Developments in Drag Reduction Methods and Devices for Road Vehicles

Abstract

This study presents new developments in novel drag reduction devices for road vehicles, focusing on the use of inflatable and alternative material rear drag reduction devices that employ both a single- and multi-cavity approach. The effectiveness of these devices is assessed through on-road testing using constant power measurements to evaluate the resulting drag reductions. Surface pressure measurements collected during testing are compared with CFD predictions, using both the RANS and HLES methods to evaluate how accurately pressure changes are modelled when the devices are fitted to the test vehicles. A novel method for analysing vehicle surface flow in real-world conditions is also introduced, involving the capture and processing of video-recorded tuft imagery to determine appropriate means and standard deviations for the surface flow behaviour. Additionally, the study presents the latest advancements in multi-cavity drag reduction device design, along with considerations on how such devices can significantly enhance the benefits of vehicle platooning.

1. Introduction

The need for improved fuel economy and drag reduction in the road transport sector has once again become critical, as it was following the oil crisis of the 1970s [1]. This renewed urgency is driven by many factors, including the ongoing climate crisis [2], the demand for improved electric vehicle driving range [3], and the volatility of fuel prices due to geopolitical situations [4]. One of the most effective ways to improve a vehicle’s fuel economy is to reduce the air resistance forces it experiences when on the road. Once a passenger car exceeds a speed of approximately 60 km/h, aerodynamic drag becomes the largest resistance force the vehicle must overcome [5]. The main issue is that the power requirement to overcome this air resistance grows in proportion to the cube of the vehicle’s speed, which is one of the primary causes of why substantial fuel economy and range detriments are observed when driving at typical motorway speeds (120 km/h) [6]. Reducing aerodynamic drag on a vehicle reduces fuel consumption; however, the relationship between these reductions is highly dependent on a number of factors, such as vehicle type and driving cycle [5].

In general, when any road vehicle undertakes a high-speed, long-distance journey, drag is the largest consumer of the fuel used for that journey. A reasonable estimate, commonly used for such a driving cycle, is that a 10% drag reduction would realise a 5% fuel saving [7,8,9]. If the driving cycle were different, such as incorporating more city-based or outer-city driving, which includes accelerations, starts and stops, then the weighting could be reduced to below 5% [10]. There are four primary forces on a road vehicle as it executes motion: aerodynamic drag, rolling resistance, acceleration forces, and grade resistance. The grade resistance is related to the forces that must be overcome when ascending hills; however, most of this can be recovered when the vehicle eventually descends the ascended gradient. Both the rolling resistance and acceleration losses are related to the vehicle’s mass. The heavier the vehicle, the more significantly these factors impact overall fuel consumption across any driving cycle. Technology such as regenerative braking for electric vehicles is an example of a way to partially recover some of the acceleration losses when the vehicle brakes/decelerates. The proportion that can be recovered is highly dependent on the vehicle and the driving cycle. To give an estimate, a recent 2024 road testing campaign of 19 electric vehicles by the German Automobile Club found that, on average, regenerative braking could regain 22% of the energy expended on flat terrain, based on a driving cycle similar to that of the WLTP [11]. Both air and rolling resistance can be regarded as total losses, such that there is no way to recover the energy spent in overcoming them. Therefore, the only way to reduce such a loss is to reduce the size of their original application force on the vehicle. At higher road speeds (100–120 km/h), aerodynamic drag can significantly exceed rolling resistance, making drag reduction one of the most effective strategies for improving fuel economy and addressing the discussed current needs and challenges in the road transport sector.

2. Literature Review

There are a number of methods and techniques used by automakers to reduce air resistance on their production vehicles [5]; however, this literature review focuses primarily on methods that can be applied to post-production vehicles. These methods can be described as appendable devices, where an end-user fits a device to their vehicle to reduce drag, save fuel, and extend driving range. A critical consideration is the relationship automakers have with drag reduction. Low-drag features are incorporated into production vehicles only to the extent that they align with consumer preferences. When market demand favours larger SUVs or crossover vehicles with particular aesthetic and functional traits [12], these often take precedence over aerodynamic performance. Since automakers are commercially driven and profit depends on meeting consumer demand, design compromises are made accordingly. This is fundamentally why regulation of a vehicle’s shape by governments is necessary [13], if substantial improvements in road transport fuel efficiency are to be achieved, as reflected in the ambitious climate targets set by many Western countries [14].

Another factor is that a single vehicle model is typically expected to serve a wide range of users, driving styles, and environments. For example, a large van might be used both for long-distance intercity transport and for local urban deliveries, depending on the user’s needs. This creates a demand for configurable vehicles, vehicles that can alter their aerodynamic profile through the use of appendable drag-reduction devices. The requirements of a high-speed intercity driver differ substantially from those of a city-based driver. At motorway speeds, more energy is spent overcoming aerodynamic drag, making drag reduction devices more valuable for such users. Appendable drag-reduction technologies fitted to post-production vehicles therefore represent a viable way to improve fleet fuel efficiency without significantly disrupting consumer preferences or the complex dynamics between manufacturers, consumers, and legislation. The rear of a vehicle is particularly well suited for the addition of aerodynamic devices, due to the significant drag caused by the low-pressure wake that forms after flow separation at the end of a bluff body [15]. A comprehensive review of rear and other vehicle-mounted drag-reduction devices was presented in [16], which summarised key developments in the field over the past 50 years. The findings relevant to the present work, specifically roof and rear appendables, are summarised next.

2.1. Non-Rear Drag Reduction Devices

Roof-mounted add-ons such as lightbars, roof racks, and signage can introduce considerable drag penalties, requiring measures to reduce their impact on fuel economy. Studies have shown that even modest roof racks can contribute meaningfully to national fuel usage, where Ref. [17] estimated that roof racks account for roughly 1% of the total light-duty vehicle fuel consumption in the US. Ref. [18] quantified the penalties for various vehicle attachments, finding fuel use increases ranging from 1 to 3% for empty roof racks and 10% for ski box fittings. Aerodynamic improvements to roof fittings such as lightbars can be achieved using shape changes and appendable devices, where Ref. [19] achieved a 20% drag reduction through a redesigned lightbar for emergency vehicles, while Ref. [20] proposed retrofitted appendable sections for the rear of existing lightbars, yielding appreciable drag improvements. The lightbar design choice for police fleets was studied in [21], where the best designs increased fuel consumption by just 6.6% compared to 11.3% for the higher drag designs. Similarly, Ref. [22] found a 6.9% improvement in fuel economy when switching from external lightbars to an internal lightbar design. In the context of roof-mounted taxi signs, Ref. [23] demonstrated that reorienting the high-drag Irish taxi sign could produce significant cost savings and reduce national emissions. The calculated fuel savings were estimated at nearly 1000 euros a year for each taxi driver who implemented the reorientation. Finally, Ref. [24] highlighted the broader need for design improvements and EU policy attention towards roof add-on components, especially given their impact on fuel usage relative to their size.

2.2. Rear Drag Reduction Devices

A wide variety of rear drag reduction strategies has been assessed in the literature, with performance depending on the shape and size of the device, along with the vehicle type. Ref. [25] demonstrated a device known as the fluid tail, which redirected air from the rear wheel arches into the rear wake, reducing drag by 18–20% on a production hatchback, while Ref. [26] integrated servo-actuated flaps into a base cavity on an SUV to improve yaw-averaged drag performance. Ref. [27] outlined work related to the development of an inflatable rear drag reduction device for a road vehicle. The paper outlined drag reduction results for a very simplified body using scale wind tunnel work, without full-scale prototyping or results for the inflatable device on a passenger car. Ref. [28] showed that inward-angled deflectors at 20 degrees significantly diminished wake turbulence on a square-back configuration. Ref. [29] demonstrated that a tapered rear cavity could more than double the drag reduction achieved by a straight cavity in direct flow. Streamlined tail extensions were studied in [30], reporting up to 60% drag reductions using elongated, tapered designs, which maintained most of the drag reduction performance when truncated. Similarly, Ref. [31] showed that truncating a full boat tail on a box van yielded only a marginal performance drop, with drag reductions falling to just 31% from 32%. Ref. [32] measured a 3.3% drag reduction with a recessed cavity on an SUV without passive base bleeding, with only a 1% extra performance improvement when the base bleeding was included, highlighting how the initial cavity contributed most of the savings. Ref. [15] presented a new type of rear drag reduction device, known as the multi-stage converging cavity, which utilised multiple angled cavities within one another to access a downstream high-pressure zone. The device then redistributed this pressure over the vehicle’s base, realising substantial base drag reductions.

