Numerical Analysis of Aerodynamic Drag Reduction for a DrivAer Automobile Model Using Rear Air Jets

Abstract

This paper presents a numerical investigation into aerodynamic drag reduction by air jets for a realistic DrivAer estateback vehicle model. Numerical simulations are conducted based on Reynolds-Averaged Navier–Stokes equations with a shear stress transport k-ω turbulence model, for optimizing the drag reduction with seven individual rear slot jets and their combination. The results demonstrate that the jets located at the upper and lower edges of the rear end could achieve the highest individual drag reduction of up to 4.82%, by suppressing recirculation bubbles, delaying flow separation, and promoting pressure recovery. The jet positioned at the lower lateral side of vehicle base reduces the drag by 4.14% through the control of the underbody vortex. Moderate performance is observed for other individual jets within the wake flow. The underlying mechanisms are elucidated by detailed analyses of wake flow fields and rear-end surface pressure distributions. On this basis, optimal performance is obtained by a multi-jet combination, incorporating the best vertical jet and three better horizontal jets, which collectively yield a remarkable 11.80% drag reduction with high energy efficiency. This work confirms that the active flow control by the rear air jets can greatly improve the aerodynamic efficiency for realistic vehicles, providing a practical approach for drag reduction in modern automotive applications.

1. Introduction

Aerodynamic drag is a dominant resistance force for ground vehicles, accounting for over 50% of the total driving resistance at highway speeds, which directly affects fuel consumption, energy efficiency, and environmental sustainability [1,2,3]. With stringent global regulations on carbon emission and fuel economy, reducing aerodynamic drag has become a critical focus in automotive design and research [4,5,6]. Studies indicate that a 10% reduction in drag can lead to approximately 5–7% improvement in fuel efficiency, translating to significant cost savings and reduced greenhouse gas emissions over the whole vehicle lifespan [7,8,9]. This urgency has driven extensive investigations into both passive and active flow control strategies to minimize the drag force [10,11,12,13].

Most of the foundational studies in vehicle aerodynamics rely on simplified models to isolate key flow phenomena and reduce complexity [14,15,16]. The Ahmed body, introduced in the 1980s, has been widely adopted as a generic bluff body to study wake structures and drag mechanisms across various slant angles [14]. The flow is characterized by a separation bubble on the rear window, longitudinal C-pillar vortices, and recirculation regions behind the vertical base, all contributing to drag coefficients [17]. Passive flow control strategies, such as rear spoilers, wheel deflectors, air curtains, and vortex generators, have been employed to manipulate these flow structures. For example, Fukuda et al. [18] reported a 2% drag reduction using a rear spoiler, while Sebben [19] achieved up to 4% reduction with front wheel deflectors. Shankar and Devardjane [20] demonstrated a 4.5% drag reduction through vortex generators on a simplified passenger vehicle. However, passive methods are limited by their fixed geometry and inability to adapt to varying driving conditions.

In contrast, active flow control techniques offer dynamic and potentially more efficient drag reduction by using external energy input to modify flow structures in real time [21,22,23,24]. These methods include steady or pulsed blowing, suction, synthetic jets, and plasma actuators. On the Ahmed body, studies have shown significant advantages of active strategies. Brunn et al. [25] used steady blowing near the C-pillar to weaken the longitudinal vortices, achieving a drag reduction of up to 10%, while Aubrun et al. [26] applied microjets on the rear window, reducing drag by 14%. Joseph et al. [13] employed pulsed jets to delay flow separation, resulting in an 8% drag reduction. More recently, combinations of multiple actuations have been explored. Zhang et al. [12] reported a 29% drag reduction on the Ahmed body using integrated blowing slots, highlighting the synergy between different control strategies. Despite these advances, most of the studies focus on overly simplified models like the Ahmed body, which lack the geometric complexity of real vehicles, such as detailed underbodies, wheels, mirrors, and engine bays, limiting the practical applicability of findings to production cars.

Recently, the DrivAer model was developed as a more realistic generic vehicle, incorporating features from the production cars like the Audi A4 and BMW 3 Series [27]. It offers modular configurations—fastback, notchback, and estateback—and includes optional details such as side mirrors, underbody geometry, and rotating wheels, providing a better representation of actual automotive flows. As a realistic generic vehicle, active flow control strategies show greater attraction, without changing the original shape of the model. However, there are currently few studies on this topic. Baek and Lee [28] investigated continuous blowing on the DrivAer estateback model, achieving up to 7.5% drag reduction at high Reynolds numbers, but their study is limited to roof and C-pillar blowing without comprehensive parametric analysis. Nabutola and Boetcher [29] assessed air-jet wheel deflectors on the notchback DrivAer, observing modest drag reductions of 1.5% at higher speeds but noting inefficiencies at lower velocities. According to these studies, a systematic investigation of active control on the wake flow of the DrivAer model, particularly for the high-drag estateback configuration, is still lacking, and the existing work fails to explore the combined effects of multiple actuations or detailed flow mechanisms.

