Abstract
The reduction of fuel consumption has become one of the main targets in the automotive industry. To achieve this objective, drag reduction plays a major role and one of the techniques that has become attractive in recent years is the use of active flow control (AFC). In the present paper, Computational Fluid Dynamics (CFD) simulations are used to study the application of synthetic jets (SJ) as AFC devices in the flow around a station wagon (SW). The main purpose of this study is to determine the viability of these devices in the overall aerodynamic performance of the vehicle but especially in drag reduction. A baseline case (no actuation) of the simulation of the flow around the SW was initially performed and the drag coefficient was validated with experimental data from a coast-down test. Using the baseline results, two zones for the synthetic jet outlets were defined in the rear part of the SW, one located in the Upper Side (US) and the other in the Lateral Side (LS). Numerical results show that the synthetic jets actuation effectively affects the dynamics of the flow and the near wake, and a reduction of the drag (∼1%) with an increment in the lift (∼20%) was observed with actuation in US. A lift coefficient reduction (∼33%) with a drag increment (∼4%) was also observed with SJ actuating in LS. Nevertheless, due to the high momentum coefficient required by the SJ, a simple estimation of the energy required to operate the SJ shows that it is higher than the energy saved due to the combination of drag reduction and lift increment.
1 Introduction
Nowadays, high fuel prices and strict environmental regulations have increased the necessity to improve road vehicle aerodynamics and fuel consumption. In the specific case of vehicles with speeds above 70 km/h, the aerodynamic drag is responsible for most of the fuel consumption (). In this way, the implementation of active flow control systems emerges as a viable alternative for the reduction of aerodynamic loads without altering the geometrical design of the vehicle.
In general, flow control can be divided into passive or active depending on the energy input requirements. Passive Flow Control (PFC) techniques include the use of geometrical elements or devices that modify the boundary layer close to the surface of the vehicle. Most of the elements for PFC have been extensively tested and used in aircraft aerodynamics with very good results. Among the elements that have been used are Vortex Generators, spoilers, flaps and other vehicle body modifications such as surface dimples, diffusers and vanes (; ). Active Flow Control (AFC) is based on the use of an actuator (fluidic or plasma ()) that requires an energy input to energize the boundary layer close to the surface of the vehicle to modify the development of the boundary layer. The main objective of AFC applied to road vehicles is related to the manipulation and control of the vortical structures in the wide separated region that a typical road vehicle has. In the case of fluidic actuators, AFC can be achieved using jets arrays in the surface of the vehicle. These jets could be operated with steady blowing or suction, pulsed or Synthetic Jets (SJ). A SJ consists of a cavity with an orifice (that connects the cavity with the outer flow) in which one of the cavity walls is a diaphragm that moves harmonically such that the air is sucked in and out from the cavity. The net mass flow from the SJ outlet is zero but the momentum is not, so that the characteristic of the outer flow can be manipulated depending on the strength of the SJ.
SJs stand out among the various modalities of active flow control and their effect on drag reduction has been demonstrated in simplified vehicles such as Ahmed body. This is a simplified ground vehicle geometry introduced as a benchmark configuration to study the fundamental aerodynamic characteristics of road vehicles. It consists of a rounded front section, a constant cross-section mid-body, and a slanted rear surface, which allows controlled investigation of flow separation and wake structures (). For example, successfully implemented pulsating jets to an Ahmed body, obtaining an 8% reduction in the drag coefficient. Additionally, using the same model but in a different study, they demonstrated that the use of pulsating micro-jets produced by micro-actuators with MEMS technology (Micro Electro Mechanical Systems) allows to obtain a similar reduction in drag, but with a better energy balance and greater efficiency compared to standard technology (). conducted wind tunnel experiments of active flow control with SJs in an Ahmed body with a slat angle of 25°. It was found that the drag reduction highly depends not only on the momentum coefficient (Cµ - See Equation 2) of the jet but also on the Reynolds number ( - where is the density, is the freestream velocity, L is the length of the body and is the viscosity). An 8.5% drag reduction was obtained for Re = 1.2 × 106 in comparison to only 6.5% of reduction at Re = 1.9 × 106. also performed experiments with an Ahmed body with a slant angle of 25° and Re = 1.4 × 106. Fluidic actuators similar to SJs were placed at the roof-slant interface of the Ahmed body using momentum coefficients between 2.4 × 10−3 and 3.7 × 10−2. Experimental results show a drag reduction of up to 15% and highly dependable on Cµ; the higher Cµ the higher drag reduction. A basic estimation of the power requirements for operating the actuator shows that for Cµ = 2.4 × 10−3 was the only case in which the power requirements were less than the power saved due to drag reduction, all other configurations show higher power demands. performed wind tunnel experiment of an Ahmed body with a slant angle of 25° with AFC based on pulsed jets. The Reynolds number based on the length of the model was 1.4 × 106 which corresponds to a freestream velocity of 30 m/s. A drag reduction of 20% was reported with a pulsed jet with a frequency of 550 Hz and Cµ = 2.75 × 10−3. It is important to mention that this Cµ corresponds to a jet peak velocity of 50 m/s which is almost twice the freestream velocity. Unfortunately, the authors did not perform an estimation of the energy saved due to drag reduction and compared it against the energy requirements due to the flow control. Nevertheless, these results confirm the need to increase the knowledge of physical phenomena occurring with and without control of the flow around ground vehicles.