In the context of heavy-duty vehicles, Ref. [33] examined a boat tail design with a shortened, angled bottom panel and found that excluding the bottom panel halved the overall drag reduction, underscoring the need for bottom surfaces on rear cavities and tails. A study by [34] confirmed that increased cavity length enhanced drag reduction, especially when combined with side skirts, with [35] documenting a 6.5% fuel saving for a road-tested practical cavity device on a heavy truck. Various appendables were studied in [36] for a pick-up truck, where combining a rear boat tail constructed from plates with a partial bed cover led to a drag reduction of 21 counts. Shortened boat tails also performed effectively in the studies outlined by [37,38], reporting drag reductions of 10.3% and 10.9% on a heavy and light-duty truck geometry, respectively, using wind tunnel tests. Ref. [39] reviewed various trailer-mounted aerodynamic devices for heavy trucks and recommended boat tail lengths between 24 and 32 inches for a viable trade-off between performance and practicality. The influence of specific panel configurations on rear cavities was explored in [40], which showed that a full enclosure with tapering of 10 degrees maximised performance, and that removing lower panels significantly reduced the drag reduction. Overall, these studies highlight that significant drag and fuel savings are realisable through the integration of a rear tail or cavity device appended to the base of a road vehicle.

2.3. General Discussion on Appendable Device Implementation

The integration of rear-mounted aerodynamic devices on passenger vehicles presents some initial challenges. These challenges, however, should not overshadow the opportunity to improve fuel efficiency. This is particularly relevant as modern vehicle designs are becoming increasingly streamlined, meaning the proportion of total drag carried by the rear will increase and therefore increase the effectiveness of any rear drag reduction device [16]. Key challenges facing the integration of these devices include how the devices are stored when not in use, their compatibility across similar vehicle types, and whether they affect access to the rear storage area. The device must also reliably resist weather degradation, vibration, and general wear and tear, as repair costs could offset the fuel savings [41]. They must also have minimal interference with driver visibility, parking sensors, and external lighting systems.

A device that doubles as a rear storage box could be a viable option for practical implementation. EU regulations such as 2019/2144 [42] and 2021/535 [43] have defined regulations for fitting such devices to the heavier class of vehicles, excluding the smaller passenger cars (M1) and vans (N1). The regulations for the heavier vehicles (M2, M3, N2, N3) prohibit such devices from increasing vehicle storage space. However, as these regulations do not apply to the smaller vehicles in the EU, such a device could be made to double as a rear storage box and a drag reduction device. Light-duty vans represent a very suitable initial market for such a device due to their flat rear towbar options to facilitate towbar mounting, and the likely no rear glazing eliminates some rear vision concerns. These devices are likely to have the same effect on a driver’s insurance as that set by the precedent for driving with rear bicycle racks, storage boxes, tents, and all the other rear-mounted protrusive fittings, which have an established precedent to work on the road. Stakeholder discussions conducted by the authors with Irish insurers confirmed that such devices aimed at improving fuel economy would not affect insurance premiums. They outlined that vehicle modifications that increase engine power and increase vehicle cornering speed are the types of modifications that must be disclosed and that often increase insurance premiums. Overall, based on the established precedent set by rear-mounted fittings such as storage boxes and bicycle racks, there is reasonable justification that rear drag reduction devices for the smaller road vehicles are viable products, which can benefit road users who need improved fuel economy and extended driving range.

2.4. Paper Overview

Outlined next is a detailed description of the road testing and CFD methodology used to evaluate the novel prototype drag reduction devices studied in this article. This includes the surface flow, surface pressure, and on-road drag change measurement methodologies. Following the outline of the CFD methodology, a results section is presented which describes a range of drag reduction results for different devices mounted on two road vehicles. Finally, a conclusion and outlook are provided, with discussion on the future implementation of such devices in the wider transport sector.

3. Road Testing Methodology

3.1. Measuring a Drag Change On-Road

The method described next for measuring a drag change on-road was first described in [44]; therefore, only a brief summary of the technique will be provided next. The method involves fixing the vehicle’s throttle pedal across two vehicle configurations. For a given, fixed throttle position, a road vehicle will reach a constant equilibrium speed for its configuration on a long flat straight road. This happens because by fixing the vehicle’s throttle pedal, the fixed power output from the engine is used to counteract both the drag and the rolling resistance force on the vehicle. It was confirmed in [44] that fixing the vehicle’s throttle pedal across configurations does produce a fixed power output from the engine, which was confirmed via three different power measurements that remained constant for multiple different configurations with two different vehicles. An example to demonstrate the method is as follows: The baseline standard vehicle has its throttle pedal fixed at 35% compression, the vehicle will then reach a constant speed on a long, flat, straight road, $V_1$. The vehicle is then configured in some way, such as by adding a kayak to its roof. When this configured vehicle travels down the same road with the same throttle pedal compression, it will reach a new speed, $V_2$. The resulting speed delta measured on the road, $V_1$–$V_2$ can then be used with the equation set discussed next to determine the percentage drag change on the vehicle.

3.1.1. Governing Equations

The derivation for the percentage drag change equation begins from the constant power statement (Equation (1)), which becomes Equation (2), as the only two forces acting on a vehicle once it reaches its equilibrium speed for a given power input are drag and rolling resistance. $P_1$ and $P_2$ represent the vehicle’s power output at the speeds $V_1$ and $V_2$.

$$P_1=P_2$$

(1)

$$\left(D_1+R_1\right)\left(V_1\right)=\left(D_2+R_2\right)\left(V_2\right)$$

(2)

A reasonable assumption to apply is that the rolling resistance force between the two configurations at the speeds $V_1$ and $V_2$ remains constant. This is valid as the measured speed delta is often less than 10 km/h, and the rolling resistance force change across such a speed delta would be minimal [45]. Applying this assumption to Equation (2), the power balance then becomes Equation (3). $C_{D1}{A}_1$ and $C_{D2}{A}_2$ denote the drag areas of the vehicle configurations 1 and 2, respectively.

$${\displaystyle \frac{1}{2}}\rho V_1^3{C}_{D1}{A}_1+R{V}_1={\displaystyle \frac{1}{2}}\rho V_2^3{C}_{D2}{A}_2+R{V}_2$$

(3)

Equation (3) can then be rearranged to isolate the drag area of the vehicle in its second configuration, which can then be subbed into the percentage drag change formula to produce Equation (4). This is the final equation of the derivation, which is used to determine the percentage change in drag for a baseline vehicle caused by any given configuration change.

$$\begin{gathered} C_{D2}{A}_2={\displaystyle \frac{\frac{1}{2}\rho V_1^3{C}_{D1}{A}_1+R\left(V_1-V_2\right)}{\frac{1}{2}\rho V_2^3}} \\ \%DragChange={\displaystyle \frac{D_2-D_1}{D_1}}={\displaystyle \frac{C_{D2}{A}_2-C_{D1}{A}_1}{C_{D1}{A}_1}}={\displaystyle \frac{C_{D2}{A}_2}{C_{D1}{A}_1}}-1 \\ \%DragChange=\left({\left({\displaystyle \frac{V_1}{V_2}}\right)}^3+{\displaystyle \frac{2R(V_1-V_2)}{\rho V_2^3{C}_{D1}{A}_1}}-1\right)100 \end{gathered}$$

(4)

The percentage drag change determined by Equation (4) is primarily determined by the values inputted for the road-measured speeds, $V_1$, and $V_2$. To apply the formula, an approximate estimate of the baseline vehicle’s drag area and rolling resistance is required. It was shown in [44] via a sensitivity analysis that only general estimates of these values are required, as the formula is relatively insensitive to the values used for the drag area, $C_{D1}{A}_1$, and R. The formula’s primary sensitivities are related to the values inputted for $V_1$ and $V_2$, highlighting the need for the accurate determination of the road-measured speeds using GPS to gain representative results.

3.1.2. Test Track and Testing Conditions

A 3.5 km section of public road was used as the test track, which can be seen in Figure 1. The test track comprised a main test section and two pretest sections, which led into the main test section from either side. To ensure minimal interference from external traffic, all road tests were conducted between the hours 1 and 4 am. The vehicle’s throttle pedal was fixed at the start of the pretest section, after which the vehicle began to reach its equilibrium speed, which usually occurs just prior to entering the main test section. At the centre of the main test section, the vehicle’s speed is recorded using dual frequency GPS, which has a speed measurement accuracy of 0.25 km/h based on the number of satellites the GPS can access along the test track. The vehicle’s speed is recorded using several runs travelling in both directions. Testing was conducted only on dry, calm nights, where the external wind speed was measured to be less than 2 km/h using a handheld hot-wire anemometer at the centre of the test track over a period of 90 s. In general, the external wind speed for most test nights was less than 1 km/h, and any slight wind was accounted for by recording the vehicle’s speed when coming from both directions. The track had substantial tree cover on either side, which added additional protection from any slight external wind that came perpendicular to the track. In general, the averaged speeds recorded when coming from both directions were approximately the same, or varied by at most 1–2 km/h due to any slight external wind conditions during testing. Any runs encountering traffic interference that would have affected the equilibrium speed recorded at the speed record point were scrapped; however, scrapping a run was uncommon due to the minimal traffic interference along the test track during the testing hours stated.

