Wilson C. Chin, PhD, earned his M.Sc. at Caltech and Ph.D. from M.I.T. both in aerospace engineering. Early on, he had served as Senior Research Aerodynamicist at Boeing and Turbomachinery Manager at Pratt & Whitney Aircraft, authoring two dozen papers on supersonic and transonic flow, panel methods, hydrodynamic stability, computational fluid-dynamics and inverse formulations. Mr. Chin would later turn his efforts to the petroleum geosciences, writing more than twenty monographs with Wiley-Scrivener and other publishers on several areas in oil and gas exploration. He has also more than a hundred papers and four dozen patents to his credit. He is the recipient of five prestigious awards from the United States Department of Energy and is a well-regarded software developer to domestic and international petroleum companies. In the present book, Mr. Chin focuses on key aerodynamic issues he had addressed, which have grown in importance, and contributes numerous insights to modern analysis methods now key to the resurgence of new types of aircraft on the drawing boards.

• Preface xiiAcknowledgements xiv1 Basic Concepts, Challenges and Methods 11.1 Governing Equations - An Unconventional Synopsis 11.2 Fundamental “Analysis” or “Forward Modeling” Ideas 61.3 Basic “Inverse” or “Indirect Modeling” Ideas 151.4 Literature Overview and Modeling Issues 201.5 References 322 Computational Methods: Subtleties, Approaches and Algorithms 332.1 Coding Suggestions and Baseline Solutions 332.1.1 Presentation Approach 332.1.2 Programming Exercises 352.1.3 Model Extensions and Challenges 362.2 Finite Difference Methods for Simple Planar Flows 392.2.1 Finite Differences - Basic Concepts 392.2.2 Formulating Steady Flow Problems 452.2.3 Steady Flow Problems 462.2.4 Wells and Internal Boundaries 552.2.5 Point Relaxation Methods 622.2.6 Observations on Relaxation Methods 642.3 Examples - Analysis, Direct or Forward Applications 752.3.1 Example 1 - Thickness Solution, Centered Slit in Box 762.3.2 Example 2 - Half-Space Thickness Solution 912.3.3 Example 3 - Centered Symmetric Wedge Flow 982.3.4 Example 4 - General Solution with Lift, Centered Slit 1012.3.5 Example 5 - Transonic Supercritical Airfoil with Type-Dependent Differencing Solution, Subsonic, Mixed Flow and Supersonic Calculations 1192.3.6 Example 6 - Three-Dimensional, Thickness Only, Finite, Half-Space Solution 1292.4 Examples - Inverse or Indirect Applications 1382.4.1 Example 1 - Constant Pressure Specification and Symmetric Thin Ellipse 1382.4.2 Example 2 - Inverse Problem, Pressure Specification, Centered Sit, Trailing Edge Closed vs Opened 1452.4.3 Example 3 - Inverse Problem, Pressure Specification, Three-Dimensional Half-Space, Closed Trailing Edge, Nonlifting Symmetric Section 1583 Advanced Physical Models and Mathematical Approaches 1653.1 Nonlinear Formulation for Low-Frequency Transonic Flow 1703.1.1 Introduction 1703.1.2 Analysis 1713.1.3 Discussion and Summary 1743.1.4 References 1753.2 Effect of Frequency in Unsteady Transonic Flow 1763.2.1 Introduction 1763.2.2 Numerical Procedure 1773.2.3 Results 1783.2.4 Concluding Remarks 1803.2.5 References 1813.3 Harmonic Analysis of Unsteady Transonic Flow 1823.3.1 Introduction 1823.3.2 Analytical and Numerical Approach 1833.3.3 Calculated Results 1843.3.4 Discussion and Closing Remarks 1853.3.5 