Optimal design of aerodynamic force supplementary devices for the improvement of fuel consumption and emissions

Abstract

One of the primary concerns in the automotive industry is energy saving, protecting the global environment and fuel consumption reduction. The main purpose of this study is to develop optimal supplementary parts for reduction of aerodynamic force of highway tractor and trailer combinations to reduce aerodynamic drag, without negatively affecting the usefulness or profitability of the vehicles. In this article, the possibility to improve the aerodynamic performance for boosting fuel economy of trucks is studied by optimal designing of supplementary devices. That will be carried out by using integrated computational fluid dynamic and genetic algorithm for simulation and geometry optimization of applied devices. Also, simulation results are verified by experimental results in wind tunnel. For this purpose, effects of various supplementary devices and configuration are added to space between cabin and cargo compartment to stabilize the vortex and decrease the drag resistance force. Finally, the geometry of appended device with considering the installation and packing conditions is optimized by using a genetic algorithm. Through the analysis of airflow contours and optimization procedure, results indicate that using two plates at the sidewalls of the gap with optimized length and installation angle can reach the maximum reduction of drag force and fuel consumption by 20 and 10%, respectively.

Keywords

Trailer energy emissions computational fluid dynamics genetic algorithm fuel tank blade drag reduction

Introduction

In recent years, with the continuous increasing of road transportation, fuel prices, and emissions, the aerodynamic styling of heavy truck becomes an important issue development of truck Cab, which is one of the main targets for truck manufacturers. In order to evaluate the vehicle aerodynamic performance, wind tunnel and finite element method (FEM) are utilized by manufactures. Wind tunnels are used to simulate air (fluid) flows over vehicles, which is in contact (friction) with the surrounding environment.^1–4 Given the high cost and required equipment for the wind tunnel, the alternative simulation method based on FEM is applied to check the vehicles aerodynamics performance (Figure 1).^5,6

Figure 1.

Pressure flow around vehicle in wind tunnel.

As shown in Figure 2, aerodynamic forces include Drag, Lift, Lateral force, Rolling Moment, Pitching Moment, and Yawing Moment. These forces are effective in fuel economy, emissions, vehicle controllability, and noise-vibration-harshness (NVH).

Figure 2.

Aerodynamic forces.

The drag force is the dominating resistance force, which acts on commercial vehicles and trucks in highway. Drag force at high speeds is one the main resistance force that increases fuel consumption significantly. Increasing speed from 55 to 65 mph, for example, increases drag by about 40%, resulting in a 10 to 15% increase in fuel consumption.^7,8 Drag reduction techniques are mainly divided into two categories; design optimal body shape in manufacturing process, which is usually in conflict with body structure and style parameters. Adding supplementary parts such as Front Fairing, Side Fairing, Rear Fairing, Roof Reflector, Corner blades, Gap seal, forebody, Back blade, and Base Flap that are illustrated in Figure 3.

Figure 3.

Adding supplementary parts for drag force reduction.

Heavy vehicles because of their large frontal area and bluff shapes are aerodynamically inefficient and take up to 65% of fuel to overcome drag. As mentioned by Hsu and Davis,⁹ it is estimated that with a drag reduction of about 40%, 10,000 USD/year/vehicle can be saved. Because of the high cost of development and required testing for any changes in sample model in the wind tunnel. So, before production, original sample FEM is utilized to analyze the influence of aerodynamic parameters and finding optimal body shape. In the case of trailers and trucks, the cab shape has huge impact on the formation of airflow around the body and creation of vortices (Figures 4 and 5). Therefore, proper design of the cabin can significantly affect the drag reduction. Previous studies^10,11 investigated the effects of different types of roof deflectors, side deflectors, and chassis fairings on vehicle aerodynamic improvements. Mazyan¹⁰ analyzed the effect of applying drag reducing devices on a sedan, sports utility vehicle (SUV), and a tractor-trailer model to improve the fuel consumption of the vehicle. They used computational fluid dynamic (CFD) to analyze the percent drag reduction due to the use of different drag reducing devices. Ortega et al.¹¹ employed a full-scale wind tunnel to investigate the changes in the drag coefficient that arise from the installation of supplementary devices for class 8 heavy vehicles. They obtained a better understanding of how different devices affect the performance of other devices installed simultaneously.¹² Singh et al.¹³ could reach drag reduction of up to 18% by implementation of base flaps in heavy and road vehicles. Håkansson and Lenngren¹⁴ presented devices for Volvo FH trailer. Their results demonstrate that fuel Aerodynamic trailer devices have a great potential of reducing drag compared with the tractor. Also, they showed that Side skirts and Frame extension have a large potential to prevent turbulence and vortices in these regions.

