This textbook and exercise book is aimed at future users of computational fluid dynamics software. In addition to the comprehensibly presented basics, the focus is on technical examples treated in detail with supplementary practical hints. Comprehension questions including applications give the beginner confidence in fundamental relationships. The original 4th German edition has been adapted to the latest program version ANSYS 18.1.
Author(s): Stefan Lecheler
Publisher: Springer
Year: 2023
Language: English
Pages: 210
City: Wiesbaden
Preface
Symbol directory
Contents
1: Introduction
1.1 Aim of This Book
1.2 Tasks of the Numerical Flow Calculation
1.3 Structure of the Book
2: Conservation Equations of Fluid Mechanics
2.1 Aim of This Chapter
2.2 Derivation of the Conservation Equations
2.2.1 Equation of Conservation of Mass
2.2.2 Conservation of Momentum Equations
2.2.3 Conservation of Energy Equation
2.3 Navier-Stokes Equations
2.3.1 Complete Navier-Stokes Equations
Navier-Stokes Equations in Scalar Form (Cartesian Coordinates)
Navier-Stokes Equations in Vector Form (Cartesian Coordinates)
Navier-Stokes Equations in Divergence Form
2.3.2 Additionally Required Equations and Quantities
2.3.3 The Substance Values
Boundary Conditions
Physical Boundary Conditions at the Inflow Edge
Physical Boundary Conditions at the Downstream Edge
Physical Boundary Conditions at the Solid State Boundary
Non-Reflective Boundary Conditions
Summary of Boundary Conditions
2.3.4 Reynolds-Averaged Navier-Stokes Equations
2.3.5 Turbulence Models
2.4 Simplification Possibilities
2.4.1 Introduction
2.4.2 Thin-Layer Navier-Stokes Equations
2.4.3 Euler Equations
2.4.4 Boundary Layer Equations
2.4.5 Potential Equation
3: Discretization of the Conservation Equations
3.1 Aim of This Chapter
3.2 What Does Discretization Mean?
3.3 Spatial Discretization
3.3.1 Discretization of the First Derivatives
3.3.2 Discretization of the Second Derivatives
3.3.3 Notes on Spatial Discretization
3.4 Time Discretization
3.4.1 Time Asymptotic or Stationary Solutions
3.4.2 Time-Accurate or Transient Solutions
3.5 Difference Equations
3.5.1 Derivation
3.5.2 Consistency, Stability and Convergence
Consistency
Stability
Convergence
3.5.3 Additive Numerical Viscosity
3.5.4 Upwind Discretization
3.5.5 Explicit and Implicit Discretization
3.5.6 CFL Number
3.5.7 Summary
4: Computational Meshes
4.1 Aim of This Chapter
4.2 Overview
4.3 Structured Meshes
4.3.1 Cartesian Meshe
4.3.2 Curvilinear Meshes
4.3.3 The Transformation of Coordinates into Curvilinear Coordinates
4.3.4 Block Structured Meshe
4.4 Unstructured Meshe
4.5 Mesh Adaptation
4.5.1 Mesh Densification
4.5.2 Adaptive Meshe
5: Solution Methods
5.1 Aim of This Chapter
5.2 Overview
5.3 Central Methods
5.3.1 Overview
5.3.2 Lax-Wendroff Method
5.3.3 Runge-Kutta Multi-Step Method
5.3.4 ADI Method
5.4 Upwind Methods
5.4.1 Overview
5.4.2 Flux Vector Splitting Method
5.4.3 Flux Difference Splitting Method
5.4.4 Summary
5.5 High-Resolution Methods
5.5.1 Overview
5.5.2 Monotonicity, TVD and Entropy Condition
5.5.3 Limiter Functions
5.5.4 Summary
5.6 Comparison of the Methods
5.6.1 Stationary Flow Through a Divergent Nozzle
5.6.2 Unsteady Flow in a Shock Wave Tube
6: Typical Workflow of a Numerical Flow Calculation
6.1 Aim of This Chapter
6.2 Overview
6.3 Generation of the Calculation Area (Geometry)
6.4 Generation of the Mesh (Meshing)
6.5 Preparation of the Flow Calculation (Setup)
6.6 Flow Calculation (Solution)
6.7 Evaluation (Results)
6.8 Validation
6.9 Introduction to the Exercise Examples
6.10 The ANSYS WORKBENCH Working Environment
7: Example Airfoil Flow
