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**APPLIED COMPUTATIONAL **

**FLUID DYNAMICS **

Edited by** Hyoung Woo Oh**

** **

** **

** **

** **

**Applied Computational Fluid Dynamics **

Edited by Hyoung Woo Oh

**Published by InTech **

Janeza Trdine 9, 51000 Rijeka, Croatia

**Copyright © 2012 InTech**

All chapters are Open Access distributed under the Creative Commons Attribution 3.0

license, which allows users to download, copy and build upon published articles even for

commercial purposes, as long as the author and publisher are properly credited, which

ensures maximum dissemination and a wider impact of our publications. After this work

has been published by InTech, authors have the right to republish it, in whole or part, in

any publication of which they are the author, and to make other personal use of the

work. Any republication, referencing or personal use of the work must explicitly identify

the original source.

As for readers, this license allows users to download, copy and build upon published

chapters even for commercial purposes, as long as the author and publisher are properly

credited, which ensures maximum dissemination and a wider impact of our publications.

**Notice **

Statements and opinions expressed in the chapters are these of the individual contributors

and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no

responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book.

**Publishing Process Manager** Jana Sertic

**Technical Editor** Teodora Smiljanic

**Cover Designer** InTech Design Team

First published March, 2012

Printed in Croatia

A free online edition of this book is available at www.intechopen.com

Additional hard copies can be obtained from orders@intechweb.org

Applied Computational Fluid Dynamics, Edited by Hyoung Woo Oh

p. cm.

ISBN 978-953-51-0271-7

Contents

**Preface IX **

Chapter 1

**Computational Fluid Dynamics 1 **

Victor Udoewa and Vinod Kumar

Chapter 2

**A Computational Fluid Dynamics Model of **

**Flow and Settling in Sedimentation Tanks 19 **

Ali Hadi Ghawi and Jozef Kriš

Chapter 3

**Advances in Computational Fluid Dynamics **

**Applied to the Greenhouse Environment 35 **

Jorge Flores-Velázquez, Guillermo De la Torre-Gea,

Enrique Rico-García, Irineo L. López-Cruz

and Abraham Rojano-Aguilar

Chapter 4

**Fluid Dynamics Analysis of **

**a Space Vehicle Entering the Mars Atmosphere 63 **

Antonio Viviani and Giuseppe Pezzella

Chapter 5

**Air Movement Within Enclosed Road-Objects **

**with Contra-Traffica CFD-Investigation 73 **

M. Muhasilovic, A. Mededovic,

E. Gacanin, K. Ciahotny and V. Koza

Chapter 6

**Computational Fluid Dynamics (CFD) and Discrete **

**Element Method (DEM) Applied to Centrifuges 97 **

Xiana Romani Fernandez, Lars Egmont Spelter

and Hermann Nirschl

Chapter 7

**CFD and Thermography Techniques **

**Applied in Cooling Systems Designs 135 **

Samuel Santos Borges and Cassiano Antunes Cezario

Chapter 8

**Computational Fluid Dynamics (CFD) **

**Modeling of Photochemical Reactors 155 **

Masroor Mohajerani, Mehrab Mehrvar and Farhad Ein-Mozaffari

VI

Contents

Chapter 9

**Aerodynamic Design of the Vertical Takeoff Hopper **

**Concept of Future Launchers Preparatory Programme 177 **

Giuseppe Pezzella

Chapter 10

**Fluid-Structure Interaction of a Radial Turbine 201 **

Zied Driss, Sarhan Karray, Hedi Kchaou and Mohamed Salah Abid

Chapter 11

**Industrial Sprays: Experimental **

**Characterization and Numerical Modeling 223 **

Avinash Khopkar, Michael D. Cloeter and Quan Yuan

Chapter 12

**Multidimensional Design **

**of Hydraulic Components and Systems 249 **

Massimo Milani, Luca Montorsi and Fabrizio Paltrinieri

Chapter 13

**Study of an Individual Air-Conditioning **

**Energy-Saving Equipment 277 **

Nguyen Anh Tuan, Wu-Chieh Wu and K-David Huang

Chapter 14

**Unsteady Differentiation of Aerodynamic **

**Coefficients: Methodology and Application 295 **

Carlo Necci and Nicola Ceresola

Chapter 15

**Use of Fluid Dynamic Simulation to **

**Improve the Design of Spouted Beds 321 **

Rodrigo Béttega, Ronaldo Guimarães Corrêa

and José Teixeira Freire

** **

Preface

This book is intended for use as a reference text to help advanced scientists and research engineers solve numerous and diverse fluid flow problems using

computational fluid dynamics (CFD). Each chapter has been contributed by the

practiced experts in the field of fluid dynamics. This material covers a wide spectrum

of CFD applications involving flow modeling in sedimentation tank, greenhouse

environment, hypersonic aerodynamics, computational scheme, cooling systems

design, photochemical reaction engineering, atmospheric reentry problem, fluid‐

structure interaction (FSI), atomization, hydraulic component design, air conditioning

system, and industrial applications of CFD.