References 1883.4 Supersonic Wave Drag for Nonplanar Singularity Distributions 1893.4.1 Introduction 1893.4.2 Analysis 1913.4.3 Summary 1933.4.4 References 1943.5 Supersonic Wave Drag for Planar Singularity Distributions 1953.5.1 Introduction 1953.5.2 Analysis 1983.5.3 Concluding Remarks 2063.5.4 References 2073.6 Pseudo-Transonic Equation with a Diffusion Term 2083.6.1 Introduction 2093.6.2 Analysis 2093.6.3 Summary 2123.6.4 References 2123.7 Numerical Solution for Viscous Transonic Flow 2133.7.1 Introduction 2133.7.2 Analysis 2133.7.3 Numerical Approach 2163.7.4 Sample Calculation 2173.7.5 Discussion 2183.7.6 References 2203.8 Type-Independent Solutions for Mixed Subsonic and Supersonic Compressible Flow 2213.8.1 Introduction 2213.8.2 Discussion 2213.8.3 Numerical Approaches 2233.8.3.1 Horizontal Line Relaxation 2233.8.3.2 Vertical Column Relaxation 2243.8.4 Summary 2253.8.5 References 2273.9 Algorithm for Inviscid Compressible Flow Using the Viscous Transonic Equation 2283.9.1 Introduction 2283.9.2 Analysis 2293.9.3 Sample Calculations 2313.9.4 Summary and Conclusions 2323.9.5 References 2333.10 Inviscid Parallel Flow Stability with Nonlinear Mean Profile Distortion 2343.10.1 Introduction 2353.10.2 Analysis 2353.10.3 Discussion and Conclusion 2393.10.4 References 2403.11 Aerodynamic Stability of Inviscid Shear Flow Over Flexible Membranes 2423.11.1 Introduction 2423.11.2 Analysis 2423.11.3 Specific Examples 2453.11.4 Discussion and Concluding Remarks 2473.11.5 References 2483.12 Goethert’s Rule with an Improved Boundary Condition 2493.12.1 Introduction 2493.12.2 Analysis 2503.12.3 Summary 2533.12.4 References 2533.13 Some Singular Aspects of Three-Dimensional Transonic Flow 2543.13.1 Analysis 2543.13.2 Discussion and Summary 2573.13.3 References 2594 General Analysis and Inverse Methods for Aerodynamic Modeling 2604.1 On the Design of Thin Subsonic Airfoils 2644.1.1 Introduction 2644.1.2 Analysis 2654.1.3 First-Order Problem 2664.1.4 Second-Order Problem 2694.1.5 Discussion and Conclusion 2714.1.6 References 2734.2 Airfoil Design in Subcritical and Supercritical Flows 2744.2.1 Introduction 2744.2.2 Streamfunction Formulation 2784.2.3 Numerical Procedure 2814.2.4 Calculated Results 2844.2.5 Discussion and Closing Remarks 2854.2.6 References 2904.3 Direct Approach to Aerodynamic Inverse Problems 2924.3.1 Introduction 2924.3.2 Theory and Examples 2954.3.2.1 Constant Density Planar Flows 2954.3.2.2 Constant Density Flows Past Three-Dimensional Finite Wings 2994.3.2.3 Compressible Flows Past Finite Wings 3014.3.2.4 Flows in Fans and Cascades 3024.3.2.5 Axisymmetric Compressible Flows 3034.3.3 Sample Calculations 3044.3.4 Closing Remarks 3074.3.5 References 3104.4 Superpotential Solution for Jet Engine External Potential and Internal Rotational Flow Interaction 3124.4.1 Introduction 3134.4.2 Rotational Flow Equations 3144.4.3 The Linearized Problem 3164.4.4 Application to Jet-Engine External Potential and Internal Rotational Flow Interaction 3184.4.5 Calculated Results and Closing Discussion 3214.4.6 References 3254.5 Thin Airfoil Theory for Planar Inviscid Shear Flow 3264.5.1 Introduction 3274.5.2 Planar Flows with Constant Vorticity 3304.5.2.1 Planar Flows: Inverse Problems 3304.5.2.2 Planar Flows: Direct Formulations 3314.5.2.3 Some Planar Analytical Solutions 3324.5.2.4 Analogy to Ringwing