Overview
Objective Reduce the aerodynamic drag of a multi-element Formula Student front wing without giving up downforce, and demonstrate that the result is a property of the geometry rather than of the mesh.
A Formula Student front wing does two jobs at once. It has to generate downforce at the front axle, and it has to do so without adding so much drag that it costs more in the acceleration and endurance events than it returns in cornering. A multi-element configuration makes that trade-off adjustable — slot gaps and element angles change the pressure recovery on the upper surfaces — but it also makes the design space large enough that guessing is not a strategy.
This study set up a CFD workflow that could answer the trade-off with numbers: build the geometry in CAD, clean it in SpaceClaim, establish a mesh that no longer changes the answer, choose a turbulence model appropriate to the flow physics, and then iterate on the geometry while holding everything else fixed.
The final geometry reduced drag by approximately 45% against the baseline while improving aerodynamic efficiency.
Design brief, requirements and constraints
The wing had to work inside Formula Student packaging and regulation limits, and the study had to be defensible: a drag number that moves because the mesh changed is not a result.
| ID | Requirement | Why | How verified |
|---|---|---|---|
| R1 | Reduce aerodynamic drag of the front wing assembly against the baseline geometry. | Drag costs lap time in the acceleration and endurance events. | Drag coefficient from converged Fluent solutions, same boundary conditions each run. |
| R2 | Do not trade the drag reduction for a loss in aerodynamic efficiency. | A wing that sheds drag by shedding downforce has not solved anything. | Lift-to-drag ratio compared against the baseline. |
| R3 | Demonstrate that reported differences are independent of mesh resolution. | Without this, every comparison between geometries is unsupported. | Mesh independence study across successively refined meshes. |
| R4 | Select a turbulence model appropriate to the flow being studied and justify it. | Adverse pressure gradients and separation on multi-element surfaces are model-sensitive. | Documented selection against the flow features of interest. |
Constraints
- Formula Student packaging and regulation envelope for front aerodynamic devices.
- Single-configuration study — no active or adjustable elements.
- Computational budget of a university workstation, which sets the practical ceiling on mesh size.
Out of scope
- Full-vehicle aerodynamics and wing-to-body interaction.
- Wind tunnel or on-track aerodynamic validation.
- Structural analysis of the wing elements and mountings.
Design decisions and rationale
Each entry states what was chosen, what else was on the table, and why the alternative was rejected.
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Iterate on geometry rather than run a single redesign
Decision Improve the wing through successive geometry revisions, re-running the same analysis on each and carrying forward only changes that improved the objective.
Alternatives considered
- One redesign, analysed once against the baseline Gives a single before-and-after number with no evidence about which change caused it, and no way to stop when a change stops helping.
- Automated parametric optimisation across the full design space The number of solver runs needed is far beyond the available compute budget for a mesh resolved well enough to trust near the surfaces.
Why this one
Iterating keeps every comparison like-for-like: one geometry change per revision, identical domain, mesh strategy, boundary conditions and solver settings. That makes it possible to attribute an improvement to a specific change rather than to the run as a whole.
Trade-off accepted More solver time overall than a single redesign, and the search is local — it finds a better wing, not provably the best one.
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Establish mesh independence before comparing any two geometries
Decision Run a mesh independence study first, and fix the mesh strategy at the resolution beyond which the aerodynamic coefficients stop changing meaningfully.
Alternatives considered
- Use one convenient mesh throughout and compare geometries directly A change in the coefficients could then be caused by the geometry, by the mesh resolving the flow differently, or by both. The result would not be defensible in a review.
- Refine to the finest mesh the hardware allows for every run Spends the entire computational budget on resolution that the independence study shows is not buying accuracy.
Why this one
Mesh independence is what separates a CFD result from a picture. It is also the first thing a reviewer looks for, because without it none of the comparisons downstream carry weight.
Trade-off accepted Several solver runs are spent before any design work starts, on meshes that are discarded afterwards.
Evidence: Mesh independence study, documented in the simulation section below.
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Judge the design on drag and efficiency together, not downforce alone
Decision Use drag coefficient as the primary objective and lift-to-drag ratio as the constraint, so a revision only counts as an improvement if it reduces drag without hurting efficiency.
Alternatives considered
- Maximise downforce Trivially achieved by adding angle of attack, at a drag penalty that costs more in the acceleration and endurance events than it returns.
- Minimise drag alone Equally trivially achieved by flattening the wing, which removes the reason for fitting one.
Why this one
The two-part objective is what makes the result meaningful: roughly 45% less drag matters because efficiency improved at the same time, not in spite of it.
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Turbulence model selection
Decision TO CONFIRM — state the model used in the final study and keep the reasoning below, which is why the choice mattered.
Alternatives considered
- Standard k-epsilon with wall functions Cheap and robust in free-shear flow, but wall functions resolve separation under an adverse pressure gradient poorly — which is exactly the flow feature that governs a multi-element wing.
- A wall-resolved model with near-wall treatment Much more demanding on near-wall cell size and therefore on total cell count, which has to be paid for out of the same computational budget.
Why this one
The behaviour that decides whether a multi-element configuration works is pressure recovery over the flap suction surfaces and whether the boundary layer stays attached through the slot gaps. Model choice changes that prediction, so it is a decision that has to be stated rather than defaulted.
TO CONFIRM — record the model you used and the near-wall resolution it required, then delete this marker.
Engineering logic and methodology
The workflow was fixed before any design work started, so that every revision was analysed identically.
- Geometry. Wing elements built and refined in CAD, then prepared in SpaceClaim: surfaces cleaned, small features that would force unnecessary mesh refinement removed, and the fluid domain extracted.
- Domain and meshing. Domain sized so the boundaries do not influence the solution around the wing, with refinement concentrated at the element surfaces, the slot gaps and the wake.
