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A COMPARISON STUDY OF LIQUID AND VAPOR PHASE DEVELOPMENT AT SPRAY BOUNDARY OF DIESEL SPRAY, BDF AND SVO SPRAY
ADAM MOHD IZHAN BIN NOOR AZAM
Report submitted in partial fulfillment of the requirement for the award of the degree of Bachelor of Mechanical Engineering with Automotive Engineering
Faculty of Mechanical Engineering
UNIVERSITY MALAYSIA PAHANG
June 2012
v
ABSTRACT
The use of biodiesel as an alternative diesel engine fuel is preferred for fossil fuel substitution. However, due to technical deficiencies, they are rarely used purely or with high percentages in unmodified diesel engines. Therefore, this project is to study spray simulation of diesel, biodiesel fuel (BDF) and straight vegetable oil (SVO) in the diesel chamber. Two main components are focused on this paper. First, the relations between the viscosities of different fuels and the spray characteristics in achieving stoichiometric air-fuel mixture are investigated. Lastly the spray liquid-vapor phase in chamber is investigated. Good spray characteristics lead to the good drivability, high combustion efficiency and stoichiometric air-fuel mixture. Therefore, Computational Fluid Dynamics (CFD) method using ANSYS Fluent simulation software is used for this purpose. The simulation of injection spray in chamber is conducted by using three type of fuel that is diesel, biodiesel and palm oil with the one 0.2mm valve covered orifice (VCO) nozzle, injection pressure at 700 MPA, ambient pressure at 10 MPA, ambient temperature at 300 K and same iteration time. The results are shown by changing the type of fuel. The simulation results showed that the spray characteristics are better for diesel at the same time iteration compared to BDF and SVO by the penetration length, cone angle and liquid-vapor phase data.
vi
ABSTRAK
Penggunaan biodiesel sebagai alternatif minyak enjin diesel lebih disukai bagi penggantian bahan api fosil. Walau bagaimanapun, disebabkan oleh kekurangan teknikal, ia jarang digunakan tulen atau dengan peratusan yang tinggi dalam enjin diesel tanpa ubah suai. Oleh itu, projek ini adalah untuk mengkaji semburan simulasi diesel, minyak biodiesel (BDF) dan minyak sayuran terus (SVO) di dalam kebuk diesel. Dua komponen utama yang diberikan tumpuan di atas kertas ini. Pertama, hubungan antara kelikatan bahan api yang berbeza dan ciri-ciri semburan dalam mencapai stoikiometri udara-minyak campuran dikaji. Akhir sekali semburan fasa cecair-wap di dalam kebuk juga dikaji.Ciri-ciri semburan yang baik membawa kepada daya pemanduan yang baik, kecekapan pembakaran yang tinggi dan stoikiometri campuran udara-bahan api. Oleh itu, kaedah Computational Fluid Dynamics (CFD) menggunakan perisian simulasi ANSYS Fluent digunakan untuk tujuan ini. Simulasi semburan suntikan di dalam kebuk dijalankan dengan menggunakan tiga jenis bahan api iaitu diesel, biodiesel dan minyak sawit dengan muncung 0.2mm meliputi muncung orifis (VCO), tekanan suntikan pada 700 MPA, tekanan awal (ambient) pada 10 MPA, suhu awal (ambient) pada 300 K dan sama masa iterasi. Hasil yang diperolehi ditunjukkan dengan menukar jenis minyak. Keputusan simulasi menunjukkan bahawa ciri-ciri semburan adalah lebih baik bagi diesel pada iterasi masa yang sama yang berbanding BDF dan SVO melalui panjang penembusan, sudut kon dan data fasa cecair-wap.
