Sim­u­la­tion-Driven Design of a Race Car Rear Wing

In the last years, we have been sup­port­ing student racing teams, such as the FaSTTUBe and the Ryerson Formula Racing Team in Canada. For the Formula Student Germany (FSG) com­pe­ti­tion, Carolina Cura recently worked on the design and shape opti­miza­tion of a race car rear wing. The FSG is a national design com­pe­ti­tion per­formed every year by students from all over Germany. In this blog post, a brief overview of her opti­miza­tion work is given, along with a few results. 

It’s All About the Downforce

In contrast to Formula 1 or similar racing com­pe­ti­tions, the main objec­tive is not con­struct­ing the fastest race car, but the best global concept is being decisive. The inter­play of design, bud­get­ing, business concept and the racing per­for­mance of the vehicle is taken into account. The racing per­for­mance is analyzed using cat­e­gories such as vehicle dynamics, handling, accel­er­a­tion, endurance and fuel effi­ciency. In contrast to ordinary vehicle aero­dy­nam­ics, race car aero­dy­nam­ics focus mainly on down­force mag­ni­tude and dis­tri­b­u­tion, whereas drag force is of sec­ondary impor­tance. Sta­bil­ity and handling of a race car strongly depend on tire per­for­mance, which is directly linked to the balance between front and rear down­force. Opti­miz­ing the loads on the front and the rear tires there­fore leads to enhanced braking per­for­mance, cor­ner­ing speed and thus also sta­bil­ity. Once the general stream­lined shape of the race car is set, the balance between rear and front down­force can be strongly influ­enced by adding so-called wings. The rear wing is known to con­tribute about as much as one third of the overall down­force of the race car. In contrast to appli­ca­tions in aviation, wings designed for race cars differ from the tra­di­tional wings in four dif­fer­ent aspects. First of all, they are designed to produce down­force, contrary to the lifting wings of an airplane. Moreover, accord­ing to these wings have to be designed to operate in (extreme) ground effect, have small aspect ratios and can have strong inter­ac­tions with other parts of the body. See the fol­low­ing figure: It can be seen how a sidewise slip of the tire occurs when sub­jected to a side force, e.g. to inertia due to cor­ner­ing. As a con­se­quence of the side slip, the direc­tion of motion is at an angle relative to the direc­tion of heading. Increas­ing the vertical force (down­force) creates less slip for the same side force or the amount of slip at a higher side force, which means that higher cor­ner­ing forces can be achieved at the expense of the same slip. 

Despite the fact that the addition of wings increases the overall drag force, faster lap times can be achieved by improv­ing the above men­tioned vehicle dynamics aspects. The top speed attain­able through drag reduc­tion is usually sec­ondary when chal­leng­ing tracks with fast corners and high speed brakings are faced. 

Geometry and CFD Analysis

In order to optimize the aero­dy­namic per­for­mance of the rear wing, the cor­re­spond­ing rear wing section con­sist­ing of three airfoils and an end plate on each side of the wing is para­me­ter­ized using CAESES. The starting point for the opti­miza­tion process is a baseline design that had already been opti­mized with regard to the posi­tion­ing of the dif­fer­ent wing elements. All viscous flow com­pu­ta­tions needed for the opti­miza­tion process are per­formed with the com­mer­cial Reynolds-averaged Navier-Stokes solver STAR-CCM+.

Two-Stage Rear Wing Opti­miza­tion Process

In the first step, a 2D section opti­miza­tion is con­ducted to under­stand and to find the optimal inter­ac­tion between the three airfoils. In a second step, a full 3D flow sim­u­la­tion is set up and auto­mated in order to optimize the end plate. In this second step, the opti­mized sections from the 2D study are extruded and combined with the end plate. Para­me­ters such as the shape of the main wing, the lon­gi­tu­di­nal and vertical position of the main and the second wing as well as the angle of attack of all three wings are varied auto­mat­i­cally. For each gen­er­ated design the meshing process and flow analysis can be auto­mated by using the software con­nec­tor from CAESES. 

Geometry Con­straints

In order to prevent unfea­si­ble designs, inequal­ity con­straints are included for the opti­miza­tion. It is nec­es­sary to prevent the airfoils from inter­sect­ing or touching each other, while the relative position and the angle of attack are varied. For this aim, two curves are defined and mon­i­tored. The first line starts at the trailing edge of the main airfoil and ends at the leading edge of the second airfoil. The second line is defined in analogy between the trailing edge of the second airfoil and the leading edge of the third airfoil. The next ani­ma­tion shows how the shape of the main airfoil, the angle of attack of all three airfoils as well as vertical and lon­gi­tu­di­nal position of main and center airfoil are varied:

2D Section Optimization

For the 2D opti­miza­tion of the three wing sections, a set of random designs is gen­er­ated using the inte­grated Sobol sampling algo­rithm of CAESES. After this Design of Exper­i­ments (DoE), a local opti­miza­tion is con­ducted for a selec­tion of promis­ing design can­di­dates. In order to change the shape of the lower section, a fast delta shift trans­for­ma­tion is applied to the original profile. The smaller sections are only rotated and trans­lated by the opti­miza­tion routine.

The opti­miza­tion finally shifted the lower section of the optimal design a bit down­wards and slightly forward. The mid wing section does not show sub­stan­tial changes in position, while the upper wing section of the best design is rotated by a few degrees. The CFD results for the opti­mized design and the baseline design are shown below. Since the baseline design was already opti­mized using a dif­fer­ent workflow, the visual dif­fer­ences in the velocity dis­tri­b­u­tion are rather small, even though the shape changes have some sub­stan­tial effect on the overall performance.

In the pictures, the suction region on the lower surfaces of the airfoils are dis­played as high nor­mal­ized veloc­i­ties. For the opti­mized airfoils, one can observe slightly higher veloc­i­ties. The pressure region on the upper surfaces remains similar for both cases, while slightly lower veloc­i­ties in the flow around the opti­mized airfoils are generated. 

3D Opti­miza­tion of the End Plate

The optimal wing designs from the 2D study are then used as fixed geometry for the 3D opti­miza­tion where the rear wing end plate is varied and analyzed. The shape of the end plate is defined by a para­met­ric CAESES model, which allows the opti­miza­tion strategy to modify the lower left and upper left corner of the plate. The pictures below show the pressure coef­fi­cient dis­tri­b­u­tion for the opti­mized end plate and the baseline end plate design. The increase in down­force is mainly due to a strong pressure increase on the pressure side, while the suction side remains similar for both cases.

Check with Full Vehicle Setup

At the end of the end plate opti­miza­tion process, pre­lim­i­nary sim­u­la­tions of the entire race car, equipped with the baseline rear wing design as well as the opti­mized rear wing design (opti­mized airfoils and end plate) are tested to assess the results. The final opti­miza­tion results give an increase of the overall down­force mag­ni­tude by 3.9% for the full vehicle setup. When split­ting up the two dif­fer­ent opti­miza­tion stages, the 2D opti­miza­tion led to a ~2.14% improve­ment of the down­force mag­ni­tude, while the 3D opti­miza­tion deliv­ered roughly 2.44% of improvement.

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