This study aims to conduct a comprehensive numerical analysis of the aerodynamic drag reduction for the DrivAer estateback model by using rear air jet actuation. The numerical setups keep consistent with the wind tunnel test conditions in Ref. [27], for achieving a stable drag coefficient that is slightly affected by further increase in Reynolds number. Under this condition, drag reduction by a rear slot jet is investigated to obtain a relatively general strategy. The numerical approach employs the Reynolds-Averaged Navier–Stokes (RANS) equations with Shear Stress Transport (SST) k-ω turbulence model, which exhibits lower accuracy compared to Detached/Large Eddy Simulation, but offers a balance between computational efficiency and accuracy for capturing the complex wake flow [28,30,31]. On these bases, the effects of air jets from seven slots positioned on the rear end of the model are investigated individually, to identify optimal jet velocities and angles for drag reduction. Then, the mechanisms underlying drag reduction are elucidated through detailed analysis of wake flow fields and surface pressure distributions. Finally, the optimal jet configurations are combined to explore synergistic effects and maximize the drag reduction of over 11% with high energy efficiency, which is the main contribution of the present work.

2. Numerical Setup

2.1. Estateback Model

The DrivAer estateback model exhibits a structural design analogous to that of sport utility vehicles characterized by a relatively high drag coefficient, thereby offering significant potential for drag reduction. In this study, the numerical simulations are conducted based on the estateback model configured with a smooth underbody and standard tires, as shown in Figure 1. This model is scaled at 1:2.5, resulting in final dimensions of 1.85 m (L) × 0.70 m (W) × 0.57 m (H), which are consistent with the experimental model in wind tunnel tests [27]. In addition, an 8 mm trim at the tire bottom simulates the compressed state under vehicle load conditions.

2.2. Governing Equation and Numerical Method

The numerical simulations are performed based on the three-dimensional (3D) incompressible RANS equations (expressed by Einstein notation):

$${\displaystyle \frac{\mathsf{\partial }{\overline{u}}_i}{\mathsf{\partial }{x}_i}}=0$$

(1)

$${\displaystyle \frac{\mathsf{\partial }{\overline{u}}_i}{\mathsf{\partial }t}}+{\overline{u}}_j{\displaystyle \frac{\mathsf{\partial }{\overline{u}}_i}{\mathsf{\partial }{x}_j}}=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\mathsf{\partial }\overline{p}}{\mathsf{\partial }{x}_i}}+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }{x}_j}}\left[\left(\nu +{\nu }_t\right)\left({\displaystyle \frac{\mathsf{\partial }{\overline{u}}_i}{\mathsf{\partial }{x}_j}}+{\displaystyle \frac{\mathsf{\partial }{\overline{u}}_j}{\mathsf{\partial }{x}_i}}\right)\right]$$

(2)

where $\overline{u_i}$, $\overline{u_j}$, and $\overline{p}$ represent the time-averaged velocity components and pressure, and x_i and x_j are the Cartesian coordinates. ρ and ν denote the air density and kinematic viscosity. ν_t is the turbulent eddy viscosity, provided by the SST k-ω turbulence model [32]:

$${\displaystyle \frac{\mathsf{\partial }k}{\mathsf{\partial }t}}+{\overline{u}}_j{\displaystyle \frac{\mathsf{\partial }k}{\mathsf{\partial }{x}_j}}=P_k-{\beta }^{*}\omega k+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }{x}_j}}\left[\left(\nu +{\sigma }_k{\nu }_t\right){\displaystyle \frac{\mathsf{\partial }k}{\mathsf{\partial }{x}_j}}\right]$$

(3)

$${\displaystyle \frac{\mathsf{\partial }\omega }{\mathsf{\partial }t}}+{\overline{u}}_j{\displaystyle \frac{\mathsf{\partial }\omega }{\mathsf{\partial }{x}_j}}=\alpha {\displaystyle \frac{\omega }{k}}{P}_k-\beta {\omega }^2+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }{x}_j}}\left[\left(\nu +{\sigma }_{\omega }{\nu }_t\right){\displaystyle \frac{\mathsf{\partial }\omega }{\mathsf{\partial }{x}_j}}\right]+2(1-F_1){\displaystyle \frac{{\sigma }_{\omega 2}}{\omega }}{\displaystyle \frac{\mathsf{\partial }k}{\mathsf{\partial }{x}_j}}{\displaystyle \frac{\mathsf{\partial }\omega }{\mathsf{\partial }{x}_j}}$$

(4)

where k, ω and P_k are the turbulent kinetic energy, the specific dissipation rate and the production of turbulent kinetic energy, and F₁ is the blending function. α, β*, β, σ_k and σ_ω are the constant coefficients [32].