The application of AFC to realistic passenger vehicle geometries remains considerably more challenging. Many of the largest aerodynamic improvements reported in the literature were obtained using simplified bluff-body configurations, such as square-back or slanted Ahmed bodies, where the wake topology is dominated by relatively organized large-scale structures. In contrast, realistic passenger vehicles generate highly three-dimensional wakes characterized by complex interactions between upper and lateral shear layers, asymmetric vortex dynamics, curvature effects, and multiple coupled separation regions. These phenomena substantially increase the complexity of the flow physics and reduce the effectiveness of localized flow control strategies. There are few experimental studies related to AFC on real passenger car geometries. For example, implemented an active flow control using steady jets on a 1:4 model of a real vehicle, and approached the application of an AFC system with micro-actuators in a real-scale production vehicle. In both cases, the control seems to be less efficient on drag coefficient than the previous results obtained with a simplified vehicle model: Heinemann et al. obtained a maximum drag decrease of 2% with a momentum coefficient Cµ = 6.8 × 10−3, and Aider et al. just a 0.8% decrease in drag with Cµ = 0.24. Also, in both studies, this drag decrease was obtained with an increase in lift, while a lift reduction was obtained at the cost of more drag. On a different approach, performed wind tunnel experiments on the DrivAer notchback model using sweeping jets as AFC technique. The momentum coefficients used in the different configurations ranged from 2 × 10−4 to 1.8 × 10−3 and that the total energy consumption of the jets was approximately 3 kW. The maximum drag reduction was 3.5% with significant changes in the downforce (between −25% to +38% depending on the actuation). These previous investigations on realistic vehicle geometries have shown that the drag reduction levels achieved using AFC are generally lower than those obtained for canonical bluff-body models. Besides this, no comparison has been reported of the power required by the actuators with respect to the actual power saved due to drag reduction. Studies involving realistic automotive configurations have reported that the effectiveness of synthetic jets and pulsed jets is strongly dependent on actuator placement, forcing frequency, jet orientation, and the interaction between the injected momentum and the naturally occurring wake instabilities. In many cases, although measurable modifications of the wake topology and aerodynamic coefficients are obtained, the global energetic efficiency of the control strategy remains limited because the momentum required to manipulate the large separated wake structures becomes comparable to or even exceeds the aerodynamic power savings.
Furthermore, recent investigations have emphasized that realistic vehicle wakes cannot be interpreted solely through classical simplified bluff-body behavior. The wake dynamics of passenger vehicles involve highly unsteady and coupled three-dimensional coherent structures that respond differently to forcing depending on the location and orientation of the actuation system. In particular, tangential or streamwise-oriented synthetic jets have been shown to provide more effective momentum transfer into the boundary layer and improved separation control compared to wall-normal actuation, especially in separated external aerodynamic flows (). Given this complexity of the flow, numerical simulations emerge as a viable tool for the understanding of the effects of synthetic jets as AFC method in realistic car geometries. There are several references found in the literature related to the simulation of AFC with SJs. For example, performed 2D simulations of a simplified vehicle model using Partially-Averaged Navier-Stokes (PANS) as turbulence model. A drag reduction of 15% was found when the SJ was actuated at a Strouhal number of 0.17, which is in very good agreement with the Large Eddy Simulations (LES) performed by . performed a computational study of the AFC with jets of the flow around an Ahmed body with a slant angle of 25°. The best case (highest drag reduction) was achieved with jets located at the rear slant surface with a reduction of 22% in the drag coefficient. The authors do not mention or compute the energy requirements of the jets used in the best case, but it is worth mentioning that the velocity of the jets was 6.62 m/s which is approximately 1/3 of the free-stream velocity (21 m/s). performed a computational study of the flow around a truck cabin with AFC at a Reynolds number of 5 × 105. The AFC had two components: 1) An oscillating motion was imposed on the cabin and 2) SJs located at the A-pillar. Numerical simulations were performed with the PANS turbulence model which was initially validated against LES. In general, in all the actuated cases a reduction of the drag was observed with an averaged value of approximately 10%. Other beneficial effects in the flow were observed such as flow stabilization and a reduction in the size of the recirculation regions. performed Large Eddy Simulation (LES) of the flow around and Ahmed body with a slat angle of 25° with a zero-mass active flow control. Numerical results show a reduction of 30%–40% in the drag coefficient. performed a technical review of SJ actuators for different applications including automotive and bluff bodies. It was identified that one of the main gaps is the scaling up from scale models such as Ahmed body to real passenger cars (3D complexity with all the geometrical details). performed a review of flow control (both active and passive) for road vehicles focused on drag reduction. More specifically, it was found that flow control based on synthetic jets have the potential for reducing drag in about 10%. It is important to mention that most of the literature reviewed in this context was related to simple geometries such as Ahmed body.
Although all these works have contributed to great progress in the study of active flow control in ground vehicles, there is still a need for further investigation of AFC techniques applied to realistic vehicle geometries, particularly regarding the relationship between wake modification, aerodynamic performance, and energetic efficiency. The main objective of the present study is to evaluate the impact of an active flow control (AFC) with synthetic jets on the aerodynamics of a Station Wagon (SW) through Computational Fluid Dynamics (CFD). In comparison to previous studies using SJs, the primary focus of the present study is to evaluate higher Reynolds numbers (almost double), higher slant angles (>30 deg) and explore AFC in more a realistic passenger vehicle configuration characterized by complex three-dimensional wake structures. The study evaluates the influence of synthetic jet location, forcing frequency, and momentum coefficient on the aerodynamic performance and wake topology. Additionally, special attention is devoted to the global energy balance associated with the actuation system in order to assess the practical viability of synthetic jet technology for automotive drag reduction applications. It is important to mention that race cars are out of the objective of this paper, neither to compare different AFC techniques that have been used in passenger cars but to focus on the use of synthetic jets in the reduction of drag and global energy consumption in this kind of vehicle. For this, a simplified CAD model of a SW based on a Subaru Legacy Outback model 1998 was used. Based on the analysis of the wake of the unactuated flow at a Reynolds number of 2.7 × 106 (), two actuation slots were configured in: a) the upper zone of the vehicle along the rear spoiler, and b) just before flow separation in the D-pillar. SJ boundary conditions are modeled as simple inlet-outlet without the details of the cavity and the motion or deformation of the diaphragm. The SJ velocity profiles were modelled with a sinusoidal signal with Cµ in the range of 3.4 × 10−4 to 1.4 × 10−2, and an actuation frequency of 250 and 400 Hz which corresponds to a reduced frequency (F+ and defined in Equation 3) of 33 and 54 respectively. All the non-dimensional parameters are based on the free-stream velocity of 19.4 m/s and a characteristic length of 2.62 m (Wheelbase) and air at a temperature of 17 °C and an altitude of 2,568 m above sea level (site of the road-test for experimental data). Finally, in order to explore the viability of AFC based in SJ in this type of ground vehicles, a systematic approach using CFD is presented, in which the primary focus is not only drag reduction but also the global energy efficiency and reduction of energy consumption in passenger cars with similar geometric characteristics of SWs.
