Low-Speed Aerodynamics

by Joseph Katz , Allen Plotkin

• ISBN13: 9780521665520
• ISBN10: 0521665523
• Edition: 2nd
• Format: Paperback
• Copyright: 2001-02-05
• Publisher: Cambridge University Press

Summary

Low-speed aerodynamics is important in the design and operation of aircraft flying at low Mach number, and ground and marine vehicles. This text offers a modern treatment of both the theory of inviscid, incompressible, and irrotational aerodynamics, and the computational techniques now available to solve complex problems. A unique feature is that the computational approach--from a single vortex element to a three-dimensional panel formulation--is interwoven throughout. This second edition features a new chapter on the laminar boundary layer (emphasis on the viscous-inviscid coupling), the latest versions of computational techniques, and additional coverage of interaction problems. The authors include a systematic treatment of two-dimensional panel methods and a detailed presentation of computational techniques for three-dimensional and unsteady flows.

Author Biography

Joseph Katz is a Professor of Aerospace Engineering and Engineering Mechanics at San Diego State University Allen Plotkin is a Professor of Aerospace Engineering and Engineering Mechanics at San Diego State University

Table of Contents

Preface	xiii
Preface to the First Edition	xv
Introduction and Background	1	(20)
Description of Fluid Motion	1	(1)
Choice of Coordinate System	2	(1)
Pathlines, Streak Lines, and Streamlines	3	(1)
Forces in a Fluid	4	(2)
Integral Form of the Fluid Dynamic Equations	6	(2)
Differential Form of the Fluid Dynamic Equations	8	(6)
Dimensional Analysis of the Fluid Dynamic Equations	14	(3)
Flow with High Reynolds Number	17	(2)
Similarity of Flows	19	(2)
Fundamentals of Inviscid, Incompressible Flow	21	(23)
Angular Velocity, Vorticity, and Circulation	21	(3)
Rate of Change of Vorticity	24	(1)
Rate of Change of Circulation: Kelvin's Theorem	25	(1)
Irrotational Flow and the Velocity Potential	26	(1)
Boundary and Infinity Conditions	27	(1)
Bernoulli's Equation for the Pressure	28	(1)
Simply and Multiply Connected Regions	29	(1)
Uniqueness of the Solution	30	(2)
Vortex Quantities	32	(2)
Two-Dimensional Vortex	34	(2)
The Biot-Savart Law	36	(2)
The Velocity Induced by a Straight Vortex Segment	38	(3)
The Stream Function	41	(3)
General Solution of the Incompressible, Potential Flow Equations	44	(31)
Statement of the Potential Flow Problem	44	(1)
The General Solution, Based on Green's Identity	44	(4)
Summary: Methodology of Solution	48	(1)
Basic Solution: Point Source	49	(2)
Basic Solution: Point Doublet	51	(3)
Basic Solution: Polynomials	54	(2)
Two-Dimensional Version of the Basic Solutions	56	(2)
Basic Solution: Vortex	58	(2)
Principle of Superposition	60	(1)
Superposition of Sources and Free Stream: Rankine's Oval	60	(2)
Superposition of Doublet and Free Stream: Flow around a Cylinder	62	(5)
Superposition of a Three-Dimensional Doublet and Free Stream: Flow around a Sphere	67	(2)
Some Remarks about the Flow over the Cylinder and the Sphere	69	(1)
Surface Distribution of the Basic Solutions	70	(5)
Small-Disturbance Flow over Three-Dimensional Wings: Formulation of the Problem	75	(19)
Definition of the Problem	75	(1)
The Boundary Condition on the Wing	76	(2)
Separation of the Thickness and the Lifting Problems	78	(1)
Symmetric Wing with Nonzero Thickness at Zero Angle of Attack	79	(3)
Zero-Thickness Cambered Wing at Angle of Attack-Lifting Surfaces	82	(3)
The Aerodynamic Loads	85	(3)
The Vortex Wake	88	(2)
Linearized Theory of Small-Disturbance Compressible Flow	90	(4)
Small-Disturbance Flow over Two-Dimensional Airfoils	94	(28)
