3–5, Pages 7–12
The study evaluates a single geometry at a single velocity with no parametric variation.
There is no assessment of ride height, yaw angle, surface modifications, or speed dependence.
No aerodynamic optimization or design guidance emerges beyond the general statement that DES resolves more structures than RANS.
As a result, the manuscript does not provide actionable insight for Baja SAE design practice or aerodynamic decision-making.
Presentation and Structure Concerns
While secondary to the technical issues above, the following further limit the manuscript’s readiness:
The Introduction (Pages 3–4) devotes extensive space to general Baja SAE context but insufficiently narrows the scientific gap being addressed.
The Methods section intermixes modeling description and justification, making reproducibility difficult.
Several figures rely on qualitative interpretation without clear scaling rationale or quantitative annotation.
Response: We sincerely thank the reviewer for this comprehensive and constructive comment.
We acknowledge that the present study evaluates a single vehicle geometry at a single operating condition, and does not include a parametric analysis (e.g., ride height, yaw angle, or speed variation). This limitation arises from the primary objective of the work, which is to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) rather than to conduct a full aerodynamic optimization study.
Following the reviewer’s suggestion, we have revised the manuscript to clarify this scope and to enhance the practical relevance of the findings. Specifically:

We have incorporated a discussion linking the identified flow features (e.g., recirculation zones, stagnation regions, and wake structures) to potential design implications for Baja SAE vehicles, such as body simplification, rear geometry shaping, and underbody flow management.

We explicitly state that the results should be interpreted as a methodological and diagnostic analysis, which can inform future parametric or optimization studies.

We have added a statement highlighting that future work should include parametric variations (velocity, yaw angle, ride height) and design optimization strategies.

Regarding presentation and structure:

The Introduction has been revised to better define the scientific gap and reduce general background content.

The Methods section has been reorganized to clearly separate modeling description from methodological justification, improving reproducibility.

Figure descriptions have been revised to emphasize their qualitative nature and to clarify interpretation limits.

References

A. Travin, M. Shur, M. Strelets, and P. Spalart. Detached-eddy simulations past a circular
cylinder. Flow, Turbulence and Combustion, 63:293–313, 1999.

O. D. Lopez and R. D. Moser, “Delayed Detached Eddy Simulation of Flow Over an Airfoil with Synthetic Jet Control,” Mecánica Computacional, vol. 27, pp. 3225–3245, 2008.
1. Scope and Framing of the Study
Abstract and Introduction, Pages 1 to 3
The abstract (Page 1) positions the study as a high-fidelity aerodynamic investigation using hybrid RANS–LES. While the numerical tools employed are indeed advanced, the scientific scope remains narrow. The manuscript focuses almost exclusively on drag coefficient, with no discussion of side force, lift, or aerodynamic moments.
For a ground vehicle, and especially for a racing or off-road competition vehicle, drag alone is an incomplete descriptor of aerodynamic performance. At minimum, a complete aerodynamic characterization should consider three forces (Cd, Cl, Cs) and three moments (rolling, pitching, yawing). Even if all quantities are not ultimately presented, the absence of discussion or justification for excluding them is a major omission.
Similarly, metrics such as L over D and front-to-rear balance percentage are central to racing vehicle aerodynamics, yet are not meaningfully addressed. This limits both the scientific value and the practical relevance of the results.

Response: We sincerely thank the reviewer for this insightful and valuable comment. We agree that a complete aerodynamic characterization of ground vehicles may include additional force components (lift and side force) and aerodynamic moments (rolling, pitching, and yawing), as well as derived performance indicators such as L/D ratio and aerodynamic balance. However, the primary objective of this study is not to provide a full aerodynamic characterization of the Baja SAE vehicle, but rather to evaluate the capability of hybrid RANS–LES (DES) modeling to capture wake dynamics and improve drag prediction compared to steady RANS approaches.

In this context, the drag coefficient (Cd) was selected as the primary metric because it is directly influenced by wake structures, flow separation, and vortex dynamics, which are the main phenomena investigated in this work. The focus on Cd is consistent with prior CFD studies aimed at assessing turbulence modeling strategies in external aerodynamics. We acknowledge that additional aerodynamic quantities such as lift (Cl), side force (Cs), and moments are highly relevant for vehicle stability and performance, particularly in racing applications. However, these quantities are more sensitive to detailed geometry, transient crosswind conditions, and suspension–ground interaction effects, which fall beyond the scope of the present study.

To address the reviewer’s concern, we have clarified the scope and limitations of the study in the revised manuscript, explicitly stating:
(i) the rationale for focusing on drag coefficient,
(ii) the intended methodological contribution of the work, and
(iii) the need for future studies to include a more comprehensive aerodynamic characterization.

2. Absence of Validation and Physical Benchmarking
Section 3, Pages 7–12
A critical limitation of this study is the complete absence of experimental validation, high-fidelity reference data, or benchmark comparison.
The manuscript presents drag coefficients from RANS and DES simulations at a single velocity of 30 km/h (Section 3.1, Page 7), but provides no comparison to wind tunnel data, coast-down tests, published Baja SAE measurements, or even simplified analytical estimates.
The claim that DES provides “more accurate” predictions (Abstract; Sections 3.1, 4, and 5) is not substantiated. The manuscript reports only a numerical difference between RANS and DES, not accuracy relative to a reference truth.
The standard deviation of Cd in DES is interpreted as improved physical realism (Page 7), yet temporal variability alone does not imply improved accuracy.
Without validation, the work remains a numerical comparison study, not a demonstrable advancement in aerodynamic prediction.

Response: We sincerely thank the reviewer for this important and insightful comment.
We fully agree that the absence of experimental validation or high-fidelity reference data limits the ability to assess the absolute accuracy of the numerical predictions. The primary objective of this study, however, is not to provide a fully validated aerodynamic characterization of the vehicle, but rather to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) in capturing wake dynamics and flow structures.
Following the reviewer’s suggestion, we have revised the manuscript to avoid statements implying absolute accuracy. Instead, we now emphasize that the DES approach provides enhanced physical fidelity and improved resolution of unsteady flow phenomena, particularly in the wake region. We also acknowledge that experimental validation (e.g., wind tunnel testing or full-scale measurements) is a critical component in aerodynamic studies. However, such experimental campaigns require specialized infrastructure and significant financial resources that were not available within the scope of the present work. In this context, and consistent with common practice in computational aerodynamics studies under similar constraints, we have incorporated a benchmarking discussion based on published literature. Specifically, the predicted drag coefficient values (Cd ≈ 1.25–1.29) fall within the expected range reported for bluff-body and off-road vehicle configurations, which typically exhibit relatively high drag due to exposed structural elements and flow separation. This comparison supports the physical plausibility of the results, although it does not replace direct experimental validation.
Additionally, we have clarified that the temporal variability observed in DES results reflects the inherently unsteady nature of the simulation, rather than being a direct indicator of improved accuracy. Finally, we explicitly state in the revised manuscript that the present study should be interpreted as a comparative numerical analysis, and that future work will include experimental validation to enable quantitative assessment of predictive accuracy.

3. Questionable Appropriateness of DES for the Problem Scale
Section 2.4, Pages 6–7
The choice and justification of DES for this application is insufficiently supported.
The vehicle operates at 30 km/h, corresponding to a Reynolds number of approximately 6.7 × 10⁵ (Page 6). This places the flow in a regime where steady or URANS models are often sufficient, especially given the simplified geometry.
The DES formulation relies on a mesh-dependent transition between RANS and LES regions, yet the manuscript provides no grid sensitivity analysis specific to DES behavior, only a drag-based mesh independence study using RANS (Section 2.2, Page 6).
The DES mesh adaptation is derived from vortex diameters observed in RANS results (Page 6), which introduces circular reasoning. If RANS does not resolve unsteady structures accurately, it cannot reliably inform LES filter sizing.
As presented, the DES implementation appears methodologically fragile and not robustly justified for this flow regime.
Response: We sincerely thank the reviewer for this detailed and technically insightful comment. We acknowledge that the Reynolds number of the present study (Re ≈ 6.7 × 10⁵) lies within a regime where steady RANS or URANS approaches are often considered sufficient for predicting global aerodynamic quantities such as drag. However, the objective of this work is not limited to the prediction of integral forces, but rather to investigate the capability of hybrid RANS–LES methods to resolve unsteady flow features, particularly in the wake region. Even at moderate Reynolds numbers, bluff-body flows such as those around Baja SAE vehicles are characterized by flow separation, vortex shedding, and complex wake dynamics. These phenomena are inherently unsteady and may not be fully captured by steady RANS models. In this context, DES was employed as a tool to enhance the physical representation of these flow structures, rather than as a strictly necessary modeling approach.

