NUMERICAL ANALYSIS OF

COOLING EFFECTS OF

A CYLINDER HEAD WATER JACKET  

 

 

 

 

 A Project Presented to

The Academic Faculty

By   

Qingzhao Wang  

 

 

 

In Fulfillment

of the Requirements for the Degree

Masters of Science in

Applied and Computational Mathematics

i 

 

ABSTRACT

The aim of this study is to discover the characteristics of the cooling water in the

cylinder head of a high-power diesel engine by using the Computational Fluid Dynamics

(CFD).

A 3-D geometric model of a cylinder head water jacket was previously constructed

using Unigraphics software. A mesh was then imposed on the model using the

preprocessor of Fluent software, GAMBIT. Three types of thermal boundaries are

defined and the standard ε−k model is utilized to carry out numerical simulations with

the CFD software Fluent. The pressure distribution, velocity field distribution, heat

transfer coefficient distribution, and temperature distribution of the cylinder head water

jacket are presented and analyzed. In addition, the impact flow rates have on the cooling

system of a cylinder head is studied. The relevant figures show that enhancement in flow

rate will increase the velocity and heat transfer coefficient of the coolant flow but in the

meanwhile bring in higher pressure loss. The design of the cylinder head water jacket is

evaluated to be satisfactory in terms of cooling effects. Simulation results are compared

with the work done by others and limited experimental data, and it is pointed out that the

disparity of heat transfer coefficients is mainly due to over simplification of the model

and inappropriate use of the turbulence model or wall function heat transfer coefficient.

Some suggestions on the types of boundary conditions and appropriate turbulence models

are proposed, which include the definition of boundary conditions on different locations

and the use of coupled simulation.

Key words: cylinder head water jacket；coolant flow；numerical

simulation；CFD

 

ii 

 

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to everyone who has assisted me in fulfilling

this project. I am especially grateful to my advisor Dr. Steven Trogdon, for allowing me

to continue carrying out the research on the topic that I started when I was a senior,

giving me useful suggestions and revising this report. He is very kind and patient in

helping me completing this project. I also want to say many thanks to Dr. Zhuangyi Liu,

for all his help throughout my study towards a master degree. I thank Dr. Daniel Pope for

his help in the CFD subject and serving on my reading committee.

Thanks also go to my friends. I enjoy the life in Duluth because of all of you. It is an

unforgettable memory.

Finally, I want to thank my family. Thank them for everything they did for me, thank

them for their permanent and unconditional support.                        

iii 

 

TABLE OF CONTENTS

ABSTRACT ....................................................................................... i 

ACKNOWLEDGEMENTS ............................................................... ii

LIST OF FIGURES .......................................................................... v

LIST OF TABLES ........................................................................... vi 

Chapter

1. INTRODUCTION ........................................................................ 1  1.1 Motivation and Significance of Study ...................................................................... 1

1.2 Historical Background .............................................................................................. 2

1.3 Outline of Thesis ...................................................................................................... 3

2. COMPUTATIONAL FLUID DYNAMICS THEORY ................. 5  2.1 Methodology ............................................................................................................ 5

2.2 Fundamental Physical Principles ............................................................................. 6

2.3 Discretization Methods ............................................................................................ 7

2.4 Turbulence Models ................................................................................................... 9

2.4.1 Overview ............................................................................................................ 9

2.4.2 The Standard ε−k Model ............................................................................ 10

2.4.3 Large Eddy Simulation and Detached Eddy Simulation .................................. 14

2.5 Near-Wall Treatments ............................................................................................. 15

2.5.1 Review of the near wall zones .......................................................................... 15

2.5.2 Momentum........................................................................................................ 16

2.5.3 Turbulence ........................................................................................................ 17

2.5.4 Energy ............................................................................................................... 18

2.5.5 Wall Function Heat Transfer Coefficient ......................................................... 18

3. GEOMETRIC AND MESH MODELS ....................................... 20  3.1 Geometric model .................................................................................................... 20

3.1.1 Characteristics of the Solid Model ................................................................... 20

iv 

 

3.1.2 Principles of Modeling ..................................................................................... 21

3.2 Mesh Model ............................................................................................................ 22

4.NUMERICAL SIMULATION OF A CYLINDER HEAD WATER JACKET .......................................................................... 24

4.1 Assumptions ............................................................................................................ 24

4.2 Solver ...................................................................................................................... 24

4.3 Definition ................................................................................................................ 25

4.3.1 Initial Condition ................................................................................................ 25

4.3.2 Boundary Conditions ........................................................................................ 25

4.3.3 Fluid Properties................................................................................................. 26

5. RESULTS AND ANALYSIS ...................................................... 27  5.1 Simulation Results with Convection Thermal Boundary ....................................... 27

5.2 Simulation Results with Fixed Heat Flux Thermal Boundary ............................... 33

5.3 Simulation Results with Fixed Temperature Thermal Boundary ........................... 35

5.4 HTC Distribution Using Wall Function Formula .................................................. 37

5.5 Effects of Flow Rates ............................................................................................. 37

5.6 Relations between Variables .................................................................................. 39

6. CONCLUSIONS AND FUTURE WORK .................................. 40  6.1 Evaluation of Cooling Effects of the Cylinder Head ............................................. 40

6.2 Evaluation of the Simulation .................................................................................. 40

6.3 Future Work ........................................................................................................... 41

REFERENCES ............................................................................... 44  

 

 

 

 

v 

 

LIST OF FIGURES

Figure 1 Subdivisions of the Near-Wall Region [17] .................................................... 16

Figure 2 Geometric Model of Cylinder Head Water Jacket .......................................... 22

Figure 3 Mesh Model ..................................................................................................... 23

Figure 4 Contour of Pressure Field Distribution ( Pa ) .................................................. 28

Figure 5 Pressures (Pa) on Nose Zones at z = 35 mm ................................................... 28

Figure 6 Contour of Velocity Field Distribution (m/s) .................................................. 29

Figure 7 Velocity Field around the Fuel Injector (m/s) ................................................. 30

Figure 8 Velocity Field on Nose Zones (m/s) ................................................................ 30

Figure 9 Contour of Surface HTC Distribution ( ( )2/W m K⋅ ) .................................... 31

Figure 10 Surface HTC ( ( )2/W m K⋅ ) on Nose Zones at x = -30 mm ......................... 32

Figure 11 Contour of Temperature Distribution (K) ..................................................... 33

Figure 12 Contour of Surface HTC Distribution ( ( )2/W m K⋅ ) ................................... 34

Figure 13 Contour of Temperature Distribution at Wall (K) ......................................... 34

Figure 14 Contour of Temperature Distribution at z = 35mm , 45mm and 55mm (K) . 35

Figure 15 Contour of Surface HTC Distribution ( ( )2/W m K⋅ ) ................................... 35

Figure 16 Contour of Wall Function HTC Distribution ( ( )2/W m K⋅ ) ........................ 36