** **

**Dr. Hyoung Woo Oh**

Department of Mechanical Engineering,

Chungju National University,

Chungju,

Korea

**1 **

**Computational Fluid Dynamics **

Victor Udoewa1 and Vinod Kumar2

*1George Washington University, *

*USAID Development Engineer, *

*AAAS Science & Technology Policy Fellow, AAAS, 2009-2011, *

*2Mechanical Engineering, *

*University of Texas at El Paso, *

*USA *

**1. Introduction **

Computational Fluid Dynamics (CFD) is the emerging field of fluid mechanics in which

fluid flow problems are solved and analyzed using computational methods and numerical

algorithms. In fluid mechanics, there are generally three routes of work in the field, three ways to conduct experiments. The first category is theoretical, or analytical, fluid mechanics.

Theoretical fluid mechanics includes theorizing, manipulating and solving equations with

pen and paper. The Navier-Stokes equation governing incompressible fluid flow is an

example of theoretical fluid mechanics. Secondly, many engineers and physicist work in the

area of experimental fluid mechanics. Experimental fluid mechanics involves conducting

actual physical experiments and studying the flow and the effect of various disturbances,

shapes, and stimuli on the flow. Examples include waves generated by pools, air flow

studies in actual wind tunnels, flow through physical pipes, etc. Lastly, a growing number

of engineers, mathematicians, computer scientists, and physicists work in the area of

computational fluid dynamics (CFD). In CFD, you may still run an experiment of waves

across water, an airplane in a wind tunnel, or flow through pipes, but now it is done through the computer Instead of actual, physical, 3D objects. A computer model is created,

and computer programmers code the equations representing the physical laws that govern

the flow of the molecules of fluid. Then the flow results (such as velocity and pressure) are output into files that can be visualized through pictures or animation so that you see the

result just as you do with physical experiments.

In cases where an analytical, or theoretical, solution exists, CFD simulations and the

mathematical models, which are coded in the computer program, are corroborated by

comparison to the exact solutions. This comparative check is called validation. CFD is not

yet to a point where solutions to problems are used without corroboration by existing,

known, analytical or exact solutions when available. Validation is not to be confused with

verification, however; validation is a check to make sure that the implemented, coded model

accurately represents the conceptual, mathematical description and the solution intended to

be modeled.

Still, there are many times when there is no analytical solution. In these cases, one often uses a computational approach. In such cases without a known solution, CFD is used to

2

Applied Computational Fluid Dynamics

approximate a solution. Most often, CFD is used when a computational solution is faster,

cheaper, or more convenient. Convenience may be due to time or safety or another reason.

If we wanted to create a database of information about 3D flow around a cylinder for different types of fluids at varying speeds, CFD is quite helpful. It would take quite a long time to change the fluid in our flow container and clean the container for every type of fluid we desired. It would also take some time to change the speed of the flow. In this case, it’s much faster to simulate it computationally. Then, anytime we wanted to change the speed of

the flow, we simply would change one number in a computer input file. Or if we wanted to

change viscosity and density for the fluid (representing a different fluid) we would just

change the corresponding values in a computer input file. In this case, CFD is faster.

Now imagine if you were doing space defense work for a government, and you were asked

to do fluid dynamics simulation of the combustion dynamics during an explosion or when a

space shuttle launched (1). It would take immeasurable amounts of money to do test

launches over and over as you studied the combustion dynamics of space shuttle thruster

ignition. And it would take large amounts of money to test explosive devices, especially

considering the damage they cause. In these cases, CFD is, again, quite helpful. The only

costs in CFD are the time of creating a computer model, choosing the right mathematical

model, coding it, and the power and computer time required to solve the equations. But it is plain to see that CFD is cheaper.

What if you were hired to help design material for the outfits of swimming athletes? Your

company gave you the job of studying sharks and their agile ability to swim and maneuver

through the water. So you start by trying to study the fluid dynamics around the shark skin

(2). How convenient is it to locate sharks and place them in some type of testing container

where you have probes and measuring devices located? How convenient is it to place

probes on the body of the shark itself? How safe is it to work with the sharks in that manner? No, it’s better to create a computer model of a shark and get the information for the shape, design, feel, and density of its skin and to use this information to run simulations. It is clear that CFD is more convenient in this situation. Sometimes a CFD simulation can be all three—safer, cheaper, and more convenient.

