The Project Poster summarizes the aims and objectives of the Final Year Dissertation. The project starts with a detailed study on the parameters that tend to affect the performance of front wings of an F1 car and goes through designing the front wings(3) with endplates and wheel, meshing it, solving/analysing the flow and finally optimising the selected geometry using Fluent Adjoint Solver for efficient performance. Adjoint optimisation technique is used to achieve optimal performance from the front wings. It's the most successful shape optimisation method as it's independent of the number of design variables exponentially reducing computational time and cost. The emphasis has been put on optimising the shape of the front wings using the Adjoint method as it’s the most efficient and computationally inexpensive method for design optimisation. The approach towards shape optimisation is downforce constrained drag minimization as it would result in keeping a constraint on downforce and reducing the drag at the same time, thus producing optima for a given downforce/drag value.

1. Drag Reduction of Front Wing of an F1 Car using Adjoint Optimisation
Optimization of Front wing of an F1 Car by Yasir Ahmed Malik, Project Supervisor: Dr. Jens Dominik Mueller
Introduction
This project deals with optimisation of front wing of an F1 car using aerodynamic
shape optimisation method. A detailed study is done on the parameters that
tend to affect the performance of multiple components including multi-element
wings (three in total), endplate and the flow around wheels. The optimisation
method chosen for the purpose of this project is the Adjoint method and a
comparison with other state-gradient methods has been included in the
literature review aswell. Two approaches can be followed when using the adjoint
method one is the continuous adjoint approach and the other being discrete
approach. Discrete approach is preferred over continuous adjoint approach as
the latter is seen to produce inconsistencies in modelling, discretization and
solution approaches that result in polluting the sensitivity information
remarkably especially for problems with wall functions and complex engineering
configurations. The emphasis has been put on optimising the shape of the front
wings using the Adjoint method as it’s the most efficient and computationally
inexpensive method for design optimisation. The approach towards shape
optimisation is lift constrained drag reduction as it would result in keeping a
constraint on lift and reducing the drag at the same time, thus producing optima
for a given lift and drag value.
The front part and especially the front wings of a formula one vehicle is
absolutely crucial to the overall performance of the car as they are not only
responsible for producing enough downforce for the front part but also they play
a very important role in guiding the flow downstream to other parts of the
vehicle including radiators and diffusers etc. (McBeath, 2011). Failing designing
an efficient front wing will disrupt the whole aerodynamics of the formula one
car. The geometry is designed in CAD, meshed in ICEM (as it is uses the most
advanced meshing techniques) and prism layers were created in T-grid(to
capture flow separation). The mesh was then exported into Fluent where the
flow was solved using 𝒌 − 𝜺 turbulence model and finally fluent adjoint solver
14.5 was used to optimize the front wing of F1 car.
Aims and Objectives
The aims of this project are:
 In depth study of front wings, endplates and flow around wheels
inorder to optimise the front wing for optimal performance
 Reducing drag generated by the front wings with lift constrained drag
minimization approach
 Front wing optimised will be able to achieve maximum efficiency (L/D)
by minimizing drag and creating enough downforce at the same time
The objectives of this project are:
 Creating a deep understanding of the different parameters affecting the
front wings, endplate and flow around wheels required for the optimal
of a formula one car
 Creating enough downforce and at the same time minimizing drag
