Title of Presentation

1. Title of Presentation Introduction of Computational Fluid Dynamics by Wangda Zuo M.Sc. –Student of Computational Engineering Lehrstuhl für Strömungsmechanik FAU Erlangen-NürnbergCauerstr. 4, D-91058 Erlangen JASS 2005, St. Petersburg 1

2. Contents • What is Computational Fluid Dynamics(CFD)? • Why and where use CFD? • Physics of Fluid • Navier-Stokes Equation • Numerical Discretization • Grids • Boundary Conditions • Numerical Staff • Case Study: Backward-Facing Step

3. What is CFD? Comparison&Analysis Fluid Mechanics Simulation Results Physics of Fluid Mathematics Computer Navier-Stokes Equations Computer Program Programming Language Numerical Methods Geometry Discretized Form Grids Fluid Problem C F D

4. Contents • What is Computational Fluid Dynamics(CFD)? • Why and where use CFD? • Physics of Fluid • Navier-Stokes Equation • Numerical Discretization • Grids • Boundary Conditions • Numerical Staff • Case Study: Backward-Facing Step

5. Why use CFD?

6. Where use CFD? Aerospace • Aerospace • Automotive • Biomedical • Chemical Processing • HVAC • Hydraulics • Power Generation • Sports • Marine Biomedicine Automotive Temperature and natural convection currents in the eye following laser heating.

7. Where use CFD? Streamlines for workstation ventilation Chemical Processing • Aerospacee • Automotive • Biomedical • Chemical Processing • HVAC(Heat Ventilation Air Condition) • Hydraulics • Power Generation • Sports • Marine reactor vessel - prediction of flow separation and residence time effects. Hydraulics HVAC

8. Where use CFD? Sports Power Generation • Aerospace • Automotive • Biomedical • Chemical Processing • HVAC • Hydraulics • Power Generation • Sports • Marine Flow around cooling towers Marine

9. Contents • What is Computational Fluid Dynamics(CFD)? • Why and where use CFD? • Physics of Fluid • Navier-Stokes Equation • Numerical Discretization • Grids • Boundary Conditions • Numerical Staff • Case Study: Backward-Facing Step

10. Density ρ • Viscosity μ: resistance to flow of a fluid Physics of Fluid • Fluid = Liquid + Gas

11. Contents • What is Computational Fluid Dynamics(CFD)? • Why and where use CFD? • Physics of Fluid • Navier-Stokes Equation • Numerical Discretization • Grids • Boundary Conditions • Numerical Staff • Case Study: Backward-Facing Step

12. Conservation Law in M out Mass Momentum Energy

13. Incompressible Navier-Stokes Equation I • Mass ConservationContinuity Equation Compressible

14. Navier-Stokes Equation II • Momentum ConservationMomentum Equation I : Local change with time II : Momentum convection III: Surface force IV: Molecular-dependent momentum exchange(diffusion) V: Mass force

15. Navier-Stokes Equation III • Momentum Equation for Incompressible Fluid

16. Navier-Stokes Equation IV • Energy ConservationEnergy Equation I : Local energy change with time II: Convective term III: Pressure work IV: Heat flux(diffusion) V: Irreversible transfer of mechanical energy into heat

17. Contents • What is Computational Fluid Dynamics(CFD)? • Why and where use CFD? • Physics of Fluid • Navier-Stokes Equation • Numerical Discretization • Grids • Boundary Conditions • Numerical Staff • Case Study: Backward-Facing Step

18. Discretization Discretization Analytical Equations Discretized Equations • Discretization Methods • Finite Difference Straightforward to apply, simple, sturctured grids • Finite Element Any geometries • Finite Volume Conservation, any geometries

19. Integrate over the Control Volume(CV) Integral Form of Navier-Stokes Equation Source in CV Local change with time in CV Flux Over the CV Surface Finite Volume I General Form of Navier-Stokes Equation Local change with time Flux Source

20. A B Finite Volume II Conservation of Finite Volume Method A B

21. Approximation of Surface Integrals ( Midpoint Rule) Interpolation Upwind Central Finite Volume III Approximation of Volume Integrals

22. Whole Domain Discretization of Continuity Equation One Control Volume

23. Time Discretization Explicit Implicit Discretization of Navier-Stokes Equation • FV Discretization of Incompressible N-S Equation Unsteady Convection Diffusion Source

24. Contents • What is Computational Fluid Dynamics(CFD)? • Why and where use CFD? • Physics of Fluid • Navier-Stokes Equation • Numerical Discretization • Grids • Boundary Conditions • Numerical Staff • Case Study: Backward-Facing Step

25. Grids • Structured Grid + all nodes have the same number of elements around it • only for simple domains • Unstructured Grid + for all geometries • irregular data structure • Block Structured Grid

26. Contents • What is Computational Fluid Dynamics(CFD)? • Why and where use CFD? • Physics of Fluid • Navier-Stokes Equation • Numerical Discretization • Grids • Boundary Conditions • Numerical Staff • Case Study: Backward-Facing Step

27. No-slip walls: u=0,v=0 Outlet, du/dx=0 dv/dy=0,dp/dx=0 Inlet ,u=c,v=0 r Periodic boundary condition in spanwise direction of an airfoil v=0, dp/dr=0,du/dr=0 o x Axisymmetric Boundary Conditions • Typical Boundary Conditions No-slip(Wall), Axisymmetric, Inlet, Outlet, Periodic

28. Contents • What is Computational Fluid Dynamics(CFD)? • Why and where use CFD? • Physics of Fluid • Navier-Stokes Equation • Numerical Discretization • Grids • Boundary Conditions • Numerical Staff • Case Study: Backward-Facing Step

29. Numerical Parameters • Under relaxation factor, convergence limit, etc. • Multigrid, Parallelization • Monitor residuals (change of results between iterations) • Number of iterations for steady flow or number of time steps for unsteady flow • Single/double precisions Solver and Numerical Parameters • Solvers • Direct: Cramer’s rule, Gauss elimination, LU decomposition • Iterative: Jacobi method, Gauss-Seidel method, SOR method

30. Contents • What is Computational Fluid Dynamics(CFD)? • Why and where use CFD? • Physics of Fluid • Navier-Stokes Equation • Numerical Discretization • Grids • Boundary Conditions • Numerical Staff • Case Study: Backward-Facing Step

31. Case Study • Backward-Facing Step Wall u Wall

32. Thank you for your attention!