2 Computational methods
This section contains all the details of the implementation of the CFD model to simulate the flow around the SW. It also shows the details of the configuration of the SJs including location and operational parameters. The following procedure is proposed to study the effects of AFC based on synthetic jets in a passenger car using CFD:
Perform a basic CFD simulation in steady state in order to understand the flow field and to determine the regions of massive flow separation (Section 2.1).
Design the SJ outlets based on the expected operating parameters of the SJs, this includes not only the geometry but also the peak velocities and frequencies of operation (Section 2.2).
Select the location and orientation of the SJ outlets on the surface of the vehicle (Section 2.2).
Modify the original CAD analyzed in the first step with the position and orientation of the SJ outlets. This includes a new mesh generation in which the SJ outlets require adequate discretization (Sections 2.3 and 2.4).
Implement the different cases with SJ, following the procedure described in Section 2.6 for each case.
2.1 Flow analysis of the unactuated flow
The geometrical model was obtained by a three-dimensional scanning process but excludes some details of the vehicle such as the engine bay, and the underfloor which was considered flat. The computational domain was generated as a box enclosing the SW model, as shown in Figure 1. The boundary conditions implemented in the model are the following: The velocity of the air at inlet (I) was set uniform at 70 km/h (19.4 m/s). The outlet boundary (O) was set to pressure outlet. The lateral (R) and top (T) boundaries of the domain were set to zero gradient. The other lateral boundary (S) was set as a symmetry boundary condition. Finally, the floor (B) is a static wall. The more relevant dimensions of the vehicle and computational domain are presented in Table 1. It is important to clarify that the model is only half of the vehicle taking advantage of the symmetry in the flow direction and thus it reduces the computational cost of the simulations.
FIGURE 1
TABLE 1
| Dimension | Value | |
|---|---|---|
| Station wagon | Height | 1,556.7 (mm) |
| Width without mirrors | 1,701.4 (mm) | |
| Length | 4,691.7 (mm) | |
| Front area | 2.12 (m2) | |
| Wheelbase (WB) | 2.62 (m) | |
| Computational domain | L | 11 × vehicle length = 51.43 m |
| Front of the model to I boundary | 3 × vehicle length | |
| Back of the model to O boundary | 7 × vehicle length | |
| W | 2.5 × vehicle width = 4.25 m | |
| H | 6 × vehicle height = 9.47 m | |
SW and computational domain dimensions.
A hybrid mesh was generated for the computational domain with 2.7 × 106 elements, it combines prisms near the vehicle surface and tetrahedrons in the rest of the domain. This number of elements was obtained after a convergence analysis that is reported on reference (). A minimum value of y+ = 0.8 was obtained while the average value was 17. The implemented model assumes incompressible, steady state, Newtonian, turbulent and three-dimensional flow. The model was implemented in the commercial software ANSYS-FLUENT v14.5. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) with spatial discretization methods of second order was used as pressure-velocity coupling. An absolute convergence criterion of 1 × 10−6 with 5,000 iterations was used.
2.2 Synthetic jets location
Numerical results of the unactuated flow were focused on the visualization and characterization of the separated flow.
Figure 2ashows the streamlines in the recirculation zone in the near wake of the vehicle. The massively separated flow in this region is the main target of the AFC. It is observed that the flow separation appears in the upper and the lateral rear part of the vehicle, leading to the formation of two three-dimensional toroidal vortices, which are characteristic in the near wake of this type of vehicle.
Figure 2bshows iso-surfaces of wall shear stress with positive magnitude in the flow direction giving an idea of the exact location where the separation region begins. Steady-state simulations of the uncontrolled flow field revealed that the dominant separation regions were located near the upper rear edge and the lateral rear regions of the station wagon. These regions correspond to the origin of the main separated shear layers and coherent vortical structures responsible for the wake development and aerodynamic drag generation. Based on this analysis, two actuator locations were selected:
Upper Side (US): located near the spoiler region to interact with the upper separating shear layer.
Lateral Side (LS): located near the lateral rear pillars to affect the side shear layers and lateral wake structures.
FIGURE 2
The objective of this actuator placement strategy was to inject momentum directly into the dominant separation regions in order to modify the wake topology and improve the aerodynamic performance. Additionally, tangential actuation was selected because streamwise-oriented synthetic jets have been reported to provide more effective momentum transfer into the boundary layer and improved separation control compared to wall-normal actuation.
The first step was the definition of the spatial arrangement of the outlet slots of the SJs. The positions selected for the implementation of the SJs were: (a) an upper area along the spoiler surface (Upper Side - US), and (b) the D-pillar of the vehicle (Lateral Side -LS) as shown in Figure 3. SJs width are typically in the order of millimeters for real aerodynamic applications, in this case both SJs width are limited to 7 mm due to space restriction, especially in the spoiler. Table 2 summarizes the most relevant geometric details of the SJs outlet that were implemented. The implementation of these two new additional zones (surfaces) in the original CAD model implied that a new mesh needs to be generated.