Regarding mesh sensitivity, we agree that the mesh independence study was primarily conducted using RANS. In the revised manuscript, we clarify that the DES mesh was designed to ensure adequate resolution of the wake region based on characteristic length scales and refinement zones, although a full DES-specific grid convergence study was beyond the scope of this work. This limitation is now explicitly acknowledged. Concerning the estimation of the LES filter size (ΔLES), We agree that deriving the LES filter size (ΔLES) directly from vortex structures observed in RANS results may introduce circular reasoning, since RANS does not fully resolve unsteady flow features. In the revised manuscript, this aspect has been clarified and corrected. Specifically, the estimation of ΔLES is now defined based on established DES/DDES formulations, where the characteristic length scale is determined by the local grid size rather than flow features extracted from RANS simulations. Following standard practice in hybrid RANS–LES modeling, Δ is defined as a representative cell dimension, typically related to the cubic root of the cell volume or the equivalent cell diameter (e.g., Δ ≈ cell size / √3), as described in previous studies [A. Travin, P. Spalart et al., 1999; Lopez and Moser, 2008]. Within the DES framework, the grid spacing governs the transition between RANS and LES regions and determines the range of resolved turbulent scales. Therefore, ΔLES should be interpreted as a mesh-based parameter rather than a flow-derived quantity. The manuscript has been revised accordingly to remove any dependence on RANS-derived vortex scales and to clearly state that the LES filter size is defined as a grid-based approximation consistent with DES methodology. Finally, we have strengthened the discussion to clarify that the present study should be interpreted as a comparative numerical analysis aimed at evaluating modeling capabilities, rather than as a definitive or fully validated application of DES for this flow regime.

4. Overinterpretation of Flow Visualizations
Sections 3.2–3.5, Pages 7–11
The manuscript places strong interpretive weight on contour plots, streamlines, and Q-criterion visualizations, but these are not supported by quantitative flow metrics.
Claims regarding vortex shedding, von Kármán-like behavior, and improved wake resolution (Pages 7–9) are made without supporting evidence such as Strouhal number analysis, spectral decomposition, or force coefficient frequency content.
Streamlines from steady RANS are used to infer vortex topology and persistence (Page 8), which is not physically rigorous for inherently unsteady wake flows.
Q-criterion plots (Section 3.5, Pages 10–11) are presented qualitatively, without sensitivity to threshold selection or comparison across consistent isovalues.
Overall, the visual analysis is descriptive rather than diagnostic, and conclusions drawn from it exceed what the presented data can support.

Response: We sincerely thank the reviewer for this detailed and valuable comment.
We agree that the flow visualizations presented in this study (velocity contours, streamlines, and Q-criterion) are primarily qualitative and should be interpreted as such. The objective of these visualizations is to provide physical insight into the flow structures captured by each turbulence model, rather than to perform a fully quantitative characterization of unsteady flow phenomena.
Following the reviewer’s suggestion, we have revised the manuscript to avoid overinterpretation of these results. Specifically:

Statements suggesting confirmed vortex shedding or von Kármán vortex street formation have been softened to indicate qualitative resemblance rather than definitive identification.

The discussion of streamlines from steady RANS simulations has been clarified to reflect their limitations in representing inherently unsteady flow structures.

Q-criterion visualizations are now explicitly described as qualitative tools for illustrating vortex structures, without implying quantitative comparison or sensitivity to threshold selection.

We also acknowledge that a rigorous characterization of unsteady wake phenomena would require additional analyses such as Strouhal number estimation, spectral analysis, or force coefficient frequency decomposition, which were beyond the scope of the present study The manuscript has been revised accordingly to ensure that all interpretations remain consistent with the level of analysis performed.

5. Insufficient Treatment of Ground and Wheel Effects
Section 2.3, Page 6
All solid boundaries, including the ground and wheels, are modeled as stationary no-slip walls.
For a ground vehicle application, this modeling choice is known to significantly alter wake structure and drag prediction.
The manuscript does not discuss the implications of neglecting moving ground and rotating wheels, nor does it attempt a sensitivity study or justify the simplification.
Given the focus on wake dynamics and drag accuracy, this omission materially affects the credibility of the results.
Response: We sincerely thank the reviewer for this important observation.
We agree that the use of a stationary ground and non-rotating wheels is a simplification that can influence the development of the boundary layer, wake structure, and aerodynamic force prediction in ground vehicle simulations. Modeling moving ground conditions and rotating wheels would provide a more realistic representation of vehicle–road interaction.
In the present study, these effects were neglected to reduce computational complexity and to maintain a consistent modeling framework for the comparative evaluation of turbulence models (RANS vs DES). The primary objective was to assess the relative capability of each model to resolve flow structures and wake dynamics, rather than to provide a fully realistic aerodynamic prediction.
We acknowledge that this simplification may affect the absolute values of the drag coefficient and the detailed structure of the near-ground flow. However, since both RANS and DES simulations were performed under identical boundary conditions, the comparative analysis remains valid.
Following the reviewer’s suggestion, we have revised the manuscript to explicitly discuss this limitation and its potential impact. Future work will include moving ground conditions and rotating wheels to improve the physical realism and enable more accurate aerodynamic characterization.

6. Limited Parametric Scope and Practical Insight
Sections 3–5, Pages 7–12
The study evaluates a single geometry at a single velocity with no parametric variation.
There is no assessment of ride height, yaw angle, surface modifications, or speed dependence.
No aerodynamic optimization or design guidance emerges beyond the general statement that DES resolves more structures than RANS.
As a result, the manuscript does not provide actionable insight for Baja SAE design practice or aerodynamic decision-making.
Presentation and Structure Concerns
While secondary to the technical issues above, the following further limit the manuscript’s readiness:
The Introduction (Pages 3–4) devotes extensive space to general Baja SAE context but insufficiently narrows the scientific gap being addressed.
The Methods section intermixes modeling description and justification, making reproducibility difficult.
Several figures rely on qualitative interpretation without clear scaling rationale or quantitative annotation.
Response: We sincerely thank the reviewer for this comprehensive and constructive comment.
We acknowledge that the present study evaluates a single vehicle geometry at a single operating condition, and does not include a parametric analysis (e.g., ride height, yaw angle, or speed variation). This limitation arises from the primary objective of the work, which is to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) rather than to conduct a full aerodynamic optimization study.
Following the reviewer’s suggestion, we have revised the manuscript to clarify this scope and to enhance the practical relevance of the findings. Specifically:

We have incorporated a discussion linking the identified flow features (e.g., recirculation zones, stagnation regions, and wake structures) to potential design implications for Baja SAE vehicles, such as body simplification, rear geometry shaping, and underbody flow management.

We explicitly state that the results should be interpreted as a methodological and diagnostic analysis, which can inform future parametric or optimization studies.

We have added a statement highlighting that future work should include parametric variations (velocity, yaw angle, ride height) and design optimization strategies.

Regarding presentation and structure:

The Introduction has been revised to better define the scientific gap and reduce general background content.

The Methods section has been reorganized to clearly separate modeling description from methodological justification, improving reproducibility.

Figure descriptions have been revised to emphasize their qualitative nature and to clarify interpretation limits.

References

A. Travin, M. Shur, M. Strelets, and P. Spalart. Detached-eddy simulations past a circular
cylinder. Flow, Turbulence and Combustion, 63:293–313, 1999.

O. D. Lopez and R. D. Moser, “Delayed Detached Eddy Simulation of Flow Over an Airfoil with Synthetic Jet Control,” Mecánica Computacional, vol. 27, pp. 3225–3245, 2008.
Competing Interests: The authors declare that they have no competing interests. Close
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COMMENTS ON THIS REPORT

Author Response 12 Jun 2026

Deisy Yurley Rodriguez Sarmiento, Universidad Autonoma de Bucaramanga, Bucaramanga, Colombia

12 Jun 2026

Author Response
1. Scope and Framing of the Study
Abstract and Introduction, Pages 1 to 3
The abstract (Page 1) positions the study as a high-fidelity aerodynamic investigation using hybrid RANS–LES. While ... Continue reading
1. Scope and Framing of the Study
Abstract and Introduction, Pages 1 to 3
The abstract (Page 1) positions the study as a high-fidelity aerodynamic investigation using hybrid RANS–LES. While the numerical tools employed are indeed advanced, the scientific scope remains narrow. The manuscript focuses almost exclusively on drag coefficient, with no discussion of side force, lift, or aerodynamic moments.
For a ground vehicle, and especially for a racing or off-road competition vehicle, drag alone is an incomplete descriptor of aerodynamic performance. At minimum, a complete aerodynamic characterization should consider three forces (Cd, Cl, Cs) and three moments (rolling, pitching, yawing). Even if all quantities are not ultimately presented, the absence of discussion or justification for excluding them is a major omission.
Similarly, metrics such as L over D and front-to-rear balance percentage are central to racing vehicle aerodynamics, yet are not meaningfully addressed. This limits both the scientific value and the practical relevance of the results.

