Computational Fluid Dynamics for Engineers

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1 Tuncer Cebeci Jian P. Shao Fassi Kafyeke Eric Laurendeau Computational Fluid Dynamics for Engineers From Panel to Navier-Stokes Methods with Computer Programs With 152 Figures, 19 Tables, 84 Problems and a CD-ROM HORIZONS PUBLISHING 4y Springer

2 Contents 1. Introduction Skin-Friction Drag Reduction Laminar Flow Control Calculations for NLF and HLFC Wings Prediction of the Maximum Lift Coefficient of Multielement Wings Aircraft Design and Power Plant Integration Prediction of Aircraft Performance Degradation Due to Icing Prediction of Ice Shapes Prediction of Aerodynamic Performance Characteristics Aerodynamics of Ground-Based Vehicles Applications of CFD to Automobiles 36 References Conservation Equations Introduction Navier-Stokes Equations Navier-Stokes Equations: Differential Form Navier-Stokes Equations: Integral Form Navier-Stokes Equations: Vector-Variable Form Navier Stokes Equations: Transformed Form Reynolds-Averaged Navier-Stokes Equations Reduced Forms of the Navier-Stokes Equations Inviscid Flow Stokes Flow Boundary Layers Stability Equations Classification of Conservation Equations 67

3 X Contents 2.7 Boundary Conditions 70 References 72 Problems Turbulence Models Introduction Zero-Equation Models Cebeci-Smith Model Baldwin-Lomax Model One-Equation Models Two-Equation Models Initial Conditions 90 References Numerical Methods for Model Parabolic and Elliptic Equations Introduction Model Equations Discretization of Derivatives with Finite Differences Finite-Difference Methods for Parabolic Equations Explicit Methods Implicit Methods: Crank-Nicolson An Implicit Method: Keller's Box Method Finite-Difference Methods for Elliptic Equations Direct Methods Iterative Methods Multigrid Method 127 References 132 Problems Numerical Methods for Model Hyperbolic Equations Introduction Explicit Methods: Two-Step Lax-Wendroff Method Explicit Methods: MacCormack Method Implicit Methods Upwind Methods Finite-Volume Methods Convergence and Stability Numerical Dissipation and Dispersion: Artificial Viscosity 170 References 173 Problems 174

4 Contents XI 6. Inviscid Flow Equations for Incompressible Flows Introduction Laplace Equation and Its Fundamental Solutions Finite-Difference Method Hess- Smith Panel Method A Panel Program for Airfoils MAIN Program Subroutine COEF Subroutine GAUSS Subroutine VPDIS Subroutine CLCM Applications of the Panel Method Flowfield and Section Characteristics of a NACA 0012 Airfoil Flow Over a Circular Cylinder Multielement Airfoils 201 Appendix 6A Finite Difference Program for a Circular Cylinder Appendix 6B Panel Program for an Airfoil 203 6B.1 MAIN Program 203 6B.2 Subroutine COEF 203 6B.3 Subroutine VPDIS 203 Appendix 6C Panel Program for Multielement Airfoils 203 6C.1 MAIN Program 203 6C.2 Subroutine COEF 204 6C.3 Subroutine VPDIS 204 6C.4 Subroutine CLCM 204 References 204 Problems Boundary-Layer Equations Introduction Standard, Inverse and Interaction Problems Numerical Method for the Standard Problem Numerical Formulation Newton's Method Computer Program BLP MAIN Subroutine INPUT Subroutine IVPL Subroutine GROWTH Subroutine COEF Subroutine SOLV3 226

5 XII Contents Subroutine OUTPUT Subroutine EDDY Applications of BLP Similar Laminar Flows Nonsimilar Flows 231 References 237 Problems Stability and Transition Introduction Solution of the Orr-Sornmerfeld Equation Numerical Formulation Eigenvalue Procedure e n -Method Computer Program STP MAIN Subroutine VELPRO Subroutine CSAVE Subroutine NEWTON Subroutine NEWTONI Applications of STP Stability Diagrams for Blasius Flow Transition Prediction for Flat Plate Flow Transition Prediction for Airfoil Flow 261 References 261 Problems Grid Generation Introduction Basic Concepts in Grid Generation and Mapping Stretched Grids Algebraic Methods Algebraic Grid Generation Using Transfinite Interpolation Differential Equation Methods Conformal Mapping Methods Parabolic Mapping Function Wind Tunnel Mapping Function Unstructured Grids Delaunay Triangulation Advancing Front Method 292 References 293

6 Contents XIII 10. Inviscid Compressible Flow Introduction Shock Jump Relations Shock Capturing The Transonic Small Disturbance (TSD) Equation Model Problem for the Transonic Small Disturbance Equation: Flow Over a Non-Lifting Airfoil Discretized Equation Solution Procedure and Sample Calculations Solution of Full-Potential Equation Boundary Conditions for the Euler Equations Stability Analysis of the Euler Equations MacCormack Method for Compressible Euler Equations Model Problem for the MacCormack Method: Unsteady Shock Tube Initial Conditions Boundary Conditions Solution Procedure and Sample Calculations Model Problem for the MacCormack Method: Quasi 1-D Nozzle Initial Conditions Boundary Conditions Solution Procedure and Sample Calculations Beam-Warming Method for Compressible Euler Equations Model Problem for the Implicit Method: Unsteady Shock Tube Solution Procedure and Sample Calculations Model Problem for the Implicit Method: Quasi-ID Nozzle Solution Procedure and Sample Calculations 325 References 326 Problems Incompressible Navier-Stokes Equations Introduction Analysis of the Incompressible Navier-Stokes Equations Boundary Conditions Artificial Compressibility Method: INS2D Discretization of the Artificial Time Derivatives Discretization of the Convective Fluxes Discretization of the Viscous Fluxes System of Discretized Equation Model Problem: Sudden Expansion Laminar Duct Flow Discretization of the Boundary Conditions 337

7 XIV Contents Initial Conditions Solution Procedure and Sample Calculations Model Problem: Laminar and Turbulent Flat Plate Flow Applications of INS2D 344 References 350 Problems Compressible Navier-Stokes Equations Introduction Compressible Navier-Stokes Equations Practical Difficulties Boundary Conditions MacCormack Method Beam-Warming Method Finite Volume Method Model Problem: Sudden Expansion Laminar Duct Flow Initial Conditions Boundary Conditions Solution Procedure and Sample Calculations 367 Appendix 12A Jacobian Matrices of Convection and Diffusion Terms E, F, E v and F v 367 Appendix 12B Treatment of the Region Close to the Boundaries for Eq. (12.5.4) 370 References 374 Problems 375 Appendix A Computer Programs on the Accompanying CD-ROM 377 Appendix B Computer Programs Available from the First Author 381 Subject Index 391

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