FIGURE 3
TABLE 2
| Geometric detail | Upper jet | Lateral jet |
|---|---|---|
| Width* (mm) | 7 | 7 |
| Length* (m) | 0.44 | 0.42 |
| Area (m2) | 3.32 × 10−3 | 2.92 × 10−3 |
| Perimeter (m) | 0.89 | 0.576 |
| Hydraulic diameter (m) | 0.015 | 0.020 |
Geometric details of the SJ outlets.
2.3 Mesh
For the mesh generation process the commercial software ICEM CFD v 17.0 was used. A hybrid mesh combining tetrahedral elements in all the computational domain and prisms over the vehicle surface except for the front area and wheels were generated. To correctly capture the viscous phenomena near the vehicle surface including the turbulent boundary layer, some parameters for prisms generation were adopted to obtain an average y + between 1 and 2. Regarding the rest of the domain, tetrahedral elements of different sizes were used. In order to guarantee a smooth transition between the prism layers and the rest of the domain, several density boxes were implemented. The part of the computational domain discretized with tetrahedral elements was divided into two regions: near-field and far-field. The near-field contains the parts of the domain that are closer to the vehicle and extents form 0.5 lengths of the vehicle up-stream up to 3 lengths of the vehicle down-stream (near-wake). The far-field contains the rest of the domain and the far-wake.
A convergence analysis was performed using four meshes with different elements size in each refinement zones, obtaining a total number of 2.0, 3.7, 4.5 and 7.5 million of elements. Table 3 shows the most important details of the four meshes used in the present study, including some quality indicators (OQ, Orthogonal Quality, AR, Aspect Ratio) while Figure 4 shows the results of the convergence analysis based on the drag coefficient CD. Table 3 also shows the CD values obtained for each mesh including the percentage of change between consecutive meshes (last row). From Figure 4 and Table 3, it is clear that the independence of the result of CD is obtained with Mesh 1 and that the change in the prediction of CD is close to 1% with respect to Mesh 2.
TABLE 3
| Mesh ID | Total elements | Tetrahedral | Prisms | Average OQ | Max. AR | CD | % Change |
|---|---|---|---|---|---|---|---|
| 1 | 7,562,029 | 6,712,786 | 849,243 | 0.83 | 2,466 | 0.4236 | 1.39 |
| 2 | 4,501,253 | 3,862,945 | 638,308 | 0.83 | 2,152 | 0.4295 | 1.98 |
| 3 | 3,710,524 | 2,945,865 | 764,659 | 0.82 | 1,925 | 0.4380 | 3.44 |
| 4 | 2,062,082 | 1,767,175 | 294,907 | 0.81 | 1,571 | 0.4531 | - |
Mesh convergence details.
FIGURE 4
In order to determine if the parameters used for the prism layer generation were satisfactory, Figure 5 shows a detail of the mesh close to the roof of the vehicle with a contour of velocity magnitude. The total thickness of the prism layer ensures that its outer edge is located outside the boundary layer, in a region where the velocity is approximately equal to the free-stream value (19.4 m/s). Figure 6 shows a general view of Mesh 1 with some details and the average size of the elements in the different boxes of densities that were used.
FIGURE 5
FIGURE 6
2.4 Boundary conditions
The implemented boundary conditions are the same as those used in the unactuated case (See Figure 1; Table 1) with the difference in the SJ outlet. The boundary condition implemented for the jets actuation was a uniform velocity inlet/outlet using a simple harmonic sinusoidal function set through a user defined function (UDF). No details of the cavity and the motion or deformation of the diaphragm were included in the model. Based on literature review, it was decided that the direction of the jets will be tangential to the surface in both actuation zones. It is well established in the literature that tangential or streamwise-oriented synthetic jets are generally more effective than wall-normal jets for aerodynamic performance enhancement, as they inject momentum directly into the boundary layer and promote reattachment more efficiently (; ; ). In the case of the upper SJ, it was implemented as a hybrid flow control device since the spoiler is considered a PFC element. Simulations were initially run by placing the jets only in the US, and subsequently, locating the jets only on the LS.
The amplitude for the velocity at the SJ outlet was defined as a function of the free flow velocity (), so that three levels were used: 0.5 , 1.5 and 3.0 . Regarding the excitation frequency, based on the literature review it is typically in the order of hundreds of Hertz, so 250Hz and 400 Hz were selected as actuation frequency in the present study. SJ actuation in the range of ∼100 Hz corresponds to approximately 2–10 times the natural shedding frequency, placing it in the so-called high-frequency forcing regime. This regime has been consistently identified in experimental studies as highly effective for bluff-body wake manipulation and drag reduction. Specifically, experimental investigations of bluff-body flows have demonstrated that forcing at frequencies moderately higher than the natural shedding frequency leads to: (i) stabilization of the separating shear layers, (ii) suppression of large-scale coherent vortex shedding, and (iii) reduction of wake width accompanied by an increase in base pressure, which directly translates into drag reduction. (; ; ).
The amplitude and actuating frequency are characterized by the following non-dimensional numbers: blowing coefficient (Cb), momentum coefficient (Cμ), and reduced frequency (F+) which are defined in Equations 1–3.Where is the peak velocity of the jet, is the free stream mean velocity, is the jet actuator area, is the vehicle frontal area, is the SJ frequency, and is the wheelbase distance. Table 4 shows the values of the non-dimensional numbers used for all the simulation cases of the present study.
