Computational Fluid Dynamic Modelling

Computational fluid dynamics (CFD) is an advanced computer-based simulation tool that enables engineers to predict the circulation patterns of fluids and gases across the surface of a vehicle. CFD models and simulations are extensively employed in the field of Formula one, as the data generated is crucial for understanding a car’s aerodynamic performance and its behaviour on the track. The fundamental principle of the simulation involves dividing the air surrounding the vehicle into small cells (a mesh), which are then analysed using mathematical equations to predict the behaviour of each cell. These equations account for a range of factors including air pressure, temperature, and turbulence. By simulating these variables, engineers can acquire valuable insights into airflow around various parts of the car and its impact on performance, obviating the need for costly wind tunnel testing or risking the car and driver on the track. Consequently, this will save both time and money.[37] 

Benefits and Limitations

Computational Fluid Dynamics offers numerous advantages, particularly in the money demanding world of Formula One. In a sport where milliseconds can be decisive, car components must be precisely designed and adjusted to optimise performance. CFD facilitates the testing of various parts without the necessity of purchasing or manufacturing them each time. Additionally, CFD provides a visual representation of flow patterns, enabling engineers to comprehend intricate flow systems in ways that are unattainable through physical experiments. 

CFD simulations enable engineers to look at a broad spectrum of design options, allowing engineers to identify designs aimed at specific objectives, such as maximising efficiency or minimising emissions. This concept of virtual prototyping permits engineer to evaluate and optimise design prior to construction of physical prototypes. Beyond the financial gain, CFD modelling can be utilised to assess the safety of a design and predict potential hazards without endangering the drivers. Consequently, CFD enables the implementation of proactive measures to mitigate risk.[38]

Like most technologies, Computational Fluid Dynamics has its limitations, dependent on the user’s proficiency with the program. Producing usable and valid simulation results requires considerable experience and expertise. In the absence of such, users may encounter errors such as oversimplified flow models, simplified boundary conditions, or uncertainties stemming from insufficient computational values per cell leading to interpolation errors. These uncertainties culminate inaccurate data, rendering the simulations results unusable.[39]

Moreover, CFD models can be computationally intensive, especially for larger models. Analysing the aerodynamics of an entire car demands a large-scale model, which in turn, requires substantial time, resources, and workforce.[40]    

Types of CFD modelling

Different types of CFD simulations exist, tailored to the desired behaviour of the system in question. Results for a given systems vary according to the type of CFD employed, as they all use their own discretisation scheme. Discretisation methods are used to transform a continuous function into a discrete function, where the solution values are defined at each point in space and time. Discretisation simply refers to the spacing between each point in the solution space. 

When a simulation aims to calculate a dynamic solution to a fluid/heat flow Multiphysics problem, the finite-difference time-domain (FDTD) method is used as we need to discretise time in addition to space. In 1D, 2D or 3D systems without time dependence, the finite element method (FEM) is used for discretisation. An alternative method for 3D systems is the finite volume method (FVM), in which the system is discretised in units of volume rather than as sets of points forming a mesh. 

Solution algorithms produce varying convergence and are only adapted to certain discretisation methods.[41] The most common solution methods include: 

  • Iterative method: Used to linearise systems of CFD equations and solve their finite difference equations. Picard, Newton, Newton-Raphson, and Uzawa are common methods.
  • Eulerian Method: For inviscid fluids and produces results that are equivalent to iterative techniques for inviscid fluids. This can be used to solve the linearised Navier-Strokes equations.
  • Newton techniques: This involves defining different regions with different material properties in a system as elements in a network, where the interface between neighbouring regions.
  • Transformation methods: Linearisation techniques used by applying an analytical or numerical transformation, the system can be linearised and solved easily using iterative method.
  • Adaptive meshing: Critical areas of the system that require high accuracy use fine mesh size, while other areas where lower accuracy can be tolerated use coarser mesh size.[41]

This report will be using Star-CCM+. This Multiphysics engineering simulation possesses the capability to accurately capture all pertinent physical phenomenon’s that influence the performance of any type of formula one rear wing. Designed as a Multiphysics Computational Fluid Dynamics software, Simcenter STAR-CCM+ enables you to minimise the level of approximations and assumptions. It offers a comprehensive, precise, and efficient array of fluid dynamics-related Multiphysics modelling capabilities. 

Simcenter STAR-CCM+ provides you with a predicted performance of a design that will closely match the real-world product. The modelling capabilities extend beyond fluid flow and heat transfer to encompass single multiphase flows, particle dynamics, reactive flows, fluid-structure interaction, aeroacoustics, rheology and electrodynamics modelling. This project will use this software due to its high accuracy and ease of use.[42]

Accuracy

This project is centred around the use of CFD software’s and therefore it is important to understand ways to ensure the accuracy and precision of these simulations. To do this all objectives, assumptions, constraints, and boundary conditions of the simulation must be defined, along with the relevant physical models and parameters. Additionally maintaining accuracy can be achieved by comparing results with previous reports and theories, which help confirm that the theory aligns with the simulation outcome. 

All software utilised are validated commercial programs. Programs such as STAR-CCM+ and SolidWorks are reputable and known for delivering accurate data when used correctly. Even though the software is reliable, data should be cross verified with public reports and research to ensure consistency across all data.[43]

A mesh study will be conducted to confirm that the simulation results are accurate and not dependent on mesh size. This study, also referred to as grid independence study, is essential for building confidence in CFD simulation results. During the mesh study, factors such as mesh density, element type, and transitions between elements will be examined to achieve the mist precise outcomes.[44]

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