Figure 4.

Effects of cab shape and height upon the drag coefficient.

Figure 5.

Effects of wind screen height and angle on air flow over cab roof.

In commercial vehicles such as trailers and trucks, drag force can be reduced by adding supplementary parts. Figure 6 demonstrates the overall effects of each regions role on vehicle drag coefficient. Also, it can be found the main supplementary parts on drag reduction, such as Roof Reflector, Corner blades, Gap seal, forebody, Skirt, Front Fairing, Back blade, and Base Flap.

Figure 6.

Percentage of drag coefficient regions on a tractor-trailer truck.

Previous studies^7,15 demonstrated that in commercial vehicles, total reduction of drag coefficient results in 12% improvement in fuel economy. Average mileages of trailers over a year is about 10,000 mile, which with considering 35 l/100 km fuel consumption rate, it consumes 56,000 l (12,300 gallon) per year. By reducing the drag coefficient reduction, about 12% of fuel consumption reduces, which is equivalent to 4000 pound for a year. Beside that with reduction of drag force, vehicles emissions and NVH reduces significantly. Kassim and Filippone¹⁶ used various aerodynamic retrofitting techniques to reduce heavy vehicle drag and fuel consumption. They numerically simulated realistic on-road operations to represent the effectiveness of these retrofits on various vehicle weights and driving cycles. Their results demonstrated that fuel economy improvement could be achieved from less than 1% to almost 9% annual mileage. Englar¹⁷ studied the effect of the gap between the tractor and trailer. He used a generic truck model for wind tunnel tests. Hyams et al.¹⁸ investigated unsteady aerodynamic flows affecting the fuel economy of Class 8 trucks by numerical solutions of the unsteady Reynolds-averaged Navier–Stokes equations using a parallel implicit flow solver have been given to investigate unsteady aerodynamic flows affecting the fuel economy of Class 8 trucks. Comparison of their numerical results with experimental shows that with increasing yaw angle, the accuracy decreases, whilst excellent agreement with experimental data was obtained for the 0° yaw angle while the 10° case had good agreement.

In this research, a comprehensive CFD study are conducted to investigate the influences of supplementary parts on drag reduction of trucks. For this purpose, geometry of main add-on parts are optimized by using genetic algorithm (GA) to reduce fuel consumption, emission, and NVH. The results of the current study provide optimal supplementary parts usage for improvement of heavy vehicle aerodynamic characteristics.

Modeling and simulation

Governing fluid equations

Two-dimensional equations governing laminate viscous incompressible flows including dimensionless momentum equation are as follows:

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} = 0 \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + \frac{\partial p}{\partial x} = \frac{1}{Re} \nabla 2 u \frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + \frac{\partial p}{\partial y} = \frac{1}{Re} \nabla 2 v

(1)

In this article, the equations are solved by using pressure-based method in external flows. Vector representation of the governing equations is as follows:

\frac{\partial W}{\partial t} + \frac{\partial F}{\partial x} + \frac{\partial G}{\partial y} = \frac{\partial R}{\partial x} + \frac{\partial S}{\partial y} W = [p u v] F = [β u u 2 + p uv] G = [β v uv v 2 + p] R = \frac{1}{Re} [0 \frac{\partial u}{\partial x \frac{\partial v}{\partial x}}] S = \frac{1}{Re} [0 \frac{\partial u}{\partial y \frac{\partial v}{\partial y}}]

(2)

where W is the state vector, G and F are non-viscous fluxes along x and y axis, R and S are viscous flux vectors.