TABLE 4
| ID | Case | ||||
|---|---|---|---|---|---|
| Upper | Lateral | ||||
| 1 | 0.159 | 3.87 × 10−4 | 3.40 × 10−4 | 33.69 | |
| 2 | 0.159 | 3.87 × 10−4 | 3.40 × 10−4 | 53.91 | |
| 3 | 0.477 | 3.48 × 10−3 | 3.06 × 10−3 | 33.69 | |
| 4 | 0.477 | 3.48 × 10−3 | 3.06 × 10−3 | 53.91 | |
| 5 | 1.592 | 1.39 × 10−2 | 1.23 × 10−2 | 33.69 | |
| 6 | 1.592 | 1.39 × 10−2 | 1.23 × 10−2 | 53.91 | |
Simulation cases with SJ operational parameters.
2.5 Governing equations
Despite the highest Mach number at the SJ outlet is 0.2, it was assumed that the flow is incompressible, isothermal, Newtonian, unsteady, turbulent and three-dimensional. For this study, the governing equations are the Unsteady Reynolds Averaged Navier-Stokes (URANS) which require a turbulence model. For completeness, the governing equations are included in this paper but for a proper understanding of these equations, references (; ; ; ; ; ) are suggested.
Conservation of mass (Equation 4):Where is the averaged velocity field and in index notation
Conservation of linear momentum (Equation 5):
Here is the density, is the absolute or molecular viscosity and is the average mechanical pressure field which is a consequence of the Stokes’s assumption in an incompressible flow. is called the Reynolds stress tensor and is given by:
Equation 6 can be written in index notation as: where represents the fluctuating components of the velocity field . Extra equations that model the Reynolds stress tensor are required; this problem is known as the closure problem.
Boussinesq approximation (See Equation 7)Where is the turbulent kinetic energy and is the Kronecker delta. is the turbulent or eddy viscosity which is a property of the flow not a physical property of the fluid. In order to close the governing equations, a turbulence model is required. There are several types of URANS turbulence model which are typically classified depending on the number of extra equations needed. In the present study, the SST turbulence model was used due to its good performance in this kind of simulations The k–ω SST turbulence model is widely recognized as one of the most reliable RANS models for external aerodynamic flows involving separation and adverse pressure gradients, such as those encountered in ground vehicles. Comparative studies on full vehicle geometries and automotive relevant configurations have shown that the SST model provides improved prediction of drag, lift, and wake structures compared to other RANS models (e.g., k–ε and Spalart–Allmaras), particularly due to its ability to accurately resolve near-wall regions and separated flows. The main variables in this model are the turbulence kinetic energy () and the turbulence frequency where represents the rate of viscous dissipation (See Equations 8, 9) (; ; ). Of course, this model is derived from the classic - model which is extensively discussed in the literature (; ).
equation:
Here, and represent the rates of production and dissipation of respectively. is the magnitude of the averaged rate-of-strain tensor and is a constant.
equation:
Here, represents the rates of production of and is the turbulent kinematic viscosity. and where , and . In the last expression and are constants and (See Equation 10) is computed from the following equations:
In Equations 11 and 12, represents the distance to the wall which is the most important parameter in any RANS model. in Equation 9 represents the dissipation of . For incompressible flow, where and are constants. in Equation 9 represents the cross-diffusion term and it allows the blending between the and the models.
Now, the turbulent Prandtl numbers for and that appear in Equations 7 and 8 as and are introduced (Equations 13,14),where and are constants. Finally, the model is completed with the new definition of the turbulent viscosity given by Equation 15.Where , and . Equation 15 limits the value of the turbulent viscosity which is typically overpredicted in the and the models.
2.6 Solver: configuration and initialization
The commercial software ANSYS FLUENT v 17 was used, and the simulations were implemented and initialized using the following procedure:
A base case (no actuation–geometry with SJ but with wall boundary condition) was initially run in steady-state and stationary bottom and wheels. This simulation was run until convergence (approximately 5,000 iterations) using first order discretization for the turbulence model.
Keeping the model in steady-state conditions, the turbulence model equations discretization was switched to second order, and the model was run for 10,000 iterations until convergence.
At this point, the bottom and wheels boundary conditions are switched to moving and rotating, respectively. The simulation was run for another 10,000 iterations until convergence is reached.
Now, the transient condition was turned on and the model was run for 3 s which corresponds to approximately 20 convective times based on the wheelbase length of the vehicle (WB), this means that where t is time in seconds. The drag coefficient was monitored during this time in order to verify convergence. The average drag coefficient value obtained at this step is labeled as Base Case result.
Finally, the SJs were turned on, and the simulation was run for at least 20 convective times (3 s) and the drag coefficient was monitored and analyzed in the last 0.13 s (which corresponds to 1 convective time).
Figure 7 shows the typical evolution of the drag coefficient monitor until step 4 (before the SJ are turned on). It is clear that there are small variations between each step in the initialization of the simulation and that the final value of the drag coefficient is smaller than the one reported in the reference work (). Finally, the pressure-velocity coupling used to solve the governing equations was the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) with spatial discretization of second order for all the equations. Simulations were run with a fixed step size of 0.5 m and 30 iterations per time step, with a convergence criterion of 1 × 10−6.
FIGURE 7
3 Results and discussion
This section is divided into four: First, a simple validation of the base case (unactuated flow) is performed in order to verify the implementation of the model. Once the model is validated, a quantitative evaluation of the effects of the SJ is done based on the numerical results of the drag and lift coefficients (aerodynamic performance); then, a qualitative analysis of the effects of the SJ actuation on the dynamics of the flow is shown. This analysis is focused on the shape and intensity of the vortical structures on the near wake of the SW. Finally, a simple quantification of the amount of energy required for the operation of the SJ is done and compared to the energy saved due to drag reduction.
3.1 Computational cost
The simulations were performed in a small cluster available at Universidad de the Andes with the following characteristics:
14 blade servers ProLiant BL460c Gen8.
Total RAM: 2688 GB (128 GB each blade.)
Each Blade has two Intel(R) Xeon(R) CPU E5-2,695 v2 @ 2.40 GHz (12 Cores) processors and two hard drives of 279 GB each one in RAID 1.
