Introduction to Molecular Beams Gas Dynamics

The following sections are included:

• PREFACE

• CONTENTS

The following sections are included:

• Introduction

• Perfect and Real Gases

• Intermolecular Forces

• Gas Internal Energy

• Distribution of the Molecules on the Available Energy States

• The Internal Energy of Polyatomic Molecules

• The Specific Heats and their Ratio

• The Molecular Velocity Distribution. Averaged Values

• The Mean Free Path and the Transport Coefficients

• Classical Dynamics of Binary Collisions

• The Collision Integrals

• Effusive Sources

• Different Regimes of a Gas in Thermal Equilibrium

• On the Possibility of a Macroscopic Description of the Gas Behaviour
  • Gas in equilibrium
  • Gas in non-equilibrium

• References and Notes

The following sections are included:

• Introduction

• The Boltzmann Transport Equation

• The Wang Chang–Uhlembeck and the Master Equations

• Energy Transfer During Collisions

• The Vibrational Energy Relaxation

• The Rotational Energy Relaxation

• References and Notes

The following sections are included:

• Introduction

• Notes on the Fluid Motion

• Kinematics of a Fluid Element

• The Forces Acting on Fluids

• More on the Forces on a Fluid Element

• The Stress–Strain Relationship for a Viscous Fluid

• The Navier–Stokes Equations

• The Reynolds Number

• The Fundamental Equations of Fluid Dynamics

• The Bernoulli Theorem for Compressible Fluids

• The Propagation of Small Disturbances through a Compressible Fluid

• The Gas Dynamic Equation

• The Boundary Layer

• The Crocco Theorem

• References and Notes

The following sections are included:

• Introduction

• Isoentropic and Stationary Flow of a Perfect Gas

• Temperature and Stagnation Pressure

• The Flux Density

• Propagation of Small Disturbances in a Gas in Equilibrium. Characteristic Lines

• The Propagation of Finite Amplitude Disturbances. Characteristic Lines

• Compression and Rarefaction Waves

• Generation of Compression and Rarefaction Waves in a Gas inside a Tube

• Evolution of the Distribution of the Finite Disturbances
  • Compression waves
  • Rarefaction waves

• References and Notes

The following sections are included:

• Introduction

• The Differential Equations of the Characteristics

• Applications

• Alternative Form of the Compatibility Equations

• Properties of the Characteristic Lines. Weak Discontinuities

• The Equations of the Planar Isoentropic Flow in the Hodograph Plane

• Weakly Perturbed Two-Dimensional Flow. Mach Lines

• The Flow Near a Curved Wall
  • Flow near a concave wall
  • Flow near a convex wall

• Reflection of Rarefaction and Compression Waves
  • Reflection from a frictionless rigid wall
  • Reflection from a constant pressure free boundary

• Intersection of Rarefaction and Compression Waves

• References and Notes

The following sections are included:

• Introduction

• Discontinuities in the Flow Fields

• Normal Shock. Shock Adiabatic

• Application to a Perfect Gas

• The Flow Variables Downstream of the Shock as Functions of the Upstream Mach Number

• The Oblique Shock

• The Relationship between the Deflection and Shock Angles

• The Detached Shock

• Shock Polars
  • Hodograph shock polar
  • Pressure-deflection shock polar (p–θ polar)

• Shock Reflection
  • Regular shock reflection (R.R.) from a planar rigid wall
  • Mach reflection (M.R.) of an oblique shock
  • Reflection of a shock from the free boundary between a moving and stagnating gas

• Shock Interactions

• References and Notes

The following sections are included:

• Introduction

• Stationary and Isoentropic Flow in Variable Section Ducts

• Expressions of the Nozzle Flow Rate

• Effects of the Discharge Pressure Reduction

• Flow Regimes of a de Laval Nozzle. The Emitted Jet

• Flow Regimes of a Converging Nozzle. The Emitted Jet

• References and Notes

The following sections are included:

• Introduction

• The Axisymmetric Under-expanded Jet Emitted from Converging Nozzle

• The Jet Dimensions

• Variations of the Flow Variables in the Continuous Regime

• Non-Equilibrium Cooling of a Monatomic Gas

• Non-Equilibrium Cooling of a Polyatomic Gas

• The Sudden Freeze Approximation

• Influence of the Relaxation of an Internal Degree of Freedom on the Flow Variables

• References and Notes

The following sections are included:

• Introduction

• Fundamental Hypotheses and the Method of Moments

• Calculation of the Collisional Term

• The Moment Equations in Reduced Forms

• Some Considerations About the Obtained Equations

• Calculation of the Parallel Speed Ratio

• Comparison with the Experimental Data

• References and Notes

The following sections are included:

• Introduction

• Characterisation of a Particle Source

• The Virtual Source and the Non-Maxwellian Distribution of ν_⊥

• Extraction of a Molecular Beam by a Skimmer

• References

The following sections are included:

• Introduction

• The Gas Expansion in the p-T Phase Diagram

• The Dimers Formation Mechanism

• The Dimers Formation Rate

• References

The following sections are included:

• Introduction

• The Energetic Balance in a Free Supersonic Jet
  • Pure monatomic gas
  • Pure biatomic gas
  • Pure polyatomic gas (non-linear molecules)
  • Mixture of two monatomic gases
  • Mixture of a monatomic gas (carrier) with a biatomic gas (sample)

• Binary Mixture
  • Mixture in equilibrium
  • Free jet of a binary mixture

• Expressions of the Molecular Beam Intensity

• References

The following sections are included:

• Appendices
  • Different Forms of Eq. (1.2.2)
  • Intermolecular Potential Energy
  • Molecular Energy Levels
  • Deduction of Eqs. (2.5.8;9;10)
  • Deduction of Eqs. (3.9.10;13)
  • Alternative Deduction of the Bernoulli Equation
  • Use of the Prandtl–Meyer Function in the Method of Characteristics
  • Planar Flow Classification
  • Characteristic Lines and Weak Discontinuities
  • Spherical Symmetry Source
  • A New Determination of the Flow Field
  • Deduction of Eqs. (8.5.1;2)
  • Deduction of Eqs. (9.2.9;10;11;12)
  • Deduction of Eqs. (9.3.5;6)
  • Deduction of Eq. (9.3.14)
  • Calculation of the Integral I₁ and I₂ in Eqs. (12.4.7;14)

• INDEX