Figure 17 Pressure Loss at Different Flow Rates .......................................................... 37

Figure 18 Average Velocity at Different Flow Rates .................................................... 38

Figure 19 Surface HTC at Different Flow Rates ........................................................... 38

vi 

 

LIST OF TABLES

 

Table 1 Values of Constants in the standard ε−k Model ............................................. 13

Table 2 Engine Characteristics ....................................................................................... 20

Table 3 Inlet Flow Rates of Study .................................................................................. 25

Table 4 Surface HTC at Different Locations ................................................................. 32

Table 5 Boundary Conditions Considered in the Model ................................................ 40

1 

 

CHAPTER 1

INTRODUCTION

1.1 Motivation and Significance of Study

Internal Combustion (IC) Engines play an important role in the modern industry. Great

efforts are put to improve the power performance and fuel economy of IC Engines. As

the speed and loading capability of IC engines increase, the thermal and mechanical load

increase greatly. Under normal working condition, the peak temperatures of burning

gases inside the cylinder of IC Engines are of the order of 2500 K, consequently the

temperatures of parts, including valves, cylinder head, and piston in contact with gases,

rise rapidly due to a large amount of heat absorbed. The substantial heat fluxes and

temperatures lead to thermal expansion and stresses, which further destroy the clearance

fits between parts and escalate the distortions and fatigue cracking of parts.

To prevent overheating, cooling must be provided for the heated surfaces. However, it

should be noted that overcooling will also cause some serious problems, such as

combustion roughness, lower overall efficiency and high emission pollution. To some

extent, further improvements on the performance of an IC Engine depend on the effective

resolution of heat transfer problems. Therefore, an optimal design of the cooling system

is required to maintain trouble-free operation of engines, which must take into account all

the considerations described above.

As one of the most complicated parts of an IC Engine, the cylinder head is directly

exposed to high combustion pressures and temperatures. In addition, it needs to house

intake and exhaust valve ports, the fuel injector and complex cooling passages [1]. Many

compromises must be made in design to satisfy all these requirements. The complicated

structure of a cylinder head leads to the difficulty in acquiring necessarily detailed

2 

 

information for design for conducting flow and heat transfer experiments. With improved

computer performance and rapid development of Computational Fluid Dynamics (CFD),

numerical simulation provides a tool for engineers to use in evaluating their design. With

the assistance of numerical simulation techniques, some basic features, such as pressure

and velocity distributions of the flow field, can be easily predicted. Coupled with

Computer-Aided Design (CAD), the structure of a cooling system for an engine can be

modified and optimized, in order to control the temperature at key zones, decrease the

power loss, and improve the reliability of parts working at high temperatures.

1.2 Historical Background

In late 1980’s, the thermocouple pyrometer was used to obtain local temperatures of the

cooling system, which have been treated as boundary conditions to compute the surface

temperature and heat flux distribution by using Finite Element Method (FEM). Following

the continuous development of computer hardware techniques and the emergence of user-

friendly software in 1990’s, computer modeling, FEM and CFD have been extensively

employed on engine design. M. Sandford and L. Postlemthwaite [2] and M. Moechel [3]

attempted to simulate the 3-D coolant flow in cylinder via CFD techniques. Under the

limitation of computer capacity at that time, and the immaturity of CFD software, many

simplifications were made. M. Sandford and L. Postlemthwaite [2] showed that the

velocity field of a cooling water jacket calculated using CFD is relatively consistent with

the experimental data by comparing results obtained from the experiments on the

simplified solid model and the numerical simulation on the corresponding computational

model. They also indicated that the numerical simulation for coolant flow in the coolant

cavities of a cylinder head was fairly reliable. M. Moechel [3] concluded that the

prediction of heat transfer in the cylinder block water jacket by numerical simulation was

not stable and reliable, and further pointed out this may be due to a sparse computational

mesh.

3 

 

With the efforts of researchers in the fields of computer science and CFD techniques,

numerical simulation of the cooling jacket has become an important tool for developing

and optimizing the cooling system by famous car makers [4-6]. It helped to improve the

flow state in several dead zones. However, progress has been made for only specific areas,

and there are few thorough analyses of the flow mechanism. It has always been a

formidable problem to simulate heat transfer process accurately. The reference [5]

indicates that most automobile companies only focus on the simulation of pressure and

velocity fields, ignoring the heat transfer part. Although some literature [7-11] dealing

with the heat transfer effects of different types of cylinder water jackets have arisen in

recent years, the resulting heat transfer coefficients differ a lot.

It is clear that further study and better design for an engine cooling system require more

precise simulation of the heat transfer process, which depends on accurate geometric

models and appropriate boundary conditions.

1.3 Outline of Thesis

In this study, the numerical simulation is carried out on a cylinder head water jacket of

the typical uprated engine 1015, and pressure, velocity and heat transfer coefficient

distributions of the coolant flow are given. The following work has been done. 1. Review one of the most widely used turbulence models, the standard ε−k model,

and comment on the applicability of the model for the present cylinder head water

jacket.

2. Discuss the choice of heat transfer coefficient formulas and derive the semi-

empirical formula for heat transfer coefficient formula.

4 

 

3. Analyze the flow field within the cylinder head water jacket using Fluent, and

evaluate the design for the cylinder head by focusing on the cooling effects in the

problematic regions around the valve seats and narrow bridges between valves.

4. Compare the simulation results with available experimental data and work done

by others [1, 7-11]. Comment on the possible reasons for large differences on heat

transfer coefficients.

5. Propose recommendations for improving the results of this study.

5 

 

CHAPTER 2

COMPUTATIONAL FLUID DYNAMICS THEORY

Problems involving fluid flow can be described by three fundamental physical principles,

mass conservation, Newton’s second law, and energy conservation, which can be

expressed in terms of mathematical equations. Computational Fluid Dynamics is a

technique that solves these equations by using numerical methods and algorithms to

obtain values at discrete points for certain prescribed boundary conditions. This technique

depends on the speed of computers, since millions of calculations are performed at one

time. CFD has been widely used in industry, and with the evolution of modern computers

it has become an indispensable tool in conducting fundamental research. On the other

hand, with the limit of the computational capacity, in many cases only approximate

solutions can be achieved.

2.1 Methodology

Solving a problem of fluid mechanics should follow the following basic procedure.

1. Preprocessing

1) Define and build a model of a geometrical body, namely the computational

domain.

2) Discretize the volume occupied by fluid.

3) Describe the physical model by mathematical equations.

4) Define fluid properties.

5) Specify appropriate boundary conditions.

2. Solution

Iterate to determine solutions to the equations.

3. Postprocessing

Analyze and visualize the resulting solution.

