Emanuel Shock Wave Dynamics

Derivatives and Related Topics
Erscheinungsjahr 2013
ISBN: 978-1-4665-6421-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 235 Seiten

Working knowledge of the relations of various quantities and their derivatives across a shock wave is useful for any advanced research involving shock waves. Although these relations can be derived in principle by any diligent student of the subject, the derivations are often not trivial, and once derived, neither the approach nor the result can be confidently verified. Comprehensive and analytical, Shock Wave Dynamics: Derivatives and Related Topics includes not only the final results but also the methods, which are of great practical value as examples of mathematical procedure in this field.

The book focuses on shock wave derivatives under various conditions and extensively covers shock-generated vorticity, including a novel analysis of triple points. Special care is given to the presentation of assumptions, implementation requirements, and the illustrative examples included for partial verification of the preceding analysis.

Designed both as a research monograph and for self study, Shock Wave Dynamics is a complete discussion of shock wave dynamics. An analytical exploration of shock wave phenomena, it will be interesting reading for experts in the field of high-speed gas dynamics. Given today's emphasis on numerical simulation, it will also be of interest to computational engineers as a source for code verification and validation.

Autoren/Hrsg.

Emanuel, George

Fachgebiete

• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre

Inhaltsverzeichnis

Introduction

General Jump Conditions
Basis Vector System and Shock Velocity
Conservation Equations
Explicit Solution
Illustrative Example

Two-Dimensional or Axisymmetric Formulation
Basis Vectors
Shock-Based Curvilinear Coordinates
Scale Factors
Application to a Two-Dimensional or Axisymmetric Shock
Transformation Equations
Basis Derivatives

Derivatives for a Two-Dimensional or Axisymmetric Shock with a Uniform Freestream
Preliminary Remarks
Jump Conditions
Tangential Derivatives
Normal Derivatives

Derivative Applications
Normal Derivatives When the Shock Is Normal to the Upstream Velocity
Intrinsic Coordinate Derivatives
Derivatives along Characteristics
Wave Reflection from a Shock Wave
Flows with a Conical Shock Wave
Special States
T Derivatives

Vorticity and Its Substantial Derivative
Preliminary Remarks
Vorticity
Substantial Derivative of the Vorticity
Generic Shock Shape
Slope, Curvature, Arc Length, and Sonic Point
Results

Shock Wave Triple-Point Morphology
Preliminary Remarks
Analysis
Solution Method
Results and Discussion

Derivatives When the Upstream Flow Is Nonuniform
Preliminary Remarks
Jump Conditions
Tangential Derivatives
Normal Derivatives
Intrinsic Coordinate Derivatives
Vorticity
Source Flow Model

General Derivative Formulation
Preliminary Remarks
Vector Relations
Elliptic Paraboloid Shock
Shock Curvatures
Vorticity
Jump Conditions and Tangential Derivatives
Normal Derivatives
Applications
Unsteady, Normal Derivative Formulation
Single Mach Reflection

Appendices
Selective Nomenclature
Oblique Shock Wave Angle
Method-of-Characteristics for a Single, First-Order Partial Differential Equation
Orthogonal Basis Derivatives
Conditions on the Downstream Side of a Two-Dimensional or Axisymmetric Shock with a Uniform Freestream
Conditions on the Downstream Side of a Two-Dimensional or Axisymmetric Shock when the Upstream Flow Is Nonuniform
Operator Formulation
General Derivative Formulation
Uniform Freestream Formulation
Elliptic Paraboloid Shock Formulation
Global, Shock-Based Coordinates
Unsteady State 2 Parameters

Problems
References