3.1.3. Testing Procedure and Test Vehicles

The throttle pedal position for the test vehicles was monitored using an OBD II Bluetooth scanner (OBDLink MX+). This scanner also provided information on the vehicle’s power output, based on measurements from quantities such as mass air flow rate and fuel injection data. As stated previously, the power output measured using three different power indicators during testing confirmed that the engine’s power output remained constant across configuration changes for a fixed throttle pedal. Prior to any speeds being recorded, the test vehicle was warmed up for approximately 20–30 min by driving it along the test track. This allowed the vehicle’s engine, tires and other moving components to reach normal operating temperatures. In general, a given vehicle configuration required 6–10 runs until the vehicle’s constant equilibrium speed could be determined. This was performed by observing a modal speed for the runs in each direction. Once the modal speed was recorded in each direction after the required number of runs, an average of these two speeds was taken, which resulted in the overall equilibrium speed recorded for a given vehicle configuration. The two test vehicles used for the study were a 2017 VW Golf Mk7 1.6 L diesel, and a 2018 Citroen Berlingo commercial van 1.6 L diesel L1 H1. Both these vehicles are shown in Figure 2.

As stated previously, to use Equation (4), a rough estimate of the test vehicle’s baseline drag area and rolling resistance were required. The VW Golf Mk7 was taken to have a $C_D$ value of 0.305 based on CFD results [44] and outline values based on online sources where the manufacturer claims the vehicle to have a $C_D$ value between 0.3 and 0.31 depending on spec [46,47]. The rolling resistance value for the VW Golf Mk7 was taken as 150 N, which was based on its mass and the road surface of the test track. This value is typical for a hatchback vehicle of this size, based on an example in [5] which outlines a similar value for a Mercedes Benz B-Class. The drag coefficient for the van was based on an online source stating it to be 0.35 [48], and the rolling resistance value was taken as 200 N, which accounts for the van’s larger mass, and condition based on a service life as a commercial van with over 100,000 km travelled. These values match those used in [44] for the same vehicles. The VW Golf Mk7 was used for this study on account of its availability to the authors as a personal vehicle, and the Citroen Berlingo van was provided by the University of the authors to assist with research activities. The frontal areas of the vehicles were measured using a CAD frontal area projection tool, which used highly detailed STL files for both vehicles. The frontal areas for the car and van were measured as 2.113 m² and 2.800 m² respectively.

To ensure a fair comparison of the drag force deltas between road measurements and CFD predictions, the denominators in the percentage drag change formulas for the CFD data use the same reference values as those used for the road data. This means that in the percentage drag change formula for the van and car, the deltas are always divided by 0.35 and 0.305, respectively, when the areas for the vehicle configurations remain constant. For both the car and van, the frontal projected areas remained constant across all rear drag reduction device configurations, including when no devices were fitted. The only case where the area changed was with the taxi sign roof fittings.

3.2. Measuring Surface Pressure On-Road

Surface pressure tests were carried out during calm wind conditions, with average external wind speeds measured below 1 km/h using a handheld hot-wire anemometer during a 90-s sampling interval at the test location. Generally, 8–10 runs were conducted for each vehicle configuration with 4–5 runs in each direction. Testing was conducted at a vehicle speed of 100 km/h, and the final average pressure values recorded at each patch were determined by averaging the data from all test runs. Within a given run, the pressure values at each patch showed highly consistent values; therefore, each patch’s pressure value was recorded with a resolution of 0.5 Pa. Within each run, each patch pressure was determined by taking the median pressure over that full run. When working with rear drag reduction devices, six pressure patches were fitted to the base of the test vehicle.

The surface pressure patches were connected to the pressure scanner via small tubing, which was run along the surface of the vehicle into the passenger-side window, which was slightly lowered to allow the tubes to enter the cabin. The pressure measurement equipment used was an EvoScann P8-D, a true differential pressure scanner capable of measuring pressure with an accuracy of ±3 Pa and a resolution of 0.06 Pa across a full-scale range of ±2000 Pa. The scanner’s static reference input was connected to the static port of a pitot-static probe located on the vehicle’s front bonnet. This reference probe was installed at a location (confirmed by prior CFD analysis) that corresponded to 0 Pa static for both the VW Golf Mk7 and Citroen Berlingo configurations. Additionally, a front-mounted pressure patch was placed on the front licence plate of the test vehicle. The main frontal stagnation point ($C_p$ = 1) for both vehicles was located at an air intake vertically beside the licence plate, which was confirmed using CFD. This meant that the pressure value recorded at the front patch was slightly less than the ideal total pressure value calculated when travelling at 100 km/h using $1/2\rho V^2$. Images of the setup and equipment are outlined in Figure 3.

The EvoScann P8-D unit includes eight available input channels and one designated reference port. During testing, six of these are used for taking surface pressure measurements of interest, one is used at the front licence plate, and one is kept open. The open port remains unconnected and exposed to the cabin’s internal static pressure for monitoring purposes. This port is monitored in post-processing to ensure that it remains relatively constant during a run when travelling at 100 km/h. Due to the slightly open window, pressure inside the vehicle can fall significantly below ambient, with observed readings reaching approximately −250 Pa while driving at 100 km/h. One noteworthy effect can be observed with this patch while the vehicle is stationary: if the air conditioning is turned on, even to its lowest power setting, this pressure port reports a noticeable drop in cabin pressure. Therefore, the inside of the test vehicle should never be used as the static reference port because internal cabin pressure is highly prone to pressure drops below 0 Pa static from air leakage through windows or through the air conditioning vents. This is why a front-mounted pitot static tube was used as a reference pressure.

3.3. Surface Flow Visualisation On-Road

To visualise surface flow, on-road testing using tufts was conducted and recorded using a GoPro Hero 12 mounted on the test vehicles as shown in Figure 4. Using video-recorded imagery to produce averaged images based on many still images offers a better understanding of the surface flow compared to just a single still image. This is particularly true when observing regions with significant transient flow features, such as behind a wheel well. Figure 4 highlights how the tufts immediately behind the front wheel are much more prone to fluctuation and how a mean is barely distinguishable due to the transience. Additionally, it shows how the car’s wing mirror deflects the surface flow underneath it slightly due to its presence. When reviewing video of tufts in transient locations, any given two stills could show significantly different positions for each tuft, hence the need for an averaging method based on a video recording. Post-processed images, as those shown in Figure 4, were created with Adobe Photoshop. By creating what is known as a “Smart Object” in Photoshop, stack features can be applied to the smart object to calculate still quantities such as mean and standard deviation.

The mean gives a general measure of the overall flow pattern, while the standard deviation gives a quantification of the level of transience on the section of interest. Where there is significant transience, the mean image will represent the tufts faintly, as there is a general lack of a mean flow in any given direction. Therefore, it can be more useful to use pixel-wise maximum projection images like those shown in (b) in Figure 4, which allow the user to visually decide for themselves the mean direction of the flow if applicable, and the level of transience located at each tuft. Post-processed images were created using four seconds of video footage captured at a frame rate of 22 fps. Videos were then sampled at 7 fps to generate a composite image of approximately 28 tufts overlaid.

4. CFD Methodology

The CFD methodology used for the RANS (Reynolds-Averaged Navier–Stokes) simulations matches that used in [44]; therefore, only the main components of the RANS methodology are summarised here for brevity. Additional detail is provided on the HLES (Hybrid Large Eddy Simulation) methodology, which was not included in the work outlined in [44].

4.1. Governing Equations

4.1.1. Reynolds-Averaged Navier Stokes

For the simulations where RANS was applied, the governing equations were based on the Reynolds-Averaged Navier-Stokes equations, described in detail in [49]. These equations can characterise the time-averaged behaviour of incompressible fluid flow. The continuity equation is presented in Equation (5), while the momentum equation is given in Equation (6). In these expressions, $u_i$ represents the velocity component in the $x_i$ direction, $\rho$ is the fluid density, P denotes pressure, t is time, and $\mu$ is the dynamic viscosity.

$${\displaystyle \frac{\partial \overline{u_i}}{\partial x_i}}=0$$

(5)

$$\rho {\displaystyle \frac{\partial \overline{u_i}\overline{u_j}}{\partial x_j}}=-{\displaystyle \frac{\partial P}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}\left(\mu {\displaystyle \frac{\partial \overline{u_i}}{\partial x_j}}-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)$$

(6)

The RANS-based simulations in this study were carried out using ANSYS Fluent, which numerically solves the governing equations together with a turbulence model. In this study, the k–$\omega$ SST model was employed [50], where k denotes the turbulent kinetic energy and $\omega$ is the specific dissipation rate. Throughout this work, a one-count change in drag refers to a variation of 0.001 in the drag coefficient, $C_D$.