Potential Flows 3334.5.2.5 Source and Vortex Interactions for Ringwings 3344.5.3 Airfoils in General Parallel Shear Flow 3354.5.4 Numerical Results 3394.5.5 Closing Remarks 3414.5.6 References 3434.5.7 Appendix I, Three-Dimensional Constant Density Flows 3444.5.8 Appendix II, Planar Compressible Shear Flow of a Gas 3454.6 Class of Shock-free Airfoils Producing the Same Surface Pressure 3484.6.1 Introduction 3484.6.2 Analysis 3504.6.3 Discussion and Conclusion 3514.6.4 References 3534.7 Engine Power Simulation for Transonic Flow-Through Nacelles 3554.7.1 Introduction 3554.7.2 Analytical and Numerical Approach 3564.7.3 Numerical Results and Closing Remarks 3574.7.4 References 3604.8 Inviscid Steady Flow Past Turbofan Mixer Nozzles 3614.8.1 Introduction 3614.8.2 Analytical Formulation 3614.8.3 Calculated Results and Closing Remarks 3634.8.4 References 3655 Engine and Airframe Integration Methods 3665.1 Big Picture Revisited 3675.2 Engine Component Analysis 3715.3 Engine Power Simulation Using Actuator Disks 3745.4 Mixers and Supersonic Nozzles 3755.5 References 377Cumulative References 379Index 396About the Author 408

Wilson C. Chin, PhD, earned his M.Sc. at Caltech and Ph.D. from M.I.T. both in aerospace engineering. Early on, he had served as Senior Research Aerodynamicist at Boeing and Turbomachinery Manager at Pratt & Whitney Aircraft, authoring two dozen papers on supersonic and transonic flow, panel methods, hydrodynamic stability, computational fluid-dynamics and inverse formulations. Mr. Chin would later turn his efforts to the petroleum geosciences, writing more than twenty monographs with Wiley-Scrivener and other publishers on several areas in oil and gas exploration. He has also more than a hundred papers and four dozen patents to his credit. He is the recipient of five prestigious awards from the United States Department of Energy and is a well-regarded software developer to domestic and international petroleum companies. In the present book, Mr. Chin focuses on key aerodynamic issues he had addressed, which have grown in importance, and contributes numerous insights to modern analysis methods now key to the resurgence of new types of aircraft on the drawing boards.

• Preface xiiAcknowledgements xiv1 Basic Concepts, Challenges and Methods 11.1 Governing Equations - An Unconventional Synopsis 11.2 Fundamental “Analysis” or “Forward Modeling” Ideas 61.3 Basic “Inverse” or “Indirect Modeling” Ideas 151.4 Literature Overview and Modeling Issues 201.5 References 322 Computational Methods: Subtleties, Approaches and Algorithms 332.1 Coding Suggestions and Baseline Solutions 332.1.1 Presentation Approach 332.1.2 Programming Exercises 352.1.3 Model Extensions and Challenges 362.2 Finite Difference Methods for Simple Planar Flows 392.2.1 Finite Differences - Basic Concepts 392.2.2 Formulating Steady Flow Problems 452.2.3 Steady Flow Problems 462.2.4 Wells and Internal Boundaries 552.2.5 Point Relaxation Methods 622.2.6 Observations on Relaxation Methods 642.3 Examples - Analysis, Direct or Forward Applications 752.3.1 Example 1 - Thickness Solution, Centered Slit in Box 762.3.2 Example 2 - Half-Space Thickness Solution 912.3.3 Example 3 - Centered Symmetric Wedge Flow 982.3.4 Example 4 - General Solution with Lift, Centered Slit 1012.3.5 Example 5 - Transonic Supercritical Airfoil with