vii
TABLE OF CONTENTS
Page
SUPERVISOR’S DECLARATION ii
STUDENT’S DECLARATION iii
ACKNOWLEDGEMENTS iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES x
LIST OF FIGURES xi
LIST OF ABBREVIATIONS xiii
LIST OF APPENDICES xiv
CHAPTER 1 INTRODUCTION
1.1 Research Introduction 1
1.2 Problem Statement 2
1.2.1 Problem 2
1.2.2 Solution of the problem 3
1.3 Objectives of the paper 3
1.4 Scopes 3
1.5 Hypothesis 4
1.6 Methodology 4
CHAPTER 2 LITERATURE REVIEW
2.1 Introduction 5
2.2 Diesel Engine 5
2.3 Alternative Fuels 6
2.3.1 Viscosity 7
2.3.2 Diesel 7
2.3.3 Bio-Diesel Fuel (BDF) 9
viii
2.3.4 Straight Vegetable Oil (SVO) 10
2.4 Spray Combustion Process 11
2.5 Spray Regimes 13
2.6 Spray Penetration 14
2.7 Computational Fluid Dynamic (CFD) 14
CHAPTER 3 METHODOLOGY
3.1 General Methodology 17
3.2 Literature Study 17
3.3 Flow Chart/Project Flow 18
3.4 3D Design Modeling 19
3.5 ANSYS Fluent Simulation Setup 19
3.5.1 Geometry 19
3.5.2 Computational Meshing Setting 20
3.5.3 Simulation Setup 20
3.5.4 Solution Setup 31
CHAPTER 4 RESULTS AND DISCUSSIONS
4.1 Introduction 33
4.2 Spray Image 33
4.3 Spray Penetration 36
4.4 Spray Cone Angle 38
4.5 Liquid-Vapor Area 40
CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusions 42
5.2 Recommendations 43
REFERENCES 44
APPENDICES 46
ix
LIST OF TABLES
Table No.
Title Page
2.1 Comparison of Viscosity among Diesel, Biodiesel and Vegetable
Oils.
7
2.2 Hydrocarbon contents in Crude Oil 8
2.3 Physical Properties of Petroleum Products 8
4.1 Spray penetration length 36
4.2 Cone angle size 39
4.3 Liquid-vapor phase area 41
x
LIST OF FIGURES
Figure No.
Title Page
2.1 Overall mechanism of Transesterification 10
2.2 SVO and BDF process. 11
2.3 The consecutive phase’s during the operation of a Diesel engine. 12
3.1 Flow Chart 18
3.2 3D Design of Injection Chamber 19
3.3 Injection Chamber mesh 20
3.4 General setup 21
3.5 Progress report 21
3.6 Model setup 22
3.7 Energy setup 22
3.8 Viscous model 23
3.9 Species model 24
3.10 Discrete phase physical model 25
3.11 Discrete phase tracking model 26
3.12 Setting injection point properties 27
3.13 Setting injection turbulent dispersion 27
3.14 Species mixture materials 28
3.15 Species droplet materials 29
3.16 Pressure outlet setting 30
3.17 Operating conditions setting 31
3.18 Solution control setting 32
4.1 Contours spray image 34
4.2 Particle track spray image 35
4.3 Spray penetration measure method 36
4.4 Penetration vs. Iteration 37
4.5 Spray cone angle measure method 38
4.6 Cone angle vs. Iteration 40
4.7 Liquid-vapor phase measure method 41
xi
LIST OF ABBREVIATIONS
BDF Biodiesel Fuels
SVO Straight Vegetable Oils
CAD Computer-aided Design
CFD Computational Fluid Dynamics
VCO Valve Covered Orifice
DPM Discrete Phase Model
xii
LIST OF APPENDICES
Appendix A Gantt Chart / Project Schedule for FYP1
Appendix B Gantt Chart / Project Schedule for FYP 2
CHAPTER 1
INTRODUCTION
1.1 Research Introduction
Nowadays, the depleting reserves of fossil fuel, increasing demands for diesels
and uncertainty in their availability have been a matter of global concern. This is
considered to be the important trigger for many initiatives to search for the alternative
source of energy, which can supplement or replace fossil fuels. The concern over
automotive pollution also been important aspects as it been environmental, medical and
philosophical, leading to strict emission requirement. These are effort around the world
to protect the environment from further deterioration.
From the automotive view, to minimize the fuel consumption rate in the diesel
engine is by improve the engine performance to reduce the energy lose in the
combustion. In the diesel engine, combustion and emission characteristics are
influenced by the fuel atomization, nozzle geometry, injection pressure, shape of inlet
port and other factors. So, in order to improve the fuel-air mixing, it is important to
understand the fuel atomization and spray formation process. So far, to improve the
combustion performance and particulate emissions, many researchers have investigated
the characteristics of the spray behavior by experimental and theoretical approaches.