using lift constrained drag minimization approach
 Front wing optimised will be able to generate optimal performance via
maximum efficiency
Discrete Adjoint Approach
The solution to the steady Navier-Stokes Equation satisfies zero residuals:
𝑹 = (𝑼(𝜶), 𝜶) = 𝟎
For steady state problem the residuals are made to converge or driven to zero
using a pseudo-timestepping scheme, resulting linearisation with respect to α
produces,
𝝏𝑹
𝝏𝑼
𝝏𝑼
𝝏𝜶
= −
𝝏𝑹
𝝏𝜶
using shorthand notation 𝑨𝒖 = 𝒇
Sensitivity of the objective function 𝑱 w.r.t 𝜶
𝒅𝑱
𝒅𝜶
=
𝝏𝑱
𝝏𝜶
+
𝝏𝑱
𝝏𝑼
𝝏𝑼
𝝏𝜶
=
𝝏𝑱
𝝏𝜶
+ 𝒈 𝑻
𝒖 =
𝝏𝑱
𝝏𝜶
𝒈 𝑻
𝑨−𝟏
𝒇
This requires an additional expensive solve for 𝑨𝒖 = 𝒇 for each design variable
𝜶𝒊, alternatively regrouping the terms in sensitivity computation:
𝒅𝑱
𝒅𝜶
=
𝝏𝑱
𝝏𝜶
𝒈 𝑻
𝑨−𝟏
𝒇 =
𝝏𝑱
𝝏𝜶
+ (𝑨−𝑻
𝒈)
𝑻
𝒇 =
𝝏𝑱
𝝏𝜶
+ 𝒗 𝑻
𝒇
This leads to the definition of the adjoint equation [1]
⇒ (
𝝏𝑹
𝝏𝑼
)
𝑻
(
𝝏𝑱
𝝏𝑹
)
𝑻
= (
𝝏𝑱
𝝏𝑼
)
𝑻
using shorthand notation 𝑨 𝑻
𝒗 = 𝒇
By using the adjoint equation the computational cost becomes independent of
the number of design variables as one only needs to solve the linear system
once for the sensitivity of one cost function w.r.t all design variables (F.
Christakopoulos and J.-D. Muller, 2012)
Results
The fact that adjoint convergence can only start once the conventional flow
solver (𝒌 − 𝜺 turbulence model in this case) has fully converged, means that the
mesh quality needs to be very good. The convergence for the coarse(without
prisms) and fine mesh(with prism layers) was completed in 354 and 684
iterations respectively. As a result pressure contours obtained are shown below;
Fig1: Pressure contours for coarse mesh(left) and Pressure Contours for fine mesh(right)
Fig 2: Velocity contours for course(left) and fine(right) on the multi-element wing
Once the flow solution was obtained for both coarse and fine mesh(with prism
layers), the best solution(in terms of closeness of the results to the experimental
values) was selected and the next stage of this project was to do adjoint
optimization for 5 design iterations using lift constrained drag minimization
approach for optimal performance of the front wing which is achieved
successfully. Upon convergence the adjoint sensitivity data was used to guide
the solution to an optimum. Here’s an illustration of that;
Fig 3: Showing Adjoint Sensitivity Info(Blue arrows point pushing in and red arrows pulling out)
After obtaining the sensitivity details, control volume morphing tool enabled to
parameterise the geometry and finally the mesh was deformed and then
conventional flow solver was run and actual change in the objective function
was calculated. Three design iterations were run for the geometry under
consideration and the geometry was optimised to its maximum using Downforce
constrained drag minimization approach. The Adjoint Solver workflow used to
produce the optima is summarized in the next section.
Adjoint Solver Workflow
 Solve the flow equations in Fluent and post process the results using
the conventional flow solver as usual.
 Pick an observable of engineering interest
 Lift, Drag, L/D, Moment on an aerofoil etc.
 Observable with penalty function added (lift constrained drag
minimization)
𝑫 + 𝜶(𝑳 − 𝑳 𝒐) 𝟐
 Choose an observable type and apply the observable operation as
required and then choose monitors
 Ratio, Product, Linear Equations and Fixed Value etc.
 Set up and solve the adjoint problem for the chosen observable
 Define solution advancement controls & convergence criteria
 Initialize & Iterate to convergence
 Post process the adjoint solution to get
 Shape sensitivity
 Sensitivity to boundary condition settings
 Contour and Vector plots
 Finally either take results and revert to CAD or morph and revert to top
i.e. solve new fluid calculation on a deformed grid for as many design
iterations as required.
References
[1] F. Christakopoulos and J.-D. Muller, Sensitivity computation and shape optimisation in
Aerodynamics using the adjoint methodology and Automatic Differentiation, 2012.
[2] McBeath, Simon (2011) Competition Car Aerodynamics: A Practical Handbook, Second
Edition, Bristol: Haynes
Drag Lift Lift Target