Unsteady Aerodynamics

Grigorios Dimitriadis, PhD, is Professor of Fluid Structure Interaction and Experimental Aerodynamics in the Aerospace and Mechanical Engineering Department, University of Liège, Belgium and Adjunct Professor in Aeroelasticity at the von Karman Institute for Fluid Dynamics, Belgium. He has published extensively on unsteady aerodynamics and related fields.

• Preface xiAbout the Companion Website xiii1 Introduction 11.1 Why Potential and Vortex Methods? 21.2 Outline of This Book 32 Unsteady Flow Fundamentals 52.1 Introduction 52.2 From Navier–Stokes to Unsteady Incompressible Potential Flow 52.2.1 Irrotational Flow 62.2.2 Laplace's and Bernoulli's Equations 72.2.3 Motion in an Incompressible, Inviscid, Irrotational Fluid 92.3 Incompressible Potential Flow Solutions 142.3.1 Green's Third Identity 212.3.2 Solutions in Two Dimensions 402.4 From Navier–Stokes to Unsteady Compressible Potential Flow 422.4.1 The Compressible Bernoulli Equation 422.4.2 The Full Potential Equation 442.4.3 The Transonic Small Disturbance Equation 462.4.4 The Linearised Small Disturbance Equation 472.4.5 The Compressible Unsteady Pressure Coefficient 492.4.6 Motion in a Compressible, Inviscid, Irrotational Fluid 522.5 Subsonic Linearised Potential Flow Solutions 532.6 Supersonic Linearised Potential Flow Solutions 612.7 Vorticity and Circulation 662.7.1 Solutions of the Vorticity Transport Equations 712.7.2 Vorticity-Moment and Kutta–Joukowski Theorems 762.7.3 TheWake and the Kutta Condition 772.8 Concluding Remarks 793 Analytical Incompressible 2D Models 833.1 Introduction 833.2 Steady Thin Airfoil Theory 833.3 Fundamentals ofWagner and Theodorsen Theory 933.3.1 Flow Induced by the Source Distribution 973.3.2 Flow Induced by the Vortex Distribution 1013.3.3 Imposing the Impermeability Boundary Condition 1043.3.4 Calculating the Loads Due to the Source Distribution 1083.3.5 Imposing the Kutta Condition 1113.4 Wagner Theory 1133.4.1 TheWagner Function 1203.4.2 Drag and Thrust 1233.4.3 General Motion 1293.4.4 Total Loads 1313.4.5 Quasi-Steady Aerodynamics 1383.5 Theodorsen Theory 1393.5.1 Theodorsen's Function 1433.5.2 Total Loads for Sinusoidal Motion 1463.5.3 General Motion 1533.6 Finite State Theory 1573.6.1 Glauert Expansions 1613.6.2 Solution of the Impermeability Equation 1703.6.3 Completing the Equations 1723.6.4 Kutta Condition and Aerodynamic Loads 1753.7 Concluding Remarks 1833.8 Exercises 1844 Numerical Incompressible 2D Models 1874.1 Introduction 1874.2 Lumped Vortex Method 1874.2.1 Unsteady Flows 1974.2.2 FreeWakes 2064.3 Gust Encounters 2124.3.1 Pitching and Plunging Wings 2164.4 Frequency Domain Formulation of the Lumped Vortex Method 2274.5 Source and Vortex Panel Method 2334.5.1 Impulsively Started Flow 2454.5.2 Thrust and Propulsive Efficiency 2544.6 Theodorsen's Function andWake Shape 2594.7 Steady and Unsteady Kutta Conditions 2614.7.1 The Unsteady Kutta Condition 2674.8 Concluding Remarks 2754.9 Exercises 2755 Finite Wings 2795.1 Introduction 2795.1.1 Rigid Wings and Flexible Wings 2805.2 Finite Wings in Steady Flow 2815.3 The Impulsively Started Elliptical Wing 2905.3.1 The Solution by Jones 2905.3.2 Unsteady Lifting Line Solution 3025.4 The Unsteady Vortex Lattice Method 3065.4.1 Impulsive Start of an Elliptical Wing 3205.4.2 Other Planforms 3265.5 Rigid Harmonic Motion 3295.5.1 Longitudinal Harmonic Motion 3295.5.2 Frequency Domain Load Calculations 3355.5.3 Lateral Harmonic Motion 3415.5.4 Aerodynamic Stability Derivatives 3455.6 The 3D Source and Doublet Panel Method 3515.7 Flexible Motion 3645.7.1 Source and Doublet Panel Method in the Frequency Domain 3725.8 Concluding Remarks 3785.9 Exercises 3796 Unsteady Compressible Flow 3836.1 Introduction 3836.2 Steady Subsonic Potential Flow 3836.3 Unsteady Subsonic Potential Flow 3906.3.1 The Doublet Lattice Method 3916.3.2 Unsteady 3D Subsonic Source and Doublet Panel Method 4026.3.3 Steady Correction of the Doublet Lattice Method 4146.3.4 Unsteady 2D Subsonic Source and Doublet Panel Method 4166.4 Unsteady Supersonic Potential Flow 4196.4.1 The Mach Box Method 4206.4.2 The Mach Panel Method 4286.5 Transonic Flow 4346.5.1 Steady Transonic Flow 4356.5.2 Time Linearised Transonic Small Perturbation Equation 4406.5.3 Unsteady Transonic Correction Methods 4436.6 Concluding Remarks 4536.7 Exercises 4547 Viscous Flow 4597.1 Introduction 4597.1.1 Steady Flow Separation Mechanisms 4617.1.2 Dynamic Stall 4667.2 Impulsively Started Flow around a 2D Flat Plate at High Angles of Attack 4727.2.1 Flow Separation Criteria 4807.3 Flow Around a 2D Circular Cylinder 4857.3.1 The Discrete Vortex Method for Bluff Bodies 4887.3.2 Modelling the Flow Past a Circular Cylinder Using the DVM 4917.4 Flow Past 2D Rectangular Cylinders 5017.4.1 Modelling the Flow Past Rectangular Cylinders Using the DVM 5027.5 Concluding Remarks 5077.6 Exercises 507A Fundamental Solutions of Laplace's Equation 511A.1 The 2D Point Source 511A.2 The 2D Point Vortex 513A.3 The Source Line Panel 515A.4 The Vortex Line Panel 518A.5 The Horseshoe Vortex 521A.6 The Vortex Line Segment 523A.7 The Vortex Ring 525A.8 The 3D Point Source 526A.9 The 3D Point Doublet 528A.10 The Source Surface Panel 528A.11 The Doublet Surface Panel 534B Fundamental Solutions of the Linearized Small Disturbance Equation 539B.1 The Subsonic Doublet Surface Panel 539B.2 The Acoustic Source Surface Panel 541B.3 The Acoustic Doublet Surface Panel 542B.4 The Supersonic Source Surface Panel 543C Wagner's Derivation of the Kutta Condition 549Reference 550Index 551