Response: We sincerely thank the reviewer for this insightful and valuable comment. We agree that a complete aerodynamic characterization of ground vehicles may include additional force components (lift and side force) and aerodynamic moments (rolling, pitching, and yawing), as well as derived performance indicators such as L/D ratio and aerodynamic balance. However, the primary objective of this study is not to provide a full aerodynamic characterization of the Baja SAE vehicle, but rather to evaluate the capability of hybrid RANS–LES (DES) modeling to capture wake dynamics and improve drag prediction compared to steady RANS approaches.

In this context, the drag coefficient (Cd) was selected as the primary metric because it is directly influenced by wake structures, flow separation, and vortex dynamics, which are the main phenomena investigated in this work. The focus on Cd is consistent with prior CFD studies aimed at assessing turbulence modeling strategies in external aerodynamics. We acknowledge that additional aerodynamic quantities such as lift (Cl), side force (Cs), and moments are highly relevant for vehicle stability and performance, particularly in racing applications. However, these quantities are more sensitive to detailed geometry, transient crosswind conditions, and suspension–ground interaction effects, which fall beyond the scope of the present study.

To address the reviewer’s concern, we have clarified the scope and limitations of the study in the revised manuscript, explicitly stating:
(i) the rationale for focusing on drag coefficient,
(ii) the intended methodological contribution of the work, and
(iii) the need for future studies to include a more comprehensive aerodynamic characterization.

2. Absence of Validation and Physical Benchmarking
Section 3, Pages 7–12
A critical limitation of this study is the complete absence of experimental validation, high-fidelity reference data, or benchmark comparison.
The manuscript presents drag coefficients from RANS and DES simulations at a single velocity of 30 km/h (Section 3.1, Page 7), but provides no comparison to wind tunnel data, coast-down tests, published Baja SAE measurements, or even simplified analytical estimates.
The claim that DES provides “more accurate” predictions (Abstract; Sections 3.1, 4, and 5) is not substantiated. The manuscript reports only a numerical difference between RANS and DES, not accuracy relative to a reference truth.
The standard deviation of Cd in DES is interpreted as improved physical realism (Page 7), yet temporal variability alone does not imply improved accuracy.
Without validation, the work remains a numerical comparison study, not a demonstrable advancement in aerodynamic prediction.

Response: We sincerely thank the reviewer for this important and insightful comment.
We fully agree that the absence of experimental validation or high-fidelity reference data limits the ability to assess the absolute accuracy of the numerical predictions. The primary objective of this study, however, is not to provide a fully validated aerodynamic characterization of the vehicle, but rather to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) in capturing wake dynamics and flow structures.
Following the reviewer’s suggestion, we have revised the manuscript to avoid statements implying absolute accuracy. Instead, we now emphasize that the DES approach provides enhanced physical fidelity and improved resolution of unsteady flow phenomena, particularly in the wake region. We also acknowledge that experimental validation (e.g., wind tunnel testing or full-scale measurements) is a critical component in aerodynamic studies. However, such experimental campaigns require specialized infrastructure and significant financial resources that were not available within the scope of the present work. In this context, and consistent with common practice in computational aerodynamics studies under similar constraints, we have incorporated a benchmarking discussion based on published literature. Specifically, the predicted drag coefficient values (Cd ≈ 1.25–1.29) fall within the expected range reported for bluff-body and off-road vehicle configurations, which typically exhibit relatively high drag due to exposed structural elements and flow separation. This comparison supports the physical plausibility of the results, although it does not replace direct experimental validation.
Additionally, we have clarified that the temporal variability observed in DES results reflects the inherently unsteady nature of the simulation, rather than being a direct indicator of improved accuracy. Finally, we explicitly state in the revised manuscript that the present study should be interpreted as a comparative numerical analysis, and that future work will include experimental validation to enable quantitative assessment of predictive accuracy.

3. Questionable Appropriateness of DES for the Problem Scale
Section 2.4, Pages 6–7
The choice and justification of DES for this application is insufficiently supported.
The vehicle operates at 30 km/h, corresponding to a Reynolds number of approximately 6.7 × 10⁵ (Page 6). This places the flow in a regime where steady or URANS models are often sufficient, especially given the simplified geometry.
The DES formulation relies on a mesh-dependent transition between RANS and LES regions, yet the manuscript provides no grid sensitivity analysis specific to DES behavior, only a drag-based mesh independence study using RANS (Section 2.2, Page 6).
The DES mesh adaptation is derived from vortex diameters observed in RANS results (Page 6), which introduces circular reasoning. If RANS does not resolve unsteady structures accurately, it cannot reliably inform LES filter sizing.
As presented, the DES implementation appears methodologically fragile and not robustly justified for this flow regime.
Response: We sincerely thank the reviewer for this detailed and technically insightful comment. We acknowledge that the Reynolds number of the present study (Re ≈ 6.7 × 10⁵) lies within a regime where steady RANS or URANS approaches are often considered sufficient for predicting global aerodynamic quantities such as drag. However, the objective of this work is not limited to the prediction of integral forces, but rather to investigate the capability of hybrid RANS–LES methods to resolve unsteady flow features, particularly in the wake region. Even at moderate Reynolds numbers, bluff-body flows such as those around Baja SAE vehicles are characterized by flow separation, vortex shedding, and complex wake dynamics. These phenomena are inherently unsteady and may not be fully captured by steady RANS models. In this context, DES was employed as a tool to enhance the physical representation of these flow structures, rather than as a strictly necessary modeling approach.

Regarding mesh sensitivity, we agree that the mesh independence study was primarily conducted using RANS. In the revised manuscript, we clarify that the DES mesh was designed to ensure adequate resolution of the wake region based on characteristic length scales and refinement zones, although a full DES-specific grid convergence study was beyond the scope of this work. This limitation is now explicitly acknowledged. Concerning the estimation of the LES filter size (ΔLES), We agree that deriving the LES filter size (ΔLES) directly from vortex structures observed in RANS results may introduce circular reasoning, since RANS does not fully resolve unsteady flow features. In the revised manuscript, this aspect has been clarified and corrected. Specifically, the estimation of ΔLES is now defined based on established DES/DDES formulations, where the characteristic length scale is determined by the local grid size rather than flow features extracted from RANS simulations. Following standard practice in hybrid RANS–LES modeling, Δ is defined as a representative cell dimension, typically related to the cubic root of the cell volume or the equivalent cell diameter (e.g., Δ ≈ cell size / √3), as described in previous studies [A. Travin, P. Spalart et al., 1999; Lopez and Moser, 2008]. Within the DES framework, the grid spacing governs the transition between RANS and LES regions and determines the range of resolved turbulent scales. Therefore, ΔLES should be interpreted as a mesh-based parameter rather than a flow-derived quantity. The manuscript has been revised accordingly to remove any dependence on RANS-derived vortex scales and to clearly state that the LES filter size is defined as a grid-based approximation consistent with DES methodology. Finally, we have strengthened the discussion to clarify that the present study should be interpreted as a comparative numerical analysis aimed at evaluating modeling capabilities, rather than as a definitive or fully validated application of DES for this flow regime.

4. Overinterpretation of Flow Visualizations
Sections 3.2–3.5, Pages 7–11
The manuscript places strong interpretive weight on contour plots, streamlines, and Q-criterion visualizations, but these are not supported by quantitative flow metrics.
Claims regarding vortex shedding, von Kármán-like behavior, and improved wake resolution (Pages 7–9) are made without supporting evidence such as Strouhal number analysis, spectral decomposition, or force coefficient frequency content.
Streamlines from steady RANS are used to infer vortex topology and persistence (Page 8), which is not physically rigorous for inherently unsteady wake flows.
Q-criterion plots (Section 3.5, Pages 10–11) are presented qualitatively, without sensitivity to threshold selection or comparison across consistent isovalues.
Overall, the visual analysis is descriptive rather than diagnostic, and conclusions drawn from it exceed what the presented data can support.

Response: We sincerely thank the reviewer for this detailed and valuable comment.
We agree that the flow visualizations presented in this study (velocity contours, streamlines, and Q-criterion) are primarily qualitative and should be interpreted as such. The objective of these visualizations is to provide physical insight into the flow structures captured by each turbulence model, rather than to perform a fully quantitative characterization of unsteady flow phenomena.
Following the reviewer’s suggestion, we have revised the manuscript to avoid overinterpretation of these results. Specifically:

Statements suggesting confirmed vortex shedding or von Kármán vortex street formation have been softened to indicate qualitative resemblance rather than definitive identification.

