Aerodynamic Drag Coefficient Analysis of Heavy-Duty Vehicle Platoons: A Hybrid Approach Integrating Wind Tunnel Experiments and CFD Simulations

Abstract

Heavy-duty vehicle (HDV) platooning, facilitated by vehicle-to-vehicle communication, plays a crucial role in transforming logistics and transportation. It reduces fuel consumption and emissions while enhancing road safety, supporting sustainable freight strategies and the integration of autonomous vehicles. This study employs a hybrid approach combining wind tunnel experiments and Computational Fluid Dynamics (CFD) simulations to analyze HDV platoon aerodynamics. The approach has two sequential phases: single-HDV simulation validation and multi-HDV platooning simulation. In the first phase, a single HDV CFD simulation is validated against NASA’s benchmarks, with optimized mesh generation, proper models, and conditions, and errors minimized below 1%. In the second phase, the validated model is used for multi-HDV platooning simulations, maintaining consistent mesh structures, physical models, and boundary conditions. Various platoon configurations are explored to assess the effects of speed, inter-vehicle spacing, and platoon size and position on aerodynamic drag, with virtual wind tunnel simulations evaluating drag coefficients. Our findings reveal that inter-vehicle spacing critically influences drag. An optimal range of 0.25 to 0.5-times the HDV length is identified to achieve an effective balance between safety and fuel efficiency, reducing platoon aerodynamic drag by 13–44% compared to single HDVs. While platoon speed is generally limited to impacting drag, it becomes more pronounced when an HDV platoon has very small inter-vehicle spacings, or in platoons exceeding five HDVs. Moreover, as the platoon size increases, the overall aerodynamic drag coefficient diminishes, particularly benefiting the rear HDV in larger platoons with smaller inter-vehicle spacing. These insights offer a comprehensive understanding of HDV platoon aerodynamics, enabling logistics enterprises to optimize platoon configurations for fuel savings, improved traffic flow, larger platoon formation, and enhanced transportation safety.

1. Introduction

Heavy-duty trucks (HDVs) now dominate freight fleets, representing 70% of freight ton-kilometers, consuming 40% of the energy used, and contributing 30% of CO₂ emissions [1,2]. Their fuel consumption ranges from 30 to 35.8 L/100 km in China [1] and 23.9 to 33.4 L/100 km in the EU [3], with fuel costs accounting for 35–38% of operating expenses [1,4]. Fuel consumption is expected to rise, especially in non-OECD (Organization for Economic Cooperation and Development) countries.

Many countries recognize the critical role of HDVs in promoting energy efficiency and decarbonization, which has led to the development of technologies to improve fuel efficiency [2]. Current research focuses on reducing aerodynamic drag and rolling resistance, improving engine efficiency, and recovering waste heat [3,5]. Since aerodynamic drag accounts for 35–55% of fuel consumption, optimizing HDV aerodynamics is crucial for achieving these objectives [6,7,8].

There are two primary drag reduction techniques for HDVs: The first approach focuses on enhancing the vehicle’s aerodynamics through modifications to its design. Key measures include the installation of side skirts, boat tails, and underbody panels, as well as addressing the gap between the tractor and trailer. Altaf et al. [9] conducted a Computational Fluid Dynamics (CFD) study on a simplified TGX Man truck model to analyze aerodynamic performance, focusing on a unique elliptical deflector positioned at the upper rear edge. This design achieved an 11.1% reduction in drag, significantly outperforming rectangular and triangular deflector designs. Miralbes et al. [10] utilized CFD methods to evaluate five rear drag reduction devices for HDVs, including four boat tail designs. These devices demonstrated drag reductions ranging from 10% to 15%. De Souza et al. [11] confirmed the effectiveness of underbody panels in reducing drag through wind tunnel experiments. Story et al. [12] discovered that fully sealing the gap between the tractor and trailer can reduce average drag by 20%.

Another effective approach is the implementation of platooning technology. This technology enables two or more HDVs to exchange real-time data on their position, speed, and acceleration/deceleration through vehicle-to-vehicle (V2V) communication. Using adaptive cruise control, automatic braking, and other advanced driver-assistance systems, following HDVs can maintain their close spacing within a platoon [13,14,15,16,17].

This technology improves aerodynamic efficiency by reducing inter-vehicle spacings. The leading HDV moves through the air, creating a low-pressure vortex which reduces the drags of subsequent HDVs. Additionally, interactions between HDVs in a platoon redistribute the airflow, reducing turbulence and lowering the overall aerodynamic drag.

Typical methods for studying the aerodynamic drag of HDV platoons include on-road measurements, wind tunnel experiments, CFD simulations, and a combination of wind tunnel and CFD techniques. Initial studies predominantly relied on on-road measurements [18]. They were sensitive to environmental factors and often incurred high costs. Wind tunnel experiments offer accurate and repeatable results in controlled environments [19,20]. However, they entail significant construction and maintenance costs, and their size and scaling limitations render them less suitable for studying long platoons and real-world scenarios. Advancements in CFD have made CFD simulations the primary tool for analyzing pneumatic drag in platoons due to the flexibility and cost-effectiveness of simulations [21,22]. However, the accuracy of CFD simulation methods depends on model selection, grid quality, boundary conditions, and computational resources, often requiring experimental validation, which many current studies on truck platooning have lacked. To overcome the limitations of standalone CFD simulations, several researchers have integrated wind tunnel experiments with CFD simulations, validating CFD models with wind tunnel data while using simulations to explore hard-to-reproduce scenarios [23,24]. This hybrid approach, though mostly used for small-scale platoons (both homogeneous and heterogeneous vehicles) due to resource constraints, still has great potential for the study of aerodynamic drag in HDV platoons.