6 

 

2.2 Fundamental Physical Principles

1. Conservation of Mass

Any flow problem must obey the mass conservation law. The governing flow

equation which results from the application of this fundamental physical principle

is called the continuity equation. The mathematical statement of this principle is

that, in any steady state process, the rate at which mass enters a system is equal to

the rate at which mass leaves the system. [12] This statement can be expressed by

equations (2-1),

( )t

0ρ ρ∂+∇⋅ =

∂V (2-1)

where ρ is the density of fluid, and is the velocity of flow. V

2. Conservation of Momentum

The resulting equation of the application of Newton’s second law to a fluid

element is called momentum equation. The momentum equation states that the

rate of increase of momentum in a control volume is equal to the sum of forces

acting on the control volume plus the net flux of momentum into the control

volume. The general form of the equation for fluid motion is as follows [12].

( ) ( )

( ) ( )

( ) ( )

yxxx zxx

xy yy zyy

yzxz zxz

u Pu ft x x yv Pv f

t y x yw Pw f

t z x y

τρ τ τz

z

z

ρ ρ

τ τ τρρ ρ

τρ τ τρ ρ

∂∂⎧ ∂ ∂∂+∇ ⋅ = − + + + +⎪ ∂ ∂ ∂ ∂ ∂⎪

⎪ ∂ ∂ ∂∂ ∂⎪ +∇⋅ = − + + + +⎨ ∂ ∂ ∂ ∂ ∂⎪⎪ ∂∂ ∂ ∂∂⎪ +∇ ⋅ = − + + + +

∂ ∂ ∂ ∂⎪⎩

V

V

V∂

(2-2)

where is the static pressure, P τ denotes the shear stresses (such as xyτ ) and

normal stresses (such as xxτ ), and f represents the body force per unit mass

acting on the fluid element.

7 

 

Conservation of momentum is also well known as the Navier-Stokes equations, in

honor of two men-the Frenchman M. Navier and the Englishman G.Stokes-who

independently obtained the equations in the first half of the nineteenth century.

3. Conservation of Energy

Applied to the flow model of a fluid element moving with the flow, this physical

principle states that the rate of change of energy inside fluid element equals the

sum of the net flux of heat into element and the rate of work done on element due

to body and surface forces [12]. The mathematical expression used in Fluent is

( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( )

yxxx

xy yyzx

yzxz zz

T TE E q k k kt x x y y

uuP vP wP u

zy

Tz z

x y z x y

v v vuz x y

ww wx y z

ρ ρ ρ

z

ττ

τ τ ττ

ττ τρ

⎛ ⎞∂ ∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞+∇ ⋅ = + + +⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠⎝ ⎠

∂∂ ∂ ∂ ∂⎛ ⎞− + + + +⎜ ⎟∂ ∂ ∂ ∂ ∂⎝ ⎠

∂ ∂ ∂∂+ + + +

∂ ∂ ∂ ∂

∂∂ ∂

∂ ∂∂ ∂

+ + + +∂ ∂ ∂

V

f V⋅

(2-3)

where E is the total energy, is the heat flux, and k is the thermal conductivity. q

2.3 Discretization Methods

Solving a fluid dynamics problem is actually solving a coupled system of

nonlinear partial differential equations, but presently, there is no general analytical

solution to these equations. Hence, appropriate numerical solutions play a significant role

in understanding the performance of fluid described by the mathematical equations.

Discretization is usually carried out as the first step for numerical evaluation and

implementation on digital computers. In such a process, a mathematical expression,

which takes on values at infinitely many points, is replaced by finitely many values at

8 

 

ues in use today.

discrete nodes or points. Nodes in a certain area form a grid. The form of governing

equations is changed from differential equations to a system of algebraic equations after

discretization. Not only should the obtained system of algebraic equations approximate

the equations to be studied, but they should also be numerically stable. The errors in the

intermediate calculations should not accumulate or cause the resulting output to be

meaningless. There are three common discretization techniq

1. Finite Element Method (FEM)

The basic idea of FEM is to divide the body into finite elements, connected by

nodes, apply the governing equations to these elements, and compute the values at

each node.

The Finite Element Method is a good choice for solving partial differential

equations over complex domains (like cars and oil pipelines), when the domain

changes (as during a solid state reaction with a moving boundary), when the

desired precision varies over the entire domain, or when the solution lacks

smoothness. For instance, in a frontal crash simulation it is possible to increase

prediction accuracy in "important" areas like the front of the car and reduce it in

its rear (thus reducing cost of the simulation). [13]

2. Finite Difference Method (FDM)

The Finite Difference Method replaces a partial derivative with a suitable

algebraic difference quotient. Most common finite-difference representations of

derivatives are based on Taylor’s series expansions. [12]

Although the FDM has its own advantages, such as high efficiency, the difference

equations do not always maintain the property of conservation, resulting in lower

accuracy.

9 

 

3. Finite Volume Method (FVM)

The finite-volume method is popular in fluid mechanics. The main idea is to

decompose the flow domain into a set of control volumes, so that the dependent

variables are conserved in the control volumes and in the whole computational

domain. The idea of the FVM determines the following advantages. [14]

1) It rigorously enforces conservation;

2) It is flexible in terms of both geometry and the variety of fluid phenomena;

3) It is directly relatable to physical quantities (mass flux, etc.)

2.4 Turbulence Models

2.4.1 Overview

In fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic,

stochastic property changes. This includes low momentum diffusion, high momentum

convection, and rapid variation of pressure and velocity in space and time. Flow that is

not turbulent is called laminar flow. The Reynolds number characterizes whether flow

conditions lead to laminar or turbulent flow. As an example, for pipe flow, a Reynolds

number above about 4000 (A Reynolds number between 2100 and 4000 is known as

transitional flow) will be turbulent. [15] Most of the flow phenomena in engineering

applications are associated with turbulence, as is the flow in an IC engine. The fluid

interaction over a large range of length scales produced by turbulence flow must be taken

into account for numerical simulations.

The basic physical properties of turbulent flow can be described by the Navier-Stokes

equations. A direct numerical simulation (DNS) captures all the relevant scales of

turbulent motion and gives the solution to a complex flow problem. However, DNS needs

a huge number of calculations, which is extremely expensive and not practical for

10 

 

complex engineering problems. Reynolds-averaged Navier-Stokes (RANS) equations are

the oldest and most widely used approach to turbulence modeling. Nowadays, RANS has

been coupled with other turbulence models to solve viscous flow problems. The time-

averaged parameters, flow status and hydrodynamic forces which are attractive to

engineers, can be obtained by RANS.

ε−k Model 2.4.2 The Standard

Based on experiments and theoretical background, many turbulence models have been

proposed, and have been reviewed in various works [16]. Among those models, the

standard ε−k model is most popular because of its comprehensive quality in

computational economy, range of applicability and physical realism.

In Fluent, the equations of conservation laws are particularized.

1. Conservation of Mass

( )j

j

vt x

0ρ ρ∂ ∂+ =

∂ ∂                                                (2-4)

where the duplicate index variable in a single term implies the operation of

summing over all the possible values. For a three dimensional space, the values

for the index could be 1, 2, 3. This notation will also be used later.  