The discussion of streamlines from steady RANS simulations has been clarified to reflect their limitations in representing inherently unsteady flow structures.

Q-criterion visualizations are now explicitly described as qualitative tools for illustrating vortex structures, without implying quantitative comparison or sensitivity to threshold selection.

We also acknowledge that a rigorous characterization of unsteady wake phenomena would require additional analyses such as Strouhal number estimation, spectral analysis, or force coefficient frequency decomposition, which were beyond the scope of the present study The manuscript has been revised accordingly to ensure that all interpretations remain consistent with the level of analysis performed.

5. Insufficient Treatment of Ground and Wheel Effects
Section 2.3, Page 6
All solid boundaries, including the ground and wheels, are modeled as stationary no-slip walls.
For a ground vehicle application, this modeling choice is known to significantly alter wake structure and drag prediction.
The manuscript does not discuss the implications of neglecting moving ground and rotating wheels, nor does it attempt a sensitivity study or justify the simplification.
Given the focus on wake dynamics and drag accuracy, this omission materially affects the credibility of the results.
Response: We sincerely thank the reviewer for this important observation.
We agree that the use of a stationary ground and non-rotating wheels is a simplification that can influence the development of the boundary layer, wake structure, and aerodynamic force prediction in ground vehicle simulations. Modeling moving ground conditions and rotating wheels would provide a more realistic representation of vehicle–road interaction.
In the present study, these effects were neglected to reduce computational complexity and to maintain a consistent modeling framework for the comparative evaluation of turbulence models (RANS vs DES). The primary objective was to assess the relative capability of each model to resolve flow structures and wake dynamics, rather than to provide a fully realistic aerodynamic prediction.
We acknowledge that this simplification may affect the absolute values of the drag coefficient and the detailed structure of the near-ground flow. However, since both RANS and DES simulations were performed under identical boundary conditions, the comparative analysis remains valid.
Following the reviewer’s suggestion, we have revised the manuscript to explicitly discuss this limitation and its potential impact. Future work will include moving ground conditions and rotating wheels to improve the physical realism and enable more accurate aerodynamic characterization.

6. Limited Parametric Scope and Practical Insight
Sections 3–5, Pages 7–12
The study evaluates a single geometry at a single velocity with no parametric variation.
There is no assessment of ride height, yaw angle, surface modifications, or speed dependence.
No aerodynamic optimization or design guidance emerges beyond the general statement that DES resolves more structures than RANS.
As a result, the manuscript does not provide actionable insight for Baja SAE design practice or aerodynamic decision-making.
Presentation and Structure Concerns
While secondary to the technical issues above, the following further limit the manuscript’s readiness:
The Introduction (Pages 3–4) devotes extensive space to general Baja SAE context but insufficiently narrows the scientific gap being addressed.
The Methods section intermixes modeling description and justification, making reproducibility difficult.
Several figures rely on qualitative interpretation without clear scaling rationale or quantitative annotation.
Response: We sincerely thank the reviewer for this comprehensive and constructive comment.
We acknowledge that the present study evaluates a single vehicle geometry at a single operating condition, and does not include a parametric analysis (e.g., ride height, yaw angle, or speed variation). This limitation arises from the primary objective of the work, which is to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) rather than to conduct a full aerodynamic optimization study.
Following the reviewer’s suggestion, we have revised the manuscript to clarify this scope and to enhance the practical relevance of the findings. Specifically:

We have incorporated a discussion linking the identified flow features (e.g., recirculation zones, stagnation regions, and wake structures) to potential design implications for Baja SAE vehicles, such as body simplification, rear geometry shaping, and underbody flow management.

We explicitly state that the results should be interpreted as a methodological and diagnostic analysis, which can inform future parametric or optimization studies.

We have added a statement highlighting that future work should include parametric variations (velocity, yaw angle, ride height) and design optimization strategies.

Regarding presentation and structure:

The Introduction has been revised to better define the scientific gap and reduce general background content.

The Methods section has been reorganized to clearly separate modeling description from methodological justification, improving reproducibility.

Figure descriptions have been revised to emphasize their qualitative nature and to clarify interpretation limits.

References

A. Travin, M. Shur, M. Strelets, and P. Spalart. Detached-eddy simulations past a circular
cylinder. Flow, Turbulence and Combustion, 63:293–313, 1999.

O. D. Lopez and R. D. Moser, “Delayed Detached Eddy Simulation of Flow Over an Airfoil with Synthetic Jet Control,” Mecánica Computacional, vol. 27, pp. 3225–3245, 2008.
1. Scope and Framing of the Study
Abstract and Introduction, Pages 1 to 3
The abstract (Page 1) positions the study as a high-fidelity aerodynamic investigation using hybrid RANS–LES. While the numerical tools employed are indeed advanced, the scientific scope remains narrow. The manuscript focuses almost exclusively on drag coefficient, with no discussion of side force, lift, or aerodynamic moments.
For a ground vehicle, and especially for a racing or off-road competition vehicle, drag alone is an incomplete descriptor of aerodynamic performance. At minimum, a complete aerodynamic characterization should consider three forces (Cd, Cl, Cs) and three moments (rolling, pitching, yawing). Even if all quantities are not ultimately presented, the absence of discussion or justification for excluding them is a major omission.
Similarly, metrics such as L over D and front-to-rear balance percentage are central to racing vehicle aerodynamics, yet are not meaningfully addressed. This limits both the scientific value and the practical relevance of the results.

Response: We sincerely thank the reviewer for this insightful and valuable comment. We agree that a complete aerodynamic characterization of ground vehicles may include additional force components (lift and side force) and aerodynamic moments (rolling, pitching, and yawing), as well as derived performance indicators such as L/D ratio and aerodynamic balance. However, the primary objective of this study is not to provide a full aerodynamic characterization of the Baja SAE vehicle, but rather to evaluate the capability of hybrid RANS–LES (DES) modeling to capture wake dynamics and improve drag prediction compared to steady RANS approaches.

In this context, the drag coefficient (Cd) was selected as the primary metric because it is directly influenced by wake structures, flow separation, and vortex dynamics, which are the main phenomena investigated in this work. The focus on Cd is consistent with prior CFD studies aimed at assessing turbulence modeling strategies in external aerodynamics. We acknowledge that additional aerodynamic quantities such as lift (Cl), side force (Cs), and moments are highly relevant for vehicle stability and performance, particularly in racing applications. However, these quantities are more sensitive to detailed geometry, transient crosswind conditions, and suspension–ground interaction effects, which fall beyond the scope of the present study.

To address the reviewer’s concern, we have clarified the scope and limitations of the study in the revised manuscript, explicitly stating:
(i) the rationale for focusing on drag coefficient,
(ii) the intended methodological contribution of the work, and
(iii) the need for future studies to include a more comprehensive aerodynamic characterization.

2. Absence of Validation and Physical Benchmarking
Section 3, Pages 7–12
A critical limitation of this study is the complete absence of experimental validation, high-fidelity reference data, or benchmark comparison.
The manuscript presents drag coefficients from RANS and DES simulations at a single velocity of 30 km/h (Section 3.1, Page 7), but provides no comparison to wind tunnel data, coast-down tests, published Baja SAE measurements, or even simplified analytical estimates.
The claim that DES provides “more accurate” predictions (Abstract; Sections 3.1, 4, and 5) is not substantiated. The manuscript reports only a numerical difference between RANS and DES, not accuracy relative to a reference truth.
The standard deviation of Cd in DES is interpreted as improved physical realism (Page 7), yet temporal variability alone does not imply improved accuracy.
Without validation, the work remains a numerical comparison study, not a demonstrable advancement in aerodynamic prediction.

Response: We sincerely thank the reviewer for this important and insightful comment.
We fully agree that the absence of experimental validation or high-fidelity reference data limits the ability to assess the absolute accuracy of the numerical predictions. The primary objective of this study, however, is not to provide a fully validated aerodynamic characterization of the vehicle, but rather to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) in capturing wake dynamics and flow structures.
Following the reviewer’s suggestion, we have revised the manuscript to avoid statements implying absolute accuracy. Instead, we now emphasize that the DES approach provides enhanced physical fidelity and improved resolution of unsteady flow phenomena, particularly in the wake region. We also acknowledge that experimental validation (e.g., wind tunnel testing or full-scale measurements) is a critical component in aerodynamic studies. However, such experimental campaigns require specialized infrastructure and significant financial resources that were not available within the scope of the present work. In this context, and consistent with common practice in computational aerodynamics studies under similar constraints, we have incorporated a benchmarking discussion based on published literature. Specifically, the predicted drag coefficient values (Cd ≈ 1.25–1.29) fall within the expected range reported for bluff-body and off-road vehicle configurations, which typically exhibit relatively high drag due to exposed structural elements and flow separation. This comparison supports the physical plausibility of the results, although it does not replace direct experimental validation.
Additionally, we have clarified that the temporal variability observed in DES results reflects the inherently unsteady nature of the simulation, rather than being a direct indicator of improved accuracy. Finally, we explicitly state in the revised manuscript that the present study should be interpreted as a comparative numerical analysis, and that future work will include experimental validation to enable quantitative assessment of predictive accuracy.

