This monograph treats, for the first time, major aspects of gas dynamics of nozzles from a general point of view. Its outstanding feature is the pre sentation of the modern theory of gas flows and modern analytical and nu merical methods, together with numerous examples of practical applications. At the same time, quite diverse physico-chemical processes, such as disso ciation and recombination, relaxation of vibrational degrees of freedom, two-phase flows wi th phase trans formati ons and e 1 ectromagneti c i nf1 uences, are considered. The material is presented in such a way as to help the reader to use numer ous methods and approaches, not only for the study of gas flows in nozzles, but also for the investigation of a wide variety of problems of physical gas dynamics in different areas of application. The number of applications which may benefit from the use of the methods and results presented in this book is constantly growing. Theoretical, numerical and analytical methods of physical gas dynamics of internal flows may be, and are nowadays, ap plied to solving the problem of preventing pollution of the air basin with toxic substances. These methods make it possible to describe the formation and transformation of toxic components in the vapour generators of thermal power plants, internal combustion engines and various metallurgical instal lations. The methods of physical gas dynamics may be used in meteorology and powder metallurgy to create ultradispersed media and predict their proper ties.
1. Introduction.- 2. General Theory of Nozzle Gas Flows.- 2.1 Basic Equations and Problem Formulation.- 2.1.1 Basic Equations.- 2.1.2 Characteristics.- 2.1.3 The Direct Problem.- 2.1.4 The Inverse Problem.- 2.2 Some Elementary Theories.- 2.2.1 One-Dimensional Theory.- 2.2.2 Radial Flows or Source/Sink Flows.- 2.2.3 Prandtl-Meyer Flow.- 2.3 Variational Problems of Gas Dynamics of Internal Flows.- 3. Numerical Methods of Studying Nozzle Gas Flows.- 3.1 Methods of Solving Relaxation Equations.- 3.2 Methods of Calculating Plane and Axisymmetric Supersonic Flows.- 3.2.1 Method of Characteristics.- 3.2.2 Shock-Smearing Methods.- 3.3 Methods of Calculating Three-Dimensional Supersonic Flows.- 3.3.1 Method of Characteristics.- 3.3.2 Difference Methods.- 3.4 Methods of Solving the Inverse Problem of the Theory of Nozzles.- 3.5 Methods of Solving the Direct Problem of the Theory of Nozzles.- 4. Asymptotic Methods in the Theory of Nozzles.- 4.1 Source-Sink Method and Inverse Problem for Incompressible Fluid.- 4.1.1 Plane Flow.- 4.1.2 Axisymmetric Flow.- 4.1.3 Three-Dimensional Flow.- 4.1.4 Solution of the Inverse Problem for Incompressible Fluid.- 4.2 Expansion in a Stream Function Series.- 4.2.1 Three-Dimensional Flow.- 4.2.2 Plane and Axisymmetric Flows.- 4.2.3 Two-Phase Flows.- 4.3 Asymptotic Methods in the Transonic Region.- 4.3.1 Method of Small Perturbations.- 4.3.2 Series Expansion in the Vicinity of a Rectilinear Sonic line.- 4.4 Solution in the Neighbourhood of the Infinite Point in the Subsonic Region.- 4.5 Method of Small Perturbations for Flows Close to Radial.- 5. Nozzles of Jet Engines.- 5.1 Flow Peculiarities in the Subsonic and Transonic Parts of a Nozzle.- 5.1.1 Nozzle with a Rectilinear Surface of Transition.- 5.1.2 Nozzle with a Curvilinear Surface of Transition.- 5.1.3 Local Deceleration Zones.- 5.1.4 Optimum Shape of the Subsonic Part of a Nozzle.- 5.1.5 Flow Rate Coefficient and Critical Pressure Drop in Nozzles with Curvilinear Transition Surfaces.- 5.1.6 Profiling of the Acceleration Part of a Jet Engine Nozzle.- 5.2 Profiling of Supersonic Parts of Jet Engine Nozzles and Impulse Losses.- 5.2.1 Profiling of Supersonic Parts of Jet Engine Nozzles.- 5.2.2 Impulse Losses.- 5.2.3 Thrust Changes Caused by Deviations from the Design Flow Regime.- 5.2.4 Numerical and Experimental Simulation of Flows in Jet Engine Nozzles.- 5.3 Main Principles of Choosing a Jet Engine Nozzle.- 6. Flows with Physico-Chemical Transformations.- 6.1 Isentropic Flows and Intermolecular Interaction.- 6.1.1 Isentropic Flows.- 6.1.2 Intermolecular Interaction.- 6.2 Flows with Nonequilibrium Chemical Reactions.- 6.2.1 Basic Equations, Method of Prediction and the One-Dimensional Approximation.- 6.2.2 Major Characteristic Features of Chemical Nonequilibrium Flows.- 6.2.3 Plane and Axisymmetric Flows.- 6.2.4 Approximate Methods of Calculating Nonequilibrium Flows.- 6.3 Flows with Vibrational Relaxation.- 6.3.1 Relaxation Equations and Methods of Prediction.- 6.3.2 Results of Calculations in the One-Dimensional Approximation.- 6.3.3 Plane and Axisymmetric Flows.- 6.4 Two-Phase Flows.- 6.4.1 Basic Concepts: One-Dimensional Approximation, Equilibrium and Frozen Flows.- 6.4.2 One-Dimensional Nonequilibrium Flows Without Phase Transitions; Impulse Losses.- 6.4.3 One-Dimensional Flows with Interacting Particles.- 6.4.4 One-Dimensional Flows with Phase Transitions.- 6.4.5 Flows in Axisymmetric and Plane Nozzles.- 6.5 Conductive Gas Nozzle Flows in the Presence of an Electromagnetic Field.- 6.6 Multilayer Nozzle Flows.- 6.6.1 One-Dimensional Approximation.- 6.6.2 Axisymmetric Flows.- 7 Special Nozzles, Three-Dimensional Flows, Viscosity Effect.- 7.1 Annular Nozzles and Wind Tunnel Nozzles.- 7.1.1 Some Schemes of Annular Nozzles and Methods of Calculation.- 7.1.2 Off-Design Flow Regimes in Annular Nozzles.- 7.1.3 Wind Tunnel Nozzles.- 7.2 Conical Nozzles.- 7.3 Swirling Nozzle Flows.- 7.3.1 Introductory Notes.- 7.3.2 Radially Balanced Flows.- 7.3.3 Axisymmetric Swirling Flows.- 7.4 Three-Dimensional Nozzle Flows.- 7.4.1 Some Results of Analytical and Experimental Studies.- 7.4.2 Method of Small Perturbations and Determination of Side Forces and Moments.- 7.4.3 Numerical Investigation of Three-Dimensional Nozzle Gas Flows.- 7.4.4 Experimental Studies of Side Forces and Moments.- 7.5 Flows at Small Reynolds Numbers.- Nomenclature.- References.