Collected Works of H. S. Tsien (1938-1956)

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Hsue-Shen Tsiens Biography

Boundary Layer in Compressible Fluids

I

II

References

Supersonic Flow over an Inclined Body of Revolution

References

Problems in Motion of Compressible Fluids and Reaction Propulsion

PART (I). Boundary Layer in Compressible Fluids

Boundary Layer in Compressible Fluids

PART (II). Supersonic Flow over an Inclined Body of Revolution

Supersonic Flow over an Inclined Body of Revolution

PART (III). Application of Tschapligin’s Transformation to Two Dimensional Subsonic Flow

Application of Tschapligin’s Transformation to Two Dimensional Subsonic Flow

PART (IV). Flight Analysis of a Sounding Rocket with Special Reference to Propulsion by Successive Impulses

Flight Analysis of a Sounding Rocket with Special Reference to Propulsion by Successive Impulses

Flight Analysis of a Sounding Rocket with Special Reference to Propulsion by Successive Impulses

Introduction

Notation

I

II

III

IV

Conclusion

References

Two-Dimensional Subsonic Flow of Compressible Fluids

Introduction

Approximation to the Adiabatic Relation

Section I

Section II

Concluding Remarks

References

The Buckling of Spherical Shells by External Pressure*

General Considerations

The Energy Expression and the Equation of Equilibrium for a Spherical Segment Under Uniform External Pressure

Approximate Solution by the Rayleigh-Ritz Method

Application to the Buckling Problem. Comparison with the Experiment

References

The Influence of Curvature on the Buckling Characteristics of Structures

Section I

Section II

Section III

Concluding Remarks

References

A Method for Predicting the Compressibility Burble

Introduction

Part I

Part II

Part III

Appendix 1

References

The Buckling of Thin Cylindrical Shells under Axial Compression

Stresses in the Median Surface and the expression for the Total Energy of the System

Calculation of the Total Energy

Relation Between the compression Stress and the Amplitude of Waves

The Relation Between the Compression Stress and the Shortening of the Shell in the Axial Direction

The Effect of the Elastic Characteristic of the testing Machine on the Buckling Phenomenon

Conclusions

References

Buckling of a Column with Non-Linear Lateral Supports

Introduction

General Theory for Straight Columns

Case of Two Equally Spaced Supports

Case of a Single Lateral Support, Effect of Initial Deflection

Case of a Single Lateral Support, Effect of Elasticity of the Testing Machine

Stability of the Equilibrium Positions Under Infinitesimal Disturbances

Conclusions

References

A Theory for the Buckling of Thin Shells

Introduction

The Criterions for Buckling

Column with a Nonlinear Elastic Lateral Support

Thin Uniform Cylindric Shell Under Axial Compression

Spherical Shells under External Pressure

Concluding Remarks

References

Heat Conduction across a Partially Insulated Wall

On the Design of the Contraction Cone for a Wind Tunnel

Formulation of the Problem

Solution of the Problem

The Results

References

Symmetrical Joukowsky Airfoils in Shear Flow

1. Problem

2. Method of solution

3. Shear flow over a circular cylinder

4. Force and moment

5. Symmetrical Joukowsky airfoils

6. Strength of circulation

7. Strengths of doublets and quadruplets

8. Lift and moment coefficients

9. Aerodynamic center

References

The “Limiting Line” in Mixed Subsonic and Supersonic Flow of Compressible Fluids

Criterion for the Breakdown of Isentropic Irrotational Flow

Axially Symmetric Flow

The Limiting Line

Limiting Hodograph and the Streamlines

Envelope of Characteristics in Hodograph Plane and Lines of Constant Velocity in Physical Plane

The Lost Solution

Continuation of Solution Beyond The Limiting Line

General Three-Dimensional Flow

References

Loss in Compressor or Turbine due to Twisted Blades

Problem

The Vortex System and the Induced Velocity

The General Blade Equation

Application I

Application II

Appendix

REFERENCE

Lifting-Line Theory for a Wing in Non-uniform Flow*

1. Introduction

2. General theory of a lifting line

3. Conditions far downstream

4. Minimum induced drag

5. Flow with velocity varying in the direction of span only

References

Atomic Energy

Introduction

The Equivalence of Energy and Mass

Atomic Structure

Nuclear Reactions

Nuclear Structure — Binding Energy

Energy Production in the Stars

Nuclear Fission — Chain Reaction

Engineering Approach to the Nuclear Reaction

References

Two-Dimensional Irrotational Mixed Subsonic and Supersonic Flow of a Compressible Fluid and the Upper Critical Mach Number

Introduction

Notations

Part I. Differential Equations of Compressible Flow and Properties of Their Particular Solutions