Vehicle longitudinal model

In order to develop longitudinal vehicle dynamics, a force balancing along the vehicle longitudinal axis yields:

M \frac{d U}{dt} = \frac{T_{e}}{R_{tire}} - F_{D} - F_{g} - F_{R}

(3)

F_{D} = \frac{1}{2} C_{D} A_{f} ρ U 2, F_{R} = μ Mg \cos θ, F_{g} = Mg \sin θ

(4)

where, M, U, and T_e are vehicle mass, longitudinal velocity, and engine torque, respectively. A_f and R_tire are cross-sectional area of the vehicle and the wheel radius, μ is the friction coefficient, C_d and ρ are the drag coefficient dependent upon shape and air density, Θ is the road grade, and g is gravitational acceleration. Power and fuel consumption relation by considering equations (3) and (4) can be deduced as:

power = MU \frac{dU}{dt}

(5)

FC = (bsfc) Power

(6)

Relationship between changes in drag and changes in fuel consumption are presented as¹⁹:

\frac{Δ FC}{FC} = \frac{Δ P}{P} = η (\frac{Δ C_{D}}{C_{D}} + \frac{Δ A_{f}}{A_{f}} + \frac{3 Δ U}{U})

(7)

η is a coefficient for presenting driving cycle and driving style, which is considered 0.5–0.7 for a truck at highways. In order to boost fuel economy, first term presents changes in shape to improve aerodynamics, in the second term make truck cross-section smaller, and finally third term is representative of vehicle speed effects.

In this article, Volvo truck FH12 specification and dimension is considered for the modeling (Figure 7). As well as the large dimensions of the complete trailer model, the governing equations will go up, which result in complication and time consuming of FEM. Because of the symmetry of the vehicle, half of the vehicle is modeled to reduce required time for procedure simulation (Figure 8).

Figure 7.

Complete vehicle model.

Figure 8.

Half-car model.

Figure 9.

Trailer model in virtual.

In order to simulate the aerodynamic behavior vehicle, as shown in Figure 9, CFD analysis of proposed model is carried out in virtual wind tunnel. Then boundary conditions are defined as Figure 10. The boundary conditions of the trailer model in 1 atm and 25℃ and steady state are defined. Boundary condition for input air is considered only as air velocity and pressure of output air intends to be zero. Also, surrounded wind tunnel walls are considered non-slip and trailer body proposed to be no friction surface. Finally, trailer meshed model is illustrated in Figure 11. Boundary conditions for CFD analysis of the trailer are presented in Table 1.

Figure 10.

Boundary condition.

Figure 11.

Wind tunnel and trailer mesh model.

Table 1.

Boundary condition specifications.

Boundary – Inlet		Boundary – Outlet
Type	Inlet	Type	Outlet
Location	Inlet	Location	Outlet
Flow regime	Subsonic	Flow regime	Subsonic
Mass and momentum	Normal speed	Mass and momentum	Static pressure
Normal speed	2.7000e+01 (m s⁻¹)	Relative pressure	0.0000e+00 (Pa)
Turbulence	Medium intensity and	Type	Symmetry
	Eddy viscosity ratio	Location	Symm

Boundary – Floor		Boundary – Body Free wall 1 and 2
Type	Wall	Type	Wall
Location	Floor	Location	Body
Mass and momentum	No slip wall	Mass and momentum	No slip wall
Wall velocity	Cartesian components	Wall roughness	Smooth wall
Wall U	2.7000e+01 [m s⁻¹]
Wall V	0.0000e+00 [m s⁻¹]
Wall W	0.0000e+00 [m s⁻¹]
Wall roughness	Smooth wall