3. Questionable Appropriateness of DES for the Problem Scale
Section 2.4, Pages 6–7
The choice and justification of DES for this application is insufficiently supported.
The vehicle operates at 30 km/h, corresponding to a Reynolds number of approximately 6.7 × 10⁵ (Page 6). This places the flow in a regime where steady or URANS models are often sufficient, especially given the simplified geometry.
The DES formulation relies on a mesh-dependent transition between RANS and LES regions, yet the manuscript provides no grid sensitivity analysis specific to DES behavior, only a drag-based mesh independence study using RANS (Section 2.2, Page 6).
The DES mesh adaptation is derived from vortex diameters observed in RANS results (Page 6), which introduces circular reasoning. If RANS does not resolve unsteady structures accurately, it cannot reliably inform LES filter sizing.
As presented, the DES implementation appears methodologically fragile and not robustly justified for this flow regime.
Response: We sincerely thank the reviewer for this detailed and technically insightful comment. We acknowledge that the Reynolds number of the present study (Re ≈ 6.7 × 10⁵) lies within a regime where steady RANS or URANS approaches are often considered sufficient for predicting global aerodynamic quantities such as drag. However, the objective of this work is not limited to the prediction of integral forces, but rather to investigate the capability of hybrid RANS–LES methods to resolve unsteady flow features, particularly in the wake region. Even at moderate Reynolds numbers, bluff-body flows such as those around Baja SAE vehicles are characterized by flow separation, vortex shedding, and complex wake dynamics. These phenomena are inherently unsteady and may not be fully captured by steady RANS models. In this context, DES was employed as a tool to enhance the physical representation of these flow structures, rather than as a strictly necessary modeling approach.

Regarding mesh sensitivity, we agree that the mesh independence study was primarily conducted using RANS. In the revised manuscript, we clarify that the DES mesh was designed to ensure adequate resolution of the wake region based on characteristic length scales and refinement zones, although a full DES-specific grid convergence study was beyond the scope of this work. This limitation is now explicitly acknowledged. Concerning the estimation of the LES filter size (ΔLES), We agree that deriving the LES filter size (ΔLES) directly from vortex structures observed in RANS results may introduce circular reasoning, since RANS does not fully resolve unsteady flow features. In the revised manuscript, this aspect has been clarified and corrected. Specifically, the estimation of ΔLES is now defined based on established DES/DDES formulations, where the characteristic length scale is determined by the local grid size rather than flow features extracted from RANS simulations. Following standard practice in hybrid RANS–LES modeling, Δ is defined as a representative cell dimension, typically related to the cubic root of the cell volume or the equivalent cell diameter (e.g., Δ ≈ cell size / √3), as described in previous studies [A. Travin, P. Spalart et al., 1999; Lopez and Moser, 2008]. Within the DES framework, the grid spacing governs the transition between RANS and LES regions and determines the range of resolved turbulent scales. Therefore, ΔLES should be interpreted as a mesh-based parameter rather than a flow-derived quantity. The manuscript has been revised accordingly to remove any dependence on RANS-derived vortex scales and to clearly state that the LES filter size is defined as a grid-based approximation consistent with DES methodology. Finally, we have strengthened the discussion to clarify that the present study should be interpreted as a comparative numerical analysis aimed at evaluating modeling capabilities, rather than as a definitive or fully validated application of DES for this flow regime.

4. Overinterpretation of Flow Visualizations
Sections 3.2–3.5, Pages 7–11
The manuscript places strong interpretive weight on contour plots, streamlines, and Q-criterion visualizations, but these are not supported by quantitative flow metrics.
Claims regarding vortex shedding, von Kármán-like behavior, and improved wake resolution (Pages 7–9) are made without supporting evidence such as Strouhal number analysis, spectral decomposition, or force coefficient frequency content.
Streamlines from steady RANS are used to infer vortex topology and persistence (Page 8), which is not physically rigorous for inherently unsteady wake flows.
Q-criterion plots (Section 3.5, Pages 10–11) are presented qualitatively, without sensitivity to threshold selection or comparison across consistent isovalues.
Overall, the visual analysis is descriptive rather than diagnostic, and conclusions drawn from it exceed what the presented data can support.

Response: We sincerely thank the reviewer for this detailed and valuable comment.
We agree that the flow visualizations presented in this study (velocity contours, streamlines, and Q-criterion) are primarily qualitative and should be interpreted as such. The objective of these visualizations is to provide physical insight into the flow structures captured by each turbulence model, rather than to perform a fully quantitative characterization of unsteady flow phenomena.
Following the reviewer’s suggestion, we have revised the manuscript to avoid overinterpretation of these results. Specifically:

Statements suggesting confirmed vortex shedding or von Kármán vortex street formation have been softened to indicate qualitative resemblance rather than definitive identification.

The discussion of streamlines from steady RANS simulations has been clarified to reflect their limitations in representing inherently unsteady flow structures.

Q-criterion visualizations are now explicitly described as qualitative tools for illustrating vortex structures, without implying quantitative comparison or sensitivity to threshold selection.

We also acknowledge that a rigorous characterization of unsteady wake phenomena would require additional analyses such as Strouhal number estimation, spectral analysis, or force coefficient frequency decomposition, which were beyond the scope of the present study The manuscript has been revised accordingly to ensure that all interpretations remain consistent with the level of analysis performed.

5. Insufficient Treatment of Ground and Wheel Effects
Section 2.3, Page 6
All solid boundaries, including the ground and wheels, are modeled as stationary no-slip walls.
For a ground vehicle application, this modeling choice is known to significantly alter wake structure and drag prediction.
The manuscript does not discuss the implications of neglecting moving ground and rotating wheels, nor does it attempt a sensitivity study or justify the simplification.
Given the focus on wake dynamics and drag accuracy, this omission materially affects the credibility of the results.
Response: We sincerely thank the reviewer for this important observation.
We agree that the use of a stationary ground and non-rotating wheels is a simplification that can influence the development of the boundary layer, wake structure, and aerodynamic force prediction in ground vehicle simulations. Modeling moving ground conditions and rotating wheels would provide a more realistic representation of vehicle–road interaction.
In the present study, these effects were neglected to reduce computational complexity and to maintain a consistent modeling framework for the comparative evaluation of turbulence models (RANS vs DES). The primary objective was to assess the relative capability of each model to resolve flow structures and wake dynamics, rather than to provide a fully realistic aerodynamic prediction.
We acknowledge that this simplification may affect the absolute values of the drag coefficient and the detailed structure of the near-ground flow. However, since both RANS and DES simulations were performed under identical boundary conditions, the comparative analysis remains valid.
Following the reviewer’s suggestion, we have revised the manuscript to explicitly discuss this limitation and its potential impact. Future work will include moving ground conditions and rotating wheels to improve the physical realism and enable more accurate aerodynamic characterization.

6. Limited Parametric Scope and Practical Insight
Sections 3–5, Pages 7–12
The study evaluates a single geometry at a single velocity with no parametric variation.
There is no assessment of ride height, yaw angle, surface modifications, or speed dependence.
No aerodynamic optimization or design guidance emerges beyond the general statement that DES resolves more structures than RANS.
As a result, the manuscript does not provide actionable insight for Baja SAE design practice or aerodynamic decision-making.
Presentation and Structure Concerns
While secondary to the technical issues above, the following further limit the manuscript’s readiness:
The Introduction (Pages 3–4) devotes extensive space to general Baja SAE context but insufficiently narrows the scientific gap being addressed.
The Methods section intermixes modeling description and justification, making reproducibility difficult.
Several figures rely on qualitative interpretation without clear scaling rationale or quantitative annotation.
Response: We sincerely thank the reviewer for this comprehensive and constructive comment.
We acknowledge that the present study evaluates a single vehicle geometry at a single operating condition, and does not include a parametric analysis (e.g., ride height, yaw angle, or speed variation). This limitation arises from the primary objective of the work, which is to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) rather than to conduct a full aerodynamic optimization study.
Following the reviewer’s suggestion, we have revised the manuscript to clarify this scope and to enhance the practical relevance of the findings. Specifically:

We have incorporated a discussion linking the identified flow features (e.g., recirculation zones, stagnation regions, and wake structures) to potential design implications for Baja SAE vehicles, such as body simplification, rear geometry shaping, and underbody flow management.