Therefore, there is substantial emphasis on improving the fuel economy without
sacrificing the engine performance, while adhering to stringent emission regulation. As
a result, biodiesel fuel have becomes main focus of alternative fuel research and become
popular worldwide especially in Europe for its cleaner combustion than diesel.
2
Biodiesel fuel is made by processing vegetable oil, animal fat, or recycled cooking
grease with alcohols or other chemical.
Biodiesel fuel is a renewable, biodegrable and oxygenous fuel with similar
physical and chemical characteristics to diesel. Not only that, it also produce lower
combustion emission and fewer greenhouse gas emission than fossil diesel.
However, there are some differences in fuel properties parameters especially the
kinematic viscosity between biodiesel fuel and diesel. In a diesel engine, the fuel
development and atomization characteristics play an important role in improvement of
combustion and engine performance, because they influence the fuel-air mixing in the
cylinder. Therefore, it is necessary to study and analyze the spray development and
atomization characteristics of various fuels in relation to its application in internal
combustion engines, mainly effect the spray behavior and spray characteristics inside
spray chamber. Among the various alternative fuels, biodiesel fuel (BDF) and straight
vegetable oil (SVO) fuels are the most popular. This is because biodiesel fuel can be
used in conventional diesel engine without modification of the engine and a diesel
engine fueled with BDF or SVO can be operated with only a partial modification of the
fuel supply system. In this project, the effect of kinematic viscosity of diesel, BDF and
SVO on liquid phase and vapor phase development at spray boundary will be
investigated.
1.2 Problem Statement
1.2.1 Problem
In the simulation software, there is no database of biodiesel fuel and straight
vegetable oil available for the flow injection simulation. It is very important to know the
spray characteristic for the diesel engine which is being operated with biodiesel fuel and
straight vegetable oil.
3
1.2.2 Solution of the problem
ANSYS Fluent is a user friendly and very suitable for every engine simulation
and being used in most fluid flow simulation research. Therefore there is an alternative
for the problem in defining fuel for the simulation. ANSYS Fluent allows the users to
create their own fuel files. Referring to the biodiesel fuel and straight vegetable oil
properties table, the biodiesel fuel and straight vegetable oil can be created. The results
gain by simulation can give overview on how the fuel properties affect the spray
characteristic.
1.3 Objectives of the paper
Generally, the objectives to be achieved in this project are stated below:
i. To observe the development of “structures like branches” inside spray
boundary.
ii. To measure the liquid and vapor phase area.
iii. To investigate the relationship between kinematic viscosity of fuel and,
liquid and vapor phase development at spray boundary.
iv. To measure the spray penetration and cone angle.
1.4 Scopes
The project is focused on:
i. Literature review
ii. Simulate the model by using FLUENT ANSYS software
iii. Result comparing with different fuel and the spray development
4
1.5 Hypothesis
The low viscosities of fuels cause good fuel atomization and increasing in spray
penetration, which leads to complete fuel combustion. This was mainly because the
increase in fuel viscosity prevented the breaking of the spray jet, resulting in an increase
in the size of the spray droplets. The larger size of the spray droplets will increase the
momentum of droplet but the resistance also increases that preventing forward
movement.
1.6 Methodology
i. Stage 1 : Literature study
Make review on literature study involving project title.
ii. Stage 2 : 3D modeling
3D modeling of the injector and engine geometry.
iii. Stage 3 : Boundary condition setting simulation
Set up boundary condition for simulation analysis.
iv. Stage 4 : Simulating analysis by using FLUENT software
Simulation analysis using FLUENT ANSYS software.
v. Stage 4 : Analysis of simulation result
Analyze result from simulation.
5
CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
This chapter covers the recent review of diesel engine powered with diesel,
biodiesel fuel and straight vegetable oil research activities are presented here. All the
studies are mainly focus on the spray characteristic and liquid-vapor phase development
for the diesel engine operating with diesel, biodiesel fuel and straight vegetable oil.
2.2 Diesel Engine
The history of diesel engine was started by Dr. Rudolf Diesel (1858 to 1913). In
1892, he present his diesel engine which the ignition of fuel by compression process.
