Book contents
- Frontmatter
- Contents
- Preface
- Preface to the First Edition
- 1 Introduction and Background
- 2 Fundamentals of Inviscid, Incompressible Flow
- 3 General Solution of the Incompressible, Potential Flow Equations
- 4 Small-Disturbance Flow over Three-Dimensional Wings: Formulation of the Problem
- 5 Small-Disturbance Flow over Two-Dimensional Airfoils
- 6 Exact Solutions with Complex Variables
- 7 Perturbation Methods
- 8 Three-Dimensional Small-Disturbance Solutions
- 9 Numerical (Panel) Methods
- 10 Singularity Elements and Influence Coefficients
- 11 Two-Dimensional Numerical Solutions
- 12 Three-Dimensional Numerical Solutions
- 13 Unsteady Incompressible Potential Flow
- 14 The Laminar Boundary Layer
- 15 Enhancement of the Potential Flow Model
- A Airfoil Integrals
- B Singularity Distribution Integrals
- C Principal Value of the Lifting Surface Integral IL
- D Sample Computer Programs
- Index
12 - Three-Dimensional Numerical Solutions
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Preface to the First Edition
- 1 Introduction and Background
- 2 Fundamentals of Inviscid, Incompressible Flow
- 3 General Solution of the Incompressible, Potential Flow Equations
- 4 Small-Disturbance Flow over Three-Dimensional Wings: Formulation of the Problem
- 5 Small-Disturbance Flow over Two-Dimensional Airfoils
- 6 Exact Solutions with Complex Variables
- 7 Perturbation Methods
- 8 Three-Dimensional Small-Disturbance Solutions
- 9 Numerical (Panel) Methods
- 10 Singularity Elements and Influence Coefficients
- 11 Two-Dimensional Numerical Solutions
- 12 Three-Dimensional Numerical Solutions
- 13 Unsteady Incompressible Potential Flow
- 14 The Laminar Boundary Layer
- 15 Enhancement of the Potential Flow Model
- A Airfoil Integrals
- B Singularity Distribution Integrals
- C Principal Value of the Lifting Surface Integral IL
- D Sample Computer Programs
- Index
Summary
Three dimensional numerical solutions based on surface singularity distributions are similar, in principle, to methods presented for the two-dimensional case. From the theoretical aspect, only the wake and the trailing-edge conditions (three-dimensional Kutta condition) will require some additional attention. The most difficult aspect in three dimensions, though, is the modeling of the geometry, especially when arbitrary geometry capability is sought.
In the first part of this chapter the geometry (of the wing) is kept relatively simple and the aerodynamics of a thin lifting surface is modeled. In principle, this simple method has all the elements of the more complex panel methods and is capable of modeling the effect of wing planform shape on the fluid dynamic loads. In addition, the examples that are being presented require only limited programming effort and, therefore, are suitable for classroom instruction. Furthermore, the introduction in class of the numerical lifting-line model (Section 12.1), next to Prandtl's lifting-line model of Section 8.1, provides additional insight and a clear explanation of the spanwise integral equation.
In the second part of this chapter the principles of panel codes capable of solving the flow over bodies with arbitrary three-dimensional geometry will be presented. Over the years many such methods were developed and improved, but recent trends indicate an increased use of the approach that is based on the combination of surface source and doublet distributions with the inner potential boundary condition (for closed bodies).
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- Chapter
- Information
- Low-Speed Aerodynamics , pp. 331 - 368Publisher: Cambridge University PressPrint publication year: 2001
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