O principal objetivo deste trabalho é a simulação tridimensional do escoamento em torno de um carro de competição. Na segunda parte deste trabalho foi realizada a simulação do escoamento em três dimensões ao redor do carro, assumindo um escoamento estatisticamente estacionário.
Nomenclature
Introduction
- Motivation and Objectives
- Race Car Aerodynamics
- Drag and Downforce
- Aerodynamic Appendices
- CFD in Racing Cars
- Main Challenges
- Thesis Outline
The drag is the component parallel to the free flow velocity V~∞ and is the sum of the friction drag and the pressure drag. In non-streamlined bodies, such as racing cars, this is the largest contributor to drag force.
Numerical Simulation Method
Mathematical model
- RANS Equations
- Turbulence model
- Domain and Boundary conditions
These are generally more accurate in shear-type flows and exhibit good far-field behavior. An advantage over k-models is the relatively higher stability in the near-wall region with a well-resolved boundary layer under adverse pressure gradients. Menter [6] pointed out the disadvantages in both and suggested a hybrid model, k-ωSST (Shear Stress Transport) which uses the standard k in the turbulent far-wall region but switches to k-ω in the near-wall region.
In this way, it combines the good behavior of k-ω within the boundary layer and in adverse pressure gradients while avoiding the high sensitivity of ω in the free stream. Since unfavorable pressure gradients and separation flow are expected, that is, in the simulation of the racing car, it is the selected turbulence model to complement the RANS equations in this work. The former assigns a value to the variable while the latter assigns a gradient of a variable in the direction normal to the domain boundary.
In the second option, the pressure level is not fixed because momentum equations and its boundary conditions only include pressure derivatives. At the top and bottom, in the aerofoil case, and top and side boundaries, in the racing car, the normal velocity component is assumed to be zero (Vy = 0) and the normal derivatives of all the remaining dependent variables are set equal to zero. On the other hand, the pressure dissipation in the direction perpendicular to the wall is assumed to be zero.
OpenFOAM
- General Features
- Performed Updates
In most commercial codes there are three options to model near-wall velocity and turbulent quantities: no-slip condition, wall functions, and automatic wall treatment. Without applying wall functions and using the no-slip condition at the wall combined with the impermeability of the surface results in accurate boundary conditions for the velocity components Vx = 0 and Vy = 0. The challenging part in a turbulent flow is determining the shear stress in murtw.
The equations are solved down to the viscous sublayer and require a more refined mesh near the wall, but yield more accurate results. Wall functions are computationally less expensive, because the shear stress at the wall is calculated via the log law function. However, modifying code can be challenging due to the lack of documentation and greater depth of the library.
However, the development community is highly fragmented due to the code being open source and the absence of a graphical interface requiring customization. Two modifications were required as the available version of OpenFOAM had some significant differences compared to the other software used, where one would not allow direct code comparison and the other could lead to iterative convergence issues. After several convergence problems in structured meshes, explicit under-relaxation was added, in addition to the implicit one already implemented.
Solution Verification
2D Airfoil Preliminary Case
- Domain and flow conditions
- Boundary conditions
- Numerical Settings
- Grid Sets
- Unstructured grid generation
- Discretization techniques
- Iterative convergence criteria
- Results
- General
- Quantities of interest
- Iterative convergence
- Computational domain size and boundary conditions
- Grid refinement strategy
- Approximation of convective terms of k and ω transport equations
- Structured versus unstructured grids
The anti-slip condition is applied to the surface of the wing profile as described in paragraph 2.1.3. The remaining grid sets (S3 to S6 and U3 to U6) remain comparable (for U) or identical (for S) to the reference grid sets in the common part of the computational domain. Refinement diffusion consists in the refinement of the neighbors of the already marked cells.
The three flow solvers tested include several options for the discretization of the convective terms of the momentum and turbulence quantities transport equations. In the case, the Pout boundary conditions at the outlet are used and first-order upwind is applied to the convective terms of the turbulence quantity transport equations. The plots contain the results of the five grids of each set and the estimated numerical uncertainties.
The most similar results of the two solvers are obtained for multi-block structured networks. In many engineering applications, it is common practice to apply first-order upwind to the convective terms of the transport equations of the turbulence quantities. Results obtained with ReFRESCO, ANSYS Fluent®, and OpenFOAM on first-order (1) and second-order (2) upwind grid sets S1 and U1 in the discretization of the convective terms of the Kandω transport equations.