Compared to gasoline engines and steam engines, this engine had number of
advantages. It is less fuel consumptions and could be dimensioned for higher power
outputs. In 1922, Robert Bosch decided to develop a fuel-injection system for diesel
engines. Those Bosch fuel-injection pumps were a stepping stone in achieving higher
running speeds in diesel engine. In 1936, Mercedes-Benz 260D (2580 cc, 50 hp) was
the first volume-production car to be fitted with a diesel engine. In diesel engines, the
spark plug and carburettor are replaced by a fuel injector. This due to the air when being
compressed to a temperature that is above the auto-ignition temperature of the fuel, and
combustion creates on contact as the fuel is injected into this hot air.
6
In diesel engines, only air is compressed during the compression stroke, which
can eliminate the possibility of auto-ignition. (Yunus and Michael, 2007). Therefore the
diesel engines can operate on much higher compression ratios, between 12 and 24. The
principle operation of Diesel engines relies on the heat within the compressed air to
cause an ignition of the fuel charge. The chemical energy stored in the fuel is then
converted into mechanical energy, which can be used to power tractors, locomotives
and freight trucks. The diesel engines also burn fuel more completely compared to
gasoline engines since they work on lower revolutions per minute (rpm) and having
higher air-fuel mass ratio. It is more efficient than spark ignition engine (gasoline)
because they operate at much higher compression ratios (Yunus and Michael, 2007).
Lower fuel cost and higher efficiency become the reason why they have been used in
large ships and emergency power generation units.
2.3 Alternative Fuels
The concept of using alternative fuels is not contemporary in its nature; it has
existed for many years. Alternative diesel engine fuels that have been researched over
the years range from coal to peanut oil. During the 1900 Paris World Fair, the French
Otto Company ran the Diesel Engine on peanut oil at the request of the French
government. A Belgian patent granted in 1937 to G. Chavanne displays the early
existence of the use of ethyl esters extracted from palm oil (Knothe et al., 1997).
However, inexpensive petroleum-based fuels prevented biodiesel fuels from
receiving much consideration, resulting in adoption of a diesel engine to specifically
burn petroleum diesel. Interruption of cheap oil supplies resulting from the 1973 oil
embargo as well as the 1990 Gulf War sparked a renewed interest and research in using
domestically grown and renewable sources for fuel production. Although the use of
biodiesel did not receive much attention in the United States until the late 1990s, it has
been used extensively in Europe for nearly a quarter of a century.
In this project, alternative fuel properties been study and research because fuel
characteristics play an important part as it effect the spray characteristics, spray
penetration, atomization, droplet size drop distribution.
7
2.3.1 Viscosity
Viscosity is a measure of a fuel’s adhesive or cohesive property and is the key
factor in estimating the required temperature for pumping, injection, storage, and
transfer of the fuel. A viscosity comparison of diesel, biodiesel, and vegetable oils is
shown in Table 2.1.
Table 2.1: Comparison of Viscosity among Diesel, Biodiesel and Vegetable Oils
[Source: Knothe et al., 1997]
2.3.2 Diesel
Diesel is processed from crude oil, a fossil fuel with broad variations in colour,
from clear to tar-black, and viscosity, from that of water to almost a solid. Crude oil
contains a complex mixture of hydrocarbons comprised of differing chain lengths and
physical and chemical properties. Hydrocarbons containing up to four carbon atoms are
gaseous in nature, those with 5 to 19 carbon atoms are usually found in liquid form, and
those with a carbon composition greater than 19 are found as solids as shown in Table
2.2.
8
Table 2.2: Hydrocarbon Contents in Crude Oil
[Source: ATSDR, 1995; OTM, 1999]
Products resulting from fractional distillation that undergo further processing
(cracking, unification and alternation) in order to acquire desired compounds are shown
in Table 2.3.
Table 2.3: Physical Properties of Petroleum Products
[Source: Freudenrich, 2001]
9
2.3.3 Bio-Diesel Fuel (BDF)
Biodiesel is defined as a fuel comprised of mono-alkyl esters of long chain fatty
acids derived from vegetable oils or animal fats. Biodiesel is typically created by
reacting fatty acids with an alcohol in the presence of a catalyst to produce the desired
mono-alkyl esters and glycerin. After reaction, the glycerin, catalyst, and any remaining
alcohol or fatty acids are removed from the mixture. The alcohol used in the reaction is
typically methanol, although ethanol and higher alcohols also have been used.
