Aerodynamic Performance Analysis on Various Wheel Con�gurations of Commercial Vehicle

In this study, the aerodynamic characteristics of wheel layouts in commercial vehicles, including dual and tandem axle wheels, were investigated using Computational Fluid Dynamics (CFD) with isolated and in-vehicle systems. For the dual wheel system, an increase in oﬀset distance reduced the drag by up to 31.2% for the Fackrell A2 wheels thanks to the decrease in the low pressure area behind the wheels. In the case of tandem wheel conﬁguration, drag increased as the axle spread increased. As the axle spread increases, the rear wheels move out of the slipstream of the front wheel, causing a sharp increase in drag, while the front wheels’ drag remains constant across all axle spreads. In a realistic commercial vehicle model, the same trend was observed. An increase in oﬀset distance reduced the drag by approximately 4.30%, and the increase in axle spread increased the drag by 4.62%. These results are expected to contribute to the improvement of fuel eﬃciency and the reduction of greenhouse gas emissions by reducing the aerodynamic drag of commercial vehicles.


Introduction
Owing to the growing concern over climate change and the environment, greenhouse gas emissions and fuel consumption regulations are becoming increasingly stringent.This trend has significantly raised the importance of aerodynamic design in vehicles.
According to the New European Driving Cycle (NEDC), about 6.7% of the fuel energy and approximately 29.5% of the energy transmitted to the wheels in passenger vehicles are consumed as aerodynamic drag.For commercial vehicles, the aerodynamic drag's impact is increasing, up to 13.6% [1].
The rotating wheel and the flow field around them significantly influence vehicle's aerodynamic performance.In open-wheel racing cars, approximately 40% of the total drag [2], 25% in passenger vehicles [3], and approximately 30% in commercial vehicles induced from the wheels, wheelhouses, and vehicle underbody [4].This proportion of aerodynamic resistance from the wheels and wheelhouses could increase in electric vehicles with smooth and simplified underbody configurations compared to internal combustion engine vehicles.
Owing to its growing importance, research on the flow field around the rotating wheels and the wheelhouse has been a long-standing field.Fackrell conducted experiments to measure the pressure on the tire surface and the drag and lift forces on rotating independent wheels [5], [6].Subsequently, Mears and Dominy et al. analyzed the drag and lift forces on the isolated racing wheel and the flow field around the wheel using advanced measurement methods like Particle Image Velocimetry (PIV) and predict the jet-flow on the rotating wheel using CFD [7], [8], [9].
Various observation techniques have emerged to measure the forces on the wheel more accurately, and modern wind tunnels capable of rotating wheels through a fivemoving belts system have facilitated studies examining the effects of wheel rotation accurately.
Mercker and Breuer analyzed the changes in lift and drag on passenger vehicles because of wheel rotation, suggesting that simulating wheel rotation reduces aerodynamic drag [10].Elofsson et al. conducted wind tunnel experiments and showed that simulating the rotation of rear tires induces upwash at the vehicle's rear, significantly impacting the vehicle's drag coefficient [11].Wiedemann described how the ground effect and rotation of the wheel in wind tunnels could alter the yaw angle of the airflow impacting the front tire, potentially causing variations in the drag coefficients of vehicle components like the front spoiler and rear wing [12].Wickern et al. analyzed technical approaches for measuring forces on rotating wheels in wind tunnels, confirming that wheel and tire drag could account for up to 25% of a vehicle's total drag [3].
Wäschle experimentally verified through Laser Doppler Velocimetry (LDV) the effects of rear tire wake interfering with the vehicle's underbody flow owing to wheel rotation and compared this with computational results [13].
The numerical study of rotating independent wheels, conducted by Axon et al., led to numerous studies using computational analysis methods [14].Croner et al.
compared their URANS analysis using the ONERA k-kL turbulence model with wind tunnel results, demonstrating that CFD flow analysis can replicate wind tunnel results and closely match PIV measurement data.Additionally, they analyzed the reasons for the oscillation of drag and lift forces over time [15].Haag et al. compared unsteady flow analysis using DDES with PIV data and has good agreement in accuracy in capturing vortices shedding from the rim based on its shape.They also highlighted the significant increase in computing resources required for flow analysis using sliding mesh techniques [16].
This literature survey shows that the flow around rotating wheels and wheelhouse has been studied through various experiments and analyses, not only for isolated wheels but also within realistic vehicle models.However, very little research has been reported on the aerodynamics of dual wheel or tandem axle wheel systems which are widely used in commercial vehicles.Recalling that more than 13.6% of energy is wasted to overcome the aerodynamic drag of commercial vehicles, understanding of aerodynamic characteristics of dual and tendem axle systems with and without vehicles is very necessary.
Therefore, this study aims to analyze the flow characteristics and the drag generation mechanism of wheels with various dual and tendem axle configurations using state-of-the-art CFD techniques.This approach facilitated a comparison of the effects of geometric configuration on aerodynamic characteristics such as drag and lift and the analysis of how these changes affect the flow field around the wheel and tire.Finally, it is expected that the understanding of flow and aerodynamic characteristics of wheel layout systems can be applied to the aerodynamic design of commercial vehicles with high efficiency with low greenhouse gas emissions.