Imagine a situation in which two paratroopers, jumping from both side doors of a military

cargo aircraft, always crash into each other down below (3). In order to analyze the fluid

dynamics of the problem to see what air flow forces are affecting the paratrooper paths, you would need to perform test jumps with paratroopers. However, that is potentially injurious

and not safe. You would also have to rent the plane, pay for the rental by hour, hire the test pilot, and pay for all the equipment for the jump. That is expensive. Lastly, the organization of the use of the military aircraft and personnel and equipment takes many months, and it

can take from 6 to 12 months to plan the test. In this case a CFD experiment is more convenient: faster, cheaper, and safer.

Usually solving CFD problems involves three stages. First there is the pre-processing stage.

In this stage, the geometric boundaries of the problem are defined. In 3D, a volume is

created (in 2D, an area) over which the equation will be solved. This volume is broken into

smaller units or cells creating a mesh (though there are meshless methods for computing

CFD problems). This may be uniform or non-uniform. Along with constitutive equations,

the particular equations are chosen for the problem in order to properly physically model

the flow. These equations may be manipulated depending on the mathematical method

being used. Boundary conditions are prescribed along the boundary. For time dependent

problems, initial conditions are prescribed.

Computational Fluid Dynamics

3

Secondly, the problem is solved numerically. At the least, we usually solve for velocity and pressure, but the list of unknowns can be longer depending on the mathematical model

(equation) chosen for the physical situation. Other unknowns may include temperature,

energy, and density. The numerical solution is usually computed iteratively for steady-state solutions. For time-dependent problems, a step in time is taken, and the equation is

numerically solved again, eventually producing a solution for every time step.

The final step in the CFD process is post-processing. In this stage, the solution is analyzed usually with the help of visualization and possibly animation for dynamic, or time-dependent, problems. It is in this stage that CFD results are usually compared to any

previous experimental results or known analytical, or theoretical, solutions. This

comparison is usually called validation. Today, confidence in CFD is growing, but we have

not arrived at the point of trusting CFD solutions without validation. Even if a particular

model is validated, we still corroborate the results of a simulation with experimental or

analytical results.

Because of the hybrid nature of CFD, advances in CFD are usually made in three areas:

computational and applied mathematics, mechanical/chemical engineering, and computer

science/electrical engineering. Some researchers work on new theoretical, mathematical

models creating new discretization methods (ways to discretize the problem in order to

numerically solve it over the discrete units or cells), or turbulence models. They might

publish in applied mathematics or computational mathematics journals. Others work on

computer architecture (such as different types of supercomputers or computer clusters),

coding techniques such as parallel programming, or speeding up the computational

processes through faster mesh generation and mesh reordering. They might publish their

results in electrical engineering or computer science journals. Lastly others might use CFD

to concentrate on new insights in the engineering aspect of the problem such as the

mechanics of bird flight or sharkskin-inspired speedo design for less water resistance, or

resistance to blood flow inherent to certain veins. They might publish their results in

engineering journals next to experimental or theoretical engineering results. Their focus is on the application more so than the math or computer science.

**2. Pre-processing **

Pre-processing refers to the work that must be done prior to the actual computational

experiment or simulation. This work can be reduced to four general areas: geometry

definition, volume division, model choice and definition, and boundary condition

definition. For the purposes of this article, we will ascribe the work of coding and the choice of computational implementation to the processing stage called simulation. Sometimes

researchers refer to mesh generation as pre-processing in general because a mesh is

generated when the volume is divided.

**2.1 Geometry definition **

The first step is to define the computational domain of the problem. The purpose of this

definition is to confine the problem to a finite space and limit the computation. It is true that a plane flying in the air has some residual effects on air flow patterns 1,000 miles away, but because of the negligible nature of those effects, we are relatively safe in looking at the effect of the plane on air flow within a reasonable vicinity of the plane thereby limiting our

4

Applied Computational Fluid Dynamics

computational work and making the problem finite. It would be quite a task to compute the

effect of the airplane on the air flow at a certain height around the entire earth.

To limit the flow in this way usually requires defining a domain inside which we will

compute the flow, outside of which we will not compute the flow. Usually the geometry of

the domain is chosen to be a box of some sort, usually a rectangular prism in 3D or a

rectangle in 2D. However, any closed shape may be chosen as long as the shape closes off

an inside computational domain from an outside space in which computations will not

take place.

A closed space does not imply, however, an empty domain box. For example imagine that

we are simulating intravenous blood flow (4) (5) around a cancerous growth. The vascular

domain is modeled by a 3D cylindrical prism (our domain box), but we still have an object

inside. In this case, our object is a semi-spherical cancerous growth on the surface of a wall of the vein. Traditionally, our domain must be totally closed, so the surface of the domain

goes from the wall of the vein, joins the surface of the cancerous growth, and continues on

the other side rejoining the wall of the vein creating a closed 3D space that does not go

under the tumor but continues over the surface of it. Likewise, if we were calculating flow

around a sphere (6), the domain box would be the outer half of the domain surface. The

inner half of the surface would be the sphere inside the domain box. Just as in the cancer

example, we are not calculating the flow inside the sphere, just as we were not calculating

the blood flow in the tumor. But the tumor and sphere form part of the boundaries of the

domain helping to close off the computational space in which we are interested in the

velocity and pressure of the fluid. Remember, domain boxes may contain objects inside

which no flow is calculated, but whose surface forms part of the surface of the domain

helping to limit the computational space and better define where the fluid flows.