Type-Dependent Differencing Solution, Subsonic, Mixed Flow and Supersonic Calculations 1192.3.6 Example 6 - Three-Dimensional, Thickness Only, Finite, Half-Space Solution 1292.4 Examples - Inverse or Indirect Applications 1382.4.1 Example 1 - Constant Pressure Specification and Symmetric Thin Ellipse 1382.4.2 Example 2 - Inverse Problem, Pressure Specification, Centered Sit, Trailing Edge Closed vs Opened 1452.4.3 Example 3 - Inverse Problem, Pressure Specification, Three-Dimensional Half-Space, Closed Trailing Edge, Nonlifting Symmetric Section 1583 Advanced Physical Models and Mathematical Approaches 1653.1 Nonlinear Formulation for Low-Frequency Transonic Flow 1703.1.1 Introduction 1703.1.2 Analysis 1713.1.3 Discussion and Summary 1743.1.4 References 1753.2 Effect of Frequency in Unsteady Transonic Flow 1763.2.1 Introduction 1763.2.2 Numerical Procedure 1773.2.3 Results 1783.2.4 Concluding Remarks 1803.2.5 References 1813.3 Harmonic Analysis of Unsteady Transonic Flow 1823.3.1 Introduction 1823.3.2 Analytical and Numerical Approach 1833.3.3 Calculated Results 1843.3.4 Discussion and Closing Remarks 1853.3.5 References 1883.4 Supersonic Wave Drag for Nonplanar Singularity Distributions 1893.4.1 Introduction 1893.4.2 Analysis 1913.4.3 Summary 1933.4.4 References 1943.5 Supersonic Wave Drag for Planar Singularity Distributions 1953.5.1 Introduction 1953.5.2 Analysis 1983.5.3 Concluding Remarks 2063.5.4 References 2073.6 Pseudo-Transonic Equation with a Diffusion Term 2083.6.1 Introduction 2093.6.2 Analysis 2093.6.3 Summary 2123.6.4 References 2123.7 Numerical Solution for Viscous Transonic Flow 2133.7.1 Introduction 2133.7.2 Analysis 2133.7.3 Numerical Approach 2163.7.4 Sample Calculation 2173.7.5 Discussion 2183.7.6 References 2203.8 Type-Independent Solutions for Mixed Subsonic and Supersonic Compressible Flow 2213.8.1 Introduction 2213.8.2 Discussion 2213.8.3 Numerical Approaches 2233.8.3.1 Horizontal Line Relaxation 2233.8.3.2 Vertical Column Relaxation 2243.8.4 Summary 2253.8.5 References 2273.9 Algorithm for Inviscid Compressible Flow Using the Viscous Transonic Equation 2283.9.1 Introduction 2283.9.2 Analysis 2293.9.3 Sample Calculations 2313.9.4 Summary and Conclusions 2323.9.5 References 2333.10 Inviscid Parallel Flow Stability with Nonlinear Mean Profile Distortion 2343.10.1 Introduction 2353.10.2 Analysis 2353.10.3 Discussion and Conclusion 2393.10.4 References 2403.11 Aerodynamic Stability of Inviscid Shear Flow Over Flexible Membranes 2423.11.1 Introduction 2423.11.2 Analysis 2423.11.3 Specific Examples 2453.11.4 Discussion and Concluding Remarks 2473.11.5 References 2483.12 Goethert’s Rule with an Improved Boundary Condition 2493.12.1 Introduction 2493.12.2 Analysis 2503.12.3 Summary 2533.12.4 References 2533.13 Some Singular Aspects of Three-Dimensional Transonic Flow 2543.13.1 Analysis 2543.13.2 Discussion and Summary 2573.13.3 References 2594 General Analysis and Inverse Methods for Aerodynamic Modeling 2604.1 On the Design of Thin Subsonic Airfoils 2644.1.1 Introduction 2644.1.2 Analysis 2654.1.3 First-Order Problem 2664.1.4 Second-Order Problem 2694.1.5 Discussion and Conclusion 2714.1.6 References 2734.2 Airfoil Design in Subcritical and Supercritical Flows 2744.2.1 Introduction 2744.2.2 Streamfunction Formulation 2784.2.3 Numerical Procedure 2814.2.4 Calculated Results 