4.1.2. Hybrid Large Eddy Simulation

HLES applies a RANS formulation within the boundary layer, transitioning to a LES formulation in the mixing layer and in regions where the flow detaches from the surface. Among the widely used HLES methods is the Stress-Blended Eddy Simulation (SBES) [51], a proprietary approach developed by ANSYS. The SBES model blends the turbulence stress tensor according to Equation (7). In theory, any RANS and LES combination can be used. When both models rely on eddy-viscosity formulations, the resulting expression simplifies as shown in Equation (8). The $f_{SBES}$ shielding function introduces some of the model’s main complexity; however, its formulation is not publicly disclosed by ANSYS. A key benefit of SBES is its ability to quickly switch/transition between the RANS and LES zones [51]. The SBES method was applied in this study when performing HLES CFD simulations.

$${\tau }_{ij}^{SBES}={\tau }_{ij}^{RANS}{f}_{SBES}+{\tau }_{ij}^{LES}(1-f_{SBES})$$

(7)

$${\nu }_{ij}^{SBES}={\nu }_{ij}^{RANS}{f}_{SBES}+{\nu }_{ij}^{LES}(1-f_{SBES})$$

(8)

4.2. Domain Setup

The geometries for both the VW Golf Mk7 and Citroen Berlingo van were created from highly detailed STL files for the vehicles, which were then wrapped and cleaned to remove extra details—generally unneeded in the evaluation of aerodynamic changes due to configuration changes on the vehicles. The wrapping and cleaning of the geometry also facilitated easier meshing of the models. The drawing of the appendable devices and general edits to the vehicle geometries were carried out using Solidworks 2021 SP3. The wheels of the geometries were represented as smooth, no spoke, or tire tread wheels, which facilitated the application of the rotating boundary condition on their surfaces. One of the main simplifications to the vehicle geometries was to model their undersides as smooth and to have no internal flows through the vehicles. As the CFD was used to evaluate changes in aerodynamics on the vehicles due to the appending of rear drag reduction devices and roof fittings, this slightly relaxes the implications of not detailing these components. Having a smooth underside on the vehicle would slightly alter the rear wakes that are simulated on the vehicles. The underside of the real VW Golf Mk7 was generally quite smooth, while the underside on the van was much less smooth. This is one of the reasons why the CFD-predicted drag deltas presented in [44] showed very close agreement with the road-measured deltas for the configuration changes to the VW Golf Mk7.

The fluid domain surrounding the geometry was generated using Ansys SpaceClaim 21R2. The domain (Figure 5) extended 5L upstream, 12L downstream, 6H vertically above, and 4.5W laterally from the vehicle, where L, H, and W represent the vehicle’s length, height, and width, respectively. The chosen domain dimensions ensured a blockage ratio below 1%. The domain’s ground surface was defined as a moving no-slip wall, moving at the same velocity as the inlet flow. A pressure outlet boundary condition with a reference pressure of 0 Pa was applied at the domain’s exit. The simulations related to the VW Golf Mk7 included a full vehicle domain, whereas the simulations for the Citroen Berlingo van were performed on a half vehicle domain, mirrored through the vehicle’s symmetry plane. This was performed to save on cell count when working with the van. A confirmation study assessing the suitability of splitting the fluid domain was conducted using the same van geometry in [44]. The study reported an absolute difference in baseline drag coefficient of only 2 counts for two van configurations, with no variation observed in the relative delta between the two configurations. For both vehicles, the remaining sky surfaces were given symmetry boundary conditions.

4.3. Mesh and Solver Settings

All models were meshed using the native meshing tool within Ansys Fluent. The surface mesh featured elements ranging from 1 mm to 8 mm in size on bulk surfaces, while finer features were resolved with elements as small as 0.1 mm. An inflation layer comprising 16 layers was grown on model surfaces, with the first cell height set at 0.035 mm to maintain a y+ value close to 1 across most of the vehicle. A poly-hexcore mesh structure filled the fluid domain. In terms of volume mesh refinement around the vehicle models, near region cells were sized at 12 mm, surrounded by progressively coarser refinement zones of 24 mm, 48 mm, and 96 mm. In the wake region, the refinement started with 12 mm elements and increased to 24 mm, 48 mm, 60 mm, and 96 mm further downstream. Additional local mesh refinements around features such as wheels, mirrors and appendables were also applied using 4–12 mm elements. The rest of the domain was capped at a maximum element size of 204.8 mm. Overall, mesh sizes ranged between 40 million and 60 million cells. A general outline of the structure of the baseline mesh used is shown in Figure 6. For the RANS simulations, turbulence was modelled using the k–$\omega$ SST model. A steady-state, pressure-based, coupled solver with pseudo-transient formulation was employed, using air properties of 1.2215 kg/m³ for density and $1.8013\times {10}^{-5}$ Pa·s for viscosity. The velocity inlet was specified as 27.78 m/s. At 27.78 m/s, the resulting Reynolds number was $8.48\times {10}^6$, based on an approximate vehicle length for both vehicles of 4.5 m. Second-order accuracy was applied to all numerical solver schemes. Each RANS simulation was run for 1250 iterations, with the aerodynamic coefficients averaged over the final 500 iterations.

For the HLES simulations, the Stress-Blended Eddy Simulation (SBES) approach within Ansys Fluent was employed, utilising the Dynamic Smagorinsky model for sub-grid scale turbulence. The RANS region of the hybrid approach used the SST turbulence model. Pressure–velocity coupling was performed using the SIMPLEC algorithm, with momentum discretisation based on the recommended bounded central differencing scheme. A first-order implicit scheme was applied for the transient formulation. To satisfy the mesh fidelity requirements of the HLES approach, a significantly refined mesh was created, incorporating additional refinement around the vehicle body and its wake. This refinement increased the total cell count for the models to over 100 million cells. Simulations started with a RANS initialisation for 1250 iterations. Following this, a series of flushing steps was conducted, including five quick flow passes with a timestep of 0.0036 s, five more at 0.0018 s, and two additional passes at 0.0009 s. After this flushing process, the final timestep of 0.00025 s was used for five flow passes, followed by the main averaging across a final six flow passes. Each timestep used five inner iterations. In total, the simulations covered approximately 4.14 s of physical time. The final timestep was selected to maintain a Courant–Friedrichs–Lewy (CFL) number below or near 1 in the vicinity of the vehicle and its wake. In localised regions where flow acceleration occurred near the vehicle surface, such as between the end of the windscreen and the start of the roof, the CFL number rose slightly above 1. To assess timestep sensitivity, a verification run was carried out using a timestep of 0.000125 s on the VW Golf Mk7 equipped with a rigid, triple cavity, rear drag reduction device. This simulation produced a drag coefficient of 0.242, which was just one count less than the 0.243 value obtained with the larger timestep. For comparison, the RANS simulation for this vehicle configuration yielded a $C_D$ value of 0.236, indicating that reducing the timestep slightly improved the agreement seen between the HLES and RANS results.

4.4. Mesh Sensitivity Study

The meshing methodology used in this study follows that of [44], which showed that the variation in $C_D$ between the baseline and finest meshes in a mesh sensitivity study of the Citroen Berlingo van was less than 1%. An additional mesh sensitivity study was conducted for the present study on the VW Golf Mk7 fitted with a taxi sign, the results of which are outlined in

Table 1. CFD-predicted $C_D$ values using the RANS methodology for the VW Golf Mk7 fitted with a taxi sign in the mesh sensitivity study.

Mesh Name	Baseline	Fine	Very Fine
Cell Count (millions)	43.2	64.3	97.9
Drag Coefficient	0.4043	0.4034	0.4031
% $C_D$ Change	–	$-0.22\%$	$-0.30\%$

. Similar to the result found in [44], the percentage difference between the baseline and very fine mesh was less than 1%, with the exact difference in $C_D$ equating to approximately 1 drag count. This result highlights the appropriateness of the baseline mesh in producing mesh-independent results for its current level of mesh refinement. The fine mesh was produced by refining the surface mesh only, reducing the maximum surface element size to 4 mm on all bulk surfaces. The very fine mesh utilised this refined surface mesh with additional volume mesh refinement both near the vehicle and in its wake.

5. Cross-Validation of Methods and Prior Validation

A validation study was performed in [44] using a series of coastdown tests to validate the correctness of the drag delta predicted using the new constant power method for the VW Golf Mk7 fitted with a taxi sign. This showed that the coastdown tests found, on average, a drag increase of 37.3% due to the taxi sign, compared to the 41.8% predicted with the new method. Additionally, the CFD methodology predicted a drag increase of 39.8%. As the road testing and CFD methodology used in this study match that in [44], this study draws on that validation to confirm the validity of the results. The level of agreement shown in the eight configurations studied in the results section of [44] also demonstrates the ability of the CFD to predict deltas that match those measured on the road.

Additionally, this article’s results section (Section 6) details comparisons between CFD and road measurements, using drag deltas, surface pressure measurements, and surface flow measurements. The level of agreement demonstrated between the results for the configurations that are rigid and non-flexible serves as additional cross-validation for the testing methodologies discussed.

6. Results and Discussion

6.1. On-Road Drag Change Measurements

All CFD-predicted drag changes stated in this section are based on the RANS methodology. The air density used for the CFD simulations, as stated in Section 4.3, was 1.2215 kg/m³. When calculating the road-measured drag change using Equation (4), the same density value was applied. Although the most appropriate value for $\rho$ is that measured on the testing night when $V_1$ and $V_2$ are recorded, the formula is highly insensitive to $\rho$. Therefore, for simplicity and consistency across tests with slightly varying air densities, and for direct comparison with CFD, a single value of 1.2215 kg/m³ was used. To demonstrate this insensitivity, if a value of 1.25 kg/m³ were used for $\rho$ when calculating the road-measured drag change in

Table 2. Drag change results for the van with the inflatable triple cavity.