**2.2 Volume division **

The second step is volume division or mesh generation. Why we must divide the volume

is not obvious until one remembers that it is easier to solve a flow problem over a smaller

area or volume than a larger one. So dividing the volume into smaller units transforms the

large problem over the entire domain into a large number of smaller problems over

smaller sub-domains. However, the real reason we divide the volume is because we seek

to find, for example, the velocity and pressure of the fluid at various points throughout

the domain volume or area. In order to do this, we fill the inner domain volume or area

with nodes—points at which we will calculate, in this instance, velocity and pressure.

Once we have filled the inner volume or area with nodes, we connect the nodes with

edges (and sides in 3D) creating smaller sub-volume or sub-area elements. For example, if

our computational box is a rectangular prism and we fill it with nodes, we can connect the

nodes to create quadrilaterals or tetrahedrals. If the domain is a rectangle and we fill the rectangle with nodes, we can connect all the nodes to create small rectangles or triangles.

This network of rectangles/triangles and quadrilaterals/tetrahedrals creates a mesh of

nodes; a mesh has been generated.

Remembering that the purpose of volume or area division is to create more manageable sub-

volumes or sub-areas, it behooves us to evenly space out the distribution of nodes. If we do not, we may find that there are large spaces (volumes or areas) with no nodes. This is problematic because it means some of the sub-volume or sub-area elements will still be

large; though our goal is to make them small.

Computational Fluid Dynamics

5

Our second goal is to make each sub-element evenly shaped. In 2D, evenness in both

directions means that 2D rectangles tend towards squares or that our triangles are equilateral.

In 3D, if evenness is desired in all 3 directions, our quadrilaterals tend toward cubes and the tetrahedrals tend to be equilateral. Oblong and unevenly shaped sub-elements also create

spaces (areas or volumes) with fewer nodes than parts of the domain with evenly shaped sub-

elements. In these cases, our second goal serves a similar purpose as our first goal: to divide the domain into smaller, more manageable sub-domains with evenly distributed nodes.

An important aspect of mesh generation is choosing the appropriate size, or refinement,

of the mesh sub-elements, such that important aspects of the flow are properly resolved.

The general rule is that no fluid particle should advance through multiple sub-elements,

cells, or units in one time step. Therefore our third goal is to increase the refinement (or the number of nodes) in areas or sub-volumes of increased fluid velocity or vorticity or

any interesting fluid flow phenomena that you would like to capture computationally.

This will allow us to visualize it later.

So far, the realm of geometry definition and mesh generation fall into the computer science

side of CFD. When generating the mesh by defining a geometry and dividing that geometric

area or volume, one must decide if one will use uniform sub-elements or non-uniform sub-

elements. Definitely in parts of the domain with special flow requiring increased refinement, the elements in those parts will not match the refinement of elements elsewhere. But in the

general flow one can still choose a uniform, structured mesh or a non-uniform, unstructured

mesh. The ability to create non-uniform meshes is important in CFD because of the physical

nature of fluids to occupy and fill any void left unoccupied. When dealing with complex geometries and small nooks, crannies, and crevices of an automobile or a model of a city

block, it helps to have unstructured, non-uniform meshes that allow for the modeler to

create the best shapes to fit the 2D or 3D space (7).

Likewise, the division of the volume or area in mesh generation requires the modeler to

choose between quadrilaterals and rectangular prisms or triangles and tetrahedrals (there

are other choices of shapes, as well, such as wedges and pyramids in 3D). Generally,

quadrilaterals and rectangular prisms have a more accurate solution than triangles and

triangular prisms, but there are ways to increase the accuracy of the latter. Because of the non-uniform and sharp geometries found in fluid problems by nature of fluids, triangles

and triangular prisms work better geometrically for CFD applications. Normally, CFD

researchers will utilize triangles and triangular prisms and then increase the number of

interpolation points inside these elements so that no accuracy is lost. Interpolation points are points inside an element at which the solution is calculated. From these interpolation points, we can approximate the solution at any location inside an element.

All of the choices in dividing the volume and discretizing the mesh have the potential to

introduce errors. Such errors, due to bad distribution of nodes or parts of the domain

where the refinement is too low, are called discretization errors. These are errors that

would disappear if we appropriately divided the