Numerical Method
The commercial CFD program, ANSYS Fluent V2023-R1, was utilized for the flow simulation of rotating wheels in a realistic vehicle model.RANS (Reynolds Averaged Navier-Stokes) equations with a Realizable k − ϵ turbulence model were used for the accurate simulation of highly turbulent three-dimensional flow.
The Moving Reference Frame (MRF) technique was used to implement the rotation of the wheel and tire to improve accuracy and efficiency [17] [18] [19] [20].It is well known that the MRF technique shows more accurate results than those of movingwall treatment [21] and efficieny increases about 4.2 times that of the sliding mesh method [16] for the simulation of the wheel rotation.
Changes in flow characteristics in accordance with geometric configurations were quantitatively compared through drag, lift, and pressure coefficients on the tire surface.
Qualitative analysis was also conducted using pressure distribution and Q-criterion iso-surface around the flow field.
Simulations were performed using 48 cores of Xeon CPUs, and it took approximately 10 hours of wall clock to obtain a converged solution using a grid system composed of 46 million cells for commercial vehicles.

Geometry Modeling
The purpose of this study is to examine changes in aerodynamic characteristics according to wheel layout and propose design guidelines for reducing the aerodynamic drag of commercial vehicles.
For this purpose, the Fackrell A2 wheel, as illustrated in Figure 1, was selected as the reference wheel shape.The diameter of the wheel is 0.416m, and the width is 0.191m.Because detailed geometric and wind tunnel test data are available, extensive validations have been performed throughout numerous research works.For the dual wheel case, offset distance was non-dimensionalized based on the wheel's diameter.Offset distance varies from 0.0D to 0.20D by increasing the distance between two wheels.For the tandem wheel case, similar non-dimensionalization was performed for the axle spread based on the wheel diameter.Analyses were conducted for the axle spread of 1.1D to 4.0D with the offset distance from 0.05D to 0.20D.

Similar approaches have been conducted for the realistic vehicle model shown in
The axle spread varies from 1.1d to 3.3d with the offset distance from 0.0d to 0.1d, while the wheel diameter is 1, 090mm, as shown in Figure 4.
Table 1 presents simulation cases with respect to the axle spread and offset distance.

Validation
The analysis technique was validated through comparison with existing experimental data [5] [6] at the inlet velocity of 18.6m/s and wheel rotating velocity of 854 rpm.For the mesh convergence study, different mesh sizes were set for the far field boundary, Body of Influence(BOI) area, MRF zone, Tire, and contact patch as shown in Table 2 while the non-dimensional wall distance y + remains constant(0.482mm).
The sesulting number of cells varies from 1.4 to 12.0 million.The distribution of y + on the tire surface obtained from the analysis results is shown in Figure 6.Except for certain parts of the rim, the non-dimensional wall distance is in the range of 30 and 100, so it is judged that the requirements of the first mesh size are generally well satisfied.For the mesh convergence study, surface pressure distributions for various mesh systems were compared with wind tunnel test values as shown in Figure 7.The pressure peak occuring around 90 drgress could not be accurately predicted due to technical difficulties ariging from the contact patch treatment between the tire and the ground.However, it can be seen that the prediction is acceptable for the flow acceleration (azimutal angle from 360 to 290 degrees), and resulting low-pressure area (azimutal angle from 90 to 290), as the number of computational meshes increases.respect to the number of computational meshes.As shown in Figure 8, there is a small discrepancy between Fackrell's experimental data [5] and the predicted ones.
However, as the number of meshes increases, predicted C d and C l converge to the wind tunnel test, which shows mesh convergence.In the point of aerodynamic drag and lift coefficients, it was observed that the system with 4.8Mil.cells showed an error of approximately 0.4% and 0.36% in C d and C l compared to those of Fackrell's experiments, respectively.
Additionally, the Q-criterion from 4.8Mil.mesh result was used to visualize the flow structure around the tire in Figure 9 (a).Comparre with other researcher's work shown in Figure 9 (b), it was confirmed that the numerical methods used in this research work accurately reproduced flow features around the isolated wheel, such as arch-shaped vortices in the tire wake, flow separation, and jetting between the tire and ground.Thus, from both quantitative and qualitative points, mesh resolution parameters for 4.8Mil.case was set to be a reference for efficient computation and used for dual and tandem wheel configurations.Figure 10 shows the detailed volume mesh of the dual and tandem wheels.In the case of the wheels in the commercial vehicle, to set up the flow domain and create the computational meshes around the vehicle with various wheel layout systems, symmetry condition was used for efficient computation.
To make the first mesh size of the viscous layer y + ∼ 30, the height of the first layer was set to 0.849mm and 0.629mm for the vehicle body and wheel & tire combination, respectively.Here, the vehicle's driving speed is 15.42m/s and the wheel rotating velocity of 135 rpm.Partial views of the computational meshes are shown in Figure 11.