2. Transformation of the Differential Equations

3. The Particular Solutions of the Differential Equations

4. The Properties of the Hypergeometric Functions of Large Order

Part II. Construction of the Solutions for Compressible Flow Around a Body

6. The Functions for Incompressible Flow

7. Conformal Mapping of Incompressible Flow on the Hodograph Plan

8. Construction of a Solution about the Origin

9. Analytic Continuation of the Solution Branch Point or Order 1

10. Continuation Logarithmic Singularity

11. Transition to Physical Plane

Part III. Improvement of the Convergence of Solution by the Asymptotic Properties of Hypergeometric Functions

13. Asymptotic Solutions of the Hypergeometric Equations

14. The Asymptotic Representation of F(av, bv; cv; τ) and F(av + β, bv + β; cv; τ)

15. Transformation of the Function W(w; τ) Branch Point of Order 1

16. Continuation: Lo garithmic Singularity

17. The Coordinate Functions x (q, θ) and y (q, θ)

Part IV. Criteria for the Upper Critical Mach Number

19. The Condition for the Limiting Line

20. The Approximate Determination of the Upper Critical Mach Number

Part V. Application — Elliptic Cylinders

22. The Functions z0(w), W0 (w) and Λ0 (w)

23. Expansions of W0 (w) and Λ0 (w)

24. The Stream Function ψ(q, θ)

25. The Coordinate Functions x(q, θ) and y(q, θ)

Conclusions

References

Appendix A Proof of Theorem (52)

Appendix B Proof of Theorem (88)

Appendix C Proof of Theorem (98)

Tables of the Hypergeometric Functions

Superaerodynamics, Mechanics of Rarefied Gases

Introduction

Mean Free Path and Realms of Fluid Mechanics

Stresses and Boundary Conditions in Slip Flow

Boundary Conditions for Slip Flows of Small Mach Number

Slip Flows at Small Mach Numbers

Free Molecule Flows at Small Mach Numbers

Free Molecule Flow at Large Mach Numbers

Free Molecule Flow Over an Inclined Plate

References

Propagation of Plane Sound Waves in Rarefied Gases

1. Introduction

2. Symbols

3. Basic Equations

4. Solution of the Differential Equations

5. Numerical Calculation

6. Results

References

Similarity Laws of Hypersonic Flows

Introduction

Differential Equation for Hypersonic Flows

Similarity Laws in Two-Dimensional Flow

Axially Symmetrical Flows

References

One-Dimensional Flows of a Gas Characterized by van der Waals Equation of State*

Introduction

Isentropic Expansion of a van der Waal Gas

Expansion in a Nozzle

Shock Wave in Supersonic Flow

Parameters for Constants a and b

Properties of Air

Tabulation of Functions for Air

Application of Results to a Hypersonic Wind Tunnel

References

Corrections on the Paper “One-Dimensional Flows of a Gas Characterized by van der Waals Equation of State”

Flow Conditions near the Intersection of a Shock Wave with Solid Boundary

1. Introduction

2. Basic Equations

3. Relations of Quantities on the Two Sides of Shock

References

Lower Buckling Load in the Non-Linear Buckling Theory for Thin Shells

Rockets and Other Thermal Jets Using Nuclear Energy: With a General Discussion on the Use of Porous Pile Materials

1. Simple Theory of Space Rockets

2. Relativistic Theory of Space Rockets

3. Idealized Optimum Design using Nuclear Energy

4. Nuclear Energy Rocket

5. Specific Examples of Nuclear Energy Rocket

6. Possibilities of Reducing the Critical Size

7. Application of Nuclear Fuel to other Thermal Jets

8. Advantages of Using Porous Pile Material

References

Engineering and Engineering Sciences*

Introduction

Contributions of an Engineering Scientist to Engineering Development

The Feasibility of a Proposal—Long Range Rockets

Rocket Propellants

Best Method of Attack— Manufacture of Fissionable Material

Reason and Remedy for a Failure — the Tacoma Narrows Bridge

Unification—Basic Research in Engineering Science

Training of an Engineering Scientist

Concluding Remarks

References

On Two-Dimensional Non-steady Motion of a Slender Body in a Compressible Fluid

1. Introduction

2. General formulation of the problem

3. Introduction of parameters

4. Theory of small perturbations

5. Further simplification in special cases

6. Influence of wind tunnel walls

7. The Case of Large Pressure Disturbance

8. The Transonic case with M1= 1

References

Wind-Tunnel Testing Problems in Superaerodynamics

Introduction

(1) Tunnel Design

(2) Flow Measurement

(3) Hot-Wire Anemometer

(4) Parameters of Flow

Appendix

References

Airfoils in Slightly Supersonic Flow

Introduction

Oblique Shock

Prandtl-Meyer Expansion

Flat Plate Airfoil

Asymmetric Wedge Airfoil

References

Interaction between Parallel Streams of Subsonic and Supersonic Velocities*

Introduction

Incident Wave

Inclined Wall

Numerical Results and Discussion

References

Appendix

Research in Rocket and Jet Propulsion*

Variable Stress

Heat Transfer

Wall-Temperature Effects

Long-Range Trajectory

References

A Generalization of Alfrey’s Theorem for Visco-elastic Media

1. Introduction

2. First boundary value problem

REFERENCE

Instruction and Research at the Daniel and Florence Guggenheim Jet Propulsion Center