These governing equations are solved by commercial software Star CCM+ (Version 2022) using the finite volume method with second-order spatial accuracy. The pressure-based segregated flow solver is adopted for the steady flow solution, by using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The under-relaxation factors of pressure and velocity are set to 0.3 and 0.7. The initial conditions are set based on the inlet velocity and outlet pressure. The computation is considered convergent when the residuals drop below 10⁻³ with minor fluctuations, and the monitored force stabilizes around a constant value over the last 1000 iterations.

2.3. Computational Domain and Boundary Condition

For this realistic vehicle model, the numerical simulation demands higher mesh resolution and therefore more computational resources. Thus, a half-model is used to balance the computational efficiency with the realistic flow representation. The size of computational domain is set to 20 × 4 × 5 m³, as shown in Figure 2. The estateback model is positioned with its head 2L from the inlet and its tail 8L from the outlet, creating a total domain length of 11L. The width and height are set to about 10W and 10H, yielding a blockage ratio of approximately 1%. This configuration ensures sufficient space for the complete flow development around this vehicle, particularly in the wake region.

To keep consistent with the wind tunnel test condition in Ref. [27], the inlet velocity V₀ is set to 40 m/s, achieving a Reynolds number of 4.87 × 10⁶. The pressure on the outlet is set to 1 atm. The rotating wall condition is applied to the wheels, while the slip wall condition is imposed on the top, side and ground boundaries. The boundary conditions are summarized in

Table 1. Summary of boundary conditions.

Boundaries	Setups
Inlet	Velocity inlet, 40 m/s, 0.5% turbulence intensity
Outlet	Pressure outlet, 1 atm
Symmetry plane	Symmetry
Top, side and ground	Slip wall
Car body	Stationary wall
Wheels	Rotating wall

.

2.4. Mesh Division and Numerical Validation

Trimmed meshes are employed with six prism layers near the model surface, ensuring that most y⁺ values are below 10 for accurately capturing the boundary layer, as shown in Figure 3. This meshing strategy enables us to generate as many 3D hexahedral grids as possible. In addition, the two refinement regions are implemented: a 32 mm cell zone around the vehicle body and a 16 mm cell zone in the wake. The total number of meshes reaches approximately 9.7 million.

Under the above numerical setup, the drag coefficient C_d (defined by Equation (5)) of the Estateback model is determined to be 0.2780. Then, the mesh independence is evaluated by varying both the prism layers and the global cell size, resulting in 5.4, 11.8, 15.4 and 20.1 million meshes. The corresponding drag coefficients are 0.2522, 0.2789, 0.2784 and 0.2792 shown in Figure 4 and

Table 2. Comparison of C_d by different mesh numbers.

	Mesh Number (Million)	Cd	ΔCd
Coarse	5.4	0.2522	−0.0258
Baseline	9.7	0.2780	---
Refined-1	11.8	0.2789	+0.0009
Refined-2	15.4	0.2784	+0.0004
Refined-3	20.1	0.2792	+0.0012

, which demonstrate convergence over 10 million meshes. Compared to the result by the baseline mesh of 9.7 million, the values of ΔC_d by the refined meshes are less than 2 counts (0.002). Thus, the baseline mesh presents the optimal balance between the computational accuracy and efficiency.

$$C_d={\displaystyle \frac{F_d}{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\rho V_0^2{A}_f}}$$

(5)

where F_d and A_f represent the aerodynamic drag force and frontal area of the model.

By using the baseline mesh, the simulation result of C_d is 0.2780 with a relative error of 4.8%, compared to the wind tunnel test data of 0.292 (with moving ground, freestream turbulence intensity of 0.4%) by a multi-component balance [27]. This error is similar to the numerical result using the same turbulence model in Ref. [31]. Further validation against the experimental pressure coefficient (C_p, defined by Equation (6)) at 12 monitoring points along the vehicle centerline (measured by pressure taps with an accuracy of ±0.15% [27]) shows good agreement, with a maximum error of less than 0.05 in Figure 5, confirming the accuracy of the numerical setup.

$$C_p={\displaystyle \frac{p-p_0}{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\rho V_0^2}}$$

(6)

where p₀ is the inlet pressure.

3. Drag Reduction by Single Slot Jet

In this section, the fundamental flow structures in the wake of the original vehicle model will be analyzed at first. Then, the positions of seven rear jet slots are determined based on the main vortical structures and the surface pressure distribution. Finally, a systematic analysis is conducted on the drag reduction performance of each individual slot jet, for identifying their optimal jet velocities and angles. The underlying flow mechanisms responsible for drag reductions and the exploration of combined slot configuration will be discussed in Section 4 and Section 5.