The connectivity is done with Infiniband at 40gbps.
All the simulations were run using 32 processes in parallel. In steady state, running 5,000 took approximately 5 h (CPU time), so that first 3 steps of the proposed procedure (Section 2.6) took 15 h. In transient mode, running 1 s took approximately 1.5 days (CPU time) using a time step of 0.5 m and 20 iterations per time step. For each case, it was required approximately 9 days, and approximately 45 days in total (six cases). This computational cost does not include post-processing of the solution data.
3.2 Base case validation
In order to verify the correct implementation of the model a comparison of the numerical drag coefficient obtained in the base case simulation is done with respect to numerical and experimental results reported in references (, ). The experimental procedure is based on the standard SAE J1263, which basically consists of a series of coast-down tests that were performed to the actual vehicle. The SW mass is measured in stationary condition using a scale and a weather station is used to measure the atmospheric conditions (wind speed, temperature, humidity and pressure) at the site of the tests. A differential GPS is used to measure the SW speed using a mobile data logger which is installed in the SW and a base station that is placed close to the test track. Table 5 summarizes the validation results and a comparison with other references found in the literature. A very good agreement is observed between the numerical and experimental results with a difference of approximately 4.6%.
TABLE 5
| Description | Type of vehicle | CD | Reference |
|---|---|---|---|
| Experimental (coastdown) | SW | 0.404 | |
| Numerical (SA Turb. model) | SW | 0.463 | |
| Numerical (SA Turb. model) | SW | 0.431 | |
| Experimental (Wind Tunnel) | SW | 0.42 | |
| Present study | SW | 0.423 | |
Validation data.
3.3 Effects of the jets on the aerodynamic performance
3.3.1 Upper side synthetic jets
Figure 8a shows the convergence of drag coefficient for simulations with jets in the upper side. It is clear that the drag coefficient has a periodic behavior due to the pulsing action of the SJ and that the amplitude directly depends on Cμ. The configuration with better results in terms of drag reduction corresponds to case 6 (). With this configuration, computational results show an average drag coefficient of 0.4202, leading to a drag reduction of 0.8% compared with the value obtained for the base case (0.4236). Regarding the lift coefficient, it also shows a periodic behavior due to the pulsing action of the SJ and similarly to CD, the amplitude directly depends on Cμ. However, lift coefficient increases as Cμ increases. This is clearly observed in 4 of the 6 cases, as shown in Figure 8b, with a maximum increment of 18% that corresponds to case 6 (). In Figure 8, the frequencies associated with the evolution of each case are primarily related to the actuation frequency (Cases 1, 3 and 5: 250 Hz and Cases 2, 4 and 6: 400 Hz).
FIGURE 8
3.3.2 Lateral side synthetic jets
When LS SJs are used, a similar behavior in the evolution of the aerodynamics coefficients is observed, i. e.,: periodic and with and amplitude highly dependable on Cμ. Nevertheless, with jet actuation only in the lateral side a clear increment in drag coefficient is obtained as shown in Figure 9a. A maximum increment in CD of +4% was achieved for case 6 () in comparison to the base case. However, in terms of lift, all the cases lead to a reduction of the lift coefficient as shown in Figure 9b. The maximum reduction is obtained for case 5 allowing a change in the lift coefficient of −32%. Figure 10 shows the variations in the drag and lift coefficients, calculated as shown in Equation 16.
FIGURE 9
FIGURE 10
As it is observed, the reduced frequency does not have a significant impact on the variations of either drag or lift coefficients; the most relevant parameter for the variations on the aerodynamics forces is the momentum coefficient. For CD, a maximum reduction of almost 1% percent is obtained for US actuation with Cμ = 1.4 × 10−2, with an increment in lift of 18%. On the other hand, for CL, a maximum reduction of 32% is obtained for Cμ = 1.2 × 10−2 implementing jets in LS, with an increment in drag of 4%. In Figure 9, the frequencies associated with the evolution of each case are primarily related to the actuation frequency (Cases 1, 3 and 5: 250 Hz and Cases 2, 4 and 6: 400 Hz).
When comparing Figures 8, 9, numerical results demonstrate a distinct difference in both lift and drag responses between the 250 Hz (Cases 1, 3, and 5) and 400 Hz (Cases 2, 4, and 6) operating conditions. As observed in both the LS and US configurations, the 400 Hz actuation naturally yields shorter convective time cycles characterized by steeper temporal gradients. Furthermore, the higher frequency consistently induces slightly larger peak-to-peak amplitude fluctuations in both lift and drag coefficients relative to the corresponding 250 Hz cases. This behavior is most distinctly evident when comparing Case 6 (400 Hz) to Case 5 (250 Hz), where the higher-frequency actuation drives a greater oscillatory amplitude across both actuator locations.
3.4 Effects of the SJ actuation on the flow
Considering that the best scenarios based only on drag reduction was case 6 (US actuation), then this case was selected to perform an analysis of the flow dynamics in the near wake. Figure 11 shows a comparison of the averaged velocity contours in the symmetry plane between the base case and the case with jet actuation. A higher velocity zone can be observed in the upper part of the wake, as would be expected due to the synthetic jet effect. The injected momentum has a clear influence on the velocity distribution of the upper part of the near wake considering the tangential direction of the SJ.
FIGURE 11
Figure 12 shows the effect of the synthetic jet actuation on the pressure distribution over the rear surface of the vehicle. It is observed that the jet actuation generates a higher negative pressure particularly close to the SJ outlet and in different zones along the slanting surface. It is also observed that there is a local reduction in pressure in the rear lower part of the surface of the SW. In general, the increment in the pressure is not significant (less than 5 Pa), which is related to the low reduction of drag.