Biodiesel fuel is now mainly being produced from soybean, rapeseed and palm
oils. Its properties are close to diesel fuels that can usually be used in diesel engines
without modification and have reduced emissions from a cleaner burn due to their
higher Oxygen content and therefore biodiesel becomes a strong candidate to replace
the diesel. It probably has better efficiency than petrol-oil. Due to the increment of
crude oil prices, limited resources of fossil oil, environmental concerns, population
increase and higher energy demand, biodiesel represents a promising alternative fuel for
use in compression ignition (diesel) engines.
In order for vegetable oils and fats to be compatible with the diesel engine, it is
necessary to reduce their viscosity. This can be accomplished by breaking down
triglyceride bonds, with the final product being referred as biodiesel. There are at least
four ways in which oils and fats can be converted into biodiesel:
i) Transesterification
ii) Blending
iii) Microemulsions
iv) Pyrolysis
Among these processes, transesterification is the most commonly used method.
The transesterification process is achieved by reaction of a triacylglycerol molecule
with an excess of alcohol in the presence of a catalyst to produce glycerol and fatty
esters as shown in Figure 2.1. Currently, the preferred alcohol is methanol (R = CH3)
10
Figure 2.1: Overall mechanism of Transesterification
[Source: Gerpen, 2005]
2.3.4 Straight Vegetable Oil (SVO)
SVO is a biodiesel fuel obtained from plant seed oil pressing. It can be used in a
non modified diesel engine just by adding a small heat exchanger in conjunction with
other minor modifications in the fuel intake system. The production of SVO with
respect to BDF is much easier because it includes fewer processes and less energy
consumption. The production process for BDF and SVO is shown in Figure 2.2.
However, the disadvantage of straight vegetable oil (SVO) was too viscous for
the fuel injectors to handle properly. Prolonged use of vegetable oil in a stock diesel
engine will lead to carbon deposits in the combustion chamber, valve sticking on seats
and stems and eventual leakage of fuel into the lubricating oil causing irreparable
engine damage. This viscosity problem left two options: modify the vegetable oil fuels
or modify the diesel engine. Early experimentation focused on reducing the viscosity of
the vegetable oil fuels by convert the vegetable oil to biodiesel.
11
Figure 2.2: SVO and BDF process.
[Source: Bernat Esteban, 2011]
2.4 Spray Combustion Process
The combustion performance and emissions are mainly influenced by the
atomization of the liquid fuel, the motion and evaporation of the fuel droplets and
mixing of fuel with air. The dynamics of spray and its combustion characteristics are
extremely important in determining, for instance, the flame stability behavior at widely
varying loads, the safe and efficient utilization of energy, as well as the mechanisms of
pollutants formation and destruction. Figure 2.3 show the consecutive phase’s occurring
during the operation of a diesel engine.
12
Figure 2.3: The consecutive phase’s during the operation of a Diesel engine.
[Source: Olga WOJDAS, 2010]
Understanding and controlling atomization and spray combustion is becoming
an essential part of the industrial applications, which have been driven by increasingly
urgent demands to improve fuel and energy efficiencies, and to drastically reduce the
emission of pollutants. The spray combustion process may be divided into several
elements, such as atomization, liquid transport, vaporization, and combustion. In
general, liquid fuel is injected through a nozzle system into the combustor chamber and
is atomized to form a spray of droplets before gas-phase combustion takes place in the
vaporized fuel. In the atomization region, the liquid dominates the flow and the liquid
fuel disintegrates into ligaments and droplets. Large liquid blobs which are bulks of
continuous liquids present in the atomization region.
13
The dense spray region has lower but still significant liquid volume fraction and
includes secondary breakup of drops and ligaments as well as drop interactions, such as
collisions and coalescence. Liquid ligaments normally present in the atomization and
dense spray regions, which are non-spherical liquid sheets, sheared off the liquid jet
column. In the dilute spray region, spherical droplets are well formed and have a strong
interaction with the turbulent airflow. In general, the spray structure depends on the
injection pressure difference, injector size, fuel viscosity and fuel density. (X. Jiang,
G.A. Siamas, K. Jagus, T.G. Karayiannis, 2010)
2.5 Spray Regimes
Diesel engine sprays are usually of the full-cone type. This means that in the idle
mode the fuel is blocked from the upstream side of the nozzle and during injection the
core of the spray is denser than the outer regions. The liquid spray can be characterized
by distinguishing spatial regimes. Starting from the nozzle exit there is an intact liquid
core. A few nozzle diameters further downstream in the so-called churning the liquid
consists of ligaments (blobs). These liquid parts are like large droplets with sizes
comparable to the nozzle diameter. Then the ligaments are breakup into many smaller
droplets in the thick zone where the volume and mass fraction of the liquid phase is
high. Further downstream the breakup process of droplets goes on and in the same time
more and more of the surrounding gas is entrained into the spray area.