We explicitly state that the results should be interpreted as a methodological and diagnostic analysis, which can inform future parametric or optimization studies.

We have added a statement highlighting that future work should include parametric variations (velocity, yaw angle, ride height) and design optimization strategies.

Regarding presentation and structure:

The Introduction has been revised to better define the scientific gap and reduce general background content.

The Methods section has been reorganized to clearly separate modeling description from methodological justification, improving reproducibility.

Figure descriptions have been revised to emphasize their qualitative nature and to clarify interpretation limits.

References

A. Travin, M. Shur, M. Strelets, and P. Spalart. Detached-eddy simulations past a circular
cylinder. Flow, Turbulence and Combustion, 63:293–313, 1999.

O. D. Lopez and R. D. Moser, “Delayed Detached Eddy Simulation of Flow Over an Airfoil with Synthetic Jet Control,” Mecánica Computacional, vol. 27, pp. 3225–3245, 2008.
Competing Interests: The authors declare that they have no competing interests. Close
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Version 2 (revision) 12 Jun 26
Version 1 03 Nov 25	read	read

Adit S Misar, University of North Carolina at Charlotte, Charlotte, USA
Luis Fernando Rodriguez, Clarkson University, Potsdam, USA

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Reviewer Report

17 Views

10 Apr 2026 | for Version 1

Luis Fernando Rodriguez, Mechanical and Aerospace Engineering, Clarkson University, Potsdam, New York, USA

17 Views Cite this report Responses(1)

Not Approved

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Mechanical Engineering: Structural Analysis and Fluid Mechanics (Turbulent Analysis).

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Responses (1)

Author Response

12 Jun 2026

Deisy Yurley Rodriguez Sarmiento, Universidad Autonoma de Bucaramanga, Bucaramanga, Colombia

Points for Improvement

Validation: The manuscript would benefit significantly from validation against experimental data, simplified benchmarks, or published results. Including such comparisons would strengthen the credibility of the conclusions.

Response: We thank the reviewer for this valuable suggestion. The importance of validation is fully acknowledged and was also raised by Reviewer 1. In response, we have revised the manuscript to clarify that the present work is a comparative numerical study of turbulence modeling approaches rather than a fully validated aerodynamic prediction.
Additionally, we have included a benchmarking discussion showing that the predicted drag coefficient values fall within ranges reported in the literature for similar bluff-body and off-road vehicle configurations, supporting the physical plausibility of the results.
The absence of experimental validation is now explicitly acknowledged as a limitation, and future work will address this through experimental and parametric studies.

Aerodynamic Metrics: Expanding the analysis beyond drag coefficient to include lift, side forces, or moments would provide a more complete characterization of vehicle performance.

Response: We thank the reviewer for this valuable suggestion. This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that a complete aerodynamic characterization would include additional force components such as lift, side force, and aerodynamic moments. However, the objective of the present study is to provide a comparative assessment of turbulence modeling approaches, focusing on wake dynamics and drag as a representative parameter of wake-induced aerodynamic losses. This scope has now been clearly stated in the revised manuscript. Additionally, we have included a statement highlighting that future work will incorporate a more comprehensive set of aerodynamic metrics to enable a complete evaluation of vehicle performance.

Turbulence Model Justification: Additional discussion on why DES is necessary for this flow regime, including comparisons with simpler models, would improve the methodological clarity.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that, although the Reynolds number considered falls within a range where steady RANS approaches can provide reasonable predictions of global aerodynamic quantities, the use of DES is motivated by its ability to better represent unsteady flow structures, particularly in the wake region. The manuscript has been revised to explicitly state that the use of DES is intended to enhance the representation of wake dynamics rather than to serve as a strictly necessary modeling approach for this flow regime. Also, the scope of the study has been clarified as a comparative evaluation of turbulence modeling approaches, rather than a fully optimized or validated aerodynamic prediction.

Boundary Conditions: The assumption of stationary ground and non-rotating wheels should be discussed in more detail, including its potential impact on results.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We have included a more detailed discussion of the assumption of stationary ground and non-rotating wheels, highlighting its potential impact on near-ground flow development, wake structure, and the absolute values of aerodynamic forces. This modeling choice has been clarified as a simplification adopted to maintain computational feasibility and ensure consistency in the comparative analysis between turbulence models.
The corresponding limitations are now explicitly stated in both the Methods and Discussion sections, and future work will incorporate moving ground conditions and rotating wheels to improve the physical realism of the simulations.

Quantitative Analysis: Complementing visualizations with quantitative metrics (e.g., frequency analysis or additional flow parameters) would strengthen the analysis.

Response: This point was also raised by Reviewer 1 and has been addressed in the revised manuscript. We clarify that the flow visualizations presented in this study are intended for qualitative analysis of flow structures rather than for quantitative characterization of unsteady phenomena. Accordingly, we have revised the manuscript to avoid overinterpretation and to explicitly state the limitations of the visual analysis. We also acknowledge that a more rigorous quantitative characterization such as frequency analysis, Strouhal number estimation, or additional flow metrics would further strengthen the analysis, but is beyond the scope of the present study. Future work will incorporate these approaches to provide a more comprehensive assessment of unsteady wake dynamics.

Scope: Exploring additional cases (such as different speeds or geometric variations) could enhance the practical impact of the work.

Response: This aspect was also raised by Reviewer 1 and has been addressed in the revised manuscript. We acknowledge that the present study is limited to a single geometry and operating condition, and therefore does not capture the influence of parameters such as velocity or geometric variations.
The scope of the work has been clarified as a comparative evaluation of turbulence modeling approaches rather than a parametric or optimization study. Additionally, we have included a discussion highlighting how the identified flow features can inform future design improvements. Future work will extend the analysis to include parametric variations, such as different speeds and geometric configurations, in order to enhance the practical applicability of the results.

Minor Comments

The introduction could more clearly define the research gap. Some figures would benefit from additional quantitative annotations. The organization of the methods section could also be improved for clarity.
Response: We thank the reviewer for these helpful suggestions.
These aspects were also raised by Reviewer 1 and have been addressed in the revised manuscript. Specifically, the Introduction has been refined to more clearly define the research gap and the scope of the study as a comparative evaluation of turbulence modeling approaches.
The Methods section has been reorganized to improve clarity and reproducibility, with a clearer distinction between model description and methodological justification.
In addition, figure descriptions have been revised to enhance clarity, and where appropriate, annotations and explanations have been improved to better support interpretation. The qualitative nature of the visualizations has also been explicitly stated.

Recommendation

The manuscript has solid potential but would benefit from revisions addressing the points above. With additional validation, expanded analysis, and clearer justification of modeling choices, the work could make a valuable contribution to the field.
Response: We sincerely thank the reviewer for the positive evaluation and constructive feedback. All the points raised have been carefully addressed in the revised manuscript. In particular, we have clarified the scope of the study, strengthened the methodological justification, and incorporated additional discussion regarding validation through literature benchmarking and the limitations of the modeling approach. These revisions aim to improve the clarity, rigor, and overall contribution of the work. We appreciate the reviewer’s comments, which have significantly helped to enhance the quality of the manuscript.

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Competing Interests

The authors declare that they have no competing interests.

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Reviewer Report

24 Views

02 Jan 2026 | for Version 1

Adit S Misar, University of North Carolina at Charlotte, Charlotte, North Carolina, USA

24 Views Cite this report Responses(1)

Not Approved

The manuscript presents drag coefficients from RANS and DES simulations at a single velocity of 30 km/h (Section 3.1, Page 7), but provides no comparison to wind tunnel data, coast-down tests, published Baja SAE measurements, or even simplified analytical estimates.
The claim that DES provides “more accurate” predictions (Abstract; Sections 3.1, 4, and 5) is not substantiated. The manuscript reports only a numerical difference between RANS and DES, not accuracy relative to a reference truth.
The standard deviation of Cd in DES is interpreted as improved physical realism (Page 7), yet temporal variability alone does not imply improved accuracy.

The vehicle operates at 30 km/h, corresponding to a Reynolds number of approximately 6.7 × 10⁵ (Page 6). This places the flow in a regime where steady or URANS models are often sufficient, especially given the simplified geometry.
The DES formulation relies on a mesh-dependent transition between RANS and LES regions, yet the manuscript provides no grid sensitivity analysis specific to DES behavior, only a drag-based mesh independence study using RANS (Section 2.2, Page 6).
The DES mesh adaptation is derived from vortex diameters observed in RANS results (Page 6), which introduces circular reasoning. If RANS does not resolve unsteady structures accurately, it cannot reliably inform LES filter sizing.