Dual Wheels
In the isolated wheel system, the aerodynamic characteristics of dual wheels with various offset distances were compared through drag and lift coefficients.Based on the Fackrell A2 wheel, a total of five cases were selected by increasing the offset distance in increments of 0.05d from 0.00d to 0.20d.As the offset distance increases, it can be seen that the pressure recovery behind the tire increases significantly.Particularly in the 0.20d case, which has the most significant offset distance, the interaction between the two tires became weaker, which means that the tires act more independently.
Also, a relatively large stagnation pressure area is observed around the front of the tire when the two tires are relatively close.The pressure coefficient distribution also shows that the decrease in the low-pressure area is not only in the flow direction (x-dir) but also in the vertical direction (z-dir) of the tire with the increase in offset distance.
When the tires are closer together (small offset distance), the confined space restricts the airflow, leading to a more substantial jetting effect as the air is forced out at high velocities from the limited openings at the ends of the tires.However, as the offset distance increases, the space between the tires widens, providing more space for the air to flow through.This larger passage area reduces the velocity and force of the air being expelled, decreasing the size of the air jet.

Tandem Wheels
The aerodynamic performance of tandem axle tires was analyzed by increasing the axle spread in cases with offset distances of 0.05d and 0.20d.The axle spread was also non-dimensionalized based on the wheel diameter and varied from 1.1d to 4.0d.
As shown in Figure 14 (a), when examining the drag coefficient for each case compared to the wind tunnel results of the single Fackrell A2 wheel, it is observed that the drag coefficient increases as the axle spread increases in both offset distance cases.However, in the offset distance of 0.05d case, the drag coefficient does not increase significantly.It remains almost constant until the axle spread reaches 2.0d; subsequently it increases sharply.In contrast, in the 0.20d offset distance case, the drag coefficient continuously increases as the axle spread increases.Conversely, as shown in  In both the 0.05d and 0.20d offset distance cases, the drag coefficient of the front tire remains almost constant, nonetheless, an increase in axle spread.Similarly to the dual tire cases, the drag coefficient of the front tire in the 0.05d case is higher than that of 0.20d.However, the rear tire shows different tendencies depending on the offset distance.In the 0.20d case, the drag coefficient of the rear tire gradually increases as the axle spread grows.Conversely, in the 0.05d case, the drag coefficient remains similar to a 2.0d axle spread but increases sharply subsequebtly.This phenomenon is shown in Figure 16, which shows the pressure coefficient distribution on the z = 0.5D plane through the center of the wheel and y = const plane through the center of the right tire.As observed in the dual tire cases, when the offset distance is close, a more extensive low-pressure area is created behind the front tire.This results in the rear tire remaining longer within the slipstream of the front tire, leading to the observed trends in drag coefficient.Therefore, the drag coefficient of the rear tire at 0.05d case increases in stiff when the axle spread is bigger than the wake size of the front tire.However, in the 0.20d case, which has a relatively large offset distance, the slipstream of the front tires is much smaller than that of the 0.05d case.Thus, even a small increase in the axle spread makes the rear tire out of the slipstream, which results in the gradual drag increase of the rear tires.

