0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

DATOS0

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

WHAT IS COMPUTATIONAL FLUID DYNAMICS

Computational fluid dynamics has certainly come of age in industrial applications and academia research. In the beginning this popular field of study was primarily limited to high-technology engineering areas of aeronautics and astronautics, but now it is a widely adopted methodology for solving complex problems in many modern engineering fields.

What actually is computational fluid dynamics? In retrospect, it has certainly become a new branch integrating not only the disciplines of fluid mechanics with mathematics but also with computer science as illustrated in Fig. 1.1.

1.1

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

WHAT IS COMPUTATIONAL FLUID DYNAMICS

CFD has also become one of the three basic methods or approaches that can be employed to solve problems in fluid dynamics and heat transfer. As demonstrated in Fig. 1.2, each approach is strongly interlinked and does not lie in isolation.

Traditionally, both experimental and analytical methods have been used to study the various aspects of fluid dynamics and to assist engineers in the design of equipment and industrial processes involving fluid flow and heat transfer. With the advent of digital computers, the computational (numerical) aspect has emerged as another viable approach. Although the analytical method is still practiced by many and experiments will continue to be significantly performed, the trend is clearly toward greater reliance on the computational approach for industrial designs, particularly when the fluid flows are very complex.

1.1

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics

1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

ADVANTAGES OF COMPUT. FLUID DYNAMICS

With the rapid advancement of digital computers, CFD is poised to remain at the forefront of cutting edge research in the sciences of fluid dynamics and heat transfer. Also, the emergence of CFD as a practical tool in modern engineering practice is steadily attracting much interest and appeal.

There are many advantages in considering computational fluid dynamics. Firstly, the theoretical development of the computational sciences focuses on the construction and solution of the governing equations and the study of various approximations to these equations.

Secondly, CFD complements experimental and analytical approaches by providing an alternative cost-effective means of simulating real fluid flows. Particularly, CFD substantially reduces lead times and costs in designs and production compared to experimental-based approach and offers the ability to solve a range of complicated flow problems where the analytical approach is lacking.

Thirdly, CFD has the capacity of simulating flow conditions that are not reproducible in experimental tests found in geophysical and biological fluid dynamics, such as nuclear accident scenarios or scenarios that are too huge or too remote to be simulated experimentally (e.g., Indonesian Tsunami of 2004).

Fourthly, CFD can provide rather detailed, visualized, and comprehensive information when compared to analytical and experimental fluid dynamics.

Nevertheless, the favorable appraisal of CFD thus far does not suggest that it will soon replace experimental testing as a means to gather information for design purposes. Instead it is considered a viable alternative.

1.2

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics

1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

APPLICATION OF COMPUT. FLUID DYNAMICS1.3

AS AN EDUCATION TOOL TO LEARN BASIC THERMAL-FLUID SCIENCE

AS A RESEARCH TOOL

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics

1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

APPLICATION OF COMPUT. FLUID DYNAMICS1.3

AEROSPACE

AUTOMOTIVE ENGINEERING

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics

1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

APPLICATION OF COMPUT. FLUID DYNAMICS1.3

CHEMICAL AND MINERAL PROCESSING

BIOMEDICAL SCIENCE AND ENGINEERING

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics

1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

APPLICATION OF COMPUT. FLUID DYNAMICS1.3

CIVIL AND ENVIRONMENTAL ENGINEERING

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics

1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

APPLICATION OF COMPUT. FLUID DYNAMICS1.3

SPORTS

POWER GENERATION

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics

1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

THE FUTURE OF COMPUT. FLUID DYNAMICS

This changing landscape is partly attributed by the rapid evolution of CFD techniques and models. For example, state-of-the-art models for simulating complex fluid mechanics problems, such as jet flames, buoyant fires, multiphase and/or multicomponent flows, are now being progressively applied especially through the availability of multipurpose commercial CFD computer programs. The increasing usage of these types of codes in industries is a clear testimony how very demanding practical problems are now being analyzed by CFD. With decreasing hardware costs and rapid computing times, engineers are increasingly relying on this reliable yet easy-to-use CFD tool for delivering accurate results as already described by the examples in the previous sections.

Additionally, significant advances in virtual technology and electronic reporting are allowing engineers to swiftly view and interrogate the CFD predictions and make necessary assessments and judgments on a given engineering design.

1.4

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

FUNDAMENTALS. INTRODUCTION

CFD is fundamentally based on the governing equations of fluid dynamics. They represent mathematical statements of the conservation laws of physics. The purpose of this chapter is to introduce the derivation and discussion of these equations, where the following physical laws are adopted:

-Mass is conserved for the fluid.

-Newton's second law, the rate of change of momentum equals the sum of forces acting on the fluid.

- First law of thermodynamics, the rate of change of energy equals the sum of rate of heat addition to and the rate of work done on the fluid.

2.1

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction

2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

FUNDAMENTALS. EQUATIONS

MASS CONSERVATION

One conservation law that is pertinent to fluid flow is matter may neither be created nor destroyed. Consider the arbitrary control volume V fixed in space and time in Fig. 3.1.The fluid moves through the fixed control volume, flowing across the control surface. Mass conservation requires that the rate of change of mass within the control volume is equivalent to the mass flux crossing the surface S of volume V. In integral form, where n is the unit normal vector.

2.2

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction

2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

FUNDAMENTALS. EQUATIONS

THE MOMENTUM EQUATION

Equations (3.24) and (3.25) derived from Newton 's second law, where v is the kinematic viscosity (v = µ/p), describe the conservation of momentum in the fluid flow and are also known as the Navier-Stokes equations.

2.2

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction

2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

FUNDAMENTALS. EQUATIONS

THE ENERGY EQUATION

The equation for the conservation of energy is derived from the consideration of the first law of thermodynamics:

2.2

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction

2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

FUNDAMENTALS. EQUATIONS

THE ADDITIONAL EQUATIONS FOR TURBULENT FLOW

Many if not most flows of engineering significance are turbulent in nature. The turbulent flow regime is, therefore, not just of theoretical interest among academics but a problematic source for engineers who need to capture the effects of turbulence in solving everyday problems.

Flows in the laminar regime are completely described by the continuity and momentum equations as aforementioned. In simple cases, they can be solved analytically. More complex flows may have to be tackled numerically with CFD techniques. It is well known that small disturbances associated with disturbances in the fluid streamlines of a laminar flow can eventually lead to a chaotic and random state of motion a turbulent condition. These disturbances may originate from the free stream of the fluid motion, or induced by the surface roughness, where they may be amplified in the direction of the flow, in which case turbulence will occur.

2.2

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction

2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

FUNDAMENTALS. EQUATIONS

GENERIC FORM OF THE GOVERNING EQUATIONS FOR CFD

2.2

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

CFD TECHNIQUES – THE BASICS3

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

CFD TECHNIQUES – THE BASICS3

FINITE-DIFFERENCE METHOD

0. DATOS

1. CHAPTER 1. Introduction

1.1 What is computational fluid dynamics1.2 Advantages of computational fluid dynamics1.3 Application of computational fluid dynamics1.4 The future of computational fluid dynamics

2. CHAPTER 3. Governing Equations for CFD - Fundamentals

2.1 Introduction2.2 Equations

3. CHAPTER 4. CFD Techniques – The Basics

CFD TECHNIQUES – THE BASICS3

FINITE-VOLUME METHOD