Jet-Propulsion Centers

Instruction and Research of Jet Propulsion

Characteristics of Rocket and Jet-Propulsion Engineering

Material Problems

Heat Transfer

Combustion

Performance of Rocket and Jet-Propelled Vehicles

References

Influence of Flame Front on the Flow Field

Flame Front

Production of Vorticity by Flame

Flame Width in a Uniform Channel

Effect of Compressibility on Flame Width

Appendix

References

Optimum Thrust Programming for a Sounding Rocket

Formulation of the Problem

Quadratic Drag Law

Linear Drag Law

Discussion of Results

Acknowledgment

References

The Emission of Radiation from Diatomic Gases. III. Numerical Emissivity Calculations for Carbon Monoxide for Low Optical Densities at 300K and Atmospheric Pressure

I. Introduction

II. Summary of Theoretical Relations

III. Representative Emissivity Calculations for CO at 300K

IV. Limits of Validity of the Treatment for Nonoverlapping Rotational Lines for CO17

V. Approximate Emissivity Calculations for Diatomic Molecules with Nonoverlapping Rotational Lines

VA Emissivity Calculations for CO at 300K for Nonoverlapping Rotational Lines, Assuming Equal Spacing and Intensity of Lines

VB Emissivity Calculations for CO at 300K for Nonoverlapping Rotational Lines Using Asymptotic Expressions for the Modified Bessel Functions

Appendix

References

The Transfer Functions of Rocket Nozzles

Flow Conditions

Formulation of the Problem in Nozzle

Solution for Small Frequency

Solution for Large Frequencies

Concluding Remarks

References

A Similarity Law for Stressing Rapidly Heated Thin-Walled Cylinders

Stresses and Strains of a Thin-Walled Cylinder

Nondimensional Quantities and Equations of Equilibrium

Infinite Cylinder Under Uniform Internal Pressure

Linearized Theory for General Secondary Loading

Similarity Law for General Loading

Example of Dimensioning the Equivalent Cold Cylinder

Junction Stress Between Cylinder and Head

Ring Stiffener Around Cylinder

References

On the Determination of Rotational Line Half-Widths of Diatomic Molecules*

I. Introduction

II. Calculation of Rotational Half-Widths from Experimental Data

References

Automatic Navigation of a Long Range Rocket Vehicle

Equations of Motion

Normal Flight Path

Disturbance Equations

Adjoint Functions for Range Correction

Cut-Off Condition

Condition for Automatic Navigation

Discussion

Appendix

References

A Method for Comparing the Performance of Power Plants for Vertical Flight

General Relation

Applications

Detail Improvement of Rocket Engine

References

Servo-Stabilization of Combustion in Rocket Motors

Time Lag in Combustion

Intrinsic Instability

System Dynamics with Servo Control

Instability Without Servo Control

Complete Stability with Servo Control

Stability Criteria

Concluding Remarks

Appendix

References

Physical Mechanics, A New Field in Engineering Science

Basic Concepts

Physical Mechanics as an Engineering Science

Use of Approximate Models

A Question of Methodology

Concluding Remarks

References

The Properties of Pure Liquids

Lennard-Jones and Devonshire Theory of Liquids

Specific Heat at Constant Volume

Thermal Expansion and Compressibility

Specific Heat at Constant Pressure

Liquid Metals

Velocity of Sound

Transport Properties

Thermal Conductivity

Concluding Remarks

Appendix

References

Similarity Laws for Stressing Heated Wings

Introduction

Basic Equations for Heated Plate

Plateat Constant Temperature

Similarity Laws for Solid Thin Wings

Alternate Test Procedure for Thin Solid Wings

Box Wing

Discussion

Appendix—Young’s Modulus Profile

References

Take-Off from Satellite Orbit

Basic Equations

Radial Thrust

Circumferential Thrust

Discussion

References

Analysis of Peak-Holding Optimalizing Control

Introduction

Principle of Operation

Formulation of the Mathematical Problem

First-Order Input and Output Groups

Design Charts

Concluding Remarks

Appendix

References

The Poincaré-Lighthill-Kuo Method

I. Introduction

II. Ordinary Differential Equations

III. Hyperbolic Partial Differential Equations

IV. Elliptic Partial Differential Equations

V. Applications to Fluid Boundary Layer Problems

VI. Concluding Remarks

References

Thermodynamic Properties of Gas at High Temperatures and Pressures

1. Equation of States of Dense Gas

2. Lennard-Jones and Devonshire Theory

3. Other Thermodynamic Functions

References

Thermonuclear Power Plants

1. Introduction

2. Thermonuclear Reaction Rate

3. Example: Deuterium Reaction

4. Thermonuclear Reaction Chamber

5. Thermonuclear Power Station

6. Ignition

7. Thermonuclear Power Industry

References

Index