In-Vehicle System
The effect of offset distance and axle spread on the aerodynamics and flow characteristics of the commercial vehicle are investigated.Simulations were conducted with various offset distances and axle spreads, as shown in Figure 4, using the configuration shown in Figure 11.
Figure 17, which compares the drag coefficient of the vehicle, reveals that an increase in tire offset distance leads to a reduction in drag coefficient regardless of the value of axle spread.Maximum decrease of aerodynamic drag can be expected up to 4.3% at the offset distance of 0.1d and axle spread of 1.1d.This indicates that widening the offset distance can effectively reduce aerodynamic drag.Otherwise, increasing the axle spread increases the drag coefficient, which is the same tendency as that of isolated tandem wheel cases.This indicates that the greater the distance between the axles, the higher the drag coefficient for both the isolated wheel and in-vehicle systems.The significant influence of offset distance on the drag coefficient can be explained by the pressure coefficient distribution on the z = 0.5D plane through the wheel axis and symmetry plane shown in Figure 18.
Figure 18 shows the pressure distributions with the offset distance of 0.0d and 0.1d at the axle spread of 1.1d.It demonstrates that an increase in the offset distance between the front and rear tires leads to pressure recovery around the tires and is consistent with previous findings from the isolated wheel system.This change in pressure distribution with increasing offset distance, as shown in Figure 18 (c)(d), raises the pressure at the rear of the vehicle, thereby reducing the overall drag of the vehicle.
On the other hand, an increase in axle spread in commercial vehicles leads to an overall increase in drag.Figure 19 shows the pressure distributions with the offset distance of 0.1d at the axle spread of 1.1d and 3.3d.As illustrated in Figure 19 of In the in-vehicle system, the variations in drag due to changes in offset distance and axle spread exhibit similar tendencies to those observed in the isolated system.This consistency in the trend is because both parameters(offset distance and axle spread) affect the pressure recovery around the wheels, which in turn influences the vehicle's overall drag.
Thus, a shorter axle spread combined with an increased offset distance significantly reduces drag.Therefore, maximizing the offset distance with a short axle spread is highly effective in reducing the drag of commercial vehicles.
This finding emphasizes the need to consider both offset distance and axle spread in tandem when designing commercial vehicles for optimal aerodynamic performance.

Conclusions
This study analyzed the flow characteristics around various wheel geometric configurations in isolated wheel systems and within commercial vehicle systems.The findings highlight that the geometric configuration of wheels significantly influences aerodynamic and flow characteristics.
1. Dual wheel cases showed a decrease in drag coefficient with increased offset distance between the tires.This drag reduction is maximized in 31.2% between 0d and 0.20d offset distances, attributed to the reduction in the size of the low-pressure area behind the tires.
2. In tandem wheel cases, an increase in axle spread across all offset distances increased the drag coefficient.Whereas the drag coefficient of the front tire remained constant for all axle spread, the rear tire's drag coefficient increased with axle spread.This increase is due to the rear tire's escape from the front tire's slipstream.
3. In the realistic commercial vehicle model, an increase in tire offset distance led to a maximum drag reduction of 4.3%, assisting in pressure recovery at the rear.Conversely, an increase in axle spread led to an increase in drag coefficient, consistent with the trend in the isolated tire system.

Fig. 2 :
Fig. 2: Detailed geometry of realistic commercial vehicle model

Fig. 3 :
Fig. 3: Description of offset distance and axle spread

Figure 2 .
Figure 2. Vehicle geometry was simplified by removing the engine bay, fuel tank, chassis systems, and so on for simulation efficiency.The dimensions of the commercial vehicle model are: width W veh = 2, 450mm, length L veh = 11, 000mm, and height

Figure 5 Fig. 4 :Fig. 5 :
Figure 5 illustrates the flow domain and detailed mesh system of the Fackrell A2 single wheel, (a) shows the simulation domain, (b) BOI (Body Of Influence) area, (c) MRF area, and (d) zoomed-up view of boundary layer meshes around contact patch between tire and ground.Because the turbulent model used in this study is a Realizable k −ϵ model, the first layer height is set to 0.482mm to get the non-dimensional wall distance y + ∼ 30 based

Fig. 6 :
Fig. 6: y + distribution on the tire surface of isolated single Fackrell A2 wheel

Fig. 10 :
Fig. 10: Detailed mesh system of isolated dual and tandem wheel based on Fackrell A2 wheel

Fig. 11 :
Fig. 11: Detailed mesh system of in-vehicle system

Figure 12 (
Figure 12 (a) and (b) show the drag and lift coefficient with respect to the offset distance.As the offset distance increases, the drag coefficient gradually decreases.In the case of the offset distance of 0.20d, the drag coefficient decreases by approximately 31.2% compared to that of the 0.0d case.Regarding the lift coefficient, a similar trend can be obserbed in Figure 12 (b).Approximately 25% of lift reduction happened as the offset distance increased.

Fig. 12 :
Fig. 12: Drag and Lift coefficient of dual wheel case

Figure 14 (
Figure 14 (b), no significant changes can be observed in the lift coefficient.

Fig. 15 :
Fig. 15: Drag coefficient of the front and the rear tire with tandem axle wheel

Fig. 17 :
Fig. 17: Drag coefficient in-vehicle system with various offset distance and axle spread

Table 1 :
Operating systems and conditions

Table 2 :
Target size for the mesh resolution