3.1. Wake Structure of Original Model

Because of the highly 3D characteristics of the vortical structures, the wake flow will be investigated using five streamwise sections (including symmetry plane) and five transverse sections, as illustrated in Figure 6. The streamwise section Y1 is positioned 150 mm from the symmetry plane, while transverse section X1 is located 60 mm downstream of the trailing edge of the vehicle model. The other adjacent sections are spaced 50 mm apart.

Figure 7 shows the vorticity distributions and velocity streamlines of the original wake flow without slot jets. The streamlines on the symmetry plane clearly reveal that the shear layers separating from the upper edge of the rear window and the lower edge of the vertical base roll up to form a pair of separated recirculation bubbles—an upper and a lower bubble—which is similar to the wake structure of the low-drag Ahmed body [17]. Correlating with the pressure distribution on the rear surface (Figure 8), it is observed that the upper and lower recirculation bubbles correspond to the low-pressure regions on the rear window and the base, respectively. A region of weaker vorticity between the two bubbles aligns with a high-pressure zone on the base surface, termed the central high-pressure region shown in Figure 8. The strengths and positions of the recirculation bubbles directly influence the pressure distribution on the rear-end surface, which determines the aerodynamic drag of the entire vehicle to a great extent.

The streamlines on streamwise sections Y1–Y4 indicate an obvious downstream movement of the upper recirculation bubble along the spanwise direction, suggesting that the vortex legs incline toward the downstream flow field. Figure 8 shows that a slight pressure recovery occurs on the upper lateral region of the base, as the vortex legs of the upper bubble move away from the rear end. Conversely, the vortex legs of the lower bubble tilt upstream, causing a pressure decrease on the lower lateral region of the base. Under the high Reynolds number of 4.87 × 10⁶, the drag coefficient tends to be stable and slightly affected by the further increase in Reynolds number [27,28]. This enhances the entrainment of the shear layers from the roof and underbody, causing the recirculation bubbles to locate at a more stable and downstream position. Consequently, the spacing between the two bubbles increases, leading to a large central high-pressure region on the base surface, as shown in Figure 8.

The flow on the lateral side of the vehicle model separates near the D-pillar. Then, driven by the pressure difference, the separated shear layer rolls up along the D-pillar toward the rear window, forming the D-pillar vortex [12]. This vortex significantly impedes the pressure recovery on the rear window, leading to a substantial increase in the drag coefficient. Actually, the rear-end of the estateback model is similar to that of the low-drag Ahmad model, and therefore the D-pillar vortex is very weak and vanishes quickly [17], leading to a small low-pressure region on the rear window in Figure 8. Instead, a pair of trailing vortices originating from the downstream tilting legs of the upper recirculation bubble shows large scale in Figure 7, which is the real source of the ‘vortex drag’ [1]. Transverse sections X1–X5 clearly depict the formation and evolution of the trailing vortex, whose scale and intensity gradually increase downstream (and then dissipate further downstream). The formation of the trailing vortex relies on the low pressure in the upper recirculation bubble, while it also exerts a downwash effect that promotes the flow reattachment on the rear window. In addition, a vortex rotating opposite to the trailing vortex can be observed near the lower part of transverse sections, called the lower vortex. This vortex primarily originates from the underbody flow rolling upwards along the lateral side of the vehicle, and suppresses the pressure recovery on the base, as shown in Figure 8.

3.2. Slot Location

Based on previous studies on the active drag reduction for the Ahmed body, seven slots (A–G) are implemented on the rear end according to the wake flow of this realistic vehicle model, as shown in Figure 9. Slots A–D are oriented horizontally, while E–G are vertical. The projected width of each slot perpendicular to the jet direction is set to 8 mm. To preserve the model aesthetics, the slots are aligned with the characteristic lines. Slots A and D are positioned at the upper and lower edges of the rear end to effectively suppress flow separation near the rear window and the base (i.e., the upper and lower recirculation bubbles), thereby enhancing the pressure recovery on these surfaces. Slots B and C are located at the lower edge of the rear window and the middle of the base surface, respectively, aiming to actively control the internal flow of the recirculation bubbles. The three vertical slots (E–G) are situated on the lateral side of the rear end to prevent the side flow rolling up towards the symmetry plane, thus reducing the intensities of trailing and lower vortices.

For the steady slot jet, its angle and velocity are two critical parameters to determine the drag reduction. The jet angle primarily affects the coupling characteristics between the slot jet and the surrounding flow field, while the jet velocity reflects the overall intensity of the interaction. The jet velocity is set to a certain percentage of the freestream velocity. The jet direction aligned with freestream is defined as 0°. Figure 9 illustrates the positive and negative jet angles of horizontal and vertical slots.