It is noted that current studies on HDV platoons focus on how inter-vehicle spacing and platoon configuration affect aerodynamic drag. These studies suggest that the average drag coefficient of HDVs in a platoon correlates closely with inter-vehicle spacing. When speed and inter-vehicle spacing are constant, platooning HDVs often lowers the average drag coefficient when compared with that in solo HDVs, resulting in reduced emissions [25]. As inter-vehicle spacing decreases, the average drag coefficient drops further, especially with small gaps [26]. However, some studies show that drag coefficients can paradoxically increase beyond a critical inter-vehicle spacing threshold for trailing HDVs [27], while excessive inter-vehicle spacing reductions may raise the drag coefficients of leading HDVs [28]. Although uniform inter-vehicle spacing is common, non-uniform configurations have also been explored in previous studies [29]. These studies indicate that drag coefficients are reduced in heterogeneous HDV platoons, with trailing HDVs benefiting from greater drag reductions as the HDV gaps shrink [30].

Platoon configurations have also drawn research attention in previous studies. Researchers have examined HDV composition [23,31], lateral offsets [32], crosswinds [33], and platoon size, with the latter emerging as a central area of investigation. Wind tunnel experiments and on-track evaluations, conducted on small platoons, have revealed that as the platoon size increases, the average drag coefficient decreases [19,34]. CFD simulations have further confirmed that as the number of HDVs increases, the overall drag coefficient gradually decreases, and it stabilizes after it reaches a certain size [35]. Notably, when the number of HDVs exceeds four, additional aerodynamic improvements diminish [29]. For a five-HDV platoon, the average drag coefficient is lower than that of smaller platoons [36]. Although the overall drag coefficient decreases, the drag behavior of individual HDVs becomes more complex. For instance, in a three-HDV platoon, drag valleys are observed at 0.5 and 0.8 vehicle lengths for the lead HDV and at 0.3 and 0.8 vehicle lengths for the middle HDV [34]. Some studies suggest that the drag coefficient of the leading HDV remains relatively unchanged, whereas that of the middle and trailing vehicles decreases to 56% and 88% of their respective single-HDV values [35]. Other research indicates that significant drag reductions predominantly occur in the lead and trailing HDVs [26].

In summary, previous studies on aerodynamic drag coefficients in HDV platooning have noticeable limitations. They lack a hybrid approach that combines experimental and computational analyzing capabilities. As such, CFD models cannot be easily validated. Additionally, previous studies have overlooked the effects of speed variations on drag, resulting in a limited robustness in reflecting real-world roadway conditions. Furthermore, previous studies have been limited to a narrow range of platoon configurations and inter-vehicle spacings. This study aims to address these limitations and enhance the understanding of aerodynamic drag factors in HDV platooning. The main contributions of this paper are as follows:

(1) Application of a hybrid approach: We employed a hybrid approach that integrates wind tunnel experiments with CFD simulations to overcome the reliance on a single experimental or computational method seen in previous studies. The CFD model parameters were calibrated using experimental data from the NASA Ames Research Center. The calibrated CFD model was then utilized to investigate the aerodynamic drag coefficients in complex multi-HDV platoon scenarios, significantly enhancing the accuracy and reliability of predictive results.

(2) Construction of a platoon scenario dataset: This study systematically formed HDV platoons with various speeds, inter-vehicle spacings, and platoon sizes. Using these platoons, we constructed a dataset that includes four different speeds, six platoon sizes, and seven inter-vehicle spacings. This dataset surpasses previous studies in terms of platoon variations, providing a solid foundation for the in-depth analysis of factors influencing platoon drag coefficients.

(3) Identification of influencing factors: We identified the effects of HDV speed, inter-vehicle spacing, and platoon size/position on aerodynamic drag coefficients.

The structure of this study is organized as follows: Section 2 outlines the research methodology, presenting a hybrid approach that integrates advanced CFD techniques with experimental data to establish simulation scenarios for multi-vehicle platoons. Section 3 describes the results of these CFD simulations, focusing on the effects of HDV speed, inter-vehicle spacing, and platoon size/position on aerodynamic drag coefficients. In Section 4, the findings, compared with those of prior studies, provide a list of HDV factors impacting the drag coefficients. Finally, the conclusion highlights the key findings and discusses their potential implications for optimizing platoon operations.

2. Methodology

This section evaluates HDV platoon aerodynamic drag using a hybrid approach that integrates advanced CFD methods with experimental data. We employ a virtual wind tunnel designed to replicate HDV aerodynamics and calibrate against NASA’s data to enhance drag coefficient (C_d) accuracy for complex multi-HDV scenarios.

Our hybrid methodology is composed of two consecutive and interconnected phases: single-HDV simulation validation and multi-HDV platooning simulation. The initial phase involves the validation of a single HDV CFD simulation using a generic conventional HDV model (vehicle model details are provided in Section 2.1), strictly adhering to NASA’s experimental criteria for wind tunnel configuration and vehicle placement. The finite volume method is applied to generate the mesh, with careful optimization of mesh sizes and structures. Appropriate physical models are selected, and boundary conditions are defined. Through iterative optimization and continuous comparison with NASA wind tunnel data, we minimize errors to below 1%. This validation establishes the reliability of the single HDV simulation model.

In the subsequent phase, CFD simulations are conducted using the validated single HDV model, incorporating its mesh structures, calibrated physical models, and predefined boundary conditions to ensure coherence. This leverages the previously established reliability, thereby eliminating the need for redundant and time-consuming revalidation. We systematically explore a comprehensive range of platoon configurations, assessing the impact of factors such as speed, inter-vehicle spacing, platoon size, and position on aerodynamic drag. The virtual wind tunnel simulations meticulously evaluate drag coefficients across various platoon configurations. Figure 1 illustrates the experimental procedure of the hybrid method employed in this study.

