Similitude and Modelling

Similitude and Modeling describes the theoretical aspects and application of similitude method using mathematical apparatus.

This book is organized into two parts encompassing 13 chapters, and begins with an introduction to a simple technological problem in similitude modeling. The first part deals with the concept, physical fundamentals, dimensional analysis, and approximate and partial modeling of similitude. This part explores also the preparation and evaluation of similitude experiments, as well as the general types of similitude invariants. The second part highlights the application areas of similitude modeling, including heat conduction and diffusion, fluid dynamics, elastic deformation, and chemical reactions.

This book will prove useful to plant and design engineers.

Contenu

Preface

A Simple Technological Problem

1. Direct Experiment

2. Test Run (The "classical Method")

3. Experiment Design

4. Dimensional Analysis

5. Analytic Solution

6. Numerical Solution

7. Similitude Modeling

8. Analogy

Part I. Theory

Chapter 1. The Concept of Similitude

Chapter 2. The Similitude Method

2.1. Geometric Similarity

2.2. Similitude of Phenomena

2.3. Physical Variables

2.4. Dimensional Homogeneity

2.5. Criteria and Invariants of Similitude

Chapter 3. Physical Fundamentals (Transport Theory)

3.1. Extensities and Intensities

3.2. Balance Equations (Continuity Equations)

3.3. A Classification of Technological Processes

Chapter 4. Types of Problems and their Solution

4.1. Types of Problems

4.2. Methods of Solution

Chapter 5. Dimensional Analysis

5.1. The Purpose of Dimensional Analysis

5.2. The Method of Dimensional Analysis

5.3. Dimensional Analysis and Similitude

Chapter 6. Modeling

6.1. The Model Concept

6.2. The Purpose of Modeling

6.3. Types of Model

6.4. Analogy

6.5. "Degrees of Freedom" and the Freedom of Choosing Model Parameters

Chapter 7. Approximate and Partial Modeling

7.1. Approximate Similitude

7.2. Two-Dimensional Approximation

7.3. Partial Modeling

7.4. Conclusions

Chapter 8. Preparation and Evaluation of Experiments

8.1. Preliminary Analysis

8.2. Measurement Errors

8.3. Design of Experiments

Chapter 9. General Types of Similitude Invariants

Part II. Applications

Chapter 10. Heat Conduction and Diffusion

10.1. Fundamental Equations

10.2. Examples

Chapter 11. Fluid Dynamics

11.1. The Fundamental Equations

11.2. Examples

Chapter 12. Elastic Deformation

12.1. The Fundamental Equations

12.2. Examples

Chapter 13. Chemical Reactions

13.1. The Fundamental Equations

13.2. Examples

In Place of a Postscript

Annotated Bibliography

Author and Subject Index