2. Conservation of Momentum

( ) ( ) iji i j

j i

Pv v vt x x jx

τρ ρ

∂∂ ∂ ∂+ = − +

∂ ∂ ∂ ∂ (2-5)

where the elements of the stress tensor, ijτ are given by  

23

jiij ij

j i l

vv vx x x

lτ μ δ⎡ ⎤⎛ ⎞∂ ⎛ ⎞∂ ∂

= + −⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟∂ ∂ ∂⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦ (2-6)

11 

 

3. Conservation of Energy

( )( )( ) j jj j

TE v E Pt x x xρ ρ κ

⎛ ⎞∂ ∂ ∂ ∂+ + = +⎜⎜∂ ∂ ∂ ∂⎝ ⎠

i ij

vτ ⎟⎟ (2-7)

where the total Energy is given by

2k kv vPE h

ρ= − + (2-8)

h being the specific enthalpy.  

Now, relative to conservation of mass and momentum, assume and

, where

'P p p= +

'i i iv u u= + p and are mean values and iu 'p and are fluctuations. After

applying standard time averaging techniques to the conservation of mass and

conservation of momentum equations, we get

'iu

( )jj

ut x

0ρ ρ∂ ∂+ =

∂ ∂ (2-9)

( ) ( ) ij iji i j

j i j j

Rpu u ut x x x x

σρ ρ

∂ ∂∂ ∂ ∂+ = − + +

∂ ∂ ∂ ∂ ∂ (2-10)

where

23

jiij ij

j i l

uu ux x x

lσ μ δ⎡ ⎤⎛ ⎞∂ ⎛ ⎞∂ ∂

= + −⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟∂ ∂ ∂⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦ (2-11)

and

' 'ij i jR u uρ= − (2-12)

The ijR are the so called Reynold’s stresses where the overbar denotes time averaging. These stresses may be approximated using the Boussinesq hypothesis [17] to yield

23

jiij t t ij

j i l

uu uR kx x x

lμ ρ μ δ⎛ ⎞∂ ⎛ ⎞∂ ∂

= + − +⎜ ⎟ ⎜⎜ ⎟∂ ∂ ∂⎝ ⎠⎝ ⎠⎟ (2-13)

where tμ is called the turbulent viscosity and k is the turbulent kinetic energy, defined as

12 

 

1 ' '2 i ik u u= (2-14)

In the ε−k model, ε stands for the rate of dissipated turbulent energy, and is defined by

2 'ij ijS Sε μ= ' (2-15)

where

''1'2

jiij

j i

uuSx x

⎛ ⎞∂∂= +⎜⎜ ∂ ∂⎝ ⎠

⎟⎟ (2-16)

The transport equations that Fluent solves for k and ε are

( ) ( ) ti k

i j k j

kk ku Gt x x x

μρ ρ μσ

⎡ ⎤⎛ ⎞∂ ∂ ∂ ∂+ = + +⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦

ρε− (2-17)

and

( ) ( )2

1 2t

i ki j j

ku Ct x x x kε

μ G Ck

ε ερε ρε μ ρσ

⎡ ⎤⎛ ⎞∂ ∂ ∂ ∂+ = + + −⎢ ⎥⎜ ⎟∂ ∂ ∂ ∂⎢ ⎥⎝ ⎠⎣ ⎦

(2-18)

where represents the generation of turbulent kinetic energy due to mean velocity kG

gradients, defined by

jk ij

i

uG R

x∂

=∂

(2-19)

When utilizing the Boussinesq hypothesis for ijR , this expression becomes

2k t ij ijG S Sμ= (2-20)

The definition of is the same as but with replaced with . The turbulent

viscosity,

ijS 'ijS 'ju ju

tμ is found to 2

tkCμμ ρε

= (2-21)

The kσ and εσ parameters are called turbulent Prandtl numbers. The default values for

the model constants are given in Table 1:

13 

 

Table 1 Values of Constants in the standard ε−k Model

   Cμ                                      1C 2C kσ              εσ   

  0.09          1.44         1.92           1.0            1.3 

It is easy to see from Equation (2-15) that ε is nonnegative, since it is a sum of the

average of squared quantities. Also, because it occurs on the right hand side of the kinetic

energy equation (2-17) for the fluctuating motions with a minus sign, it is clear that it can

act only to reduce the kinetic energy of the flow. Therefore it causes a negative rate of

change of kinetic energy, hence the name dissipation. Physically, energy is dissipated

because of the work done by the fluctuating viscous stresses in resisting deformation of

the fluid material by the fluctuating strain rates [15].

Fluent uses the Reynolds’ analogy to turbulent momentum transfer to model the energy

equation. The modeled equation is

( ) ( )( ) ( )j eff ji ieffj j j

TE v E Pt x x xρ ρ κ τ

⎛ ⎞∂ ∂ ∂ ∂+ + = +⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠

v (2-22)

where

Prp t

efft

c μκ κ= + (2-23)

and ( ) is ji effτ jiτ with μ replaced with eff tμ μ μ= +

Prt

, the effective viscosity. The

default value for the turbulent Prandtl number, is 0.85.

The standard ε−k performs rather well in most flow problems, and it fits the

experimental data for the various locations far from walls, but due to the Reynolds’

hypothesis, this two-equations model has some deficiencies, which mainly include [16]:

14 

 

1. the inability to account for rotational strain or shear,

2. the inaccurate prediction of normal Reynolds stress anisotropies,

3. the inability to account for the amplification or the relaxation of the components if

the Reynolds stress tensor.

To overcome the difficulty that the standard ε−k model has in some cases, several other

turbulence models have been developed. Some are still two-equations models based on

the standard ε−k model, such as Realizable ε−k model, Re-Normalization Group

(RNG) ε−k model, Lam-Bremhorst (LB) ε−k model, Launder-Sharma (LS) ε−k model, and so on. The Reynolds Stress Model (RSM) appeared with the

introduction of transport equations for each Reynolds component. To reduce the

computational efforts on tons of transport equations, the Algebraic Stress Model (ASM)

has been proposed. In order to obtain a closed system, some certain unknown correlations

must be modeled. Like the ε−k model, ASM model is not an ideal tool for slalom. The

k ω− model is an empirical model based on the turbulent kinetic energy k and the

specific dissipation rateω . However, this model is over sensitive to the change of

boundary conditions. Thus, Menter [18] advocated using the k ω− model for near-wall

zones, and the ε−k model for zones far away from walls.

2.4.3 Large Eddy Simulation and Detached Eddy Simulation

RANS models are primary means in turbulence numerical simulations, but it will lose

some details and significant information of turbulent flows, which is a fatal weakness.