Optimization

In order to minimize the drag force with considering the shape and layout of add-on parts, a constrained optimization procedure are developed based on GA. For this purpose, as shown in Figure 12, the length (L) and angle (θ) of the sidewall (supplementary part) are considered as variables to minimize drag force while its layout and variables range are assumed as a constraint function. GAs are adaptive heuristic search algorithm based on the evolutionary ideas of natural selection and genetics. As such, they represent an intelligent exploitation of a random search used to solve optimization problems. GA operates on a population of individuals (potential solutions), each of which is an encoded string (chromosome), containing the decision variables (genes). After an initial population is randomly generated, the algorithm evolves the through three operators:

Selection which equates to survival of the fittest in the defined range of variables;

Crossover which represents mating between individuals to produce new population;

Mutation which introduces random modifications to avoid local minimums.

Figure 12.

Ga procedure.

This process is continued for the number of iterations or to reach a defined value range. The GA parameters and their range in which used here are listed in Table 2.

Table 2.

Parameters and variables amount and range.

Parameter or variable	Value
Number of variable	2
Length range	[0, 1]
Angle range	[0, 20]
Population size	20
Iteration	50
Crossover percent	0.7
Mutation percent	0.3
Mutation rate	0.02
Fitness scaling	Ranking
Parent selection	Tournament selection

In this article, the optimization problem of vehicle aerodynamic force is examined by variation of the truck sidewall geometry change. For this purpose, the length and angle of the side wall (supplementary part) as variables are optimized by GA to minimize drag force and prevent fluid separation by considering its layout and installation. The optimal selection of parameters for drag force minimization is then formulated as a constrained optimization problem as follows^20,21:

{Minimize}_{x \in X} J (x) s . t . h_{i} (x) \leq 0, i = 1, 2, \dots, n_{con}

(8)

where x is a solution to the problem including a vector of the control strategy parameters within the solution space X, which some of them are shown in Figure 13. X defines the lower and upper bounds of the parameters. Moreover, J(x) is the objective function and each inequality h_i(x) represents one of the nonlinear constraints discussed above. Finally, n_con is the number of constraints.

Figure 13.

Some of the optimization parameters are shown.

Results

Validation

To validate the simulation, obtained results in this article are compared with experimental and test results.²² In other words, due to high costs of optimization procedure in experimental and test procedures, several FEM simulation is utilized and optimized, then based on best solution, sample model is developed and tested. The accuracy of developed model depends on geometry, element, and material. In aerodynamic models, boundary conditions and fluid parameters should be determined properly.

Stenvall²² compared the aerodynamic performance (drag force and coefficient) for various trailers (Volvo, Scania, Mercedes, Renault, DAF). Figure 14 demonstrates the resistance force increase relative to the speed. It is obvious that Volvo FH driven at summer has the best performance at high speeds, because of the combination of low wind speeds, low air density, and a proper aerodynamic shape.

Figure 14.

Force increase relative to the resistance at 5 km/h.²²

Also in Stenvall,²² experimental aerodynamic coefficient for various trailers based on various parameters are calculated in Table 2. These results are used for comparison with simulation and optimization results of Volvo trailer body.

Because of that, the tests for trucks FH12 was carried out without the cargo in the wind tunnel, so for comparison, the simulation results with experimental one, trailer body for FEM analysis is modeled without cargo. Simulation model is presented in Figure 15 and air density and wind speed are considered 1.294 kg/m³ and 23.6 m/s.

Figure 15.

Pressure counter and air flow around FH12 model.

Simulation results in Figure 15 presents drag force as 2672 N. In comparison with actual one (2300 N) in Stenvall,²² it is 9% more, which is due to simplification of the model curves.

Optimal structure for drag reduction

As shown in Figure 6, one of the main add-on parts in reduction of drag force are front fairing and filler plates installed on the gap between the cargo compartment and cab.