Configuration Name	${\mathit{V}}_1$ (km/h)	${\mathit{V}}_2$ (km/h)	Road-Measured $\Delta$ Drag	CFD Predicted $\Delta$ Drag
Van with Inflatable Triple Cavity	99	103.25	$-13.5\%$	$-16.3\%$ *

* CFD prediction based on idealised geometry for the device.

, the result would shift only from 13.52% to 13.48%, confirming the suitability of using a single air density value.

An important consideration when interpreting the CFD-predicted drag changes for the inflatable and foam cavity devices is that the simulations are based on idealised CAD geometries. In practice, discrepancies existed between the CAD models supplied to the manufacturer and the final manufactured devices. The degree of sealing between each device and the vehicle rear also has a significant impact on the drag reduction achieved, with tighter seals generally producing greater benefits. Accurately representing the exact level of sealing in CAD is difficult due to the shape uncertainties when working with such devices. Therefore, the CFD-predicted drag changes for the inflatable and foam devices should be viewed as idealised indicators for the performance achievable under optimal manufacturing and sealing conditions.

6.1.1. Van with Inflatable Triple Cavity

A rigid triple-cavity device for the Citroen Berlingo van was first outlined in [44]. An inflatable version of this device was developed in an attempt to preserve similar performance while offering the added benefits of reduced weight, lower cost, and easier storage. Figure 7 outlines the final manufactured version of this device. A key limitation of inflatable devices is that their section thickness must be significantly greater than that of rigid devices. By having a thickened section for the cavities, the rear projected surface area of the multi-cavity device is increased, which can negatively affect drag reduction, as those rear surfaces are subjected to pressures below ambient static pressure. This is especially the case for the outer and middle cavity, but less so for the inner cavity, which can have a positive pressure exerted on its rear face as it makes contact with a downstream high-pressure bubble. Details on how a multi-cavity device reduces drag using this downstream high-pressure bubble are outlined in detail in [15,44]. The contrast between the manufactured inflatable and the idealised inflatable is shown in Figure 8, where the idealised version is free from any rippled surfaces and, most importantly, the end of the outer cavity features a taper. This taper was omitted from the real inflatable by the manufacturer due to the difficulty of incorporating it into the inflatable design. This tapered surface is needed to help the device converge the wake and reduce drag. By not having the taper, the drag reduction realised by the manufactured device was always going to be less than that for the idealised version.

One other interesting feature outlined in Figure 7, is that the device uses a silver reflective heat shield on its underside in the vicinity of the vehicle’s exhaust pipe. This triple-cavity device was one of the first inflatable devices to be manufactured and road tested in this study. On the first attempt at road testing with this device, the device was punctured due to the heat from the exhaust gases after approximately 30 min of driving. Following this incident, all subsequent inflatable devices were fitted with a heat shield in this area. This heat shield solution was very effective at protecting the devices, as no future ruptures of any inflatables due to exhaust heat occurred. This device can be inflated in approximately 2 to 3 min using a high-power, high-flow-rate pump (shown in Figure 7). The device attaches to the vehicle via hooks that engage the panel gap between the doors and body, with straps linking the hooks to O-rings on the inflatable’s surface. Brake lights, indicator signals, and the rear licence plate are still visible when the device is attached to the vehicle.

Table 2 outlines the drag reduction results for this device on the van. The road-measured drag reduction based on the road-measured speeds $V_1$ and $V_2$ was 13.5%. When driving on the road with this inflatable device, the van is noticeably quieter, as the level of turbulence in the van’s wake is significantly reduced due to the presence of the device. It was also observed to handle better in corners, likely due to a more stable base wake in the slightly yawed flow encountered during cornering. The CFD-predicted drag change using an idealised model for the device was found to be 16.3%. This was based on the delta between the CFD-predicted $C_D$ for the baseline van (0.297) and that for the inflatable device (0.240), divided by the road value for the van’s $C_D$, 0.35, outlined previously in Section 3.1.3. To quantify the effect the level of sealing between the device and the vehicle has on the drag reduction, an additional CFD simulation was performed. This showed that if the device was perfectly sealed against the van, the $C_D$ value for the device drops to 0.228, producing a drag reduction of 19.7%. This highlights the need for caution when comparing road-measured results with CFD predictions for flexible or slightly deformable devices. In the context of how multi-cavity devices perform in yawed flow, such as that observed during a crosswind, Ref. [15] showed through a crosswind study that a multi-cavity device was able to maintain its performance when subjected to such flows, providing drag reduction percentages similar to those seen in direct flow.

6.1.2. Van with Inflatable Single Cavity

Having demonstrated that an inflatable triple-cavity device could be constructed, a single-cavity device was developed to offer similar performance. This was achieved mainly by changing the shape of the bottom section, removing the taper and raising it slightly from the bottom trailing edge of the van. This change was made because the bottom taper on the triple-cavity device did not have attached flow, and it reduced performance by increasing the rear projected surface area exposed to underpressured flow. Additionally, removing the inner two cavities reduced the rear projected area, which helped further increase drag reduction, as the device now carried less self-drag. Figure 9 outlines the manufactured inflatable single cavity, while

Table 3. Drag change results for the van with the inflatable single cavity.

Configuration Name	${\mathit{V}}_1$ (km/h)	${\mathit{V}}_2$ (km/h)	Road-Measured $\Delta$ Drag	CFD Predicted $\Delta$ Drag
Van with Inflatable Single Cavity	106.75	109.75	$-9.0\%$	$-18.0\%$ *

* CFD prediction based on idealised geometry for the device.

details the road-measured and CFD-predicted drag reductions. It is notable that the CFD-predicted drag reduction for the single cavity (−18.0%) is greater than that for the triple cavity (−16.3%). This is mainly due to the single cavity’s improved outer cavity design. If another inner cavity were designed to go inside this single cavity, the drag reduction would further improve; however, the improvement would not be as substantial as that seen when working with rigid thin section cavities. Therefore, due to the added self-drag associated with the thicker sections of inflatable devices, implementing them as single cavities is generally more practical, as the marginal gains from using multiple cavities are not large enough to justify the extra material and size.

The road-measured speed, $V_1$, for the unconfigured van outlined in Table 3, is notably much higher than that detailed in Table 2. This was because the road testing associated with the triple-cavity device was performed with 35% throttle compression across configurations, while 37% was used for the single-cavity device. The 35% throttle compression was chosen for the triple-cavity testing in order to keep the recorded road speeds closer to 100 km/h, as it was expected that the $V_2$ for the triple-cavity device would be quite large if testing were performed at 37% throttle compression. The road-measured drag reduction for the inflatable single-cavity device (−9.0%) was notably much lower than that predicted by the CFD (−18.0%) for an idealised device. The cause of the deviation was primarily due to the sizing of the manufactured device, which was slightly too large for the base of the vehicle. This over-sizing issue can be observed in Figure 9, where the top and sides of the inflatable slightly protrude out past the base of the van into the flow. Additionally, the stated CFD-predicted value is based on a tightly sealed inflatable against the rear of the van. This level of sealing was not present on the real device, particularly on the side sections near the van’s lights. Another major cause of the discrepancy is the shape deviations, particularly the rippled surface and the general absence of tapering on the top and sides, which differ significantly from the idealised device.

6.1.3. Car with Foam Cavity

One of the main disadvantages of inflatable devices is the difficulty in making their shape match the desired form drawn and studied in CAD and CFD. A solution to this was to construct a single-cavity device from foam for the VW Golf, CNC milled to allow a closer match between the CAD geometry and the real device. The foam device shown in Figure 10 was constructed from EPS foam, wrapped in aluminium tape, and coated in polyurea paint to provide added strength, waterproofing and general weather resistance. The final device was a very close match with the CFD model in terms of its overall shape. The CFD model for this device predicted a drag reduction of 27.5% as detailed in

Table 4. Drag change results for the car with the foam cavity.

Configuration Name	${\mathit{V}}_1$ (km/h)	${\mathit{V}}_2$ (km/h)	Road-Measured $\Delta$ Drag	CFD Predicted $\Delta$ Drag
Car with Foam Cavity	99	104.5	$-17.4\%$	$-27.5\%$ *

* CFD prediction based on idealised geometry for the device.

. This idealised reduction is based on a perfect seal between the device and the rear of the car, combined with perfect alignment of the device. The main discrepancies between the real device and the CFD model were related to a reduced level of sealing, and the alignment of the device. On the night when this device was road tested, the device was slightly misaligned such that the device was tilted backwards slightly. This can be partially seen in the top left image of Figure 10. This was only observed when reviewing the images of the road-tested device after the testing and comparing them with how the CFD model had the device aligned.

Even with these deviations, the road-tested device still achieved an appreciable 17.4% drag reduction. If the device were better sealed and correctly aligned, it would very likely produce a drag reduction in excess of 20%. Driving with this device on the VW Golf had a very noticeable effect on its speed and acceleration, with the car reaching highway speeds with substantially less throttle effort. The device was light enough to be installed on the vehicle by a single individual. Additionally, when viewed from the rear, both the licence plate and rear lighting systems were visible with only minor obstruction. This device could be further refined by reducing its section thickness, taking its current size down from approximately 150 mm to 75 mm. This would improve both rear visibility and the realised drag reduction, as reducing the rear projected surface would lower the self-drag on the cavity’s rear face.

