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11 Introduction of Computational Fluid Dynamics by Wangda Zuo M.Sc. –Student of Computational Engineering Lehrstuhl für Strömungsmechanik FAU Erlangen-Nürnberg.

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Presentation on theme: "11 Introduction of Computational Fluid Dynamics by Wangda Zuo M.Sc. –Student of Computational Engineering Lehrstuhl für Strömungsmechanik FAU Erlangen-Nürnberg."— Presentation transcript:

1 11 Introduction of Computational Fluid Dynamics by Wangda Zuo M.Sc. –Student of Computational Engineering Lehrstuhl für Strömungsmechanik FAU Erlangen-Nürnberg Cauerstr. 4, D Erlangen JASS 2005, St. Petersburg Title of Presentation

2 2  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 Contents

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

4 4  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 Contents

5 5 Why use CFD? Simulation(CFD)Experiment CostCheapExpensive TimeShortLong ScaleAnySmall/Middle InformationAllMeasured Points RepeatableAllSome SecuritySafeSome Dangerous

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

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

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

9 9  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 Contents

10 10  Density ρ Physics of Fluid  Fluid = Liquid + Gas SubstanceAir(18ºC)Water(20ºC)Honey(20ºC) Density(kg/m 3 ) Viscosity(P)1.82e e-2190  Viscosity μ: resistance to flow of a fluid

11 11  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 Contents

12 12 Conservation Law inout M Mass Momentum Energy

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

14 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 15 Navier-Stokes Equation III  Momentum Equation for Incompressible Fluid

16 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 17  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 Contents

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

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

20 20 Finite Volume II Conservation of Finite Volume Method AB AB

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

22 22 Discretization of Continuity Equation One Control Volume Whole Domain

23 23 Discretization of Navier-Stokes Equation  FV Discretization of Incompressible N-S Equation ConvectionDiffusion  Time Discretization Explicit Implicit SourceUnsteady

24 24  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 Contents

25 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 26  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 Contents

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

28 28  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 Contents

29 29 Solver and Numerical Parameters  Solvers Direct: Cramer’s rule, Gauss elimination, LU decomposition Iterative: Jacobi method, Gauss-Seidel method, SOR method  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

30 30  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 Contents

31 31 Case Study  Backward-Facing Step u Wall

32 32 Thank you for your attention!


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