1. Introduction

Computational / Coloured Fluid Dynamics

Flow through…

• water turbines

• solar heater

• wind turbines

• steam turbines

• vector (u,v,w) —> x, y, z direction

• T

• p

Kind of problems:

• 1D/2D/3D

• (in)viscid

• (in)compressible

• laminar/turbulent

• single/multi-phase

• (un)steady

• temperature constant/changing

• system in rest / moving geometry

• only fluid / fluid and solid

• Detailed analysis and physical insight

• Quick test of new design concepts

• Less need of prototypes and experiments

• Reduced costs

—> But validation is also needed because is can not replace tests (errors and uncertainities)

• Empirical models (turbulences)

• Model vs. Reality (geometry)

• Numerical (stops too early)

• Hexahedron

• Tetrahedron

• Prism

• Pyramid

• Polyhedron

1. Preprocessing

   1. Geometry model

   2. Numerical grid

   3. Model selection

   4. Boundary conditions

   5. Initial conditions

   6. Solving conditions

2. Solving

3. Postprocessing and analysis

4. Optimization

5. Automation

• Internal flow

  • CSM —> Open surface

  • CFD —> Closed surface

• External flow

  • Flow around a body

• Subdivision of the region

• Element types: hexahedran, tetrahedran, prism, pyramid

• Grid <—> solution error

• Accuracy

• H-Grid —> not very accurat (90 ° everywhere)

• C-Grid

• O-Grid

• Hybrid mesh

• Polyhedron (fits everywhere)

= Cell types from structured and unstructured techniques (hexahedron and tetrahedron) combined with prism and pyramids

—> Achieve the best accuracy and geometry flexibility

Example: Flow around a car —> Sublayer and outer mesh with hexa —> Connection: cut volumes = polyhedral cells

—> Velocity, mass flow rate, static pressure….

1. Inlet

2. Outlet

3. Wall

   • Slip (without friction)

   • No-Slip (with friction) —> Smooth/Rough, Moving/Fixed

4. Symmetry

5. Periodicity (replying again and again)

   • Translation

   • Rotation

1. Convection

2. Conduction

3. Transmission = 1. + 2.

Boundary conditions

1. Dirichlet condition (T = const.)

2. Neumann condition (heat flux = const.)

3. Robin condition

Unknowns in 2D

• p - Pressure

• u - Velocity

• v - Temperature

Equations

1. Mass conservation

2. x momentum

3. y momentum

—> Have a look on the results

1. Quantitative analysis

   • Integration

   • Averaging

   • Forces, moments, losses

2. Automation

   • Macros

   • Batch operation

• 0D: Efficiency

• 1D: Average pressure change along axis

• 2D: Blade-to-Blade

• 3D: Streamlines

• 4D: Animations (time-varying)

Stopping criteria

• Max. number of iterations

• Residuals —> error getting very small

1. Accuracy

   • Discretization error

   • Truncation error

2. Robustness

   • Segregated solution

   • Coupled solution

3. Speed

   • Parallelisation

   • Multigrid methods

4. Scalability

   • Different Grids

Target quantities

• Heat transfer

• Maximum Nusselt number

  Nu = alpha*l / lambda