2.1. Virtual Wind Tunnel and HDV

Simcenter STAR-CCM+ 2020.1 Build 15.02.007, a general-purpose CFD simulation software platform, is used in this study to build a virtual wind tunnel and accommodate HDVs in the tunnel. A 1:8-scale generic tractor-trailer HDV model developed by the US Department of Energy (DOE) and known as the General Conventional Model (GCM), is imported into the virtual wind tunnel. This HDV model features a simplified underbody to facilitate grid generation and reduce flow complexities. The virtual HDV has dimensions of 2.46 m (length) × 0.324 m (width) × 0.518 m (height), and its frontal area is 0.154 m². It represents an actual HDV with the dimensions of 19.7 m in length, 2.59 m in width, and 4.15 m in height. The virtual HDV has a solid blockage of 2.2% (well below the 5.0% threshold), insignificant to the blocking effect, and thus is neglected in this study. The virtual HDV is positioned 5 m behind the wind tunnel’s inlet, and is elevated 1.5 cm above the wind tunnel floor using four supporting bases. The rear end of the virtual HDV to the wind tunnel’s outlet is set to be 6 L, where L is the length of the virtual HDV (see Figure 2). Other installation details of the virtual HDV replicate those outlined in the report of Storms et al. and align with the setup details of the physical HDV used in the wind tunnel experiments of NASA’s Ames Research Center [37].

The virtual wind tunnel has a cross section of 7 ft (height) × 10 ft (width) (2.13 m × 3.05 m). The length of the virtual wind tunnel varies depending on the number of HDVs in a platoon. For a wind tunnel containing only one HDV, the length of the tunnel is 22.2 m. When a platoon contains multiple HDVs, the virtual wind tunnel is extended to cover all the platooning HDVs in series. It is noted that an inter-vehicle space is provided between any two consecutive HDVs. The space between the wind tunnel’s inlet and the first platooning HDV remains 5 m. Similarly, 6 L is reserved for the space between the rear end of the last HDV to the outlet of the wind tunnel.

2.2. Controlling Equations and Turbulence Model Selection

The airflows or winds applied to HDVs are treated as steady, isothermal, and incompressible three-dimensional turbulent flows [32]. The external flow field of HDVs is primarily viscous and is typically analyzed using the Navier–Stokes (N–S) equations. In this study, a realizable κ-ε turbulence model is developed to describe the complex flow phenomena at a high Reynolds number and to solve the nonlinear N–S equations. This model effectively captures the aerodynamic characteristics of the computational domain and determines the aerodynamic drag coefficients associated with the HDVs.

2.2.1. Controlling Equations

Fluid flow adheres to three fundamental laws: mass conservation, momentum conservation, and energy conservation, which describe the velocities, pressures, and temperatures within fluids. These principles are embodied in the N–S equations, with the mass and momentum conservation equations being particularly crucial for analyzing the external flows of HDVs. The mass conservation equation is presented as follows [38]:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla \cdot \left(\rho \overrightarrow{U}\right)=0$$

(1)

where ρ represents the fluid density and t denotes time. $\overrightarrow{U}$ = (u, v, w) is a velocity vector with components u, v, w along the x, y, z direction, respectively. $\nabla$ is the divergence operator, representing the divergence of the mass flux; it indicates the net outflow of mass from a region. This continuity equation ensures the conservation of mass within a fluid system. The momentum equations, based on Newton’s second law, reflect momentum conservation in fluid flow. These can be described as follows [38]:

$$\begin{array}{l}{\displaystyle \frac{\partial \left(\rho u\right)}{\partial t}}+\nabla \cdot \left(\rho u\overrightarrow{U}\right)=-{\displaystyle \frac{\partial p}{\partial x}}+\mu \left({\displaystyle \frac{{\partial }^{2}u}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}u}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}u}{\partial z^2}}\right)+f_x\\ {\displaystyle \frac{\partial \left(\rho v\right)}{\partial t}}+\nabla \cdot \left(\rho v\overrightarrow{U}\right)=-{\displaystyle \frac{\partial p}{\partial y}}+\mu \left({\displaystyle \frac{{\partial }^{2}v}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}v}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}v}{\partial z^2}}\right)+f_y\\ {\displaystyle \frac{\partial \left(\rho w\right)}{\partial t}}+\nabla \cdot \left(\rho w\overrightarrow{U}\right)=-{\displaystyle \frac{\partial p}{\partial z}}+\mu \left({\displaystyle \frac{{\partial }^{2}w}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}w}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}w}{\partial z^2}}\right)+f_z\end{array}$$

(2)

where p is the pressure, and f_x, f_y, f_z are the body forces acting on a fluid per unit volume in each direction. μ represents the dynamic viscosity of a fluid, describing its internal friction. ∂ρu/∂x, ∂ρv/∂y, ∂ρw/∂z represent the rate of momentum change in each direction. The second terms are the divergence of the momentum flux tensor, accounting for momentum changes as the fluid moves. −∂p/∂x, −∂p/∂y, −∂p/∂z represent pressure forces. The second terms on the right side denote viscous forces due to internal friction. These equations provide a complete description of viscous fluid motion in the x, y, z directions, balancing inertial, pressure, viscous, and body forces for an analysis of fluid behavior in three-dimensional space.