The DNS method can make up for the deficiency, but consume a large amount of

computations. A simulation method between a RANS model and a DNS model has

thereupon been developed, namely the Large Eddy Simulation (LES). In this method,

small eddies are approximated by Subgrid Scale Model (SSM), while large eddies are

described by N-S equations.

15 

 

The difficulty arises when using LSE to simulate the near-wall flows, thus the idea to

switch the model to LES in regions suitable for LES calculations and RANS in near-wall

regions has been adapted, namely the so-called Detached Eddy Simulation (DES). The

DES methods proposed respectively by Shur [19] and Strelets [20] have already been

applied in some famous CFD commercial software packages.

2.5 Near-Wall Treatments

2.5.1 Review of the near wall zones

The ε−k models, the RSM, and the LES are primarily valid for fully turbulent flows,

namely high-Reynolds-number flows. For the near-wall regions, the turbulent flows are

significantly influenced by the presence of walls, where the Reynolds number of

turbulence is so small that viscous effects predominate over turbulent ones. In turbulent

flows solution variables may have large gradients in the near-wall regions; numerical

methods must therefore be capable of resolving these large gradients in order to make

accurate predictions.

Numerous experiments have shown that boundary layers have three zones usually, a

laminar zone, followed by a transition zone and a turbulent zone, which is illustrated in

the Figure 1 plotted in semi-log coordinates.

16 

 

Figure 1 Subdivisions of the Near-Wall Region [17]

There are two traditional approaches to modeling the near-wall region. In one approach,

the viscosity-affected inner region (laminar zone) is not resolved. Instead, semi-empirical

formulas called "wall functions'' are used to bridge the viscosity-affected region between

the wall and the fully-turbulent region. In the other approach, which is called the “near-

wall modeling” approach, the turbulence models are modified to enable the viscosity-

affected region to be resolved with a mesh all the way to the wall, including the laminar

zone.

2.5.2 Momentum

In order to describe the flow of the nearby wall and prepare for the derivation of the

standard wall functions, the following two dimensionless quantities have been introduced,

one for velocity, and the other for distance.

( ) , 11.225 1 ln , 11.225

y yU

Ey yκ

∗ ∗

∗∗ ∗

⎧ <⎪= ⎨

>⎪⎩

[21] (2-24)

17 

 

where 1/4 1/2

*

/P P

w

U C kU μ

τ ρ≡ , and

1/4 1/2* P PC k y

y μρμ

≡

and ( )von K rm n constant 0.4187á áκ = =

( )empirical constant 9.793E = =

, mean velocity of the fluid at point PU = P is a point in the near wall regionP

turbulence kinetic energy at point Pk P=

distance from point to the wall Py P=

dynamic viscosity of the fluidμ =

wall shear stresswτ =

2.5.3 Turbulence

In the ε−k models, the k equation is solved in the whole domain including the wall-

adjacent cells. The boundary condition for imposed at the wall is [17] k

0kn∂

=∂ (2-25)

where is the local coordinate normal to the wall. n

The production of kinetic energy, is computed from kG

PP

wwwk

ykCyuG

21

41

μκρ

τττ =∂∂

≈

(2-26)

and the rate of dissipated turbulent energy ε is computed from

P

P

ykC

κε μ

23

43

= (2-27)

The production of kinetic energy, , and its dissipation rate, kG ε , at the wall-adjacent cells are the source terms in the equation. k

18 

 

2.5.4 Energy

Reynolds' analogy between momentum and energy transport gives a similar logarithmic

law for mean temperature. For a pressure-based solver, the temperature wall function has

the following form,

( )( )

1/4*

1*

*

/2 ,Pr

Pr ,

1 l n

T

T

tw P p P

t

y y y

ET T

y P y yc C k

Tq

μρ

κ

∗ ∗

∗ ∗

⎧− ⎪≡ = ⎨ ⎡ ⎤

⎪ ⎢ ⎥

<

>⎣ ⎦

+⎩

(2-28)

where 3/4

0.007Pr/PrPr9.24 1 1 0.28Pr

t

t

P −⎡ ⎤⎛ ⎞

e⎡ ⎤= − +⎜ ⎟ ⎣ ⎦⎝ ⎠⎢ ⎥⎢ ⎥⎣ ⎦

[21], is the dimensionless thermal

sublayer thickness, and computed as the

*Ty

y∗ value at which the linear law and the

logarithmic law intersect [17].

turbulent kinetic energy at point PPk =

density of fluidρ =

specific heat of fluidpc =

wall heat fluxq =

temperature at the cell adjacent to wallPT =

temperature at the wallwT =

( )molecular Prandtl number Pr /p fc kμ=

( )turbulent Prandtl number 0.85 at the P lr wt = la

2.5.5 Wall Function Heat Transfer Coefficient

The heat transfer coefficient, in thermodynamics and in mechanical and chemical

engineering, is used in calculating the heat transfer, typically by convection or phase

change between a fluid and a solid [15]. It is defined by

effrefw

qhT T

=−

(2-29)

which, after utilizing the logarithmic law for mean temperature, yields

19 

 

( )( )

1/4 1/2

eff *ref ref

w P p P

w w

T T c C kqhT T T T T

μρ−= =

− − (2-30)

where ref PT T≠ , and depends on the value of *T y∗ .

Assume ref PT T= and , then Equation (2-30) is reduced to *Ty y∗ >

( )

1/4 1/2 1/4 1/2 1/4 1/2

eff * PrP 1 lnr

p p p p p p

tt Ey

C C k C C k C C kh

T U PP

μ μ

κ

ρ ρ ρ

∗∗

= = = μ

⎡ ⎤ ⎡ + ⎤⎣ ⎦⎢ ⎥⎣ ⎦+

(2-31)

20 

 

CHAPTER 3

GEOMETRIC AND MESH MODELS

3.1 Geometric model

3.1.1 Characteristics of the Solid Model

The geometric model of the cylinder head was created using the software Unigraphics

(UG) modeling software, which is useful in component and surface modeling, virtual

assembly, and in generating engineering drawings.

The component studied in this project is one cylinder head of an eight-cylinder 1015

high-power diesel engine. Some of the characteristic parameters of the investigated

engine are presented in the table below.

Table 2 Engine Characteristics

Engine Type Diesel TC Cylinders 8V Bore 132mm Stroke 145mm Displacement 16L Compression Ratio 17 Rated Power 440kW Rated Engine Speed 2100r/min

The 1015 engine has a split structure, namely one cylinder head for one cylinder. The

cooling system of this engine is distinguished by the manner in which coolant is

distributed. The cylinder block water jackets are connected in series, while the cylinder

head water jackets are connected in parallel. This design enables the coolant collected in

21 

 

cylinder blocks to enter each cylinder head separately through transfer channels

separately, which is also the reason why only one cylinder head has been investigated.

3.1.2 Principles of Modeling

Based on experience gained from the repeated modeling and numerical simulation

process, the following principles of modeling are recommended.