3.3. Drag Reduction

This section investigates the drag reductions of horizontal and vertical slots under different jet velocities and angles to identify the optimal parameters for each slot jet. Based on the analysis in Section 3.1, slot jets aligned with freestream are more likely to suppress the developments of the upper/lower recirculation bubbles and the trailing/lower vortices, potentially yielding better drag reduction. In addition, the optimal jet velocities for different angles are generally similar [12]. Thus, for each slot, the optimal jet velocity is first determined at a fixed angle of 0°, and then the jet angle is optimized. However, for slots exhibiting poor drag reduction (or even adverse effects) and unclear trends with jet velocities, it indicates a severely unsuitable initial jet angle. In such a case, the optimal angle is identified first, followed by velocity optimization.

Since slot jet actuation consumes energy, the drag reduction and energy consumption must be considered together. The net power saving ΔP [33] evaluates the practical benefit of active flow control:

$$\Delta P={\displaystyle \frac{1}{2}}\rho V_0^3{A}_f\left(C_{d0}-C_{d1}\right)-{\displaystyle \frac{1}{2}}\rho V_j^3{A}_j$$

(7)

where C_d0 and C_d1 are the drag coefficients without and with slot jet actuation, and V_j and A_j are the jet velocity and slot area. In addition, it is noted that the term ‘Ref.’ in all subsequent figures denotes the baseline drag coefficient of 0.2780 and the corresponding flow fields without jet actuation, providing a reference for assessing drag reduction performance.

3.3.1. Horizontal Slot

For horizontal slots A–D, the jet angle is initially fixed at 0° to determine the optimal jet velocity for the best drag reduction. According to Figure 10a, slots A, C, and D achieve optimal drag reductions at jet velocities of 60%, 30%, and 60% of the driving speed. The corresponding drag coefficients are reduced to 0.2729, 0.2727, and 0.2663 with drag reduction rates of 1.83%, 1.91%, and 4.21%, respectively. Then, under the optimal velocities, the optimal jet angles for the three slots are determined, as shown in Figure 10b. The best drag reductions occur at angles of −20°, −5°, and +10°, respectively, reducing the drag coefficients to 0.2676, 0.2691 and 0.2646 with drag reductions of 3.74%, 3.20%, and 4.82%. In addition, the net power savings for these configurations are all positive in

Table 3. Optimal drag reduction parameters for horizontal slots.

Slot	Jet Velocity	Jet Angle	Cd	Reduction Rate	Net Power Saving
A	60%	−20°	0.2676	3.74%	105.87 W
B	45%	50°	0.2706	2.66%	74.87 W
C	30%	−5°	0.2691	3.20%	111.35 W
D	60%	10°	0.2646	4.82%	128.68 W

, which means the feasibility of their practical application.

For slot B, a 0° jet not only fails to reduce the drag, but has a negative impact on the drag reduction. This indicates a highly suboptimal initial angle. Thus, the jet angle is first optimized at 100% driving speed. Figure 11a shows that the best drag reduction occurs at 50°, reducing the drag coefficient to 0.2742 with a small reduction rate of 1.37%. Then, the optimal jet velocity is achieved at 45% driving speed, as shown in Figure 11b. The drag coefficient can be reduced to 0.2706 (reduction rate of 2.66%) with a positive net power saving. The performance of slot B is inferior to the other horizontal slots, which is consistent with the conclusion for the Ahmad body [12].

The optimal jet parameters for the horizontal slots are summarized in Table 3. Among them, slots A and D at the upper and lower edges of the rear end yield the best results. Their optimal angles directing inward into the wake make the two jets act as the extended fluid walls of the roof and the underbody, smoothing the shear layer–wake interactions and enlarging the central high-pressure region. Inner slots B and C transport kinetic energy downstream to move the upper and lower bubbles downstream, improving the pressure recovery on the rear window and the base surface, respectively. Notably, slot C achieves considerable drag reduction at the lowest jet velocity, but the net power saving is still lower than slot D with a higher jet velocity.

3.3.2. Vertical Slot

Following the same methodology, the optimal jet velocities for vertical slots E-G are first determined at a fixed angle of 0°, as shown in Figure 12a. Slots F and G achieve optimal drag reductions at 90% and 65% driving speed, reducing drag coefficients to 0.2731 and 0.2665 with drag reduction rates of 1.76% and 4.14%, respectively. Slot E instead increases the drag, without a clear correlation with the jet velocity, but shows a local minimum drag coefficient at 100% driving speed. Then, it is tentatively regarded as the reference jet velocity for the subsequent angle optimization. Figure 12b shows that the best drag reductions for slots E-G occur at angles of 5°, −5°, and 0°, reducing drag coefficients to 0.2726, 0.2727, and 0.2665 with drag reduction rates of 1.94%, 1.91% and 4.14%, respectively. However, the net power saving is negative for slot E, and it causes a sharp drag increase when the jet angle exceeds 10°.