2.2.2. Realizable k-ε Turbulence Model

The realizable k-ε turbulence model, an improved two-equation closure model, improves the standard k-ε turbulence model by providing more accurate results in complex flows and the separation of boundary layers. It utilizes two transport equations to describe turbulent kinetic energy (k) and its dissipation rate (ε), where the former represents the energy in turbulent motions and the latter indicates the rate at which turbulent kinetic energy is converted into thermal energy, as shown in Equations (3) and (4) [39]:

$${\displaystyle \frac{\partial \left(\rho k\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho k{u}_j\right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]+P_k-\rho \epsilon$$

(3)

$${\displaystyle \frac{\partial \left(\rho \epsilon \right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho \epsilon u_j\right)}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+\rho C_{1}S\epsilon -\rho C_2{\displaystyle \frac{{\epsilon }^2}{k+\sqrt{\nu \epsilon }}}+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}{C}_{3\epsilon }{P}_b$$

(4)

$$\begin{array}{ccc}{\mu }_t=\rho C_{\mu }{\displaystyle \frac{k^2}{\epsilon }}& & C_{\mu }={\displaystyle \frac{1}{A_0+A_s\frac{k{U}^{*}}{\epsilon }}}\end{array}$$

(5)

where x_j and u_j denote the spatial and velocity coordinate components, indicating position and velocity in the fluid coordinate system across different directions. P_k is the production term for k due to turbulent shear stresses. σ_k and σ_ε are the turbulent Prandtl numbers for k and ε, typically valued at 1.0 and 1.3, respectively. The constants C₁, C₂, C_1ε, and C_3ε are used to shape the behavior of the turbulence model under different flow conditions. S is a scalar invariant based on the mean strain rate, ν indicates kinematic viscosity and internal friction, and P_b is the buoyancy generation term. The turbulent viscosity μ_t, calculated by Equation (5), quantifies the enhanced momentum transfer due to turbulence. The parameter C_μ, crucial to model performance, is dynamically adjusted in the realizable k-ε model based on the mean strain and rotation rate tensors U*. The constants A₀ and A_s are also utilized in this adjustment.

2.3. CFD Simulation Method for a Single HDV

2.3.1. Meshing Structure

STAR-CCM+ utilizes a finite volume method to “mesh” the aerodynamic behaviors of the virtual wind tunnel and the platooning HDVs. It treats the wind tunnel (outside the HDVs) as a computational domain. It discretizes and partitions the domain into small volumes or meshes. Each partitioned mesh is a control entity with its own aerodynamic characteristics (that is, mass, air pressure, and airflow speed). The finer the meshes, the more accurate the aerodynamic characteristics determined by our CFD method, but the greater the consumption of computing resources.

To ensure the computational results are independent of mesh size, this study incorporates a mesh independence analysis. The process begins with an initial mesh generation, followed by iterative refinement to progressively reduce the mesh size until the drag coefficient exhibits only a negligible change between consecutive refinements. This iteration continues until the drag coefficient difference falls below 0.003 or is less than 5% [40].

Triangular surface meshes are created to represent the surface of any HDVs in the virtual wind tunnel. Figure 3 presents the surface meshes for a single HDV. Through a process of mesh independence iterative refinement, the size of the triangular surface meshes was determined to be 4.4 mm, to better balance the accuracy and the computation load of our CFD model.

Volumetric meshes are used to represent the computational domain (see Figure 4). In considering that airflow disturbances primarily occur around the HDVs, our CFD model densifies the meshes in regions near the HDVs where the airflows change rapidly, while larger meshes are used outside of these regions to reduce the computational burden. Additionally, volumetric meshes are employed to form three layers of volume meshes in the computational domain: coarse meshes with a side length of 100 mm, finer meshes with a side length of 50 mm, and the finest meshes with a side length of 25 mm. The finest meshes are closest to the HDVs, while the finer meshes are between the finest and coarse meshes. Additionally, a six-layer set of prism meshes with a thickness of 6 mm is also generated on the surface of HDVs to accurately capture the turbulence at the surface joins of each HDV. In total, there are 5,832,579 cells, 17,488,495 faces, and 6,344,171 vertices, modeling the virtual wind tunnel housing an HDV. To validate the mesh quality, we employed five well-established parameters: the face validity, cell quality, volume change, cell skewness angle, and chevron quality indicator. The assessment results demonstrate the high quality of our generated mesh, ensuring its suitability and reliability for subsequent analyses and simulations.

2.3.2. Boundary Conditions

The wind at the speed of 51.45 km/h enters from the inlet of the virtual wind tunnel and exits from the outlet. The inlet is a velocity inlet experiencing airflows that are applied to platooning HDVs, while the outlet is a pressure outlet with gauge pressures of 0 Pa. This study employs a relative motion methodology. The top and side surfaces of the computational domain are designated as symmetric planes. The ground is modeled as a moving ground with the same speed but opposite direction as the incoming airflow, and the HDV surface is treated as a no-slip wall to accurately simulate the relative movement between the HDV and the actual ground. This study adopts the turbulence intensity of 0.0025, which was used in NASA’s wind tunnel experiments. Additionally, for the turbulence viscosity ratio, a default value of 10 is employed, considered appropriate for moderate turbulence and being widely used in most experiments.

2.4. Calibration of the Virtual Wind Tunnel’s Settings

Besides the settings of the virtual wind tunnel, the convergence of our CFD model was also assessed in our study. During the CFD simulations, six variables or residuals of continuity, turbulent kinetic energy, turbulent dissipation, momentums in the X/Y/Z directions were closely monitored in the virtual wind tunnel. The simulation was stopped when one of the residuals or variables was lower than 10⁻³. It was noted that after 1000 iterations, the residuals of all six variables were below 10⁻³. This indicates that the CFD simulations of the single HDV reached their convergence.

After the virtual wind tunnel is configured for the HDVs, its settings need to be calibrated. In this study, we used the physical wind tunnel established by the NASA Ames Research Center as a baseline to calibrate the settings of the meshes and boundary conditions for the virtual wind tunnel. The aerodynamic drag coefficient was determined to be 0.4267.

