Introduction of Computational Fluid Dynamics by Wangda Zuo

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

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

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

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

Simulation(CFD) Experiment Cost Cheap Expensive Time Short Long Scale Any Small/Middle Information All Measured Points Repeatable All Some Security Safe Some Dangerous 5 Why use CFD?

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

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 Streamlines for workstation ventilation 7 Where use CFD?

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

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

Ø Fluid = Liquid + Gas Ø Density ρ ØViscosity μ: resistance to flow of a fluid Substance Density(kg/m 3) Viscosity(P) 10 Air(18ºC) Water(20ºC) Honey(20ºC) 1. 275 1000 1446 1. 82 e-4 1. 002 e-2 190 Physics of Fluid

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

in M out Mass Momentum Energy 12 Conservation Law

Ø Mass Conservation Continuity Equation Compressible Incompressible 13 Navier-Stokes Equation I

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

ØMomentum Equation for Incompressible Fluid 15 Navier-Stokes Equation III

Ø 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 16 Navier-Stokes Equation IV

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

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

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

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

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

One Control Volume Whole Domain 22 Discretization of Continuity Equation

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

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

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

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

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

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

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

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

Ø Backward-Facing Step Wall u Wall 31 Case Study

Thank you for your attention! 32