Mercedes G-Class W463 Numerical Simulation

1. Introduction

The goal of this project is to carry out a CFD simulation of the 2018 Mercedes G-Class W463 using OpenFOAM.

The Mercedes-Benz G-Class is an iconic vehicle, originally designed in the late 1970s as a robust and versatile off-road model. Over the decades, it has become a symbol of durability and prestige, while retaining its characteristic boxy design and high ground clearance.

2. Geometry

The geometry is a simplified model of the G-Class, available at the following link: https://grabcad.com/library/mercedes-g-class-for-cfd-1

Using a simplified geometry instead of the original reduces the complexity of the mesh, leading to faster preprocessing, lower computational cost, and improved numerical stability. However, since it is not the exact geometry, it cannot capture the full physical realism. The goal of this study, however, is to gain insights and identify flow trends, and the geometry used here is sufficient to achieve these objectives.

3. Physics/Numerics

• Steady state
• Constant density, ρ = 1.2 kg·m^-3
• k-ω SST turbulence model
• Second-order schemes

4. Boundary conditions

• Flow velocity, U = 30 m·s^-1 = 108 km·h^-1, with moving ground and rotating wheels
• Freestream turbulence values from Spalart and Rumsey, using a reference chord length of 1.85 m (height of the car). This leads to:
  • k = 0.0009 m²·s^-2
  • ω = 90.91 s^-1

5. Fluid domain

The car length is L = 4.6 m. The fluid domain used is the following:

6. Meshing

a. General mesh

• Meshing with snappyHexMesh
• Refinement of the tires
• Two refinement boxes around the car: one at 0.5 m (fine) and another at 2 m (coarser)
• Three progressively coarser refinement boxes to capture the car’s wake

b. Mesh quality

• 18,224,493 cells with a dominance of hexahedral cells (17,315,550)
• Maximum aspect ratio: 30.63
• Mesh non-orthogonality: max = 64.98, average = 5.97
• Maximum skewness: 3.2

c. Inflation layers

• Six layers with a final layer thickness of 30% relative to the surface mesh and an expansion ratio of 1.2
• Aim of 30 < y+ < 300 on the entire car and the ground

The following images show the distribution of y+ on the car within the range of 30–300. Most of the car falls within the range, except for certain areas, particularly around the windshield.

d. Visualisation of the mesh

7. Solving

• simpleFoam solver
• The case was run until all force coefficients no longer varied
• The simulation was performed for 7500 iterations on 4 cores

8. Post-processing

a. Drag and lift forces

The following forces represent the forces acting on the car along the X and Z directions :

Fx [N]	Fz [N]
972.19	-185.557

b. Drag and lift coefficients

In aerodynamics, lift and drag forces are typically normalized by the product of the freestream dynamic pressure and a reference area, allowing comparisons between different flow conditions and geometries. The resulting dimensionless quantities are the lift and drag coefficients, denoted C_L and C_D, respectively. The reference area used to calculate the coefficients is A_ref = 3.17 m².

CD	CL
0.571	-0.104

c. Pressure coefficient

The pressure coefficient, C_p, is a dimensionless quantity used to describe how the local static pressure differs from the freestream pressure. It is calculated by dividing this pressure difference by the freestream dynamic pressure. This normalization makes it possible to compare pressure distributions obtained under different flow conditions. A positive C_p indicates a pressure above the freestream value, while a negative C_p indicates a lower pressure.

d. Velocity

e. Skin-friction coefficient

The skin-friction coefficient, C_f, is a dimensionless quantity that measures the friction exerted by the airflow on a surface. It is obtained by normalizing the wall shear stress by the freestream dynamic pressure. In the Cf images, Line Integral Convolution (LIC) is used to visualize the direction of the wall shear stress and, therefore, the direction of the flow near the surface.

f. Streamlines

The next image is obtained using Surface LIC (Line Integral Convolution) on a slice plane.

g. Total-pressure coefficient

Total pressure represents the mechanical energy carried. For an incompressible flow, it is the sum of the static and dynamic pressures. The total-pressure coefficient, C_pT, is defined as the difference between the local total pressure and the freestream static pressure, normalized by the freestream dynamic pressure. It is particularly useful for identifying regions where the flow has lost energy, due to viscous effects for example.