Using the NASA’s physical wind tunnel configuration and testing results, we fine-tuned, for a single HDV, the mesh structure and the computational domain’s dimensions in the virtual wind tunnel, while keeping the Mach and Reynolds numbers and other boundary settings the same as the NASA wind tunnel. Through iterative refinement, a mesh structure was determined for the virtual wind tunnel, and the aerodynamic drag coefficient was determined to be 0.4241 for the single HDV, with an error of −0.61% when compared to NASA’s result (0.4267).

To further validate the accuracy of the CFD simulations, we tapped a set of sensors in the computational domain and compared the static relative pressures (or the virtual C_p values) obtained from these sensors to those within the NASA wind tunnel tests (or the NASA C_p values). Figure 5 illustrates the C_p distributions of these sensors along the testing HDV, with 0° yaw. The HDV was positioned at x = 13.33 cm, and the rear end of the HDV was at x = 259.39 cm. Visually, the virtual C_p values were consistently close to the NASA C_p values. The root mean square error (RMSE) between the two sets of C_p values was 0.0394, which indicates an excellent match between the two settings for the wind tunnel experiments.

2.5. HDV Platoon Configurations

After calibrating the virtual wind tunnel, we assumed that the settings and the boundary conditions for one HDV were applicable to the virtual wind tunnel containing multiple HDVs in a platoon. In this study, a series of platoons with multi-HDVs were placed within the virtual wind tunnel and CFD simulations were conducted using the mesh method. The boundary conditions were consistent with those for a single HDV. Additionally, we, for the simplicity of the CFD modeling process, assumed that all HDVs within a platoon share identical shapes and masses. Our study explored the aerodynamic drags of multiple HDVs in platoons, considering the effects of speed, inter-vehicle spacing, and platoon size and position. Moreover, the length of the virtual wind tunnel was extended to cover all the HDVs in a platoon. The distance between the rear of the last HDV and the exit of the wind tunnel was elongated to six times the length of a single HDV. Figure 6 illustrates the key terms of a platoon configuration containing multiple HDVs.

Platooning is particularly effective at higher speeds, reducing fuel consumption by 42% [41], but the relationship between HDV speed and aerodynamic drag is not well-documented. In China, freight HDVs operate between 70 and 100 km/h. Analyzing how HDV speed variations affect the platoon’s aerodynamic drag coefficient within this range is crucial.

Previous research has highlighted the impact of inter-vehicle spacing on aerodynamic drag, finding the inter-vehicle spacing a key factor in determining the drag coefficient. Our study examined aerodynamic drag coefficients across varying inter-vehicle spacings (from 0.125 to 2-times the length of an HDV), with a minimum inter-vehicle spacing of approximately 2.46 m. While this inter-vehicle spacing may be considered less safe in some studies, including it in our analysis enhances understanding of the aerodynamics between closely spaced HDVs.

Previous research has shown that larger platoons increase road capacity, but overly large platoons can cause unstable traffic flow and higher safety risks [42]. A 5–10 autonomous vehicle or six HDV platoon is considered optimal for energy savings [43]. Additionally, an HDV’s position in a platoon affects its aerodynamics. Current research often focuses on differences between lead and following HDVs, with less attention to aerodynamics at various positions. Our study addresses this by analyzing the impact of HDV position on aerodynamic drag.

Our research team developed 140 platooning configurations for CFD analysis. These configurations cover the HDV speeds of 70, 80, 90, and 100 km/h, the inter-vehicle spacings of 0.125 L, 0.25 L, 0.5 L, 0.75 L, 1 L, 1.5 L, and 2 L of the HDV length (L), and the platoon sizes of 2, 3, 4, 5, and 6 HDVs. Using these configurations, we have determined 560 (4 × 7 × (2 + 3 + 4 + 5 + 6)) sets of aerodynamic drag coefficients, C_dⁱ(v, ds, N), where i = {1, 2,…, N}, v is the speed of the ith HDV in a platoon configuration, d_s is the inter-vehicle spacing between the ith HDV and (i + 1)th HDV, and N is the number of the HDVs in a platoon configuration. For example, C_d²(70, 0.75 L, 4) indicates the aerodynamic drag coefficient of the second HDV in a 4-HDV platoon traveling at 70 km/h with a 0.75 L inter-vehicle spacing. In this study, a baseline set of aerodynamic drag coefficients is defined by C_d⁰(v), representing a single HDV driving on the truck lane at the speed of v = {70, 80, 90, 100}.

The computations for this study were executed on the AMD 256 queue of the BSCC-A2 supercomputing system in the Parallel Supercomputing Cloud Platform (Beijng PARATERA Tech Co., Ltd., Beijing, China) to manage and schedule computational tasks. The computing nodes are configured with AMD EPYC 7452 32-Core Processors, featuring 64 cores and 256 GB memory. For platoon formations consisting of four or fewer HDVs, a single node was sufficient, while for larger platoons involving five to six HDVs, two nodes were utilized to handle the increased computational load. The entire simulation process consumed approximately 200 h in total.

3. Results of CFD Simulations on Platooning HDVs

In this study, the aerodynamic drag coefficient of the i^th HDV in a platoon at a specific speed v is defined as C_dⁱ(v, d_s, N), the baseline aerodynamic drag coefficient at a specific speed v is C_d⁰(v), and the ratio of two drag coefficients is φ_i(v, d_s, N) = C_dⁱ(v, d_s, N)/C_d⁰(v). This ratio represents the normalized aerodynamic drag coefficient, which facilitates a more explicit and meaningful comparison across different operational scenarios. We assess the ratios of 140 platooning configurations from the view of HDV speed, inter-vehicle spacing, the position of an HDV in a platoon, and the size of the platoon. Our findings are as follows:

3.1. HDV Speed

The aerodynamic drag coefficient of a single HDV, C_d⁰(v), was observed to directly correlate with its operating speed. For the speeds of 70, 80, 90, and 100 km/h, the corresponding aerodynamic drag coefficient was measured to be 0.4342, 0.4321, 0.4303, and 0.4289, respectively.