Symmetric Airfoil with Nonzero Thickness at Zero Angle of Attack	94	(6)
Zero-Thickness Airfoil at Angle of Attack	100	(4)
Classical Solution of the Lifting Problem	104	(2)
Aerodynamic Forces and Moments on a Thin Airfoil	106	(8)
The Lumped-Vortex Element	114	(6)
Summary and Conclusions from Thin Airfoil Theory	120	(2)
Exact Solutions with Complex Variables	122	(29)
Summary of Complex Variable Theory	122	(3)
The Complex Potential	125	(1)
Simple Examples	126	(2)
Uniform Stream and Singular Solutions	126	(1)
Flow in a Corner	127	(1)
Blasius Formula, Kutta-Joukowski Theorem	128	(1)
Conformal Mapping and the Joukowski Transformation	128	(9)
Flat Plate Airfoil	130	(1)
Leading-Edge Suction	131	(2)
Flow Normal to a Flat Plate	133	(1)
Circular Arc Airfoil	134	(1)
Symmetric Joukowski Airfoil	135	(2)
Airfoil with Finite Trailing-Edge Angle	137	(1)
Summary of Pressure Distributions for Exact Airfoil Solutions	138	(3)
Method of Images	141	(5)
Generalized Kutta-Joukowski Theorem	146	(5)
Perturbation Methods	151	(16)
Thin-Airfoil Problem	151	(3)
Second-Order Solution	154	(3)
Leading-Edge Solution	157	(3)
Matched Asymptotic Expansions	160	(3)
Thin Airfoil between Wind Tunnel Walls	163	(4)
Three-Dimensional Small-Disturbance Solutions	167	(39)
Finite Wing: The Lifting Line Model	167	(17)
Definition of the Problem	167	(1)
The Lifting-Line Model	168	(4)
The Aerodynamic Loads	172	(1)
The Elliptic Lift Distribution	173	(5)
General Spanwise Circulation Distribution	178	(3)
Twisted Elliptic Wing	181	(2)
Conclusions from Lifting-Line Theory	183	(1)
Slender Wing Theory	184	(11)
Definition of the Problem	184	(2)
Solution of the Flow over Slender Pointed Wings	186	(6)
The Method of R. T. Jones	192	(2)
Conclusions from Slender Wing Theory	194	(1)
Slender Body Theory	195	(6)
Axisymmetric Longitudinal Flow Past a Slender Body of Revolution	196	(2)
Transverse Flow Past a Slender Body of Revolution	198	(1)
Pressure and Force Information	199	(2)
Conclusions from Slender Body Theory	201	(1)
Far Field Calculation of Induced Drag	201	(5)
Numerical (Panel) Methods	206	(24)
Basic Formulation	206	(1)
The Boundary Conditions	207	(2)
Physical Considerations	209	(4)
Reduction of the Problem to a Set of Linear Algebraic Equations	213	(3)
Aerodynamic Loads	216	(1)
Preliminary Considerations, Prior to Establishing Numerical Solutions	217	(3)
Steps toward Constructing a Numerical Solution	220	(2)
Example: Solution of Thin Airfoil with the Lumped-Vortex Element	222	(4)
Accounting for Effects of Compressibility and Viscosity	226	(4)
Singularity Elements and Influence Coefficients	230	(32)
Two-Dimensional Point Singularity Elements	230	(2)
Two-Dimensional Point Source	230	(1)
Two-Dimensional Point Doublet	231	(1)
Two-Dimensional Point Vortex	231	(1)
Two-Dimensional Constant-Strength Singularity Elements	232	(5)
Constant-Strength Source Distribution	233	(2)
Constant-Strength Doublet Distribution	235	(1)
Constant-Strength Vortex Distribution	236	(1)
Two-Dimensional Linear-Strength Singularity Elements	237	(7)
Linear Source Distribution	238	(1)
Linear Doublet Distribution	239	(2)
Linear Vortex Distribution	241	(1)
Quadratic Doublet Distribution	242	(2)
Three-Dimensional Constant-Strength Singularity Elements	244	(14)
Quadrilateral Source	245	(2)
Quadrilateral Doublet	247	(3)
Constant Doublet Panel Equivalence to Vortex Ring	250	(1)
Comparison of Near and Far Field Formulas	251	(1)
Constant-Strength Vortex Line Segment	251	(4)
Vortex Ring	255	(1)
Horseshoe Vortex	256	(2)
Three-Dimensional Higher Order Elements	258	(4)
Two-Dimensional Numerical Solutions	262	(69)
Point Singularity Solutions	262	(14)
Discrete Vortex Method	263	(9)
Discrete Source Method	272	(4)