2844.2.5 Discussion and Closing Remarks 2854.2.6 References 2904.3 Direct Approach to Aerodynamic Inverse Problems 2924.3.1 Introduction 2924.3.2 Theory and Examples 2954.3.2.1 Constant Density Planar Flows 2954.3.2.2 Constant Density Flows Past Three-Dimensional Finite Wings 2994.3.2.3 Compressible Flows Past Finite Wings 3014.3.2.4 Flows in Fans and Cascades 3024.3.2.5 Axisymmetric Compressible Flows 3034.3.3 Sample Calculations 3044.3.4 Closing Remarks 3074.3.5 References 3104.4 Superpotential Solution for Jet Engine External Potential and Internal Rotational Flow Interaction 3124.4.1 Introduction 3134.4.2 Rotational Flow Equations 3144.4.3 The Linearized Problem 3164.4.4 Application to Jet-Engine External Potential and Internal Rotational Flow Interaction 3184.4.5 Calculated Results and Closing Discussion 3214.4.6 References 3254.5 Thin Airfoil Theory for Planar Inviscid Shear Flow 3264.5.1 Introduction 3274.5.2 Planar Flows with Constant Vorticity 3304.5.2.1 Planar Flows: Inverse Problems 3304.5.2.2 Planar Flows: Direct Formulations 3314.5.2.3 Some Planar Analytical Solutions 3324.5.2.4 Analogy to Ringwing Potential Flows 3334.5.2.5 Source and Vortex Interactions for Ringwings 3344.5.3 Airfoils in General Parallel Shear Flow 3354.5.4 Numerical Results 3394.5.5 Closing Remarks 3414.5.6 References 3434.5.7 Appendix I, Three-Dimensional Constant Density Flows 3444.5.8 Appendix II, Planar Compressible Shear Flow of a Gas 3454.6 Class of Shock-free Airfoils Producing the Same Surface Pressure 3484.6.1 Introduction 3484.6.2 Analysis 3504.6.3 Discussion and Conclusion 3514.6.4 References 3534.7 Engine Power Simulation for Transonic Flow-Through Nacelles 3554.7.1 Introduction 3554.7.2 Analytical and Numerical Approach 3564.7.3 Numerical Results and Closing Remarks 3574.7.4 References 3604.8 Inviscid Steady Flow Past Turbofan Mixer Nozzles 3614.8.1 Introduction 3614.8.2 Analytical Formulation 3614.8.3 Calculated Results and Closing Remarks 3634.8.4 References 3655 Engine and Airframe Integration Methods 3665.1 Big Picture Revisited 3675.2 Engine Component Analysis 3715.3 Engine Power Simulation Using Actuator Disks 3745.4 Mixers and Supersonic Nozzles 3755.5 References 377Cumulative References 379Index 396About the Author 408

Wilson C. Chin, PhD, earned his M.Sc. at Caltech and Ph.D. from M.I.T. both in aerospace engineering. Early on, he had served as Senior Research Aerodynamicist at Boeing and Turbomachinery Manager at Pratt & Whitney Aircraft, authoring two dozen papers on supersonic and transonic flow, panel methods, hydrodynamic stability, computational fluid-dynamics and inverse formulations. Mr. Chin would later turn his efforts to the petroleum geosciences, writing more than twenty monographs with Wiley-Scrivener and other publishers on several areas in oil and gas exploration. He has also more than a hundred papers and four dozen patents to his credit. He is the recipient of five prestigious awards from the United States Department of Energy and is a well-regarded software developer to domestic and international petroleum companies. In the present book, Mr. Chin focuses on key aerodynamic issues he had addressed, which have grown in importance, and contributes numerous insights to modern analysis methods now key to the resurgence of new types of aircraft on the drawing boards.