The optimal drag reductions for the vertical slots are summarized in

Table 4. Optimal drag reduction parameters for vertical slots.

Slot	Jet Velocity	Jet Angle	Cd	Reduction Rate	Net Power Saving
E	100%	5°	0.2726	1.94%	−86.2 W
F	90%	−5°	0.2727	1.91%	11.0 W
G	65%	0°	0.2665	4.14%	131.5 W

. The optimal jet angles are all close to the freestream, which is consistent with our assumption based on the wake flow structures. Slot G effectively controls the lower vortex near the underbody and then promotes pressure recovery on the base surface, yielding the maximum drag reduction rate. Slots E and F present minimal drag reductions, because the rear end of the estateback model resembles the low-drag Ahmed body where the trailing vortex is weaker. Thus, the active controls for the trailing vortex produce insignificant benefits. In addition, slot jet E is not feasible in practical application because of its negative net power saving.

4. Underlying Flow Mechanism of Single Slot Jet

This section will provide a comprehensive analysis of the underlying flow mechanisms responsible for drag reduction by the seven slot jets, based on the wake flow structure and the surface pressure distribution. The discussion is divided into two parts for horizontal slot jets A–D and vertical slot jets E–G, respectively.

4.1. Drag Reduction Mechanism of Horizontal Slot Jet

According to the conclusions in Section 3, horizontal slots A and D located at the upper and lower edges of the rear end yield the most significant drag reduction, while slots B and C positioned at the lower edge of rear window and the middle of vertical base exhibit relatively weaker performance. Thus, the drag reduction mechanisms of these two groups of horizontal slots are analyzed separately below.

4.1.1. Slots A and D

The jet angles of slots A and D are both aligned with the local flow direction. Thus, the slot jets act like extended “fluid walls” to prolong the roof and the underbody surfaces. This allows a smoother coupling of the shear layers (at the upper/lower edges of the rear end) and the wake flow.

Figure 13 shows that slot jet A delays the flow separation point on the rear window. Then, the upper recirculation bubble becomes smaller and moves downstream, increasing the spacing between the upper and lower recirculation bubbles. In addition, the movement of the upper recirculation bubble increases the pressure on the rear window, which could effectively suppress the formation and development of the D-pillar vortex and the trailing vortex, as shown in Figure 14. As a result, the central high-pressure region is expanded greatly, and the pressure on the rear window side can be further improved, as shown in Figure 15. However, the vortex on the roof is induced by the slot jet A, but it dissipates rapidly downstream and does not seriously affect the pressure recovery on the rear window. These flow modifications ultimately lead to a significant improvement of the pressure recovery on the entire rear-end surface shown in Figure 15, resulting in substantial drag reduction.

Similarly, slot jet D delays the lower recirculation bubble, and indirectly causes an obvious downstream movement of the upper recirculation bubble. The spacing between the two bubbles is also markedly increased, as shown in Figure 13. These contribute to the improved pressure recovery on the rear window and the central high-pressure region, as shown in Figure 15. In addition, Figure 14 shows that the trailing vortex is noticeably suppressed, enhancing the pressure recovery on the rear window side, but another vortex induced by this slot jet appears near the lower vortex. This vortex leads to the inward contraction of the central high-pressure region, but does not seriously affect the pressure recovery on the base, as shown in Figure 15. Overall, the flow control by slot jet D yields better drag reduction than that achieved by slot A.

4.1.2. Slots B and C

Slot B is located at the lower edge of the rear window, within the mid-region of the upper recirculation bubble. Its jet could generate an additional pair of small, high-intensity recirculation bubbles behind the rear window, which significantly shifts the large upper recirculation bubble downstream and suppresses the development of the trailing vortex, as shown in Figure 16 and Figure 17. According to the pressure distribution on the rear surface of Figure 18, this pair of small bubbles creates another small local high-pressure region on the rear window. In addition, although the trailing vortex is suppressed, the small lower bubble with stronger intensity extends across the entire window, leading to much lower pressure distribution at the bottom and the lateral side of the window. Nonetheless, the overall pressure recovery on the rear window is slightly improved (Figure 18). As for the base surface, the movement of the upper recirculation bubble and the increased spacing between the upper/lower bubbles result in an expanded central high-pressure region with higher pressure recovery.