Gap between cab and container

The gap between cab and cargo filled by three method. In the first method, as shown in Figure 16(a), plates are installed on the sidewalls of cabin transversely. In the second method, two side plates are used to stabilize the vortex of air through the gap between the cargo compartment and the cab (Figure 16(b)). Figure 16(c) illustrates the third configuration that one plate mounted in the center of gap transversely. In this method, air vortexes are stabilized, which reduces drag force and improves aerodynamic performance.

Figure 16.

Various configuration of filler plates installed on the gap between the cargo compartment and cab: (a) Two plates at side walls; (b) two plates at center; (c) one plate at center.

Front fairings

As shown in Figure 17, this device is installed on around cargo compartment front surface. It deflects airflow and prevents flow separation, which causes reduction of drag force. Figure 18 illustrates pressure counter and airflow velocity around trailer.

Figure 17.

Trailer model with front fairings.

Figure 18.

Pressure counter and airflow velocity around trailer with front fairings.

Efficiency of various add-on devices on drag reduction

These supplementary parts are added simultaneously on FH12 trailer. Simulation results for various configurations are presented in Table 3.

Table 3.

Calculation example of aerodynamic resistance assuming constant rolling resistances.²²

Vehicle	Air density (p) (kg/m³)	Frontal area (A) (m₃)	Force at 85 km/h (F_D) (N)	Vehicle speed (v)	Wind speed (wind)	Drag coefficient (C_D)	Yaw angle ( $\circ$ )	Correcte drag coefficient (C_D)
Scania R-series	1.283	9.7	2600	23.6	(3.5)	0.75	8	0.62
Mercedes actors	1.280		2600		(1)	0.75	2.5	0.71
Volvo FH winter	1.294		2300		3	0.58	–	0.58
Renault premium	1.268		3300		(1.5)	0.96	3.5	0.91
DAF XF	1.268		2700		2.5	0.71	–	0.71
Volvo FH summer	1.228		2000		0.5	0.59	–	0.59

It is fairing obvious that installation of two plates at gap sidewalls provide the most efficiency between various configurations in drag reduction. In other words, the optimal device among studied add-on devices is two filler plates installed on the gap sidewalls between the cargo compartment and cab. Therefore, in the optimization procedure, its geometry optimizes by using GA.

Geometry optimization of supplementary part

In this section, the dimensions of the sidewall piece mounted on the trailer Volvo FH12 model (as a device which provides most impacts on drag reduction) are optimized for enhancing minimum drag force. The main dimensions of this part are the angle and length of piece. So, the main objective of GA is determining the optimized value of its angle and length to reduce drag force. GA parameters are presented in Table 5. Also, the optimization procedure for 50 iterations and the best selected next generations are illustrated in Figures 19 and 20, respectively.

Table 4.

Effects of various add-on devices on drag force.

Configuration description	Air velocity (m/s)	Air density (kg/m³)	Drag force (N)	Drag reduction
Basic model	30	1.294	5215.6	–
One plate at center of gap	30	1.294	5201.2	0.27%
Two plates at center of gap	30	1.294	5198.3	0.33%
Front fairing	30	1.294	5207.8	0.15%
Two plates at sidewalls of gap	30	1.294	5179.3	0.7%

Table 5.

Optimization results.

Angle (°)	Length (m)	Drag force (N)	Drag reduction
0	0	5215.6	–
0	1	5179.3	0.07%
0	0.8	5171.2	0.86%
0	0.6	5174.6	0.78%
0	0.4	5189.6	0.5%
5	1	5175.9	0.76%
10	1	5170.3	0.87%
10.52	0.74	5169.4	0.88%
11.34	0.79	5170.2	0.88%
12.2	0.76	5176.3	0.75%
9.65	0.85	5173.3	0.79%
15	1	5180.8	0.66%
10	0.8	5172.7	0.82%
5	0.6	5178.9	0.7%
10	0.6	5183.6	0.61%
10	0.4	5189.7	0.5%

Figure 19.

Solution convergence in GA iterations.

Figure 20.

Child generation for 20 initial population.

Table 5 presents the optimization results for 50 iterations and selected solutions are with various length and angles are determined for each case.