• Preface xiiAcknowledgements xiv1 Basic Concepts, Challenges and Methods 11.1 Governing Equations - An Unconventional Synopsis 11.2 Fundamental “Analysis” or “Forward Modeling” Ideas 61.3 Basic “Inverse” or “Indirect Modeling” Ideas 151.4 Literature Overview and Modeling Issues 201.5 References 322 Computational Methods: Subtleties, Approaches and Algorithms 332.1 Coding Suggestions and Baseline Solutions 332.1.1 Presentation Approach 332.1.2 Programming Exercises 352.1.3 Model Extensions and Challenges 362.2 Finite Difference Methods for Simple Planar Flows 392.2.1 Finite Differences - Basic Concepts 392.2.2 Formulating Steady Flow Problems 452.2.3 Steady Flow Problems 462.2.4 Wells and Internal Boundaries 552.2.5 Point Relaxation Methods 622.2.6 Observations on Relaxation Methods 642.3 Examples - Analysis, Direct or Forward Applications 752.3.1 Example 1 - Thickness Solution, Centered Slit in Box 762.3.2 Example 2 - Half-Space Thickness Solution 912.3.3 Example 3 - Centered Symmetric Wedge Flow 982.3.4 Example 4 - General Solution with Lift, Centered Slit 1012.3.5 Example 5 - Transonic Supercritical Airfoil with Type-Dependent Differencing Solution, Subsonic, Mixed Flow and Supersonic Calculations 1192.3.6 Example 6 - Three-Dimensional, Thickness Only, Finite, Half-Space Solution 1292.4 Examples - Inverse or Indirect Applications 1382.4.1 Example 1 - Constant Pressure Specification and Symmetric Thin Ellipse 1382.4.2 Example 2 - Inverse Problem, Pressure Specification, Centered Sit, Trailing Edge Closed vs Opened 1452.4.3 Example 3 - Inverse Problem, Pressure Specification, Three-Dimensional Half-Space, Closed Trailing Edge, Nonlifting Symmetric Section 1583 Advanced Physical Models and Mathematical Approaches 1653.1 Nonlinear Formulation for Low-Frequency Transonic Flow 1703.1.1 Introduction 1703.1.2 Analysis 1713.1.3 Discussion and Summary 1743.1.4 References 1753.2 Effect of Frequency in Unsteady Transonic Flow 1763.2.1 Introduction 1763.2.2 Numerical Procedure 1773.2.3 Results 1783.2.4 Concluding Remarks 1803.2.5 References 1813.3 Harmonic Analysis of Unsteady Transonic Flow 1823.3.1 Introduction 1823.3.2 Analytical and Numerical Approach 1833.3.3 Calculated Results 1843.3.4 Discussion and Closing Remarks 1853.3.5 References 1883.4 Supersonic Wave Drag for Nonplanar Singularity Distributions 1893.4.1 Introduction 1893.4.2 Analysis 1913.4.3 Summary 1933.4.4 References 1943.5 Supersonic Wave Drag for Planar Singularity Distributions 1953.5.1 Introduction 1953.5.2 Analysis 1983.5.3 Concluding Remarks 2063.5.4 References 2073.6 Pseudo-Transonic Equation with a Diffusion Term 2083.6.1 Introduction 2093.6.2 Analysis 2093.6.3 Summary 2123.6.4 References 2123.7 Numerical Solution for Viscous Transonic Flow 2133.7.1 Introduction 2133.7.2 Analysis 2133.7.3 Numerical Approach 2163.7.4 Sample Calculation 2173.7.5 Discussion 2183.7.6 References 2203.8 Type-Independent Solutions for Mixed Subsonic and Supersonic Compressible Flow 2213.8.1 Introduction 2213.8.2 Discussion 2213.8.3 Numerical Approaches 2233.8.3.1 Horizontal Line Relaxation 2233.8.3.2 Vertical Column Relaxation 2243.8.4 Summary 2253.8.5 References 2273.9 Algorithm for Inviscid Compressible Flow Using the Viscous Transonic Equation 2283.9.1 Introduction 2283.9.2 Analysis 2293.9.3 Sample Calculations 2313.9.4 Summary and Conclusions 2323.9.5 References 