Slot C is located near the lower recirculation bubble. Figure 16 shows that this jet shifts the lower bubble downstream and transports kinetic energy to the base flow, compensating for the viscous dissipation caused by the lower bubble. This significantly increases the pressure on the lower part of the base surface, as shown in Figure 18. In addition, the upper recirculation bubble also indirectly moves downstream, leading to a considerable pressure increase on the rear window. The increased spacing between the upper and lower bubbles causes the central high-pressure region to move upward, with substantially improved pressure recovery. Furthermore, the formation of the trailing vortex is greatly suppressed according to Figure 17, which enhances the pressure recovery on the lateral side of the rear window.

4.2. Drag Reduction Mechanism of Vertical Slot Jet

The three vertical slot jets E–G are positioned along the lateral side of the rear end, with their jet directions closely aligned with the incoming flow. This configuration could effectively weaken the entrainment of the side flow toward the symmetry plane, thereby suppressing both the trailing vortex and the lower vortex.

Slot E is located near the D-pillar. Its jet impedes the entrainment of the separated flow from the lateral side toward the rear window, allowing the upper recirculation bubble to fully develop and shift its vortex core downstream, as shown in Figure 19. Meanwhile, the trailing vortex formation and its intensity are greatly suppressed, as shown in Figure 20. These modifications greatly enhance the pressure recovery on the rear window (Figure 21). Moreover, the downwash effect of the trailing vortex on the upper recirculation bubble is considerably weakened, causing the upper bubble to move upward and increasing the spacing between the two recirculation bubbles. This leads to the upward shift of the central high-pressure region with higher pressure recovery.

Slot F is positioned at the lateral side edge (upper part) of the base. This jet directly reduces the entrainment of the separated side flow rolling up towards the base surface, thereby improving the pressure recovery on the base side and expanding the high-pressure region, as shown in Figure 21. The recirculation bubbles and the trailing vortex have no obvious changes (Figure 19 and Figure 20), and then the rear window remains a low-pressure distribution (Figure 21). As a result, this slot jet shows the smallest effect on the drag reduction, which is consistent with the result in Section 3.3.2.

Slot G is situated at the lateral side edge (lower part) of the base. This jet could effectively suppress the lower vortex intensity near the underbody (Figure 20), increasing the pressure on the lateral side of the base surface (Figure 21). Meanwhile, the lower recirculation bubble develops more fully and then lifts the upper recirculation bubble (Figure 19), which benefits the pressure recovery on the base and the rear window (Figure 21). The increased pressure on rear window indirectly weakens the trailing vortex (Figure 20), further improving the pressure recovery on the window side (Figure 21). In addition, the larger spacing between two recirculation bubbles (Figure 19) expands the high-pressure region with the higher pressure distribution (Figure 21). All these factors contribute to a significant improvement of the pressure recovery on the rear surface, making the drag reduction far superior to that by slots E and F.

5. Combined Slot Jet Configuration

This section investigates the optimal combination of multiple slot jets to achieve maximum drag reduction. The parameters for each slot jet are selected based on their individual optimal values identified in the previous sections. Although the coupled effects among different jets may prevent this approach from achieving the global optimum, the resulting drag reduction rate from the best configuration obtained here is close to the sum of the individual drag reduction rates, which demonstrates the feasibility and efficiency of this optimization approach to a certain extent.

5.1. Combination Strategy and Drag Reduction Performance

Based on the conclusions in Section 3, the most effective horizontal jets are from slots A and D, while slots B and C also achieve considerable drag reductions (approximately 3%). Among the vertical slots, slot G performs best, whereas slots E and F yield negligible drag reduction (less than 2%). Moreover, slot E exhibits a negative net power saving, making it impractical. Therefore, the optimization begins with the combination of the best horizontal slots (A and D), followed by the gradual incorporation of other slots to maximize the drag reduction.

As summarized in

Table 5. Drag reduction by combined slots.

Slot	Cd	Reduction Rate	Net Power Saving
A+D	0.2621	5.72%	131.3 W
A+D+G	0.2561	7.88%	191.0 W
A+B+D+G	0.2452	11.80%	311.3 W
A+B+C+D+G	0.2531	8.96%	203.5 W
A+B+D+E+F+G	0.2435	12.41%	194.2 W

, the combination of slots A and D reduces the drag coefficient to 0.2621, corresponding to a drag reduction of 5.72%, which is less than the sum of their individual contributions because of the overlapping drag reduction mechanisms between the two slots. Then, the best vertical slot G is further added to reduce the drag coefficient to 0.2561, achieving a drag reduction of 7.88% with a high net power saving of 191.0 W. Slots A, D and G are all located at the edges of the rear end. Next, incorporating the internal horizontal slot B (at the lower edge of the rear window) can substantially reduce the drag coefficient to 0.2452, yielding a remarkable drag reduction of 11.80% which is close to the sum of the maximum individual drag reductions of slots ABDG (15.36%). In addition, the net power saving remains very high (311.3 W), indicating excellent energy efficiency. Although slot B alone performs poorly, it plays a significant role in the combined configuration. However, adding slot C increases the drag coefficient to 0.2531 with drag reduction reduced to 8.96%, and therefore it should be abandoned in the combination. Finally, further incorporating slots E and F into the optimal combination (ABDG) slightly reduces the drag coefficient to 0.2435 with a drag reduction of 12.41%, but the net power saving drops significantly to 194.2 W. Considering both the drag reduction and energy efficiency, the optimal combination is determined to be slots A+B+D+G.