Result demonstrates that GA with considering packaging and installations constraints determines the best optimal solution of device geometry. It demonstrates that the best angle and length are 10.52° and 0.74 m, which results in 0.88% drag reduction (force 45.8 N reduces). Figure 21 depicts the airflow and velocity counter around the trailer with optimized sidewall device mounted on the trailer Volvo FH12.

Figure 21.

Airflow and velocity counter around trailer.

Fuel tank blade

In this article, we develop a blade for fuel tank to reduce the drag and fuel consumption. Simulation results for velocity streamline around fuel tank and vehicle with blade is shown in Figure 22. Also, the drag force and coefficient for with and without fuel tank blade are presented in Table 6.

Figure 22.

Velocity streamline with fuel tank blade.

Table 6.

Effects of fuel tank blade and optimization on drag.

Model	Cd	Angle	Length	Vwind	Af	Fd (drag force)
Base model	0.5837	0	0	1.5	1.294	2302
With blade	0.5817	3	20	1.5	1.294	2300
Optimal blade	0.5789	8.5	29.56	1.5	1.294	2289

It is obvious that with addition an optimized orib blade of fuel tank, drag coeffiecient and force reduce about 0.3% and 0.5%, respectively.

Fuel consumption and emissions

In this section, fuel consumption are compared in two cases; optimized supplementary parts and initial one. As shown in Figure 23 by optimizing the supplementary parts, fuel rate over a traveled path reduces significantly by 20%. Fuel consumption reduction decreases the emissions and the cost of energy. Overall, fuel consumption rate and mileages of trailers are considered to be 40 l/km and 10,000 km per year.^23,24 According to these assumptions, 800 l fuel can be saved in each trailer, which results in a significant reduction of emissions and costs in transportation system.

Figure 23.

Engine operation and fuel rate comparision in two cases.

Conclusion

Fuel consumption is always one of the key issues in the truck design, which significantly effects on emissions and costs. Therefore, the primary objective of this article is to design and optimize the drag force reduction devices, which has the main role in improving fuel efficiency and emissions. For this purpose, a trailer with optimized appended devices was developed and effects of each of them on the reduction of drag force investigated. At the first step, in order to verify the proposed model and simulation, enhanced results for the basic model were compared with the experimental data in wind tunnel.²² Then main add-on devices effects on improving aerodynamic performance compared. Results indicated that the installation of two plates at gap sidewalls provide the most efficiency in drag and fuel consumption reduction. Finally, to minimize the drag force, the geometry of plates at the sidewalls optimized by GA with considering the installation and packing constraints, which results in obtaining the optimal length and angle of installation. Findings showed that with installation, the optimized plates at the side of the gap between cabin and cargo compartment, drag force reduces about 20%, which, it can reduce fuel consumption about 4 to 10% over a year. Also, it was shown that with using all optimal supplementary devices, fuel rate reduces about 800 l for each trailer in a year, which can cause a significant emission and energy cost reduction in the transportation system.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Yaghoub Pourasad received his PhD degree in electrical engineering from the Khajenasir University, Tehran, in 2010. Now, he is an assistant professor in the Department of Electrical Engineering, Urimia University of Technology. His current research interests include electrical engineering, signal processing and optimal design.

Amirhossein Ghanati received his MSc degree in Executive MBA in Industrial Marketing Management from the Uppsala University (Sweden), in 2007. Now, he is vice president for design & engineering in automotive industries of Mine and Trade ministry in Iran.

Mehrdad Khosravi received his BS and MS in mechanical engineering from IAU in 2012 and 2015, respectively. His research interests include computational fluid dynamics, automotive system and aerodynamics.

References

Zhu

. Wind tunnel investigations of aerodynamic coefficients of road vehicles on bridge deck. J Fluids Struct 2012; 30: 35–50.

Chen

. Study of aerodynamic configuration design and wind tunnel test for solar powered buoyancy-lifting vehicle in the near-space. Proc Eng 2015; 99: 67–72.