The aerodynamic drag coefficients of multiple HDVs in a platoon are also governed by the speed of these HDVs. Figure 7 illustrates a platoon at various speeds and with an inter-vehicle spacing of 0.125 L between HDVs. When two HDVs are in a platoon, the second HDV experiences a declining φ_i(v, d_s, N) when compared to the first HDV at a specific speed. When a platoon has 3, 4, 5, or 6 HDVs, φ_i(v, d_s, N) presents a V-shape. Additionally, a slight upward trend is exhibited in φ_i(v, d_s, N), as speed increases from 70 to 100 km/h, with this trend being more pronounced in following HDVs. This trend is consistent across different scenarios, where φ_i(v, d_s, N) augments with increasing speed. This trend is less noticeable for the lead HDV, with relative extreme ranges of [0.12%, 1.48%] across different speeds. For following HDVs, the impact of speed is more significant, with relative extreme ranges of [0.13%, 6.52%]. As inter-vehicle spacing decreases, this effect intensifies. For example, at an inter-vehicle spacing of 0.125 L, the relative extreme ranges expand to [2.02%, 6.52%].

The influence of HDV speed on the average aerodynamic drag coefficient of a platoon varies across different scenarios. Figure 8 illustrates the impact of HDV speed on the average aerodynamic drag coefficient ${\overline{C}}_d\left(v,d_s,N\right)$ for different platoon sizes at inter-vehicle spacings of 0.125 L and 1.5 L. The results demonstrate that the influence of speed is more pronounced at smaller inter-vehicle spacings. Specifically, at 0.125 L, the relative extreme ranges of the average aerodynamic drag coefficient across different speeds ranged from 3.58% to 4.80%. When the inter-vehicle spacing is expanded to 1.5 L, this range narrowed to [0.91%, 1.30%]. Additionally, at inter-vehicle spacings of less than 0.5 L, increasing the speed from 70 km/h to 100 km/h results in a 2.77–4.92% increase in the average aerodynamic drag coefficient of the platoon, with this trend becoming more pronounced as the platoon size increases. This indicates that HDV speed is a significant factor in influencing aerodynamic drag under the conditions of smaller inter-vehicle spacings or larger platoon sizes. However, when the inter-vehicle spacing exceeds 1 L, or when the inter-vehicle spacing is greater than 0.5 L and the platoon size is less than five HDVs, the impact of HDV speed on aerodynamic drag can be considered negligible.

This phenomenon may potentially be attributed to the fact that under the conditions of relatively small inter-vehicle spacings, the airflows between HDVs interact strongly. In such circumstances, alterations in speed induce modifications in the airflows, which subsequently affect the interference of the airflows between the HDVs. Consequently, this exerts a more pronounced influence on the drag coefficient. Concurrently, when the platoon size is relatively large, accompanied by an increment in the number of HDVs, the overall blocking and perturbing effects of the entire platoon on the airflows are augmented.

3.2. Inter-Vehicle Spacing

Figure 9 highlights the variations of φ_i(v, d_s, N) under different inter-vehicle spacings for an HDV–HDV platoon. As the inter-vehicle spacing increases, the aerodynamic drag coefficients of both HDVs increase. Additionally, the trailing HDV experiences a φ_i(v, d_s, N) lower than the leading HDV because the leading HDV shields the trailing HDV from a significant portion of the oncoming flow, resulting in a notable reduction of aerodynamic drag in the trailing HDV. Furthermore, the trailing HDV’s aerodynamic performance is particularly sensitive to changes in the inter-vehicle spacing. As the inter-vehicle spacing increases from 0.125 L to 0.75 L, the φ_i(v, d_s, N) rises. When the inter-vehicle spacing is at 1 L or more, the leading HDV’s aerodynamic drag matches the baseline case (with a single HDV), while the trailing HDV experiences a reduction of φ_i(v, d_s, N), approximately 20% compared to the baseline case.

Figure 10 demonstrates the impacts of inter-vehicle spacings on φ_i(v, d_s, N) when a platoon moves at a speed of 100 km/h. Similar to the HDV–HDV platoon experiment, a positive correlation exists between inter-vehicle spacings and φ_i(v, d_s, N). Reducing the inter-vehicle spacings leads to a decrease in φ_i(v, d_s, N). Furthermore, the leading HDV performs aerodynamically consistently with that observed in the HDV–HDV configuration, with a significant reduction in φ_i(v, d_s, N) when the inter-vehicle spacing falls below 0.5 L. However, this reduction diminishes rapidly once the inter-vehicle spacing exceeds 0.5 L, becoming negligible when it reaches one vehicle length or 1 L. In the multiple-HDV configurations, the middle HDVs (or the HDVs from 2^nd to N − 1th) share similar aerodynamic behavior (that is, from low to high φ_i(v, d_s, N)). They reduce φ_i(v, d_s, N) substantially (42–65%). It is worth noting that the aerodynamic features of the last HDV are particularly interesting; when the inter-vehicle spacing is small, the last HDV experiences the highest φ_i(v, d_s, N) among the N − 1 number of HDVs ahead (or the HDVs except the leading HDV). As the inter-vehicle spacing exceeds 0.5 L, the last HDV experiences a gradual reduction in drag coefficient. When the inter-vehicle spacing surpasses one vehicle length or 1 L, the last vehicle exhibits the lowest aerodynamic drag coefficient within its platoon.