5.2. Flow Mechanism of Optimal Slot Combination

The flow mechanisms underlying the best-performing combination (slots ABDG) will be analyzed in this section. As shown in Figure 22, the jets from the three edge slots (ADG) act as the extended “fluid walls”, leading to a smoother coupling of the shear layer from vehicle side with the wake flow. This delays the separation point on the rear window, and the recirculation bubbles obviously move downstream with lower intensity and larger spacing. These are beneficial for the pressure recovery on the rear end and meanwhile enlarge the central high-pressure region. In addition, slot jet B generates an additional pair of small recirculation bubbles, which further shifts the upper recirculation bubble downstream and suppresses the development of the trailing vortex (Figure 23), enhancing the pressure recovery and creating an additional high-pressure region on the rear window (Figure 24). These flow modifications collectively result in a great improvement in the pressure recovery on both the rear window and the base surface, with the most notable increase in the central high-pressure region which also expands considerably (Figure 24).

The vorticity distributions on transverse sections in Figure 23 reveal that the increased pressure on the rear window and the movement of the recirculation bubbles greatly suppress the formation and intensity of the D-pillar and trailing vortices, thereby enhancing the pressure recovery on the rear window side (Figure 24). In addition, slot jet G directly suppresses the lower vortex near the underbody (Figure 23), increasing the pressure on the lower side of the base (Figure 24). However, slot jets A and D interact with the incoming flows from the roof and the underbody, generating two additional vortices above the trailing vortex and the lower vortex, respectively (Figure 23). The two vortices dissipate quickly downstream and have negligible impact on the pressure recovery on the side of the rear end surface (Figure 24). In addition, the vortex near the base side greatly strengthens (Figure 23), leading to a noticeable pressure drop in the upper corner of the base surface (Figure 24). Apparently, this region is very small and would not significantly impact the overall drag reduction performance.

6. Conclusions and Future Work

This study comprehensively investigates the application of active flow control via rear slot jets to reduce the aerodynamic drag on a realistic vehicle model, and provides insights into the underlying flow mechanisms, performance optimization and practical applicability.

Slots A and D, positioned at the upper and lower edges of the rear end, perform the best individually in the horizontal slot jets, with the drag reductions of 3.74% and 4.82%, respectively. These jets act as the extended fluid walls, smoothing shear layer–wake interactions, moving recirculation bubbles downstream, and enlarging the central high-pressure region. The best vertical slot G, situated at the lateral side edge (lower part) of the base, achieves a 4.14% drag reduction by effectively suppressing the lower vortex and enhancing the base pressure recovery. Slots B and C offer moderate reductions (~3%), while slots E and F show minimal effects (≤2%), with slot E exhibiting negative net power saving.

The combined configuration of slots A+B+D+G yields a considerable drag reduction rate of 11.80% with high net power saving, demonstrating the highly efficient energy utilization and flow control synergy. Adding slot C reduces the performance, while incorporating slots E and F only slightly improves the drag reduction to 12.41% at a much lower energy efficiency. The best-performing slots delay separation point and suppress key vortical structures (including D-pillar, trailing, and lower vortices), leading to the downstream movement of the recirculation bubbles, the increased spacing between upper/lower bubbles, and the significant expansion of the central high-pressure region. These ultimately promote the entire pressure recovery on the rear end and greatly reduce the aerodynamic drag of the vehicle.

In conclusion, this work demonstrates that the targeted active flow control using rear slot jets could potentially enhance the aerodynamic performance in realistic vehicle models, achieving considerable drag reduction and energy savings according to the numerical analyses. These results provide valuable insights into the design of active flow control systems for realistic vehicle geometries, contributing to the development of aerodynamic drag reduction strategies and the improved energy efficiency in automotive applications.

Future work will focus on experimental validation through wind tunnel tests to verify the accuracy and practical applicability of the active drag reduction effects. Additionally, we plan to explore the integration of slot jet actuation with wheel spoilers, aiming to develop an adaptive wheel drag reduction system that can dynamically adjust to varying driving conditions.