Car Simulation
Problem assumptions and Computational capabilities
Domain and flow conditions
Boundary conditions
Geometry
- Geometry Description
- CAD Model Preparation
The underfloor is composed of a large flat zone with the same width of the car and a long skid plate, closer to the ground, that goes from the front of the floor to the beginning of the diffuser. The diffuser is located at the rear of the car, towards the underfloor and close to the ground. It has 4 main channels, symmetrical 2 by 2, relative to the XZ plane passing through the center of the motor.
All channels are completely straight and have the same angle of 12.5 degrees relative to the surface. The baseline AOA for this wing is 4 degrees from the plane defined by the underside of the car (underfloor). At the front, shown in Figure 4.3(a), two are integrated into the front bumper, with the intake section receiving undisturbed flow.
In Figure 4.3(a), the first channel can be seen in the front bumper, between the two front radiators. Therefore, they have been simplified to a cylinder-like shape where the area in contact with the ground is flat to avoid meshing problems, Figure 4.12. Finally, all radiators, Figs 4.14 and 4.15, power train line, Fig 4.13, front and rear brake ducts, Figs 4.14 and 4.15 respectively, were closed as internal flows are not within the scope of this work.
Mesh Generation
- Initial Parameters
- Mesh Topology
- Surface Mesh
- Proximity Refinements
- Viscous Layers
- Mesh Quality
A general surface refinement was defined to capture an accurate representation of the geometry, with an element size of 10 mm. However, unlike the 2D case, the complexity of the geometry requires refinements on specific surfaces, not only to capture relevant small edges and curvatures, to keep the geometric details as close to reality as possible, but also to avoid mesh issues such as negative cells. The bottom surface of the diffuser guide vanes is thin and 3 to 4 times smaller than the target element size of the mesh in that area.
1Refinement diffusion consists of refining the neighbors of the cells already marked for refinement. Since the mesh size was on the order of 40 million cells and due to time and resource constraints, it was not possible to calculate the shear stress at the wall by its definition,τw=µ∆U. Unlike NUMECA HEXPRESS®, NUMECA OMNIS® has no built-in tool to calculate either the height of the first cell near the wall(1) or the thickness of the boundary layer.
The boundary layer thickness is calculated using the height of the first cell, number of layers and. The pressure side of the rear wing was completely outside the target value, as shown in Figure 4.24. The lower velocity on the pressure side of the blade also as a lower wall shear stress, as shown in Figure 4.25(b), resulting in a(yn+)2 below that obtained in the suction side.
Numerical Settings
Post Processing and Result Analysis
- Convergence and Forces
- Flow Pattern Analysis
- Unsteady Flow
As mentioned above, the downforce of the subfloor is severely compromised as most of the flow escapes through the gap between the subfloor and the splitter. At the leading edge curvature of the end plate, the flow accelerates and, in combination with the high pressure on top of the wing, generates a vortex that. 2To reduce excessive high pressure openings on the upper part of the end plate are sometimes adopted in the flow direction to allow a small pressure drop.
In (9), Figure 4.34, it is possible to see how the flow towards the leading edge accelerates for a short distance to reach a maximum along the longitudinal direction of the splitter. Between the splitter and subfloor there is a significant gap (11) which creates a low velocity region with recirculation due to the sudden expansion of the flow. The sudden transition from the flat bottom surface of the splitter and the gap to the subfloor does not allow any pressure recovery, leading to a flow behavior similar to a free jet and consequently all the downforce is lost in the splitter.
In Figure 4.35 and according to (13), the zone of high speed near the surface of the body corresponds to more intense streamlines curvatures and thus by definition to a low pressure zone, which explains the lift generated by the car body. In both cross-sections there is a large recirculation zone (15) at the back of the car and in both channels of the diffuser. These cells were located at the tip of the hindwing, near the junction with the endplate.
Conclusions
Achievements
Adequate cell quality throughout the mesh proved difficult to achieve as achieving the (y+n)2 target over the entire surface of the machine proved difficult. It was found that a significant lag in the rear wing reduces the downforce generated. This was mainly due to a large gap between the lower floor and the divider, which reduces the flow rate under the body.
The high pressure area in the front of the car was reduced and the received flow was undisturbed. However, the rear jets did not work in the best conditions because there was a low velocity region that suggested flow separation in part of the channel.
Future Work
Bibliography
Appendix A
Pininfarina H2 Speed Drawing