FIGURE 12
Figure 13 shows streamlines plotted with velocity contours of the near wake in the symmetry plane. A general observation is that the SJ energizes the upper part of the near wake, so that the shape of the separation bubble is changed and shifted towards the ground. A decrease in size of the separation bubble is observed when the base case is compared with the US actuation case 6. Despite the increase in size of the two toroidal vortices for the case with jet actuation, the total size of the separation bubble is reduced because of the synthetic jet effect on the top of the vehicle. The X and Y vortex increase in 12% and 6% respectively, but the total size of the separation bubble is reduced by 3% approximately, considering the distance traced between the rear side of the vehicle and the saddle point S. The key mechanism responsible for this behavior is related to the momentum injection and wake reorganization produced by the synthetic jet. The actuation introduces periodic momentum that enhances the mixing between the separated shear layer and the surrounding flow. Therefore, the additional momentum introduced by the synthetic jet promotes earlier reattachment and partial suppression of the recirculation bubble, which leads to a reduction of the separated region behind the vehicle. At the same time, the injected momentum modifies the global wake topology. The observed increase in the spatial extent of the vortical structures should not be interpreted as an increase in vortex strength or recirculation intensity. Instead, the actuation redistributes vorticity over a larger region, producing wider but less concentrated coherent structures. Simultaneously, the additional momentum introduced into the separated shear layer promotes earlier reattachment and reduces the recirculation length behind the vehicle. Therefore, the increase in vortex size and the reduction in the separation region are not contradictory phenomena, but rather a consequence of the wake reorganization induced by the synthetic jet forcing, where enhanced mixing and momentum redistribution lead to a shorter separation bubble and a broader, less concentrated wake structure. The toroidal vortices identified in the wake are not simply strengthening in place; instead, the redistribution of vorticity and enhanced entrainment causes these coherent structures to expand spatially while their circulation is redistributed over a larger region. To complement these observations, Figure 14 shows the average 3D streamlines close to the SJ outlet for both base case and case 6. A clear influence of the actuation is observed in the dynamics of the flow, by bending the streamlines towards the vehicle surface. One of the main objectives of the SJ is to control the sizes and shape of the vortical structures in the near wake and in this way have an impact on the aerodynamic coefficients, in this case drag reduction.
FIGURE 13
FIGURE 14
In terms of the average vorticity field in the near wake, Figure 15 presents a comparison of the vorticity in the flow direction on a transverse plane just at the rear end of the SW (0.1 m downstream). For the base case, the appearance of the characteristic pairs of counter-rotating vortices is observed. However, observing the difference between the base case and case 6, an alteration in the vorticity regions A+ and C ± is clearly observed accompanied by a certain reduction in the vorticity magnitude. This observation also shows the effectiveness of the SJ to make not only local changes in the flow field but also in a more general aspect, manipulating the vortical structures in the near wake.
FIGURE 15
3.5 Energy balance
An energy balance analysis is performed for the best scenario in drag reduction (case 6 - US) and compare to the base case. A very simple estimation of the power required for jet actuation Pjet (Equation 17) is compared to the saved power Psaved (Equation 18) due to the drag reduction and lift enhancement. Typically, only drag is included in this estimation () but in the present study the effects of lift enhancement in the power consumption were considered since the rolling resistance coefficient was estimated from experiments.
In Equations 17 and 18, δCD and δCL represent the reduction in drag and increment lift coefficients between the base and the actuated cases respectively, Ujet is the averaged velocity of the jet and fr is the rolling resistance coefficient which has a value of 0.0132.
Table 6 shows the results of the energy balance for the cases with US actuation. It is clear that none of the simulation cases were effective since the energy required for actuation is higher than the energy saved due to aerodynamic performance. The best-case scenario with respect to energy balance is case 2 in which the saved power is only approximately 80% of the power required to operate the SJs. However, the amount of power saved is less than 1 W which is insignificant for the purpose of fuel consumption reduction. On the other hand, in case 6, the energy saved is approximately 14 W, but the energy required for the operation of the SJ is approximately 80 W. These estimations do not include the efficiency of the SJ in the conversion of mechanical/electrical energy into kinetic energy in the flow at the SJ outlet.
TABLE 6
| Case | Pjet(W) | Psaved(W) | Psaved/Pjet | ||
|---|---|---|---|---|---|
| 1 | 6.79 × 10−5 | −9.87 × 10−4 | 0.38 | 0.21 | 0.55 |
| 2 | 9.30 × 10−5 | −8.89 × 10−4 | 0.38 | 0.30 | 0.81 |
| 3 | 7.67 × 10−4 | 1.64 × 10−3 | 10.13 | 2.96 | 0.29 |
| 4 | 8.36 × 10−4 | 1.92 × 10−3 | 10.13 | 3.23 | 0.32 |
| 5 | 3.35 × 10−3 | 1.27 × 10−2 | 81.02 | 13.19 | 0.16 |
| 6 | 3.41 × 10−3 | 1.32 × 10−2 | 81.02 | 13.43 | 0.17 |
Energy balance for actuation with upper side SJ.
Although the synthetic jet actuation produced measurable modifications in the wake topology and aerodynamic coefficients, the global energetic efficiency of the control strategy remained unfavorable. Several factors contribute to this behavior. First, the wake generated by the station wagon geometry is highly three-dimensional and characterized by large-scale separated flow structures with substantial momentum deficits. Consequently, significant momentum injection is required to produce noticeable modifications in the global wake dynamics. As the momentum coefficient and jet velocity increase, the power required for actuation becomes considerable relative to the aerodynamic gains obtained. Second, the effectiveness of the synthetic jets strongly depends on the interaction between the injected momentum and the local shear-layer dynamics. The results obtained in the present study show that upper-side actuation produced modest drag reductions, whereas lateral-side actuation generated drag increases despite reducing lift. This behavior highlights the sensitivity of realistic vehicle wakes to actuator placement and forcing conditions.
