CAE Notes

Introduction to Computer Aided Engineering (CAE)

• CAE uses computer systems to analyze CAD geometry, refine designs, and validate product behavior.
• It does not change the basic nature of the design process.

Types of CAE

• Finite Element Analysis (FEA):
  • Solid mechanics analysis (stress/strain).
  • Heat Transfer.
  • Other continuous fields.
• Computational Fluid Dynamics (CFD):
  • Study of fluids in motion through simulation.
  • Heat transfer, mass transfer, chemical reactions, etc.

Finite Element Analysis (FEA)

• FEA simulates physical phenomena using the Finite Element Method (FEM).
• Reduces the need for physical prototypes and experiments; optimizes components during design.

Computational Fluid Dynamics (CFD)

• Predicts fluid flow, heat transfer, mass transfer, chemical reactions by solving governing mathematical equations numerically.

CAE in Design

• CAE allows rapid design revisions without extensive physical prototyping.
• Helps to:
  • Reduce physical prototyping and testing.
  • Optimize designs.
  • Learn about complex behavior.
  • Find unmeasurable results.

Formulation of the Mathematical Model

• The CAD model defines:
  • Physical working volume (solution domain).
  • Material properties assigned to the domain.
  • Conditions applied to model faces (domain boundaries).

Creating the Finite Element Model

• Domain Discretization: Splitting the domain into smaller sub-domains (elements) through meshing.
• Breaks the object into calculable chunks, approximating displacement variation using polynomials.

From Infinite to Finite

• FEA premise: Break down a larger (continuous - infinite DOF) model into smaller (finite DOF) pieces by meshing.
• Make calculations at a limited number of points across the original domain, then stitch this collection of local solutions together to build a global solution that represents the whole solid object.

Computational Fluid Dynamics (CFD) Explained

• CFD is a numerical tool used to solve the algebraic form of the governing partial differential equations of fluid flow.
• Can be described as a ‘portable wind tunnel’.
• CFD is used to conduct ‘numerical experiments’.
• Built on fluid dynamics principles.

CFD Disciplines

• Include:
  • Computer science
  • Parallel computing
  • Numerical analysis
  • Applied mathematics
  • Application fields

CFD Applications

• Suitable when:
  • Physical experiments are hazardous or dangerous.
  • Experiments are practically impossible (e.g., designing hypersonic aircraft).
  • Experimental equipment interferes with results.
  • Parametric experiments are required, especially with geometry changes.

CFD Workflow

• Step 0: Define the aim of the CFD.
• Step 1: Create a CAD model.
• Step 2: Subdivide the domain into control volumes.
• Step 3: Define physics and models; apply conservation equations (mass, momentum, energy).
• Step 4: Run the solver and post-process results.

How CFD Solves Flow Problems

• Uses the Navier-Stokes equations (conservation of mass, momentum, and energy).
• Requires problem domain discretization (meshing into control volumes).

Mesh Topology

• Variable mesh refinement is strategically used to capture flow characteristic variations.

Why the First Layer of Cells Matters

• Fluids behave differently near surfaces; the thin layer is called the boundary layer.
• This is where friction, viscous drag, and heat transfer occur.

What Is y+

• $y+$ is a dimensionless number describing the distance of the first mesh layer from a wall.
• Indicates if the mesh is fine enough to resolve near-wall effects.
• Depends on distance from the wall, fluid velocity, and viscosity.

Why Does y+ Matter?

• If $y+$ is too high:
  • Mesh skips important flow effects.
  • Results become less accurate.
• If $y+$ is too low:
  • Simulation takes longer.
  • May not work with simpler models.

How Good is Good Enough?

• For wall functions (simpler approach): $y+ ≈ 30–300$
• For detailed modelling: $y+ ≈ 1$

Boundary Conditions

• Applied to every surface that has been ‘chopped’ between the real world and the simulated domain.

Commercial Codes

• Proprietary CFD software packages with support, user-friendly interfaces, and documentation.
• Examples: ANSYS Fluent, Siemens STAR-CCM+, COMSOL Multiphysics, Autodesk CFD.

SimScale

• A cloud-based CAE platform (includes CFD, FEA).
• Runs in a web browser, eliminating the need for high-end local hardware.
• Uses the OpenFOAM solver but is a commercial platform with pre-configured workflows and support.

CFD Advantages

• In-depth results and visualization.
• Systems with multiple physics can be experimented upon individually.
• Cheaper and less time-consuming.
• Can solve problems without theoretical or analytical solutions.

CFD Drawbacks

• No exact solution.
• Requires validation using theoretical or experimental results.
• Can be difficult and/or time-consuming for certain problems.