6.1.4. Car with Inflatable Double Cavity

As the rear of the VW Golf was smaller than that of the Citroen Berlingo van, constructing a triple-cavity inflatable device for it was not feasible, given the required section thickness for each cavity when made from inflatable material. Therefore, to demonstrate a multi-cavity inflatable device on the passenger car, a double-cavity variant was designed and manufactured, as shown in Figure 11. This device was made primarily for studying its usability instead of pursuing a maximum drag reduction. This was due to the van inflatable device results, which indicated that when manufacturing rear devices from inflatable material, the gains from using multi-cavity variants are only marginal due to manufacturable shape constraints. A major issue with this device was the lack of support for the inner cavity when connected to the outer cavity. To help support it, a cable tie chain was used to connect the ends of the top surfaces of the outer and inner cavity, which can be seen in the images of Figure 11. Even with this support, the inner cavity was observed to bounce/oscillate slightly in the vertical direction when on the road during testing. Therefore, the road-measured drag reduction presented in

Table 5. Drag change results for the car with the inflatable double cavity.

Configuration Name	${\mathit{V}}_1$ (km/h)	${\mathit{V}}_2$ (km/h)	Road-Measured $\Delta$ Drag	CFD Predicted $\Delta$ Drag
Car with Inflatable Double Cavity	102.5	105	$-8.0\%$	$-16.4\%$ *

* CFD prediction based on idealised geometry for the device.

was always unlikely to match that predicted with the CFD model. The bouncing issue, combined with a general lack of sealing between the device and the lower rear of the VW Golf, is primarily what caused the road-measured reduction to realise just 8% compared to the 16.4% predicted with CFD. Figure 11 includes an image showing the level of sealing between the underside of the device and the car for the CFD model, which was tightly sealed. This contrasted with the manufactured device, which had a noticeable gap in this region.

6.1.5. Car with Adapted Inflatable Double Cavity

Given that the inner cavity of the car’s inflatable double cavity was prone to bouncing, an adapted version was created by cutting it away. This effectively made a single-cavity device for the car using just the outer section of the original double cavity. Figure 12 shows this device, while

Table 6. Drag change results for the car with the adapted (inner-removed) inflatable double cavity.

Configuration Name	${\mathit{V}}_1$ (km/h)	${\mathit{V}}_2$ (km/h)	Road-Measured $\Delta$ Drag
Car with Adapted Inflatable Double Cavity	102	103.5	$-5.0\%$

presents its road-measured results. Removing the inner cavity did reduce the device’s performance, demonstrating just a 5% drag reduction for its adapted single-cavity variant in comparison to its original 8% drag reduction as a double-cavity. While the realised drag reduction was smaller, the adapted version of this device was significantly more practical and user-friendly. This is shown in the lower images of Figure 12, which illustrate how the device can be easily manoeuvred to allow access to the vehicle’s rear storage space. Reaching through the centre of the device to open the boot was made easier with the inner cavity removed. Additionally, the device can be easily flipped onto the roof of the car to access the boot, or it can remain attached to the hatch as the boot opens. Another benefit of this smaller device is that it can be quickly deflated and easily stored in the boot, taking up less space as a result of the reduced material. The original double cavity can be stored and manoeuvred in a similar way, but it requires more effort and must be fully deflated to fit in the boot, whereas the single variant requires only partial deflation.

6.1.6. Car with Inflatable Single Cavity

The final inflatable drag reduction device prototyped and tested was based on the foam cavity device outlined previously in Section 6.1.3. Two versions of this device were made using two different materials, both of which are shown in Figure 13. The road-tested device, which produced the results shown in

Table 7. Drag change results for the car with the inflatable single cavity.

Configuration Name	${\mathit{V}}_1$ (km/h)	${\mathit{V}}_2$ (km/h)	Road-Measured $\Delta$ Drag
Car with Inflatable Single Cavity	101	103.5	$-8.2\%$

, was constructed from the clear PVC material, which was used for all previously outlined inflatables. A tougher version made from a white PVC material was also produced, which was not road tested as it had the exact same shape as the clear version of the device. The tougher white material was made to assess its added resistance to heat from the exhaust pipe and its enhanced puncture resistance. These two devices also suffered from the same gap issue seen with previous inflatables, with a significant space between the underside of the device and the lower rear of the car. This is shown in the images of Figure 13.

This single inflatable device realised a 8.2% drag reduction when road tested, which was notably less than that for the foam cavity (17.4%), on which it was based. The loss in performance is mostly due to shape deviations in the handmade inflatable devices, which were not present in the CNC-milled foam device. The main shape issues included the general lack of tapering at the end of the device, combined with the previously discussed gap issue. The main conclusion to draw from the road testing results for all the discussed inflatable devices is that shape deviations generate substantial losses in performance. Even when working with more precisely crafted devices such as the foam cavity, issues around alignment and ensuring a tight gap between the device and the vehicle can lead to performance losses. Therefore, to enhance performance, an additional material or membrane should be fitted between the device and the rear of the vehicle to help ensure a tighter seal. Additionally, when working with production versions of such devices compared to the prototype shapes studied here, the level of shape deviation between the devices and that studied in CFD will be significantly less, leading to closer matches between the predicted and road-measured results.

6.1.7. Car with Taxi Sign and Drag-Reducing Roof Ramp

Prior research conducted into the Irish taxi sign [23,44] has shown it to add substantial drag when mounted to any baseline vehicle. Ref. [44] found that when mounted on the VW Golf Mk7, this taxi sign increased drag by 41.8% when measured on the road, matching closely with the 39.8% predicted using CFD. To help reduce this drag increase, Ref. [23] proposed a drag-reducing roof ramp that would be fitted ahead of the taxi sign, which would reduce drag by reducing the frontal stagnation on the roof fitting, while helping the flow wrap around the taxi sign, benefiting downstream pressure recovery. As part of this present study, the proposed roof ramp was manufactured and road tested, as outlined by Figure 14. As this appendable device was constructed from rigid material and its positioning was easily matched with that used in the CAD and CFD, the correlation between the predicted drag reduction using CFD and what was measured on the road was expected to be much higher than that for the previously outlined rear drag reduction devices.

Table 8. CFD-predicted and road-measured drag change results for the VW Golf Mk7 fitted with a taxi sign and a drag reducing roof ramp.

VW Golf	CFD ${\mathit{C}}_{\mathit{D}}$	Area (m2)	CFD Predicted $\Delta$ Drag	Measured Speeds (km/h)	Road-Measured $\Delta$ Drag
with Taxi Sign	0.404	2.230	–	$V_1=92.25$	–
with Taxi Sign and Ramp	0.345	2.246	$-14.0\%$	$V_2=96.25$	$-13.5\%$

outlines how this was confirmed in the results, where the predicted drag reduction of 14.0% matched closely with that measured on the road (13.5%). The surface pressure plot of Figure 14 shows how the front-facing curved section of the ramp is subjected to negative pressures, which produce significant thrust on the ramp, benefiting the overall drag reduction. The skin friction plot of Figure 14 shows how the flow wraps around the roof fittings, with the curvature lines meeting at the roof’s centreline ahead of the VW Golf’s vortex generator/antenna, which aids downstream pressure recovery. With the ramp not fitted, the flow wrapping and subsequent pressure recovery are significantly reduced, observable by the curvature lines meeting much further downstream (shown later in Figure 18), behind the vortex generator/antenna.

6.2. Surface Pressure Measurements

6.2.1. Van with Rigid Triple Cavity

The inflatable triple-cavity device for the Citroen Berlingo van, previously detailed in Section 6.1.1, was based on a rigid triple-cavity device that was first studied in [44]. This rigid device (shown in Figure 15) was used in this present study to quantify the changes to the van’s base pressure map once the device was fitted. Six base pressure patches, labelled A–F, were fitted to the van’s rear, which was divided horizontally into three sections, with patches A–B, C–D, and E–F representing the top, middle, and lower sections, respectively.

Table 9. Pressure deltas recorded at each of the six patches shown in Figure 15 using the three different measurement methods, with an outline for the errors between the CFD methods and the experiment.

Patch Pressure Difference $\Delta \mathit{P}$ (Pa)	A	B	C	D	E	F
Road-Measured	24	20	34	52	64	75
RANS	58	63	52	91	36	49
HLES	23	32	30	46	69	87
RANS Error	34	43	18	39	$-28$	$-26$
HLES Error	$-1$	12	$-4$	$-6$	5	12

outlines the recorded pressure deltas on each of the six patches for the three measurement methods. The road-measured pressure deltas show that the largest base pressure increase occurred on the lower section of the van once the device was fitted, with patches E and F reporting increases of 64 Pa and 75 Pa, respectively. The next largest pressure increase was recorded on the middle section, with the top section showing the lowest pressure rise.