7.1 Generation of the Calculation Area (Geometry)
7.2 Generation of the Mesh (Meshing)
7.2.1 Starting the MESHING Program and Creating a Standard Mesh
7.2.2 Refinement of the Computational Mesh on the Profile
7.2.3 Associative Naming of the Boundaries
7.2.4 Exiting the MESHING Program
7.3 Preparation of the Flow Calculation (Setup)
7.3.1 Starting the CFX-PRE Program
7.3.2 Definition of the Calculation Parameters
7.3.3 Definition of the Physical Boundary Conditions
7.3.4 Inflow Boundary
7.3.5 Outflow Boundary
7.3.6 Solid Boundary
7.3.7 Symmetry Planes
7.3.8 Periodic Boundary Conditions
7.3.9 Exiting the CFX-PRE Program
7.4 Calculation of the Flow (Solution)
7.4.1 Starting the CFX-SOLVER Program
7.4.2 Monitoring Convergence Behaviour
7.4.3 Exiting the CFX-SOLVER Program
7.5 Evaluation (Results)
7.5.1 Starting the CFD-POST Program
7.5.2 Generation of Isoline Images
7.5.3 Vector Image Creation
7.5.4 Streamline Image Generation
7.5.5 Generation of Diagrams
7.5.6 Calculation of Integral Values
7.5.7 Preparation of a Report
7.5.8 Exiting the CFD-POST Program
8: Example Internal Pipe Flow
8.1 Generation of the Calculation Area (Geometry)
8.1.1 Importing a CAD File
8.1.2 Generation of the Computational Domain with the Program DESIGN MODELER
8.2 Generation of the Mesh (Meshing)
8.2.1 Starting the MESHING Program and Creating a Standard Mesh
8.2.2 Refinement of the Mesh on the Pipe Walls
8.2.3 Associative Naming of the Boundaries
8.2.4 Exiting the MESHING Program
8.3 Preparation of the Flow Calculation (Setup)
8.3.1 Starting the CFX-PRE Program
8.3.2 Definition of the Calculation Parameters
8.3.3 Definition of the Physical Boundary Conditions
8.3.4 Inflow Rim in Front
8.3.5 Inflow Rim Top
8.3.6 Outflow Boundary
8.3.7 Solid Boundary
8.3.8 Symmetry Plane
8.3.9 Exiting the CFX-PRE Program
8.4 Calculation of the Flow (Solution)
8.4.1 Starting the CFX-SOLVER Program
8.4.2 Monitoring Convergence Behaviour
8.4.3 Exiting the CFX-SOLVER Program
8.5 Evaluation (Results)
8.5.1 Starting the CFD-POST Program
8.5.2 Generation of Isoline Images
8.5.3 Vector Image Creation
8.5.4 Streamline Image Generation
8.5.5 Exiting the CFD-POST Program
9: Example Double Tube Heat Exchanger
9.1 Generation of the Calculation Area (Geometry)
9.2 Generation of the Mesh (Meshing)
9.2.1 Starting the MESHING Program and Creating a Standard Mesh
9.2.2 Refinement of the Mesh on the Pipe Walls
9.2.3 Associative Naming of the Border Areas
9.2.4 Exiting the MESHING Program
9.3 Preparation of the Flow Calculation (Setup)
9.3.1 Starting the CFX-PRE Program
9.3.2 Definition of the Calculation Parameters
9.3.3 Definition of the Physical Boundary Conditions
9.3.4 Inflow Boundaries for Fluid Inside and Fluid Outside
9.3.5 Outlet Boundaries for Fluid Inside and Fluid Outside
9.3.6 Solid Boundaries for Fluid Outer and Tube End Faces
9.3.7 Symmetry Planes for Fluid Inside, Fluid Outside and Pipe
9.3.8 Interface Planes Between Fluid and Pipe
9.3.9 Exiting the CFX-PRE Program
9.4 Calculation of the Flow (Solution)
9.4.1 Starting the CFX-Solver Program
9.4.2 Monitoring Convergence Behaviour
9.4.3 Exiting the CFX-Solver Program
9.5 Evaluation (Results)
9.5.1 Starting the CFD-POST Program
9.5.2 Generation of Isoline Images
9.5.3 Vector Image Creation
9.5.4 Generation of Diagrams
10: Example Parameter Variation
Answers to the Target Control
Answers to Sect. 2.1 Conservation Equations of Fluid Mechanics
Answers to Sect. 3.1 Discretization of the Conservation Equations
Answers to Sect. 4.1 Computational Meshes
Answers to Sect. 5.1 Solution Methods
Answers to Sect. 6.1 Typical Workflow of a Numerical Flow Calculation
References
Index