 

1. Embodiment of features of the structure and flow

A cylinder head consists of the firedeck, side plate, fuel injector protection sleeve and

valve guide. It can be described as a box that has been trimmed by intake and exhaust

ports and padded by intake and exhaust valves, and fuel injector. All these features create

a rather irregular cylinder head structure with special cavities and bores, which

complicate the process of building a water jacket model, since the shape and position of

parts in cylinder head determine the shape of the water jacket. Moreover, the most

complicated areas in the cylinder head usually happen to be key places where

investigators put most emphases. In those locations, either the velocity and heat fields

have large gradients, or advection is significant. Therefore, the geometric features of

these parts should be modeled as accurately as possible.

2. Impact on mesh generation

Complexity of the solid models may result in potential difficulty in mesh generation, poor

quality of the mesh model and unnecessary work. To simulate viscous effects near walls,

it is usually needed to create a boundary layer, which requires some simplification in

order to avoid unacceptable meshes due to severe curvature change of surfaces.

It can be concluded that building the solid model is a trade-off process between the above

two principles. Appropriate simplification is needed on the premise that most geometric

details have been retained.

22 

 

The completed cylinder head solid model is displayed below.

Figure 2 Geometric Model of Cylinder Head Water Jacket

3.2 Mesh Model

A high quality mesh model is one of the most important factors that determine the

successful prediction of the behavior of an objective. The geometric model of cylinder

head water jacket was imported to GAMBIT, a preprocessor of the CFD software Fluent.

Tetrahedral volume meshing elements were chosen to generate the mesh model.

23 

 

The mesh model is shown below, which contains 130365 cells and 29150 nodes.

Figure 3 Mesh Model

Using a 0-1 scale for mesh quality with 0 representing the best and 1 the poorest, more

than 90 percent of the cells are of the scale less than 0.5, which implies a high quality of

the mesh model.

24 

 

CHAPTER 4

NUMERICAL SIMULATION OF A CYLINDER HEAD WATER JACKET

Numerical Simulation was carried using the CFD software Fluent, which is widely used

to simulate a large range of fluid problems, including Laminar or Turbulence, Newtonian

or non-Newtonian flow, steady or unsteady flow, compressible or incompressible flow,

and viscous or nonviscous flow.

4.1 Assumptions

In the numerical simulations, the coolant flow in coolant cavities of a cylinder head was

assumed to be 3D steady state, incompressible turbulent flow, and the viscosity in the

near wall region was taken into account, while boiling of the coolant and roughness of

walls were ignored.

Under the fixed-speed working condition of an IC engine, although the thermal loadings

of a cylinder head vary considerably in time due to the cyclical nature of engine operation,

the computations were performed assuming that steady-state was presented on the basis

of time-averaged values. At low heat fluxes the primary means of heat transfer is pure

forced convection. Only at high fluxes will film boiling occur and result in a large

increase in wall temperature [22]. For the present simulation settings, the effect of boiling

in the coolant is negligible.

4.2 Solver The turbulence model employed for the study is the standard ε−k model. The standard

wall function was utilized for the near-wall region. A pressure based solver was used

with an implicit, first-order upwind scheme.

25 

 

The Reynolds number of the studied flow was on the order of , which suggests the

flow is fully turbulent far away from the wall. The standard

510

ε−k model is therefore

worth trying in this situation.

4.3 Definition

4.3.1 Initial Condition

For a steady-state flow problem, the solution is unique in many cases whatever initial

condition is given. However, an appropriate initial condition will accelerate the

convergence of results. The initial condition was defined by default in Fluent.

4.3.2 Boundary Conditions

1. Inlet Boundary

Type: Mass flow inlet

Temperature: 373K

Flow rates used in this study were calculated and obtained under four typical conditions

with different rated powers. The values of the flow rates are shown in the following table.

Table 3 Inlet Flow Rates of Study

Rated Power (kW) 440 700 800 1000 Inlet Flow Rate (kg/s) 1.0508 1.4449 1.5587 1.8383

2. Outlet Boundary Type: Pressure outlet

Pressure: 1.2 bar

26 

 

3. Wall Boundary

Three types of thermal conditions at the wall surface in Fluent were applied and

compared with each other.

1) Fixed heat flux

The value used for the heat flux is 150 , see reference[22]. kW

2) Fixed temperature

The value used for the temperature at the wall surface is 418 , which is the empirical

data often used for the heating surface of the cylinder head.

K

3) Convection

The values used for heat transfer coefficient 3000 ( )2/W m K⋅ and free stream

temperature 418 K were taken from the literature [1].

4.3.3 Fluid Properties

All CFD simulations were carried out using the coolant mixture of water (50%) and

glycol (50%) at a constant inlet temperature 373 Kelvin. The fluid properties are listed

below.

Density: 1008.8 3/kg m

Specific heat capacity: 3592.3 / ( )J kg K⋅

Dynamic viscosity: 0.000675 / ( )kg m s⋅

Thermal conductivity: 0.39964 / ( )W m K⋅

Freezing point: 238 K (-35 ) C°

Boiling point of glycol: 470 K (197 ) C°

27 

 

CHAPTER 5

RESULTS AND ANALYSIS

With the high quality mesh model, the solutions converge within half an hour after 400-

600 iterations, depending on the cases studied. In this paper, the results of pressure field,

velocity field and temperature field are presented and analyzed. More attention is paid to

the heat transfer process. The influence of flow rates on those parameters mentioned

above is discussed.

Refer to Figure 2 for the definition of coordinates. The bottom of the cylinder head water

jacket, where inlet and outlet are located, is referred to as the datum plane, and the center

of the fuel injector bore on this plane is the origin. The positive z-axis is directed toward

the top of cylinder head water jacket, the positive y-axis is directed toward the paper, and

the positive x-axis is directed toward the outlet.

Because the computation of the pressure and velocity fields is independent of the

temperature, the simulation results of these two fields will only be presented once, for all

three thermal boundary conditions. The results shown were calculated at the inlet flow

rate of 1.0508 if they were not specified. /kg s

5.1 Simulation Results with Convection Thermal Boundary

1. Pressure Field Distribution

28 

 

Figure 4 Contour of Pressure Field Distribution ( Pa )

It can be seen from the contour of pressure that the outlet displayed the lowest pressure,

while the side plate presented the highest pressure, which indicated that the largest

pressure drop occurs between the inlet and outlet. The interior of the water jacket does

not have obvious pressure drop. The pressure loss between the inlet and outlet is

calculated to be 8.4177 kPa, which is a good indicator of low resistance in flow and

potential to enhance mechanical efficiency.

Figure 5 Pressures (Pa) on Nose Zones at z = 35 mm

29 

 

Focusing on the nose zones, the narrow bridges between intake ports, exhaust ports,

intake and exhaust ports, and two ports and the fuel injector, it is noticed from Figure 5

that the pressure varies between 129 kPa and 132 kPa, which is a small difference that

reduces the possibility of bubble producing, and therefore the destruction of the cylinder

head.