The HLES method successfully predicted this trend with relatively high accuracy, with four out of the six patches demonstrating an error of 6 Pa or less. In contrast, the RANS methodology predicted a noticeably different change to the van’s base pressure map, predicting a greater pressure increase in the upper section compared to the lower section. The limitations of RANS in accurately predicting base pressure distributions for squareback geometries are well documented in the literature. Notably, the AutoCFD workshops [52,53] provide a relevant example, where simulations on a squareback Windsor body using RANS models showed significant discrepancies compared to experimental results, whereas scale-resolving methods demonstrated improved agreement. While RANS struggles to predict the exact shape change to the base pressure map as a result of the rear device, it remains valuable in predicting overall changes in $C_D$ during development. For this device, the RANS method predicted a total drag reduction of 65 counts once fitted to the van, while the HLES method predicted a slightly higher 76 counts. Ref. [44] demonstrated that predictions of drag force changes using RANS showed a high level of agreement with on-road measurements when appendable devices were fitted to road vehicles. For example, the road-measured drag reduction for this device on the van reported in [44] was 17.5%, which correlated closely with the 18.6% reduction predicted using RANS. In contrast, the HLES method would have predicted a notably higher reduction. When working with CAD models of vehicles that have smooth undersides and no internal flows, RANS can produce results that more closely match road measurements due to a potential beneficial cancellation of errors. A rear drag reduction device is likely to produce a greater drag reduction when fitted to a vehicle with a smooth underside, as the lower turbulence and improved flow attachment in the underside flow interact more effectively with the device, leading to enhanced downstream pressure recovery and increased base pressure. Vehicles with messy undersides will experience the opposite effect, reducing the effectiveness of the device. Therefore, the lower drag reductions predicted using RANS are more likely to align with on-road measurements due to a beneficial cancellation of errors when simulating such CAD geometries.

6.2.2. Car with Foam Cavity

The foam cavity device fitted to the VW Golf Mk7, outlined in Section 6.1.3, was equipped with six base pressure patches, as shown in Figure 16. This was performed to correlate the road-measured drag reduction of 17.4% with a corresponding average base pressure increase resulting from the device. Due to the difficulty in CAD modelling the exact level of sealing between the car and the device, no comparisons are made to the CFD pressure changes, as the CFD base pressure measurements are highly sensitive to the represented/modelled level of sealing between the device and the car.

Table 10. Pressure measurements from each of the six pressure patches (as shown in Figure 16) for the VW Golf Mk7, with and without the foam cavity.

Road-Measured Patch Pressure (Pa)	A	B	C	D	E	F
VW Golf Mk7	$-107$	$-110$	$-114$	$-111$	$-100$	$-94$
VW Golf Mk7 with Foam Cavity	$-59$	$-58$	$-58$	$-63$	$-58$	$-61$
Delta	48	52	56	48	42	33
∣% Base Pressure Increase∣	$45\%$	$47\%$	$49\%$	$43\%$	$42\%$	$35\%$

outlines the road-measured patch pressures for each of the six patches for both vehicle configurations. The rear of the car experiences a substantial base pressure increase with the device, as it taps into a higher downstream pressure and distributes this over its base. The cavity, particularly with its end tapers, enhances downstream static pressure recovery, benefiting the overall base pressure increase on the car’s rear. The top (A–B) and middle (C–D) sections experienced the largest pressure increase, with reported deltas of approximately 50 Pa over both sections.

Based on the percentage base pressure increases for the six patches in Table 10, the overall average base pressure rise for the rear is likely between 40% and 50% as a result of the device. A CFD analysis of the baseline car revealed that approximately 50% of the total drag force is carried by the rear alone. For the real vehicle, this value is likely slightly less when accounting for the vehicle’s internal flows, detailed wheels, and less smooth underside. Therefore, the true portion of the total drag force carried by the VW Golf’s rear is likely between 40 and 50%. Taking this as 45% for the purpose of applying a weighting to the measured base pressure increase of 40–50%, the estimated drag reduction for this base pressure rise is likely between 18% and 22.5%. This estimate does not account for the additional self-drag present on the foam cavity, particularly on its angled tapers and end faces, due to their rear-projected surfaces. When accounting for this, the drag reduction is likely closer to the 18% estimate rather than the higher value of 22.5%. Therefore, the road-measured drag reduction of 17.4% shows reasonably good agreement with the estimated drag reduction, based on the measured base pressure increases.

6.2.3. Car with Taxi Sign

The design of the drag-reducing roof ramp described in Section 6.1.7 was motivated by findings in [44], which showed that the Irish taxi sign significantly increased aerodynamic drag. CFD simulations indicated that the taxi sign increased the drag force on the VW Golf Mk7 by 39.8%, closely aligning with the 41.8% increase measured during on-road testing. To investigate the source of this drag increase, surface pressure measurements were taken on the VW Golf both with and without the taxi sign. These measurements used the six original base-pressure patches (A–F) shown in Figure 16, supplemented by four additional roof patches (G–J) illustrated in Figure 17. Both the RANS and HLES methods predicted similar increases in $C_D$ from the addition of the taxi sign, with RANS indicating an increase of 99 counts and HLES predicting 96 counts. Both indicated that the drag increase resulted from an approximate 20 count loss of beneficial thrust ahead of the taxi sign (roof and windscreen), 60 counts of self-drag on the sign itself, 10 counts on the rear roof, and 10 counts on the vehicle’s rear. These are approximate values based on the overall increase of around 100 counts predicted by both approaches. The most notable result is that both methods predicted only marginal increases in drag at the rear of the vehicle.

Table 11. Pressure measurements for the six base pressure patches (Figure 16) and the additional four roof patches (Figure 17) for the VW Golf Mk7, with and without the taxi sign.

Patch Pressures (Pa)	Road Measured			CFD HLES
	VW Golf	with Taxi Sign	$\Delta$	VW Golf	with Taxi Sign	$\Delta$
A	$-107$	$-160$	$-53$	$-109$	$-167$	$-58$
B	$-110$	$-144$	$-34$	$-106$	$-115$	$-9$
C	$-114$	$-135$	$-21$	$-112$	$-107$	5
D	$-111$	$-127$	$-16$	$-114$	$-100$	14
E	$-100$	$-122$	$-22$	$-83$	$-99$	$-16$
F	$-94$	$-114$	$-20$	$-72$	$-64$	8
G	$-314$	41	355	$-224$	82	306
H	–	153	–	–	214	–
I	–	$-429$	$-582$	–	$-372$	$-586$
J	$-241$	$-351$	$-110$	$-186$	$-382$	$-196$

compares the road-measured pressures with those predicted using the HLES methodology. Focusing first on the base pressure patches (A–F), the road measurements indicate a notable reduction in pressure at the vehicle base caused by the presence of the taxi sign. The most significant decrease occurs on the top of the rear (patches A and B), as expected, while the remaining patches (C–F) show pressure reductions of approximately 20 Pa each. In contrast, the HLES predictions do not effectively capture this drop in base pressure. Only patch A demonstrates good agreement with the road-measured values. Patches C, D, and F, in particular, predict positive pressure deltas, which differ significantly from the observed pressure drops of around $-20$ Pa measured on the road. The absence of an appreciable base pressure reduction in the HLES results helps explain why the CFD predicted only a 10 count increase in rear drag due to the taxi sign.

The pressure difference across the front and rear of the taxi sign (patches H–I) shows very close agreement between the road measurements (–582 Pa) and the HLES predictions (–586 Pa), indicating that the CFD likely did predict the correct self-drag component on the taxi sign. However, the roof patches ahead of the taxi sign (G) and behind it (J) exhibit noticeable differences in both absolute and delta values when comparing the road data to the HLES results. It is therefore likely that the CFD’s accurate prediction of the overall 40% road-measured drag increase resulted from offsetting errors, where an underprediction of the rear drag component was compensated by an overprediction of the upstream thrust loss and downstream roof drag. Overall, the results in Table 11 illustrate how CFD can struggle to resolve local pressure variations accurately across the vehicle surface, while still producing a reliable estimate of the total change in drag force.

6.3. Surface Flow Measurements—Car with Taxi Sign

As outlined by the surface flow measurement methodology detailed in Section 3.3, averaged images of tufts produced from video-recorded imagery provide a better understanding of surface flow in transient regions compared to reviewing instantaneous single images. The wake of the taxi sign is one such region, where instantaneous images reveal little about the overall surface flow behind the sign. Figure 18 presents an averaged image of the surface flow in the wake of the taxi sign, alongside CFD predictions of the same flow. Four distinct regions, labelled 1–4, are identifiable in the averaged image and show good agreement with the CFD. Region 1 highlights how the flow begins to wrap inwards far downstream in the wake of the taxi sign. It was previously shown in Section 6.1.7 that the drag-reducing roof ramp enabled the downstream flow to wrap inwards earlier and more effectively (Figure 14), aiding downstream pressure recovery and overall drag reduction. Region 2 illustrates how some of the flow is able to pass beneath the centre of the taxi sign at high speed, which is captured by the very straight alignment of the tufts in the top image of Figure 18. This compares well with the lower CFD skin friction plot, where a green/orange-coloured zone is clearly identifiable in this region, highlighting this fast-moving, attached flow.

Figure 18. Comparison between the road-measured surface flow and that predicted using CFD for the VW Golf Mk7 fitted with the Irish taxi sign.