Constant-Strength Singularity Solutions (Using the Neumann B.C.)	276	(12)
Constant Strength Source Method	276	(4)
Constant-Strength Double Method	280	(4)
Constant-Strength Vortex Method	284	(4)
Constant-Potential (Dirichlet Boundary Condition) Methods	288	(10)
Combined Source and Doublet Method	290	(4)
Constant-Strength Doublet Method	294	(4)
Linearly Varying Singularity Strength Methods (Using the Neumann B.C.)	298	(8)
Linear-Strength Source Method	299	(4)
Linear-Strength Vortex Method	303	(3)
Linearly Varying Singularity Strength Methods (Using the Dirichlet B.C.)	306	(9)
Linear Source/Doublet Method	306	(6)
Linear Doublet Method	312	(3)
Methods Based on Quadratic Doublet Distribution (Using the Dirichlet B.C.)	315	(8)
Linear Source/Quadratic Doublet Method	315	(5)
Quadratic Doublet Method	320	(3)
Some Conclusions about Panel Methods	323	(8)
Three-Dimensional Numerical Solutions	331	(38)
Lifting-Line Solution by Horseshoe Elements	331	(7)
Modeling of Symmetry and Reflections from Solid Boundaries	338	(2)
Lifting-Surface Solution by Vortex Ring Elements	340	(11)
Introduction to Panel Codes: A Brief History	351	(2)
First-Order Potential-Based Panel Methods	353	(5)
Higher Order Panel Methods	358	(2)
Sample Solutions with Panel Codes	360	(9)
Unsteady Incompressible Potential Flow	369	(79)
Formulation of the Problem and Choice of Coordinates	369	(4)
Method of Solution	373	(2)
Additional Physical Considerations	375	(1)
Computation of Pressures	376	(1)
Examples for the Unsteady Boundary Condition	377	(3)
Summary of Solution Methodology	380	(1)
Sudden Acceleration of a Flat Plate	381	(6)
The Added Mass	385	(2)
Unsteady Motion of a Two-Dimensional Thin Airfoil	387	(13)
Kinematics	388	(1)
Wake Model	389	(2)
Solution by the Time-Stepping Method	391	(3)
Fluid Dynamic Loads	394	(6)
Unsteady Motion of a Slender Wing	400	(7)
Kinematics	401	(1)
Solution of the Flow over the Unsteady Slender Wing	401	(6)
Algorithm for Unsteady Airfoil Using the Lumped-Vortex Element	407	(9)
Some Remarks about the Unsteady Kutta Condition	416	(3)
Unsteady Lifting-Surface Solution by Vortex Ring Elements	419	(14)
Unsteady Panel Methods	433	(15)
The Laminar Boundary Layer	448	(35)
The Concept of the Boundary Layer	448	(4)
Boundary Layer on a Curved Surface	452	(5)
Similar Solutions to the Boundary Layer Equations	457	(6)
The von Karman Integral Momentum Equation	463	(4)
Solutions Using the von Karman Integral Equation	467	(4)
Approximate Polynomial Solution	468	(1)
The Correlation Method of Thwaites	469	(2)
Weak Interactions, the Goldstein Singularity, and Wakes	471	(2)
Two-Equation Integral Boundary Layer Method	473	(2)
Viscous-Inviscid Interaction Method	475	(4)
Concluding Example: The Flow over a Symmetric Airfoil	479	(4)
Enhancement of the Potential Flow Model	483	(54)
Wake Rollup	483	(4)
Coupling between Potential Flow and Boundary Layer Solvers	487	(8)
The Laminar/Turbulent Boundary Layer and Transition	487	(4)
Viscous-Inviscid Coupling, Including Turbulent Boundary Layer	491	(4)
Influence of Viscous Flow Effects on Airfoil Design	495	(10)
Low Drag Considerations	498	(1)
High Lift Considerations	499	(6)
Flow over Wings at High Angles of Attack	505	(23)
Flow Separation on Wings with Unswept Leading Edge - Experimental Observations	508	(2)
Flow Separation on Wings with Unswept Leading Edge - Modeling	510	(6)
Flow Separation on Wings with Highly Swept Leading Edge - Experimental Observations	516	(7)
Modeling of Highly Swept Leading-Edge Separation	523	(5)
Possible Additional Features of Panel Codes	528	(9)
A Airfoil Integrals	537	(3)
B Singularity Distribution Integrals	540	(5)
C Principal Value of the Lifting Surface Integral IL	545	(1)
D Sample Computer Programs	546	(65)
Index	611