2333.10 Inviscid Parallel Flow Stability with Nonlinear Mean Profile Distortion 2343.10.1 Introduction 2353.10.2 Analysis 2353.10.3 Discussion and Conclusion 2393.10.4 References 2403.11 Aerodynamic Stability of Inviscid Shear Flow Over Flexible Membranes 2423.11.1 Introduction 2423.11.2 Analysis 2423.11.3 Specific Examples 2453.11.4 Discussion and Concluding Remarks 2473.11.5 References 2483.12 Goethert’s Rule with an Improved Boundary Condition 2493.12.1 Introduction 2493.12.2 Analysis 2503.12.3 Summary 2533.12.4 References 2533.13 Some Singular Aspects of Three-Dimensional Transonic Flow 2543.13.1 Analysis 2543.13.2 Discussion and Summary 2573.13.3 References 2594 General Analysis and Inverse Methods for Aerodynamic Modeling 2604.1 On the Design of Thin Subsonic Airfoils 2644.1.1 Introduction 2644.1.2 Analysis 2654.1.3 First-Order Problem 2664.1.4 Second-Order Problem 2694.1.5 Discussion and Conclusion 2714.1.6 References 2734.2 Airfoil Design in Subcritical and Supercritical Flows 2744.2.1 Introduction 2744.2.2 Streamfunction Formulation 2784.2.3 Numerical Procedure 2814.2.4 Calculated Results 2844.2.5 Discussion and Closing Remarks 2854.2.6 References 2904.3 Direct Approach to Aerodynamic Inverse Problems 2924.3.1 Introduction 2924.3.2 Theory and Examples 2954.3.2.1 Constant Density Planar Flows 2954.3.2.2 Constant Density Flows Past Three-Dimensional Finite Wings 2994.3.2.3 Compressible Flows Past Finite Wings 3014.3.2.4 Flows in Fans and Cascades 3024.3.2.5 Axisymmetric Compressible Flows 3034.3.3 Sample Calculations 3044.3.4 Closing Remarks 3074.3.5 References 3104.4 Superpotential Solution for Jet Engine External Potential and Internal Rotational Flow Interaction 3124.4.1 Introduction 3134.4.2 Rotational Flow Equations 3144.4.3 The Linearized Problem 3164.4.4 Application to Jet-Engine External Potential and Internal Rotational Flow Interaction 3184.4.5 Calculated Results and Closing Discussion 3214.4.6 References 3254.5 Thin Airfoil Theory for Planar Inviscid Shear Flow 3264.5.1 Introduction 3274.5.2 Planar Flows with Constant Vorticity 3304.5.2.1 Planar Flows: Inverse Problems 3304.5.2.2 Planar Flows: Direct Formulations 3314.5.2.3 Some Planar Analytical Solutions 3324.5.2.4 Analogy to Ringwing Potential Flows 3334.5.2.5 Source and Vortex Interactions for Ringwings 3344.5.3 Airfoils in General Parallel Shear Flow 3354.5.4 Numerical Results 3394.5.5 Closing Remarks 3414.5.6 References 3434.5.7 Appendix I, Three-Dimensional Constant Density Flows 3444.5.8 Appendix II, Planar Compressible Shear Flow of a Gas 3454.6 Class of Shock-free Airfoils Producing the Same Surface Pressure 3484.6.1 Introduction 3484.6.2 Analysis 3504.6.3 Discussion and Conclusion 3514.6.4 References 3534.7 Engine Power Simulation for Transonic Flow-Through Nacelles 3554.7.1 Introduction 3554.7.2 Analytical and Numerical Approach 3564.7.3 Numerical Results and Closing Remarks 3574.7.4 References 3604.8 Inviscid Steady Flow Past Turbofan Mixer Nozzles 3614.8.1 Introduction 3614.8.2 Analytical Formulation 3614.8.3 Calculated Results and Closing Remarks 3634.8.4 References 3655 Engine and Airframe Integration Methods 3665.1 Big Picture Revisited 3675.2 Engine Component Analysis 3715.3 Engine Power Simulation Using Actuator Disks 3745.4 Mixers and Supersonic Nozzles 3755.5 References 377Cumulative References 379Index 396About the Author 408