- Mesh independence. Successively refined meshes run at identical conditions until the aerodynamic coefficients stopped changing meaningfully. That resolution was then fixed for the rest of the study.
- Turbulence model selection. Model chosen against the flow features that govern the result — adverse pressure gradient and separation on the flap suction surfaces.
- Baseline run. Converged solution on the baseline geometry, establishing the reference drag and lift coefficients.
- Iteration. One geometry change per revision, re-run under identical settings, compared on drag and lift-to-drag ratio. Changes that improved the objective were carried forward; changes that did not were reverted.
- Analysis. Static pressure distribution over the element surfaces and velocity contours through the slot gaps and wake, used to explain why each revision behaved as it did rather than only recording that it did.
Calculations
Drag and lift coefficients — the quantities being compared
Every comparison in this study is between non-dimensional coefficients rather than raw forces, so that any run at a different reference velocity remains directly comparable.
Assumptions
- Incompressible flow. At Formula Student speeds the Mach number is far below 0.3, so density is constant.
- Steady-state, fully developed flow. Transient effects during a corner entry are outside the scope.
- Sea-level air at 15 °C, ISA standard conditions.
- Reference area A is held identical across every geometry revision, so the coefficients remain comparable.
| Symbol | Meaning | Value | Unit | Source |
|---|---|---|---|---|
| F_D | Drag force | \mathrm{N} | ||
| F_L | Lift force (downforce, acting downwards) | \mathrm{N} | ||
| \rho | Air density | 1.225 | \mathrm{kg/m^3} | ISA sea level, 15 °C |
| V | Freestream velocity | \mathrm{m/s} | TO CONFIRM — inlet velocity used in the study | |
| A | Reference area | \mathrm{m^2} | TO CONFIRM — reference area used in Fluent | |
| C_D,\ C_L | Drag and lift coefficients | – |
-
Rearranged, this gives the force the wing actually applies at a given speed — which is what matters for the tyres and for the mountings.
F_D = \tfrac{1}{2}\,\rho\,V^2 A\,C_D -
Because the dynamic pressure term is quadratic in velocity, a wing assessed at one speed scales predictably to another provided the flow regime does not change.
\frac{F_D(V_2)}{F_D(V_1)} = \left(\frac{V_2}{V_1}\right)^{2}
Fluent reports the coefficients directly once the reference values are set. Check that the reference area and velocity in the Fluent reference values panel match the ones quoted here, otherwise the coefficients are scaled against something other than what you think.
How the drag reduction and the efficiency figure are defined
Stating the definition matters as much as the number: "45% less drag" is only meaningful once it is clear what it is 45% of.
Assumptions
- Both geometries evaluated at identical freestream velocity, reference area, mesh strategy and solver settings.
- Both solutions converged to the same criteria.
| Symbol | Meaning | Value | Unit | Source |
|---|---|---|---|---|
| C_{D,0} | Drag coefficient of the baseline geometry | – | TO CONFIRM — from the baseline run | |
| C_{D,f} | Drag coefficient of the final optimised geometry | – | TO CONFIRM — from the final run | |
| E | Aerodynamic efficiency, lift-to-drag ratio | – |
-
The headline result of the study, stated as a reduction relative to the baseline.
\Delta_{\%} \approx 45\%~45% reduction in drag
TO CONFIRM — substitute your baseline and final drag coefficients here so the working is visible.
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Aerodynamic efficiency is the ratio that stops a drag reduction from being achieved by simply removing downforce. It improved alongside the drag reduction.
E = \frac{C_L}{C_D}
Result Approximately 45% lower drag than the baseline, with aerodynamic efficiency improved rather than traded away.
The two figures have to be read together. Either one on its own can be moved in the right direction by a change that makes the wing worse.
Simulation setup and results
| Software | ANSYS Fluent |
|---|---|
| Solver | TO CONFIRM — pressure-based / density-based, steady or transient, and the pressure-velocity coupling scheme |
| Domain | TO CONFIRM — domain dimensions in chord lengths, and whether a symmetry plane was used |
| Turbulence model | TO CONFIRM — the model used in the final study |
Mesh
- TypeTO CONFIRM — element type, e.g. polyhedral, tetrahedral with inflation, poly-hexcore
- ElementsTO CONFIRM — final cell count
- y+TO CONFIRM — y+ range achieved on the element surfaces
- InflationTO CONFIRM — number of layers and growth rate
The aerodynamic coefficients were computed on successively refined meshes under identical boundary conditions and solver settings. Refinement continued until further refinement no longer changed the coefficients meaningfully, and that resolution was then held fixed for every geometry revision in the study.
This is the step that makes the rest of the comparisons valid: it establishes that a change in drag between two geometries is caused by the geometry and not by the mesh resolving the flow differently.
Convergence
TO CONFIRM — state the residual levels reached and, more usefully, confirm that the drag and lift monitors were flat over the final iterations. A monitor that has stopped moving is stronger evidence of convergence than a residual threshold on its own.
Results
Analysis focused on two things:
Static pressure distribution over the element surfaces, which shows where the wing is actually generating load and where pressure recovery is running out on the flap suction surfaces. This is what identifies the element angle and slot gap that are limiting the configuration.
Velocity contours through the slot gaps and into the wake, which show whether the flow stays attached through the gaps and how much momentum deficit the wing leaves behind it. Separation appearing in the contours is the direct explanation for a revision that added drag without adding downforce.
Read together, these are what turned each iteration from "the number moved" into a reason the number moved — and that reasoning is what drove the next geometry change.
Export the contour plots from Fluent at a readable resolution, drop them into assets/img/projects/formula-student-front-wing-cfd/, and uncomment the figures block above.