2. Velocity Field Distribution

Figure 6 Contour of Velocity Field Distribution (m/s)

The average velocity magnitude over the whole flow field is 0.892 m/s, which meets the

need of flow rate 0.5 m/s for cooling the engine. [7]

Some key zones were investigated particularly.

1) Exhaust port

The design for this cylinder head forced the flow to go around the exhaust port first,

where most of the heat was output, then cooled down the fuel injector and finally the

intake port. It is seen that the velocity of the flow around the exhaust port was higher than

other locations, which ensures that the cylinder head is relatively evenly cooled. Because

of the small inlet and outlet diameters, the velocity at these locations was largest.

30 

 

2) Fuel injector

Figure 7 Velocity Field around the Fuel Injector (m/s)

The upper part of the fuel injector hole is narrower than the lower part. Such a design

coordinates with the flow regularity that the flow comes from the under part of the hole

and up to the top of the cylinder head, which ensures a relatively high velocity of the flow

on the top. In this case, the velocity changed from 0.7m/s to 1.25m/s.

3) Nose zones

Figure 8 Velocity Field on Nose Zones (m/s)

31 

 

The higher flow rate in the narrow bridges between intake and exhaust valves ensured the

cooling effects in the most problematic regions.

3. Heat Transfer Coefficient Distribution

The cooling effects can be reflected directly by the heat transfer coefficient (HTC). The

HTC shown below is the surface HTC provided by Fluent.

The simulation results of the surface heat transfer coefficients are as follows:

1) Wall

Figure 9 Contour of Surface HTC Distribution ( ( )2/W m K⋅ ) The area-averaged surface HTC is calculated to be 836.52 ( )2/W m K⋅ .

2) Specific regions

32 

 

Figure 10 Surface HTC ( ( )2/W m K⋅ ) on Nose Zones at x = -30 mm

Figure 10 displayed the surface heat transfer coefficient distribution of the narrow bridge

regions at x =-30 . Data at different locations and on different height planes was

collected and summarized in the table below.

mm

Table 4 Surface HTC at Different Locations

HTC

Section

Exhaust

valves

Intake and

exhaust valves

Intake valves Fuel injector

z=18mm 600-750 —— —— ——

z=20mm 700-900 600-800 —— 600-700

z=25mm 900-1000 800-900 700-800 700-800

z=30mm 900-1200 800-900 750-900 900-1100

The fire deck is located at the plane where z = 0.

33 

 

4. Temperature Distribution

Figure 11 Contour of Temperature Distribution (K)

With the limitation of the boundary conditions, the temperature distribution was

displayed in the range of 373K and 418K. The bottom contacted with the fire deck, was

of extremely high temperature, which is reasonable in the sense of the structure

characteristics and work principle of the cylinder head. The temperatures around the wall

of the annular cavities, where the fresh air and exhaust passed, were ranging from 384K

to 397K, which showed acceptable cooling effects of the cylinder head.

By comparison of HTC and temperature distributions, it is evident that the regions with

high heat transfer coefficient correspond to ones with low temperature, and vice versa.

This also implies the inherent relations between the velocity and heat transfer coefficient,

which will be discussed in Section 5.5. 5.2 Simulation Results with Fixed Heat Flux Thermal Boundary

1. Heat Transfer Coefficient Distribution

34 

 

Figure 12 Contour of Surface HTC Distribution ( ) ( )2/W m K⋅

The area-averaged surface HTC at the wall is 1287.0704 ( )2/W m K⋅ , indicating a

relatively good cooling effect.

2. Temperature distribution

1) At the wall surface

Figure 13 Contour of Temperature Distribution at Wall (K)

35 

 

2) Sections orthogonal to z-axis

Figure 14 Contour of Temperature Distribution at z = 35mm , 45mm and 55mm (K)

The contour of the wall surface shows that the hottest part is located at the narrow bridge

on the heating surface, but the magnitude exceeds the boiling point of glycol, which

means either it is not realistic, or the design of the cylinder head will cause destruction

due to film boiling. 5.3 Simulation Results with Fixed Temperature Thermal Boundary Heat Transfer Coefficient Distribution

Figure 15 Contour of Surface HTC Distribution ( ( )2/W m K⋅ )

36 

 

The area-averaged surface HTC at the wall is 2142.2268 ( )2/W m K⋅

2m

, which is greater

than the results of convection and fixed heat flux thermal boundaries. Moreover, the area-

averaged total surface heat flux reaches 277706.5 , which is almost twice the

referenced [22] heat flux of 150 . In a cylinder head of an engine, the

temperature varies from point to point, which depends on the location of the heat source

and the detailed structures of different regions. It is not practical to assume the

temperature is constant over the wall surface, but the simulation conducted under the

fixed temperature thermal boundary provided a profile of the heat transfer coefficient,

which depicted the general distribution, but not the exact value of the heat transfer

coefficient.

/W2/kW m

5.4 HTC Distribution Using Wall Function Formula

The wall function HTC is based on the semi-empirical formula for HTC (refer to

Equation 2.31), in spite of the different thermal boundaries chosen. Therefore, the wall

function HTCs in the previously described three types of wall boundary conditions give

the same result, the contour of which is shown in Figure 16.

Figure 16 Contour of Wall Function HTC Distribution ( ( )2/W m K⋅ )

37 

 

In addition, the surface HTC and wall function HTC distributions present similar profiles.

It means that locations of high HTC and low HTC are almost the same in different

contours, but the magnitudes of HTC at these locations are different. It can be expected

that the wall function HTC will be more reliable when heat flux or temperature gradient

is sufficiently large.

5.5 Effects of Flow Rates

As the engine has been strengthened, it’s necessary to check the consequent effects on the

cooling system. Four typical working conditions (refer to Table 3) were taken into

account, as listed in figures below.

The convection thermal boundary condition is the most reasonable one for numerical

simulation, which gives not only the variations of the pressure field, velocity field,

temperature field and heat transfer coefficient field at different zones, but also the

magnitudes of these parameters at particular points, which are close to the experimental

data. Therefore, the simulation results used below are obtained from this condition.

1. Pressure Loss

Pressure loss is computed by taking the difference of area-averaged pressures at

the inlet and outlet.

Figure 17 Pressure Losses at Different Flow Rates

38 

 

2. Velocity

The velocity presented below is the volume-averged velocity calculted over the

interier of the water jacket.

Figure 18 Average Velocity at Different Flow Rates

3. Surface HTC with Convection Boundary Condition The surface heat transfer coefficient is the area-averaged HTC at the surface of

the water jacket.

Figure 19 Surface HTC at Different Flow Rates

39 

 

With the increase of rated power, the inlet flow rate increases, the velocity and heat

transfer coefficient increase consequently. However, the pressure loss will increase too,

which indicates the decrease of the torque efficiency. It is known that if the pressure loss

exceeds 50 , the resistance of the cooling system will be large, and loss of the power

will be considered to be high.

kPa

5.6 Relations between Variables

1. Enhancement in flow rate will strengthen the cooling effects to some extent, but

in the meanwhile bring in higher pressure loss of the flow.