Claims regarding vortex shedding, von Kármán-like behavior, and improved wake resolution (Pages 7–9) are made without supporting evidence such as Strouhal number analysis, spectral decomposition, or force coefficient frequency content.
Streamlines from steady RANS are used to infer vortex topology and persistence (Page 8), which is not physically rigorous for inherently unsteady wake flows.
Q-criterion plots (Section 3.5, Pages 10–11) are presented qualitatively, without sensitivity to threshold selection or comparison across consistent isovalues.

For a ground vehicle application, this modeling choice is known to significantly alter wake structure and drag prediction.
The manuscript does not discuss the implications of neglecting moving ground and rotating wheels, nor does it attempt a sensitivity study or justify the simplification.
Given the focus on wake dynamics and drag accuracy, this omission materially affects the credibility of the results.

6. Limited Parametric Scope and Practical Insight
Sections 3–5, Pages 7–12
The study evaluates a single geometry at a single velocity with no parametric variation.

There is no assessment of ride height, yaw angle, surface modifications, or speed dependence.
No aerodynamic optimization or design guidance emerges beyond the general statement that DES resolves more structures than RANS.
As a result, the manuscript does not provide actionable insight for Baja SAE design practice or aerodynamic decision-making.

Presentation and Structure Concerns
While secondary to the technical issues above, the following further limit the manuscript’s readiness:

The Introduction (Pages 3–4) devotes extensive space to general Baja SAE context but insufficiently narrows the scientific gap being addressed.
The Methods section intermixes modeling description and justification, making reproducibility difficult.
Several figures rely on qualitative interpretation without clear scaling rationale or quantitative annotation.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

No
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Partly
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Motorsports, CFD, Turbulence, Aerodynamics, Vehicle Dynamics.

Respond to this report

Responses (1)

Author Response

12 Jun 2026

Deisy Yurley Rodriguez Sarmiento, Universidad Autonoma de Bucaramanga, Bucaramanga, Colombia

1. Scope and Framing of the Study
Abstract and Introduction, Pages 1 to 3
The abstract (Page 1) positions the study as a high-fidelity aerodynamic investigation using hybrid RANS–LES. While the numerical tools employed are indeed advanced, the scientific scope remains narrow. The manuscript focuses almost exclusively on drag coefficient, with no discussion of side force, lift, or aerodynamic moments.
For a ground vehicle, and especially for a racing or off-road competition vehicle, drag alone is an incomplete descriptor of aerodynamic performance. At minimum, a complete aerodynamic characterization should consider three forces (Cd, Cl, Cs) and three moments (rolling, pitching, yawing). Even if all quantities are not ultimately presented, the absence of discussion or justification for excluding them is a major omission.
Similarly, metrics such as L over D and front-to-rear balance percentage are central to racing vehicle aerodynamics, yet are not meaningfully addressed. This limits both the scientific value and the practical relevance of the results.

Response: We sincerely thank the reviewer for this insightful and valuable comment. We agree that a complete aerodynamic characterization of ground vehicles may include additional force components (lift and side force) and aerodynamic moments (rolling, pitching, and yawing), as well as derived performance indicators such as L/D ratio and aerodynamic balance. However, the primary objective of this study is not to provide a full aerodynamic characterization of the Baja SAE vehicle, but rather to evaluate the capability of hybrid RANS–LES (DES) modeling to capture wake dynamics and improve drag prediction compared to steady RANS approaches.

In this context, the drag coefficient (Cd) was selected as the primary metric because it is directly influenced by wake structures, flow separation, and vortex dynamics, which are the main phenomena investigated in this work. The focus on Cd is consistent with prior CFD studies aimed at assessing turbulence modeling strategies in external aerodynamics. We acknowledge that additional aerodynamic quantities such as lift (Cl), side force (Cs), and moments are highly relevant for vehicle stability and performance, particularly in racing applications. However, these quantities are more sensitive to detailed geometry, transient crosswind conditions, and suspension–ground interaction effects, which fall beyond the scope of the present study.

To address the reviewer’s concern, we have clarified the scope and limitations of the study in the revised manuscript, explicitly stating:
(i) the rationale for focusing on drag coefficient,
(ii) the intended methodological contribution of the work, and
(iii) the need for future studies to include a more comprehensive aerodynamic characterization.

2. Absence of Validation and Physical Benchmarking
Section 3, Pages 7–12
A critical limitation of this study is the complete absence of experimental validation, high-fidelity reference data, or benchmark comparison.
The manuscript presents drag coefficients from RANS and DES simulations at a single velocity of 30 km/h (Section 3.1, Page 7), but provides no comparison to wind tunnel data, coast-down tests, published Baja SAE measurements, or even simplified analytical estimates.
The claim that DES provides “more accurate” predictions (Abstract; Sections 3.1, 4, and 5) is not substantiated. The manuscript reports only a numerical difference between RANS and DES, not accuracy relative to a reference truth.
The standard deviation of Cd in DES is interpreted as improved physical realism (Page 7), yet temporal variability alone does not imply improved accuracy.
Without validation, the work remains a numerical comparison study, not a demonstrable advancement in aerodynamic prediction.

Response: We sincerely thank the reviewer for this important and insightful comment.
We fully agree that the absence of experimental validation or high-fidelity reference data limits the ability to assess the absolute accuracy of the numerical predictions. The primary objective of this study, however, is not to provide a fully validated aerodynamic characterization of the vehicle, but rather to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) in capturing wake dynamics and flow structures.
Following the reviewer’s suggestion, we have revised the manuscript to avoid statements implying absolute accuracy. Instead, we now emphasize that the DES approach provides enhanced physical fidelity and improved resolution of unsteady flow phenomena, particularly in the wake region. We also acknowledge that experimental validation (e.g., wind tunnel testing or full-scale measurements) is a critical component in aerodynamic studies. However, such experimental campaigns require specialized infrastructure and significant financial resources that were not available within the scope of the present work. In this context, and consistent with common practice in computational aerodynamics studies under similar constraints, we have incorporated a benchmarking discussion based on published literature. Specifically, the predicted drag coefficient values (Cd ≈ 1.25–1.29) fall within the expected range reported for bluff-body and off-road vehicle configurations, which typically exhibit relatively high drag due to exposed structural elements and flow separation. This comparison supports the physical plausibility of the results, although it does not replace direct experimental validation.
Additionally, we have clarified that the temporal variability observed in DES results reflects the inherently unsteady nature of the simulation, rather than being a direct indicator of improved accuracy. Finally, we explicitly state in the revised manuscript that the present study should be interpreted as a comparative numerical analysis, and that future work will include experimental validation to enable quantitative assessment of predictive accuracy.

3. Questionable Appropriateness of DES for the Problem Scale
Section 2.4, Pages 6–7
The choice and justification of DES for this application is insufficiently supported.
The vehicle operates at 30 km/h, corresponding to a Reynolds number of approximately 6.7 × 10⁵ (Page 6). This places the flow in a regime where steady or URANS models are often sufficient, especially given the simplified geometry.
The DES formulation relies on a mesh-dependent transition between RANS and LES regions, yet the manuscript provides no grid sensitivity analysis specific to DES behavior, only a drag-based mesh independence study using RANS (Section 2.2, Page 6).
The DES mesh adaptation is derived from vortex diameters observed in RANS results (Page 6), which introduces circular reasoning. If RANS does not resolve unsteady structures accurately, it cannot reliably inform LES filter sizing.
As presented, the DES implementation appears methodologically fragile and not robustly justified for this flow regime.
Response: We sincerely thank the reviewer for this detailed and technically insightful comment. We acknowledge that the Reynolds number of the present study (Re ≈ 6.7 × 10⁵) lies within a regime where steady RANS or URANS approaches are often considered sufficient for predicting global aerodynamic quantities such as drag. However, the objective of this work is not limited to the prediction of integral forces, but rather to investigate the capability of hybrid RANS–LES methods to resolve unsteady flow features, particularly in the wake region. Even at moderate Reynolds numbers, bluff-body flows such as those around Baja SAE vehicles are characterized by flow separation, vortex shedding, and complex wake dynamics. These phenomena are inherently unsteady and may not be fully captured by steady RANS models. In this context, DES was employed as a tool to enhance the physical representation of these flow structures, rather than as a strictly necessary modeling approach.