Furthermore, the synthetic jet actuation modifies the wake dynamics through periodic momentum injection and enhanced shear-layer entrainment. Consequently, the observed increase in the spatial extent of the vortical structures should not be interpreted as an increase in vortex strength or recirculation intensity. Instead, the actuation redistributes vorticity over a larger region, producing wider but less concentrated coherent structures. Simultaneously, the additional momentum introduced into the separated shear layer promotes earlier reattachment and reduces the recirculation length behind the vehicle. Finally, the present results also reflect current limitations associated with the use of synthetic jets for large-scale external aerodynamic applications. While synthetic jets are highly effective for local separation control problems, manipulating the large separated wakes typical of passenger vehicles requires relatively high actuation authority, which can reduce the net energetic benefit of the control strategy.
4 Conclusion
A computational study for an active flow control based on SJ in a station wagon was presented, including an analysis of the aerodynamic performance. Combining prisms over the vehicle surface and tetrahedrons in the rest of the domain, a hybrid mesh with 7.5 × 106 elements was generated with several refinement sections and two actuation slots over the vehicle spoiler and on the D-Pillar of the SW. Simulations in transient state were run with the commercial software ANSYS FLUENT v17.0. Synthetic jets actuation was implemented tangentially to the surface, and the velocity magnitude was modelled by a harmonic sinusoidal function.
Numerical results show a drag reduction and lift increase for all the cases with only US jets, with a maximum reduction of 0.8% in drag (Case 6) and 18% of lift increase with a momentum coefficient of 1.4 × 10−2. Similar results are reported in the literature for AFC on real vehicle models (; ). For the cases with only lateral jets (LS), a drag increment and a reduction in lift is obtained, being 4% the maximum drag increase and 32% the maximum decrease for lift with Cμ = 1.2 × 10−2. This lift reduction could be a suitable control strategy for applications that require additional downforce sources in certain driving conditions such as sportscars. In this case, the control with only lateral jets with Cμ = 3.5 × 10−3 could be a good alternative due to the lift reduction obtained of 18% with only 2% drag increase. The steady and unsteady responses across both the drag and lift coefficients reveals a stark contrast in the aerodynamic efficacy of the two actuator locations. The Lateral Side (LS) actuation introduces severe unsteady penalties, characterized by massive peak-to-peak force fluctuations in both lift and drag, without yielding a beneficial shift in the time-averaged aerodynamic performance. In fact, high-intensity actuation at the LS location predominantly serves to violently disrupt the flow field. Conversely, the upper surface (US) location demonstrates a highly favourable control authority. It successfully achieves the dual benefit of reducing the mean drag while simultaneously increasing the mean lift (shifting the baseline CL positively), all while maintaining remarkably low-amplitude structural oscillations. This strongly suggests that the US location is far superior at favourably modifying the global flow field and suppressing detrimental shedding features with minimal unsteady loading penalties.
Regarding the dynamics of the averaged flow in the near wake, case 6 with upper jets shows a decrease in the size of the separation bubble coupled with an increase of pressure distribution in the rear part of the vehicle. Moreover, it was observed that the vorticity magnitude is affected by the jet’s actuation leading to an increase for the upper vortices (labeled as A) and decreasing for the lower ones (labeled as C).
In terms of energy performance for case 6, the power required for jets actuation resulted being 8 times the saved power in drag. Based on the results of the present study, AFC with SJ seems to be not suitable from an energy performance point of view. There are great needs in the research and understanding of the dynamics of the unactuated flow around ground vehicles and how to correctly locate, design and operate the SJs, so that the flow control strategy is attractive not only from the aerodynamic performance but also from the energy balance point of view.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
OL: Writing – review and editing, Supervision, Project administration. DB: Software, Data curation, Writing – original draft, Visualization, Investigation. LM: Writing – review and editing.
Funding
The author(s) declared that financial support was not received for this work and/or its publication.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was used in the creation of this manuscript. For the revised version Generative AI (Gemini with nano banana) was used to improved (mainly visualization of colors (contrast), colorbar and numbers) of figures 1, 6, 12 and 13.
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Abbreviations
AFC, Active Flow Control; AR, Aspect Ratio; CFD, Computational Fluid Dynamics; CD, Drag coefficient; CL, Lift Coefficient; Cb, Blowing coefficient; Cμ, Momentum coefficient; F+, Reduced frequency; LES, Large Eddy Simulation; LS, Lateral Side - Actuation; OQ, Orthogonal Quality; Pjet, Required synthetic jet power; Psaved, Power saved due to synthetic jet actuation; PFC, Passive Flow Control; Re, Reynolds number; SA, Spalart–Allmaras; SJ, Synthetic Jet; SST, Shear Stress Transport; SW, Station Wagon; , Free stream velocity; URANS, Unsteady Reynolds-Averaged Navier–Stokes; US, Upper Side - Actuation.
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Summary
Keywords
active flow control, aerodynamics, computational fluid dynamics, station wagon, synthetic jets
Citation
Lopez Mejia OD, Blanco DE and Muñoz LE (2026) Active flow control with synthetic jets in a station wagon – a CFD study. Front. Aerosp. Eng. 5:1805951. doi: 10.3389/fpace.2026.1805951
Received
06 February 2026
Revised
11 May 2026
Accepted
14 May 2026
Published
08 June 2026
Volume
5 - 2026
Edited by
Mingtai Chen, North Carolina State University, United States
Reviewed by
Jie Hua, Embry–Riddle Aeronautical University, United States
Aldo Benavides-Morán, National University of Colombia, Colombia
Updates
Copyright
© 2026 Lopez Mejia, Blanco and Muñoz.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Omar D. Lopez Mejia, od.lopez20@uniandes.edu.co
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.