2. The variation of heat transfer coefficient has close relationship with that of the

velocity. It is seen from the velocity contour and the surface heat transfer

coefficient contour that higher velocity leads to higher heat transfer coefficient.

From the semi-empirical formula of the heat transfer coefficient, this can be

proved.

40 

 

CHAPTER 6

CONCLUSIONS AND FUTURE WORK

6.1 Evaluation of Cooling Effects of the Cylinder Head

In general, the work of this cylinder head water jacket satisfied the demand of cooling

effects, which can be analyzed in the following ways.

1. The coolant in cylinder head performed a good flow rate distribution, and

relatively even pressure distribution.

2. The arrangement of the parts in cylinder head provided necessary forces to

enhance the cooling in problematic zones, so that the intake and exhaust valves

and the fuel injector will not be too hot to break down.

6.2 Evaluation of the Simulation

The flow field and heat field of the cylinder head water jacket were computed based on

the boundary condition values, which were obtained from the experiments and experience.

However, they should also be tested and verified by available information.

The following table provides some information of the coolant-side heat transfer process,

which was reported in the literature [23].

Table 5 Boundary Conditions Considered in the Model

41 

 

)

In spite of the different types of engines studied, the results should not be of way too big

differences.

By the careful comparison with all available, but limited papers [7-11] on the heat

transfer analysis of a cylinder head, it can be seen that the simulation results of the

pressure and flow rate distributions are relatively consistent with each other, while the

results on heat transfer vary a lot.

According to the information given in the above table, this present study showed more

accurate simulation results. Moreover, it should be noticed that many of the investigators

obtained rather high heat transfer coefficients, even higher than , which

deviated from the experimental data. The main causes of the disparity may lie on two

aspects:

410 ( 2/W m K⋅

1. The geometric model and mesh model are over simplified or some of the

important characteristics of the structure are ignored.

2. The chosen turbulence model is not appropriate for the studied model, and the

wall function HTC is not an acceptable prediction for the HTC profile of the

coolant flow given the boundary conditions described previously.

6.3 Future Work

It has been years that researchers put efforts on a realistic and reliable simulation of the

cooling system of the cylinder head. Until now, there are a variety of results especially in

heat transfer coefficient, some of which are not consistent with the experimental data.

This study is another attempt to better describe the heat transfer process in a cylinder

head. The results are closer to the limitedly available information obtained directly from

the experiments, but they still need to be improved on the following potential aspects.

42 

 

1. Boundary conditions

This study already showed that the convection thermal boundary for the wall is the best

way of simulating the heat transfer process, and the same value was considered for the

whole wall surface. However, it is evident that different zones of the wall are exposed to

different environment, resulting in different boundary conditions which should be set

separately according to the locations of the zones.

To achieve this purpose, boundary layers should be employed to divide the model into

different areas in Gambit, which will take effect when adding wall boundaries in Fluent.

2. Turbulence model and semi-empirical HTC formula

The classical two-equation ε−k model has been widely used with its accuracy and

universality. The simplicity is also an advantage of this model, which is based on and

developed from the Reynolds' analogy. All the assumptions of the Reynolds' analogy

made the problems simpler and easier to solve. Nevertheless, the ε−k model can not

reflect the Reynolds’ relaxation effect along the stream line, so it’s not the best

simulation tool for more complex flow in engineering.

It is shown that the standard wall function described the distribution of heat field with

relatively high heat transfer coefficients, which were inconsistent with the available

experimental results. The semi-empirical heat transfer coefficient formula could be

improved further, which needs to be investigated.

3. Coupled simulation

In this study, the entity is the water jacket of a cylinder head. If we can set up the solid

cylinder head model as well, both structural and fluid simulations can be carried on to

obtain a more satisfactory result. Finite Element Method will be applied in this kind of

simulation.

43 

 

4. Improvement of design

Once the cooling effects of the current model were figured out, it is significant to make

some change in design to achieve a better cooling model, to carry on simulations and

evaluate the new model, and to modify it again, which is a repeating process. For this

cylinder head model, it is worth trying to add a water hole in order to strengthen the

cooling effect around the fuel injector.

44 

 

REFERENCES

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Correlation Study.SAE TECHNICAL PAPER SERIES, 930068.

[3] Mark D.Moechel. Computational Fluid Dynamic (CFD) Analysis of a Six

Cylinder Diesel Engine Cooling System with Experimental Correlations.

SAE TECHNICAL PAPER SERIES, 941081.1994.

[4] Franz J.Laimbock, Gerhard Meister et al. Application in Compact Engine

Development. SAE TECHNICAL PAPER SERIES, 982016.

[5] Toyoshige SHIBATA, Hideo MATSUI, Masao TSUBOUCHI et al. KATSURADA.

Evaluation of CFD Tools Applied to Engine Coolant Flow Analysis, MITSUBISHI

MOTORS TECHNICAL REVIEW 2004, (16):56-60.

[6] Curtis M.Hill, Glenn D.Miller, Robert C. Gardner. 2005 Ford GT Powertrain-

Supercharged Supercar. SAE TECHNICAL PAPER SERIES, 2004-0101252.

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Jacket CFD Analysis[J]. Transaction of CSICE, 2003, Vol.21, No.2: 125-129.

[8] Haie Chen, Fanchen Meng, Jianlong Song, Jun Li, CFD Analysis on Engine Cooling

Jackets[J]. Design Computation Research, 1000-3703(2003).

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Cooling Water Flow around Cylinder liner for Heavy Duty Diesel Engine [J].

Chinese Internal Combustion Engine Engineering, 2004, Vol.25 No.4: 32-35.

[12] John Anderson, Computational Fluid Dynamics. The basics with applications

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[M].1995.

[13] Jacob Fish, Ted Belytschko, A First Course in Finite Elements [M]. Wiley, 2007.

[14] http://www.chmltech.com/cfd/introduction.pdf.

[15] Wikipedia-Turbulence.

[16] B. E. Launder and D. B. Spalding, The Numerical Computation of Turbulent Flows.

Computer Methods in Applied Mechanics and Engineering, 3:269-289, 1974.

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[18] Menter, F. R., Two-Equation Eddy-Viscosity Turbulence Models for Engineering

Applications, AIAA Journal, Vol. 32, No. 8, August 1994, pp. 1598-1605

[19] M. Shur, P.R.Spalart, M. Strelets et al. Detached-Eddy Simulation of an Airfoil at

High Angle of Attack. In4th Int. Symposium on Eng. Turb. Modeling and Experiments,

Corsica, France, May 1999.

[20] Travin A, Shur M, Strelets M, et al. Detached-Eddy Simulations past a Circular

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