The following images show the isosurface of the total-pressure coefficient at a value of 0. This representation helps identify the sources of drag.

9. Conclusion

In this report, I will not provide a detailed explanation of the car’s aerodynamics, as this is not the main objective of the project, but I will give a brief overview.

The first and most obvious observation is that the G-Class has poor aerodynamic performance, as reflected by its high drag coefficient. This vehicle was not designed for aerodynamic efficiency but rather for off-road capability. One major drawback is its height, which generates a large wake zone behind the car. The isosurface plots of C_pT clearly show this effect, with a significant volume associated with drag generation.

The general shape of the car also creates problems. Its boxy geometry, especially the flat front, makes it difficult for the airflow to escape smoothly, resulting in regions of high pressure and therefore increased drag. The elevated body exposes the wheels directly to the flow, which further adds to drag. Finally, the windshield is not inclined enough, which also increases drag.

Ferrari F2004 Numerical Simulation

1. Introduction

The goal of this project is to carry out a CFD simulation of the Ferrari F2004 using OpenFOAM.

The Ferrari F2004 is one of the most iconic and dominant single-seaters in Formula 1 history. Designed by Scuderia Ferrari for the 2004 World Championship season, it was the result of the work of Rory Byrne (aerodynamics and design), Ross Brawn (technical director) and Paolo Martinelli (engine). Powered by a 3.0-litre naturally aspirated V10 engine, the Ferrari Tipo 053, the F2004 combined raw power, remarkable reliability and aerodynamic efficiency.

This single-seater distinguished itself through its unrivalled dominance, giving Michael Schumacher his seventh and final world title and Ferrari its sixth consecutive constructors' title. It won 15 of the 18 races in the 2004 season, making it one of the most successful cars in history.

The aerodynamics of the F2004 represented the culmination of the V10 era, before the major regulatory changes introduced in 2005. It was notable for its exceptional balance between downforce and drag, efficient flow management around the sidepods and a high-performance rear diffuser. Its design was a refined evolution of the F2003-GA, with a lighter chassis, a lower centre of gravity and outstanding mechanical reliability.

2. Geometry

The geometry is a simplified model of the Ferrari F2004, available at the following link: Ferrari F2004 simplified CAD model

The car model is simplified in several areas. The seat is fully closed to prevent airflow from entering the cockpit, and only the driver’s head is kept, as it has a significant impact on drag. Smaller aerodynamic details such as winglets on the sidepods and some bargeboard elements are left out. The side deflector attached to the sidepod is also missing, as well as the mirrors and supports of the bargeboards. Regarding the underbody, it may not match the original one, since finding accurate references is difficult.

The air intakes are not modelled as functional. In reality, the airflow would be directed into the engine or radiators, but here they are closed surfaces, meaning that the flow simply impacts them. On the other hand, the front and rear wings are close to the real design. I am aware that the absence of some elements can cause deviations compared with the actual car, but the objective of this project is to capture the general airflow trends around this Formula 1 car.

3. Physics/Numerics

• Steady state
• Constant density, ρ = 1.225 kg·m^-3
• k-ω SST turbulence model
• Second-order schemes

4. Boundary conditions

• Flow velocity, U = 50 m·s^-1 = 180 km·h^-1, with moving ground and rotating wheels
• Symmetry plane, with half of the car simulated
• Freestream turbulence using a reference length of 2.42 m, based on the wheelbase, and a turbulence intensity of 1%. This leads to:
  • k = 0.375 m²·s^-2
  • ω = 0.59399 s^-1

5. Fluid domain

The car length is L = 4.47 m. The fluid domain used is the following:

6. Meshing

a. General mesh

• Mesh generated with snappyHexMesh
• Refinement of the tires, front wing, rear wing, underbody and bargeboards
• Two refinement boxes around the car: one at 0.5 m (fine) and another at 1 m (coarser)
• Three progressively coarser refinement boxes to capture the wake of the car

b. Mesh quality

• 20,940,958 cells, with a dominance of hexahedral cells (93%)
• Maximum aspect ratio: 30.0128
• Mesh non-orthogonality: maximum = 64.9858 and average = 7.26472
• Maximum skewness: 3.93352

c. Inflation layers

• Five layers with a final layer thickness of 40% relative to the surface mesh and an expansion ratio of 1.2
• The resulting average y+ value over the entire car and ground is approximately 44, which requires the use of wall functions

The following images show the distribution of y+ on the car within the range of 30–300. Most of the car falls within this range, except for certain areas, particularly around the rear suspension.

d. Visualisation of the mesh

7. Solving

• simpleFoam solver
• The GAMG (Geometric Algebraic Multi-Grid) solver is used for the pressure equation, while PBiCGStab (Preconditioned Bi-Conjugate Gradient Stabilized) is selected for velocity and turbulence variables equations
• The simulation was run for 5000 iterations
• Running on 4 cores, it took 6 days

• It took approximately 1000 iterations to reach a pseudo-steady state. I then decided to start averaging the coefficients from iteration 2000

8. Post-processing

a. Drag and lift coefficient results

When assessing the aerodynamic performance of vehicles, aerodynamic coefficients alone do not always provide the most relevant comparison, as vehicle dimensions are constrained and cannot simply be scaled up or down. For example, a vehicle can have a lower lift coefficient than another while generating more lift because of its larger reference area. It is therefore useful to consider the products SC_L and SC_D, commonly referred to as lift area and drag area. At a given dynamic pressure, these quantities are directly proportional to the lift and drag forces. In this study, the reference area is S = 1.24 m².

SCL [m²]	SCD [m²]	|CL/CD|
-0.997	0.897	1.11

b. Downforce and drag contributions of the different components

The following images show the forces in the X and Z directions. They help to understand the drag and downforce produced by each component.

Components	Downforce contribution [%]	Drag contribution [%]
Bodywork + Suspension + Driver	-46.66	34.19
Underbody	78.88	7.24
Front tire	1.55	15.95
Front wing	28.95	2.83
Rear tire	1.86	17.66
Rear wing	36.97	13.59
Bargeboards	-1.55	8.53

As shown in the table, most of the downforce is generated by the underbody, rear wing and front wing. The underbody plays a crucial role in a Formula 1 car, as it produces the majority of the downforce. In terms of drag, the bodywork accounts for the largest contribution.

c. Pressure coefficient

The pressure coefficient, C_p, is a dimensionless quantity used to describe how the local static pressure differs from the freestream pressure. It is calculated by dividing this pressure difference by the freestream dynamic pressure. This normalization makes it possible to compare pressure distributions obtained under different flow conditions. A positive C_p indicates a pressure above the freestream value, while a negative C_p indicates a lower pressure.

d. Velocity

e. Skin-friction coefficient

The skin-friction coefficient, C_f, is a dimensionless quantity that measures the friction exerted by the airflow on a surface. It is obtained by normalizing the wall shear stress by the freestream dynamic pressure. In the Cf images, Line Integral Convolution (LIC) is used to visualize the direction of the wall shear stress and, therefore, the direction of the flow near the surface.

f. Streamlines

The next image is obtained using Surface LIC (Line Integral Convolution) on a slice plane.

g. Total-pressure coefficient

Total pressure represents the mechanical energy carried. For an incompressible flow, it is the sum of the static and dynamic pressures. The total-pressure coefficient, C_pT, is defined as the difference between the local total pressure and the freestream static pressure, normalized by the freestream dynamic pressure. It is particularly useful for identifying regions where the flow has lost energy, due to viscous effects for example.

The following video represents the isosurface of the total-pressure coefficient when it is equal to 0. This representation helps identify the main sources of drag.

9. Conclusion

In this project, the goal was not to perfectly replicate the real aerodynamic performance of the Ferrari F2004, but rather to understand the main flow structures and aerodynamic behaviour. The results highlight how each component contributes to downforce and drag, confirming the crucial role of the underbody and wings in achieving aerodynamic efficiency. Overall, this simulation provides valuable insight into how race cars balance downforce and drag.