This peculiar behavior results from the fact that, when inter-vehicle spacings are reduced, the following HDV enters the low-pressure region formed by the wake of the leading HDV. This interaction markedly reduces the pressure differences between the adjacent HDVs, resulting in a decrease in φ_i(v, d_s, N). Conversely, when the inter-vehicle spacing increases, the following HDV transitions from the low-pressure wake region of the leading HDV. This shift results in a decrease of the slip-streaming effect and an intensification of dynamic pressure (directly proportional to the square of the fluid’s velocity) for the trailing HDV. Consequently, the drag-reducing influence of the wake on the trailing HDV is significantly diminished, leading to the higher φ_i(v, d_s, N) value. Figure 11 illustrates the slip-stream effect in a four-HDV platoon at the inter-vehicle spaces of 0.25 L and 1.5 L.

The influence of inter-vehicle spacing on the average aerodynamic drag coefficient of a platoon is highly significant. Figure 12 illustrates the ${\overline{C}}_d\left(v,d_s,N\right)$ variation in platoons of different sizes as a function of inter-vehicle spacing at a constant speed of 90 km/h. As the inter-vehicle spacing increases, the average aerodynamic drag coefficient for all platoon sizes demonstrates a marked increase. However, beyond an inter-vehicle spacing of 0.5 L, this upward trend becomes more gradual and displays the characteristics of a sigmoidal function for input values greater than 0. Notably, at inter-vehicle spacings below 0.5 L, increasing the platoon size substantially reduces the aerodynamic drag coefficient. This phenomenon can be attributed to the reduced inter-vehicle spacing, which enables trailing HDVs to more effectively utilize the wake generated by the leading HDV, thereby reducing air resistance. Conversely, at inter-vehicle spacings exceeding 0.75 L, the influence of platoon size on the aerodynamic drag coefficient diminishes, indicating that at larger inter-vehicle spacings, increasing platoon size has a limited impact on reducing overall aerodynamic drag. These findings suggest the necessity of balancing inter-vehicle spacing and platoon size when optimizing platoon configurations to achieve optimal aerodynamic performance and fuel efficiency.

3.3. Platoon Size and Position

The size of a platoon is crucial for fuel consumption, and the position of an HDV within a platoon also affects aerodynamics. Current research tends to focus on the differences in aerodynamic drag between the leading HDV and the following HDVs, with less attention paid to the aerodynamics at different positions. Our study pioneers this area by assessing the aerodynamic impacts of HDVs from the view of the HDV positions within platoons.

This study examines platoon sizes ranging from 2 to 6 HDVs. Figure 13 provides the φ_i(v, d_s, N) of HDVs within a platoon at 90 km/h. It describes a set of 42 cases (seven inter-vehicle spacings (0.125 L, 0.25 L, 0.5 L, 0.75 L, 1 L, 1.5 L, and 2 L) with six platoon sizes (two HDVs, three HDVs, four HDVs, five HDVs, and six HDVs)). The horizontal axis in each case represents the platoon size, while the vertical axis shows the φ_i(v, d_s, N) values. Each row in this figure represents φ_i(v, d_s, N) at a specific inter-vehicle spacing, while each column denotes the positions of the platooning HDVs. For instance, the top-left case illustrates the φ_i(v, d_s, N) values of the second HDV in a platoon ranging from two to six HDVs, with an inter-vehicle spacing of 0.125 L.

The experimental results demonstrate that the φ_i(v, d_s, N) values for the lead HDV remained remarkably consistent across all platoon sizes, with minimal variations that were nearly negligible. For HDVs positioned in the middle of the platoon (i.e., i ∈ [2, N − 1]), the φ_i(v, d_s, N) values showed only minor differences regardless of platoon size. However, the rear HDV (i.e., i = N) exhibited distinct behavior. Under typical inter-vehicle spacing, the φ_i(v, d_s, N) value of the rear HDV in a smaller platoon (e.g., with i = 4, and N = 4) was higher than that of the HDV in the same position within a larger platoon (i = 4, and N = 5). Consequently, from the perspective of reducing aerodynamic drag, the rear HDV has a greater incentive to encourage additional HDVs to join the platoon, thereby increasing the platoon size and effectively decreasing its own wind resistance. This discrepancy is particularly prominent with narrower inter-vehicle spacings, but as the inter-vehicle spacing increases, the diminishing trend becomes less obvious. Once the inter-vehicle spacing exceeds one vehicle length (1 L), the φ_i(v, d_s, N) values in the same position across different platoon sizes become almost indistinguishable. This also implies that decreasing inter-vehicle spacing motivates HDVs to form larger platoons, aiming to reduce the aerodynamic drag coefficient.

Figure 14 depicts the trend of the average aerodynamic drag coefficient of a platoon across varying sizes. For a fixed inter-vehicle spacing, the ${\overline{C}}_d\left(v,d_s,N\right)$ declines as the platoon size increases, but this reduction diminishes with greater inter-vehicle spacing. This behavior can be attributed to the low-pressure wake region generated by the front HDV in truck platooning, which significantly affects the aerodynamic drag experienced by the rear HDVs. Specifically, when the inter-vehicle spacing is less than 0.5 L, the rear HDVs are entirely within the wake region of the front HDVs, resulting in a substantial reduction in aerodynamic drag. As the inter-vehicle spacing increases, the rear HDV gradually moves out of the wake region, leading to a recovery of the airflow pressure to higher values. Consequently, the protective effect of the wake on the rear HDV diminishes, and the extent of aerodynamic drag reduction decreases accordingly. Cross-analyzing inter-vehicle spacing and platoon size confirms that, at smaller inter-vehicle spacings, expanding the platoon size has a more pronounced effect on lowering the aerodynamic drag coefficient.