Gilkeson CA, Toropov VV, Thompson HM, et al. Aerodynamic shape optimization of a low drag fairing for small livestock trailers. In: 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, Victoria, British Columbia, Canada, 2008.

Mahmoodi-k

Davoodabadi

Višnjić

. Stress and dynamic analysis of optimized trailer chassis. Tech Gazette 2014; 21: 599–608.

Shukri IA and Akram AM. Improvement of aerodynamics characteristic of heavy trucks. In: 3rd International conference on trends in mechanical and industrial engineering (ICTMIE'2013), Kuala Lumpur, Malaysia, 8–9 January 2013.

Ortega J and Salari K. Investigation of a trailer underbody fairing for heavy vehicle aerodynamic D-reduction, SAE International, Document Number: 2008-01-2601, 2008.

WSP Development and Transportation. Longer semi-trailer feasibility study and impact assessment, UK: Cambridge, Department of Transport, 2010.

Gao

Smith

Daw

. The evaluation of developing vehicle technologies on the fuel economy of long-haul trucks. Energy Conver Manage 2015; 16: 766–781.

Hsu

Davis

. Drag reduction of tractor-trailers using optimized add-on devices. J Fluids Eng 2010; 132: 084504.

10.

Mazyan WI. Numerical simulations of drag-reducing devices for ground vehicles. PhD Thesis, American University, 2013.

11.

Ortega J, Salari K, Brown A, et al. Aerodynamic drag reduction of class 8 heavy vehicles: a full-scale wind tunnel study. LLNL-TR-628153 Report, 2013.

12.

Bruneau

Gilliéron

Mortazavi

. Flow manipulation around the Ahmed body with a rear window using passive strategies. Comptes Rendus Mecanique 2007; 335: 213–218.

13.

Singh

Rai

Puri

. Effect of moving surfaces on the aerodynamic drag of road vehicles. Proc IMechE D: J Automobile Eng 2005; 219: 803–816.

14.

Håkansson C and Lenngren MJ. CFD analysis of aerodynamic trailer devices for drag reduction of heavy duty trucks. Master’s Thesis, Chalmers University of Technology, Göteborg, Sweden, 2010.

15.

Khaled

Elhage

Harambat

. Some innovative concepts for car drag reduction: A parametric analysis of aerodynamic forces on a simplified body. J Wind Eng Ind Aerodyn 2012; 107–108: 36–47.

16.

Kassim

Filippone

. Fuel savings on a heavy vehicle via aerodynamic drag reduction. Transport Res D: Transp Environ 2010; 15: 275–284.

17.

Englar RJ. Advanced aerodynamic devices to improve the performance, economics, handling and safety of heavy vehicles. SAE Technical Paper, 2001, 2001-01-2072.

18.

Hyams

Sreenivas

Pankajakshan

. Computational simulation of model and full scale Class 8 trucks with drag reduction devices. Comput Fluids 2011; 41: 27–40.

19.

Bellman M. Numerical drag reduction studies on generic truck. MS thesis, Washington University, Saint Louis, Missouri, 2009.

20.

Mashadi

Mahmoodi-k

Ahmadizadeh

. Development a new power management strategy for power split hybrid electric vehicles. Transp Res D: Transp Environ 2015; 37: 79–96.

21.

Montazeri-Gh

Mahmoodi

. An optimal energy management development for various configuration of plug-in and hybrid electric vehicle. J Central South Univ 2015; 22: 1737–1747.

22.

Stenvall H. Driving resistance analysis of long haulage trucks at Volvo. Master’s Thesis, Chalmers University of Technology, Göteborg, Sweden, 2010.

23.

Dindarloo

Siami-Irdemoosa

. Determinants of fuel consumption in mining trucks. Energy 2016; 112: 232–240.

24.

Ehsani

Ahmadi

Fadai

. Modeling of vehicle fuel consumption and carbon dioxide emission in road transport. Renew Sustain Energy Rev 2016; 53: 1638–1648.