Figure 18. Comparison between the road-measured surface flow and that predicted using CFD for the VW Golf Mk7 fitted with the Irish taxi sign.

Region 3 is identified as the end of a recirculation bubble directly behind the taxi sign along the vehicle’s centreline, indicated by the vertical standing tufts. Identifying Region 3 using only instantaneous images was difficult and generally inconclusive. In contrast, the averaged image clearly reveals its presence. The CFD predicts this feature effectively, as shown by the vector plot along the symmetry plane in the lower image of Figure 18. Finally, Region 4 shows a zone of reversed flow in the wake of the taxi sign, extending along the centre of the roof to noticeably far downstream. This extensive reversed flow region is also visible in the CFD vector plot, which indicates a similar downstream extent. Overall, Figure 18 demonstrates the usefulness of averaged tuft imagery in understanding overall surface flow patterns in highly transient regions, providing a reliable basis for meaningful, validatable comparisons against CFD-predicted surface flow behaviour.

6.4. Platooning with Multi-Cavity Devices

To conclude the results section, a study into the potential benefits of vehicle platooning with passenger cars employing appendable rear drag reduction devices is presented. A two-vehicle platoon comprising of two VW Golf Mk7s, spaced two vehicle lengths apart (approximately 9 m), was simulated for the four possible permutations of the two vehicles with and without a triple-cavity rear drag reduction device. Figure 19 highlights this triple-cavity device while

Table 12. Drag coefficients for the leader and follower cars (VW Golf Mk7s) in the platooning study, where the leader and follower were optionally configured with a triple-cavity rear drag reduction device.

Configuration Name	Leader ${\mathit{C}}_{\mathit{D}}$	Follower ${\mathit{C}}_{\mathit{D}}$	Leader $\Delta {\mathit{C}}_{\mathit{D}}$ (Counts)	Follower $\Delta {\mathit{C}}_{\mathit{D}}$ (Counts)
Car Only	0.305	–	–	–
Car Triple Cavity (TC) Only	0.236	–	–	–
Car + Car	0.302	0.233	$-3$	$-72$
TC + Car	0.233	0.235	$-3$	$-70$
Car + TC	0.301	0.191	$-4$	$-45$
TC + TC	0.234	0.186	$-2$	$-50$

outlines the respective $C_D$ values for both the leading and following vehicle in the platoon for the four possible permutations. When the car is fitted with the triple-cavity device, it is referred to as “TC” in Table 12. When this device was fitted to the isolated vehicle (not in the platoon), its $C_D$ reduced to 0.236, producing a 22.6% drag reduction. The general trend for the leader vehicle from Table 12, is that it experiences only a marginal drag reduction of 2 to 4 counts. As the deltas between the four permutations for the lead vehicle’s drag reduction only vary by 1 to 2 counts, it is not conclusive to say that one specific type of permutation is optimal for reducing drag on the lead vehicle.

When the baseline car was the follower vehicle, it experienced a drag reduction of approximately 70 counts, with only a 2 count extra benefit when the lead vehicle was the more bluff baseline vehicle (72 count). Hence, the added benefit of 2 counts out of 70 is not large enough to conclusively state that drafting/platooning is better for the follower vehicle when the lead vehicle is not fitted with a rear drag reduction device. In the scenario where the follower vehicle was fitted with a rear drag reduction device, there was a significant difference in the observed delta, dependent on the lead vehicle’s configuration. If the lead vehicle was also fitted with a rear drag reduction device, there was an additional 5 count benefit for the follower vehicle (50 counts total). Therefore, it can be conclusively observed that when both the leading and following vehicles are fitted with rear drag reduction devices, the following vehicle experiences an enhanced reduction in drag. The cause of this is likely all due to the less turbulent wake produced by the lead vehicle when fitted with a drag reduction device. This helps the follower vehicle’s device produce an enhanced drag reduction as the device is designed to work optimally in the less turbulent air, which is a closer match to what it experiences when it is an isolated vehicle.

Overall, the benefits of using a drag reduction device and those of drafting/platooning are seen to stack for the follower vehicle. For example, the device, when fitted to the VW Golf, reduces drag by 22.6%, and when this device drafts behind a car in a best-case scenario (leader also fitted with a device), it realises another 50 counts of extra platooning/drafting drag reduction (0.186 vs 0.236, 21.2%). This reduction closely matches the reduction for the VW Golf following the VW Golf (0.233 vs 0.305), at 23.6%. As the overall drag reduction for the follower vehicle in the best-case scenario is 39% (0.186 vs 0.305), the effective 20% reductions (device and platooning effect) approximately stack to make the overall drag reduction of nearly 40%.

This result is significant for future vehicle-to-vehicle (V2V) communication systems, where autonomous passenger cars might be used as vehicle trains for transporting people and goods long distances at high speeds. Hence, attaching rear drag reduction devices to platooning vehicles provides an approximate overall stacking benefit.

7. Conclusions

• A detailed look at some of the latest developments in appendable drag reduction technology for road vehicles was presented, showing results for five inflatable rear-cavity devices, one foam device, a rigid triple-cavity device, and a drag-reducing roof ramp. Of the inflatable devices presented, findings include those for the single, double, and triple-cavity variants. These devices were road tested and simulated using CFD on two road vehicles: a VW Golf Mk7 and a Citroen Berlingo van.
• The best-performing road-tested inflatable device was a triple cavity mounted to the van, which reduced drag by 13.5%. Overall, inflatable devices were found to have practical benefits over rigid devices, including easier storage and mounting. However, their drag reduction performance was closely linked to their manufactured shape and the level of sealing between the inflatable and the rear of the vehicle. Producing an inflatable device that matches the CAD model used in the CFD studies during development can be difficult, and performance degradation was observed due to shape deviations such as rippled surfaces, thickened sections, lack of tapering, and incomplete sealing with the vehicle.
• Due to the thickened section required when working with inflatable devices, an additional self-drag penalty is incurred, as the increase in rear-projected surface area results in an added rearward drag force. This contrasts with thin-section rigid devices, where a panel can have near-negligible self-drag. This led to the conclusion that implementing inflatable devices as multi-cavity variants offers only marginal benefits, as the added drag reduction can be offset by the increased self-drag from the thicker cavity sections.
• The observed driving properties of the test vehicles when fitted with a rear drag reduction device were noticeably improved over the standard vehicles. Clear increases in acceleration, reduced throttle effort for maintaining road speeds, and improved handling while cornering were all observed when driving with some of the most effective rear devices outlined in this article.
• Road testing with a foam cavity device mounted to the VW Golf Mk7 was found to reduce drag by nearly 20%, with corresponding base pressure measurements indicating the device offered a near 50% increase in base pressure inside the cavity. Additionally, base pressure measurements taken from a van fitted with a rigid triple-cavity device also showed substantial base pressure increases. When compared with CFD, scale-resolving methods such as Hybrid-LES were found to offer much closer agreement with the road-measured pressure deltas than the RANS methods, even though both CFD approaches predicted similar overall drag deltas for the device.
• A drag-reducing roof ramp was developed to reduce the drag penalty resulting from a roof-mounted taxi sign. The ramp was found to reduce drag by 13.5% as measured on the road, which correlated well with the CFD-predicted 14% drag reduction. Surface flow measurements were taken in the wake of the taxi sign using video-recorded images of tufts, which were then averaged to produce a single still image. This averaged image provided a much better understanding of the flow features compared to simply reviewing a series of still tuft images. The averaged image showed a high level of correlation with CFD predictions, highlighting the effectiveness of the video-recorded method in seeking meaningful and validatable results against simulation.
• Finally, a platooning study was performed using two passenger cars fitted with triple-cavity rear drag reduction devices. The study showed that the benefits from platooning and from the use of the devices were found to stack for the following vehicle, which experienced a substantial overall drag reduction. This highlights the potential for using rear devices in future autonomous vehicle technology to improve overall fuel savings in platooning vehicle trains.

Outlook

Overall, there is a clear need in the road transport sector for improved fuel economy, and appendable drag reduction technology offers a viable solution to help address this, particularly for road users who frequently undertake long-distance, high-speed journeys. The rear of a road vehicle is the most suitable location for such a device. A rear-mounted cavity device can be constructed from a range of materials, including rigid, inflatable, or foam, each offering different trade-offs between practicality and performance. Current EU legislation does not prohibit or regulate the mounting of rear drag reduction devices on smaller road vehicles (M1, N1), provided they do not obstruct rear visibility, lighting systems, or number plates.

A rear drag reduction device could therefore be designed for smaller road vehicles that doubles as a rear-mounted storage box, which can be configured into a cavity device. The van category (N1) is particularly suitable for this, given its flat rear end, additional towbar mounting options, and the high potential for aerodynamic benefit, since the rear of the van typically contributes a large proportion of the vehicle’s total drag. Reducing this component would result in substantial fuel savings. Appendable devices are intended to serve as a bridge technology, addressing the needs of some users today, until future legislation or evolving requirements prompt automakers to integrate rear drag reduction solutions, such as cavity structures, into production vehicles. This could occur either as standard equipment, optional extras, or by providing standardised mounting points along with a list of approved aftermarket suppliers for such devices.