4. Discussion

Previous research on platooning by Kospach et al. investigated the aerodynamic drag coefficients at speeds of 60 km/h, 80 km/h, and 90 km/h. Their findings revealed that the relative deviation of aerodynamic drag coefficients across these speeds was less than 2%, indicating that speed variations have a minimal effect on aerodynamic drag coefficients [44]. Building on this work, our study further explores the effects of HDV speed, demonstrating that significant influences primarily arise under conditions of reduced inter-vehicle spacing and larger platoon sizes. Specifically, when the inter-vehicle spacing exceeds 1 L or is greater than 0.5 L for platoon sizes of fewer than five HDVs, the impact of speed on aerodynamic drag becomes negligible.

In contrast, previous work by Robertson et al. analyzed a platoon of eight 1/20 scaled lorries at an inter-vehicle spacing of 0.5 L, 1 L, and 1.5 L. They found that the average aerodynamic drag coefficient for the entire platoon decreased with decreasing inter-vehicle spacing. Individual lorries within the platoon exhibited lower aerodynamic drag coefficients compared to isolated lorries, with the minimum drag occurring at the second truck for 0.5 L inter-vehicle spacing and at the rear lorry for the other two inter-vehicle spacings [45]. This finding contrasts with our results, where in platoons of three to six HDVs, the minimum aerodynamic drag coefficients peak at the second-to-last HDV under small inter-vehicle spacing conditions (less than half an HDV length). The disparities in the results could be attributed to variations in specific details of the vehicle models used, including vehicle shapes, body accessories, and size proportions, which can impact airflow patterns and consequently modify aerodynamic drag characteristics. Additionally, inconsistencies in experimental environmental conditions may contribute to the observed differences. Furthermore, drag coefficients decrease more rapidly for middle HDVs compared to rear HDVs at certain inter-vehicle spacings, although overall trends remain downward. Notably, Robertson et al.’s analysis focused solely on individual truck coefficients, omitting the overall platoon dynamics, which our study addresses by examining the average drag coefficients across different platoon sizes and inter-vehicle spacings.

Our observations suggest that the maximum and minimum drag peaks do not adhere to a straightforward monotonic pattern, potentially influenced by the structural attributes of the truck models used, as well as the methodological approach and experimental conditions.

5. Conclusions

This study employs a hybrid approach, combining wind tunnel experiments with CFD simulations to conduct an in-depth analysis of the aerodynamic drag in HDV platoons. Utilizing a 1:8 scaled HDV model developed by the U.S. DOE and calibrating it with wind tunnel data from the NASA Ames Research Center, we ensure the accuracy and reliability of aerodynamic drag coefficient predictions under various operating conditions. The synergistic application of CFD simulations and empirical wind tunnel tests has generated a dataset that closely aligns with physical experiments, significantly enhancing the credibility and precision of aerodynamic drag coefficient calculations. This robust comparative analysis lays a solid foundation for a more profound comprehension of aerodynamic interactions within multi-vehicle HDV platoons.

This study systematically analyzed the aerodynamic drag coefficient of HDV platoons by setting 140 CFD simulation scenarios, examining the impact of the operating speed, inter-vehicle spacing, and platoon size/position. Specifically, our findings have added an insightful observation that the effect of speed on the aerodynamic drag coefficient of platoons is limited, only becoming noticeably influential under the conditions of smaller inter-vehicle spacings and larger platoon sizes. This observation expands the understanding of the relationship between aerodynamic drag coefficients and platoon operating speed.

Our findings underscore the critical role of inter-vehicle spacing as the most influential factor on aerodynamic drag coefficients, with reduced inter-vehicle spacing leading to a significant decrease in drag coefficient. However, excessively small inter-vehicle spacing raises safety issues due to transmission delays and variations in braking performance. Additionally, minimal inter-vehicle spacing in platooned HDVs can cause inadequate ventilation, which could hinder cooling and lead to overheating and subsequent malfunctions. To balance safety and fuel efficiency, an inter-vehicle space is suggested in this study to be 0.25 to 0.5-times the HDV length (5 to 10 m in real-world conditions), which is already achievable in practical scenarios.

Our research reveals that as platoon size increases, there is an initial significant decrease in the overall aerodynamic drag coefficient, followed by a leveling-off of the reduction rate. The aerodynamic drag of the lead and middle HDVs remains relatively consistent across different platoon sizes and positions. However, the rear HDV is more strongly affected by changes in size, particularly when the inter-vehicle spacing is less than one vehicle length. This indicates that the rear HDV benefits more from expanding the platoon size to reduce its drag. This also suggests that reducing inter-vehicle spacing encourages the formation of larger platoons, which in turn lowers the aerodynamic drag of each HDV.

These insights are crucial for optimizing HDV platoon operations. Fleet operators and logistics enterprises can tailor parameters based on vehicle performance, road conditions, and platoon size. Our research highlights optimal inter-vehicle spacing as a strategic tool for maintaining safety and reducing aerodynamic drag, leading to energy savings, lower CO₂ emissions, and improved environmental sustainability. Compact inter-vehicle spacing also enhances road capacity and traffic flow efficiency. Furthermore, increasing the platoon size significantly reduces overall aerodynamic drag, particularly in platoons of three or more HDVs compared to conventional two-HDV formations. This allows better departure scheduling strategies to form larger platoons.

However, this study has several limitations. It is important to recognize that the mesh structure employed in this study, which was initially validated for a single HDV, may possess certain limitations in accurately capturing the complex details and effects of multi-HDV interactions. It did not account for the impact of diverse vehicle models on aerodynamic drag, limiting the findings to specific or similar models. Differences in vehicle configurations and dimensions can lead to varied aerodynamic behaviors within the platoon. Additionally, the long-term effects of speed variations on drag were not fully explored, despite speed fluctuations being common in real-world driving conditions.

Future research should consider the aerodynamic traits of different vehicle models, building models that integrate their unique features and analyzing their drag coefficient variations. The long-term impacts of speed changes on aerodynamic drag should also be examined. While our research method improves prediction accuracy, further experimental validation may be necessary for practical applications.