This results in a diverging behavior with a characteristic spray angle. The
regimes after the thick zone are the thin zone (low volume but still high mass fraction of
liquid) and the dilute zone (negligible volume and low mass fraction of liquid),
respectively.
In a hot environment the position at which all liquid droplets are evaporated is
called the liquid length. From (automotive) experiments this liquid length is found to be
approximately constant after a short development time. From that point on the
evaporated fuel continues to penetrate the surrounding gas and is denoted as vapor
length. In a typical diesel injection timeframe (few milliseconds) the vapor length does
not reach a steady state.
14
2.6 Spray Penetration
The spray penetration is defined as the maximum distance from the nozzle to the
tip of the spray at any given time and is one of the most important characteristics of the
combustion process. If the spray penetration is too long, there is a risk of impingement
on the wall of the combustion chamber, which may lead to fuel wastage and the
formation of soot. This normally occurs when the chamber wall is cold and where there
is limited air motion. However, a short penetration will reduce mixing efficiency hence
resulting in poor combustion. Hence the information of spray tip penetration would be
useful for the design of the engine combustion chamber.
2.7 Computational Fluid Dynamic (CFD)
Computational fluid dynamics or known as CFD is defined as the process and
set of methodologies that enables the computer to provide numerical simulation of
fluids flows. Computational fluid dynamics is a technology that is used to analyze the
dynamics of anything that can flow regardless in liquid or gaseous state. It is also a
software tool that can model or simulate a flow or phenomena of any system or device
under analysis (Hirsh. 2007). CFD is computed using a set of partial different equations
to predict the flow behavior. Besides that, it is also used for analyzing heat transfer
model, mass flow rate, phase change, chemical reaction such as combustion, turbulence
model, mechanical movement, deformation of solid structure and many more.
The word simulation is to indicate that the usage of computer in solving
numerically the laws that govern the movement of fluids in or around a material system,
where its geometry is also modeled on the computer. Hence, the whole system is
transformed into virtual environment or virtual product. This can be opposed to an
experimental investigation, characterized by a material model or prototype of a system
in measuring the flow properties in a prototype of an engine.
15
Simulations used nowadays are mostly 3D simulation and 2D simulation. Both
simulations differ a lot in generating data and analysis of material. 3D simulation gives
the higher ability in drawing the geometrical complexity by offering un-uniform surface
of a material to be simulated. This ability gives a more real-time data by creating a near
real-time scenario (Hirsch, 2007). The data generated are more reliable for analysis. In
contrast, 2D simulation which offers less geometrical complexities are mostly used to
simulate a general overview of the scenario.
The creation of the product is definition phase, which covers the specification
and geometrical definition. It is based on Computer-Aided Design (CAD) software,
which allows creating, and defining the geometry of the system, in or its details. The
CAD definition of the geometry is required an unavoidable input to the CFD simulation
task.
CFD always preferred method over the conventional design method because it is
cheaper and save a lot of time. Before, there is such technology, usually engineers need
to build a real model for testing and redo the model again until optimum result is
obtained. Such a long procedure would consume more money and time. With the aid of
CFD software, engineer can simulate different set of parameters for testing to get the
optimum result before working on the real prototype without any additional cost (Lim,
2004).
In automotive industry for instance the time required for the design and
production of new car and engine model has been reduce from 6 to 8 years in the 1970’s
to roughly 36 months in 2005, with the announced objective of 24 to 18 months in the
new future. This is driven by the method known as CFD with the help of fast growing
computer hardware performance (Hirsch, 2007).
Air was used as fluid media, which was assumed to be steady and
incompressible. High Reynolds number k-epsilon turbulence model was used in the
CFD model. This turbulence model is widely used in industrial applications. The
equations of mass and momentum were solved using SIMPLE algorithm to get velocity
and pressure in the fluid domain. The assumption of an isotropic turbulence field used
in this turbulence model was valid for the current application.
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