Regarding mesh sensitivity, we agree that the mesh independence study was primarily conducted using RANS. In the revised manuscript, we clarify that the DES mesh was designed to ensure adequate resolution of the wake region based on characteristic length scales and refinement zones, although a full DES-specific grid convergence study was beyond the scope of this work. This limitation is now explicitly acknowledged. Concerning the estimation of the LES filter size (ΔLES), We agree that deriving the LES filter size (ΔLES) directly from vortex structures observed in RANS results may introduce circular reasoning, since RANS does not fully resolve unsteady flow features. In the revised manuscript, this aspect has been clarified and corrected. Specifically, the estimation of ΔLES is now defined based on established DES/DDES formulations, where the characteristic length scale is determined by the local grid size rather than flow features extracted from RANS simulations. Following standard practice in hybrid RANS–LES modeling, Δ is defined as a representative cell dimension, typically related to the cubic root of the cell volume or the equivalent cell diameter (e.g., Δ ≈ cell size / √3), as described in previous studies [A. Travin, P. Spalart et al., 1999; Lopez and Moser, 2008]. Within the DES framework, the grid spacing governs the transition between RANS and LES regions and determines the range of resolved turbulent scales. Therefore, ΔLES should be interpreted as a mesh-based parameter rather than a flow-derived quantity. The manuscript has been revised accordingly to remove any dependence on RANS-derived vortex scales and to clearly state that the LES filter size is defined as a grid-based approximation consistent with DES methodology. Finally, we have strengthened the discussion to clarify that the present study should be interpreted as a comparative numerical analysis aimed at evaluating modeling capabilities, rather than as a definitive or fully validated application of DES for this flow regime.

4. Overinterpretation of Flow Visualizations
Sections 3.2–3.5, Pages 7–11
The manuscript places strong interpretive weight on contour plots, streamlines, and Q-criterion visualizations, but these are not supported by quantitative flow metrics.
Claims regarding vortex shedding, von Kármán-like behavior, and improved wake resolution (Pages 7–9) are made without supporting evidence such as Strouhal number analysis, spectral decomposition, or force coefficient frequency content.
Streamlines from steady RANS are used to infer vortex topology and persistence (Page 8), which is not physically rigorous for inherently unsteady wake flows.
Q-criterion plots (Section 3.5, Pages 10–11) are presented qualitatively, without sensitivity to threshold selection or comparison across consistent isovalues.
Overall, the visual analysis is descriptive rather than diagnostic, and conclusions drawn from it exceed what the presented data can support.

Response: We sincerely thank the reviewer for this detailed and valuable comment.
We agree that the flow visualizations presented in this study (velocity contours, streamlines, and Q-criterion) are primarily qualitative and should be interpreted as such. The objective of these visualizations is to provide physical insight into the flow structures captured by each turbulence model, rather than to perform a fully quantitative characterization of unsteady flow phenomena.
Following the reviewer’s suggestion, we have revised the manuscript to avoid overinterpretation of these results. Specifically:

Statements suggesting confirmed vortex shedding or von Kármán vortex street formation have been softened to indicate qualitative resemblance rather than definitive identification.
The discussion of streamlines from steady RANS simulations has been clarified to reflect their limitations in representing inherently unsteady flow structures.
Q-criterion visualizations are now explicitly described as qualitative tools for illustrating vortex structures, without implying quantitative comparison or sensitivity to threshold selection.

We also acknowledge that a rigorous characterization of unsteady wake phenomena would require additional analyses such as Strouhal number estimation, spectral analysis, or force coefficient frequency decomposition, which were beyond the scope of the present study The manuscript has been revised accordingly to ensure that all interpretations remain consistent with the level of analysis performed.

5. Insufficient Treatment of Ground and Wheel Effects
Section 2.3, Page 6
All solid boundaries, including the ground and wheels, are modeled as stationary no-slip walls.
For a ground vehicle application, this modeling choice is known to significantly alter wake structure and drag prediction.
The manuscript does not discuss the implications of neglecting moving ground and rotating wheels, nor does it attempt a sensitivity study or justify the simplification.
Given the focus on wake dynamics and drag accuracy, this omission materially affects the credibility of the results.
Response: We sincerely thank the reviewer for this important observation.
We agree that the use of a stationary ground and non-rotating wheels is a simplification that can influence the development of the boundary layer, wake structure, and aerodynamic force prediction in ground vehicle simulations. Modeling moving ground conditions and rotating wheels would provide a more realistic representation of vehicle–road interaction.
In the present study, these effects were neglected to reduce computational complexity and to maintain a consistent modeling framework for the comparative evaluation of turbulence models (RANS vs DES). The primary objective was to assess the relative capability of each model to resolve flow structures and wake dynamics, rather than to provide a fully realistic aerodynamic prediction.
We acknowledge that this simplification may affect the absolute values of the drag coefficient and the detailed structure of the near-ground flow. However, since both RANS and DES simulations were performed under identical boundary conditions, the comparative analysis remains valid.
Following the reviewer’s suggestion, we have revised the manuscript to explicitly discuss this limitation and its potential impact. Future work will include moving ground conditions and rotating wheels to improve the physical realism and enable more accurate aerodynamic characterization.

6. Limited Parametric Scope and Practical Insight
Sections 3–5, Pages 7–12
The study evaluates a single geometry at a single velocity with no parametric variation.
There is no assessment of ride height, yaw angle, surface modifications, or speed dependence.
No aerodynamic optimization or design guidance emerges beyond the general statement that DES resolves more structures than RANS.
As a result, the manuscript does not provide actionable insight for Baja SAE design practice or aerodynamic decision-making.
Presentation and Structure Concerns
While secondary to the technical issues above, the following further limit the manuscript’s readiness:
The Introduction (Pages 3–4) devotes extensive space to general Baja SAE context but insufficiently narrows the scientific gap being addressed.
The Methods section intermixes modeling description and justification, making reproducibility difficult.
Several figures rely on qualitative interpretation without clear scaling rationale or quantitative annotation.
Response: We sincerely thank the reviewer for this comprehensive and constructive comment.
We acknowledge that the present study evaluates a single vehicle geometry at a single operating condition, and does not include a parametric analysis (e.g., ride height, yaw angle, or speed variation). This limitation arises from the primary objective of the work, which is to perform a comparative assessment of turbulence modeling approaches (RANS vs hybrid RANS–LES) rather than to conduct a full aerodynamic optimization study.
Following the reviewer’s suggestion, we have revised the manuscript to clarify this scope and to enhance the practical relevance of the findings. Specifically:

We have incorporated a discussion linking the identified flow features (e.g., recirculation zones, stagnation regions, and wake structures) to potential design implications for Baja SAE vehicles, such as body simplification, rear geometry shaping, and underbody flow management.
We explicitly state that the results should be interpreted as a methodological and diagnostic analysis, which can inform future parametric or optimization studies.
We have added a statement highlighting that future work should include parametric variations (velocity, yaw angle, ride height) and design optimization strategies.

Regarding presentation and structure:

The Introduction has been revised to better define the scientific gap and reduce general background content.
The Methods section has been reorganized to clearly separate modeling description from methodological justification, improving reproducibility.
Figure descriptions have been revised to emphasize their qualitative nature and to clarify interpretation limits.

References

A. Travin, M. Shur, M. Strelets, and P. Spalart. Detached-eddy simulations past a circular
cylinder. Flow, Turbulence and Combustion, 63:293–313, 1999.

O. D. Lopez and R. D. Moser, “Delayed Detached Eddy Simulation of Flow Over an Airfoil with Synthetic Jet Control,” Mecánica Computacional, vol. 27, pp. 3225–3245, 2008.

View more View less

Competing Interests

The authors declare that they have no competing interests.

Alongside their report, reviewers assign a status to the article:

Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested

Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.

Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions

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Aerodynamic Performance of a Baja SAE Vehicle Using Hybrid RANS-LES Approach

Abstract

Keywords

1. Introduction

Table 1. Overview of relevant studies involving Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) applied to structural and aerodynamic optimisation of Baja SAE vehicles.

2. Methods

2.1 Geometry and computational domain

Figure 1. Vehicle geometry and computational domain.

Table 2. Vehicle and computational domain dimensions.

2.2 Meshing

Figure 2. A) Computational domain and vehicle mesh; B) Detail of the prism layer on the vehicle; C) Body of influence boxes.

2.3 RANS Model implementation

2.4 DES Model adaptation

Figure 3. Mesh adaptation from RANS to DES.

3. Results

3.1 Drag coefficient

3.2 Pressure and velocity field

Figure 4. Velocity field and streamlines in symmetry plane.

Figure 5. A) Pressure contour in the symmetry plane and on the vehicle surface by the RANS model; B) Pressure distribution on the vehicle surface; C) Pressure contour in the symmetry plane by the DES model.

3.3 Vorticity field analysis in the near and far wake

3.4 Theoretical framework of vorticity dynamics

3.5 3D Visualization of vortex structures

Figure 7. Isocontours of Q-criterion showing vortex structures around the vehicle and in the near wake region.

4. Discussion

5. Conclusion

Use of artificial intelligence

Data availability statement

Extended data

References

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