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 k − ε 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 k − ε 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 ( W / ( m 2 ⋅ K ) ) .................................... 31
Figure 10 Surface HTC ( W / ( m 2 ⋅ K ) ) on Nose Zones at x = -30 mm ......................... 32
Figure 11 Contour of Temperature Distribution (K) ..................................................... 33
Figure 12 Contour of Surface HTC Distribution ( W / ( m 2 ⋅ 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 ( W / ( m 2 ⋅ K ) ) ................................... 35
Figure 16 Contour of Wall Function HTC Distribution ( W / ( m 2 ⋅ 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 k − ε 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 userfriendly 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 k − ε 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 semiempirical 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),
∂ρ
+ ∇ ⋅ ( ρ V) = 0
∂t
(2-1)
where ρ is the density of fluid, and V is the velocity of flow.
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].
⎧ ∂ ( ρu )
∂P ∂τ xx ∂τ yx ∂τ zx
+ ∇ ⋅ ( ρ uV ) = −
+
+
+
+ ρ fx
⎪
z
t
x
x
y
∂
∂
∂
∂
∂
⎪
⎪⎪ ∂ ( ρ v )
∂P ∂τ xy ∂τ yy ∂τ zy
+ ∇ ⋅ ( ρ vV ) = −
+
+
+
+ ρ fy
⎨
z
t
y
x
y
∂
∂
∂
∂
∂
⎪
⎪ ∂ ( ρ w)
∂P ∂τ xz ∂τ yz ∂τ zx
⎪
+ ∇ ⋅ ( ρ wV ) = −
+
+
+
+ ρ fz
∂z
∂x
∂y
∂z
⎪⎩ ∂t
where P is the static pressure, τ denotes the shear stresses (such as τ xy ) and
normal stresses (such as τ xx ), and f represents the body force per unit mass
acting on the fluid element.
(2-2)
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
∂T
∂
∂
∂T
∂ ⎛ ∂T ⎞ ∂
( ρ E ) + ∇ ⋅ ( ρ EV ) = ρ q + ⎜⎛ k ⎟⎞ + ⎜ k ⎟ + ⎜⎛ k ⎟⎞
∂t
∂x ⎝ ∂x ⎠ ∂y ⎝ ∂y ⎠ ∂z ⎝ ∂z ⎠
⎛ ∂ ( uP ) ∂ ( vP ) ∂ ( wP ) ⎞ ∂ ( uτ xx ) ∂ ( uτ yx )
−⎜
+
+
+
⎟+
∂y
∂z ⎠
∂x
∂y
⎝ ∂x
∂ ( uτ zx ) ∂ ( vτ xy ) ∂ ( vτ yy ) ∂ ( vτ zy )
+
+
+
+
∂z
∂x
∂y
∂z
+
(2-3)
∂ ( wτ xz ) ∂ ( wτ yz ) ∂ ( wτ zz )
+
+
+ ρf ⋅ V
∂x
∂y
∂z
where E is the total energy, q is the heat flux, and k is the thermal conductivity.
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 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 techniques in use today.
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 timeaveraged parameters, flow status and hydrodynamic forces which are attractive to
engineers, can be obtained by RANS.
2.4.2 The Standard k − ε Model
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 k − ε 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
∂ρ
∂
+
( ρ v j ) = 0 (2-4)
∂t ∂x j
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
∂
∂
∂P ∂τ ij
( ρ vi ) +
( ρ vi v j ) = −
+
∂t
∂x j
∂xi ∂x j
(2-5)
where the elements of the stress tensor, τ ij are given by
⎡⎛ ∂v ∂v j ⎞ 2 ⎛ ∂v ⎞ ⎤
i
+
⎟⎟ − ⎜ l ⎟ δ ij ⎥
⎜
3 ⎝ ∂xl ⎠ ⎥⎦
∂
x
∂
x
⎢⎣⎝ j
i ⎠
τ ij = μ ⎢⎜
(2-6)
11 3. Conservation of Energy
∂
∂
∂
(ρ E) +
v j ( ρ E + P )) =
(
∂t
∂x j
∂x j
⎛ ∂T
⎞
+ τ ji vi ⎟
⎜⎜ κ
⎟
⎝ ∂x j
⎠
(2-7)
where the total Energy is given by
E = h−
P
ρ
+
vk vk
2
(2-8)
h being the specific enthalpy. Now, relative to conservation of mass and momentum, assume P = p + p ' and
vi = ui + ui ' , where p and ui are mean values and p ' and ui ' are fluctuations. After
applying standard time averaging techniques to the conservation of mass and
conservation of momentum equations, we get
∂ρ
∂
+
(ρu j ) = 0
∂t ∂x j
(2-9)
∂
∂
∂p ∂σ ij ∂Rij
+
+
( ρ ui ) +
( ρ ui u j ) = −
∂t
∂x j
∂xi ∂x j ∂x j
(2-10)
where
⎡⎛ ∂u ∂u j ⎞ 2 ⎛ ∂u
i
+
⎟⎟ − ⎜ l
⎜
x
x
3 ⎝ ∂xl
∂
∂
⎢⎣⎝ j
i ⎠
σ ij = μ ⎢⎜
⎞ ⎤
⎟ δ ij ⎥
⎠ ⎥⎦
(2-11)
and
Rij = − ρ ui ' u j '
(2-12)
The Rij 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
⎛ ∂u ∂u ⎞ 2 ⎛
∂u ⎞
Rij = μt ⎜ i + j ⎟ − ⎜ ρ k + μt l ⎟ δ ij
⎜ ∂x j ∂xi ⎟ 3
∂xl ⎠
⎝
⎝
⎠
(2-13)
where μt is called the turbulent viscosity and k is the turbulent kinetic energy, defined as
12 1
k = ui ' ui '
2
(2-14)
In the k − ε model, ε stands for the rate of dissipated turbulent energy, and is defined by
ε = 2 μ Sij ' Sij '
(2-15)
1 ⎛ ∂u ' ∂u ' ⎞
Sij ' = ⎜ i + j ⎟
2 ⎜⎝ ∂x j
∂xi ⎟⎠
(2-16)
where
The transport equations that Fluent solves for k and ε are
∂
∂
∂
( ρ k ) + ( ρ kui ) =
∂t
∂xi
∂x j
⎡⎛
μt
⎢⎜ μ +
σk
⎣⎢⎝
⎞ ∂k ⎤
⎥ + Gk − ρε
⎟
⎠ ∂x j ⎦⎥
(2-17)
and
∂
∂
∂
( ρε ) + ( ρε ui ) =
∂t
∂xi
∂x j
⎡⎛
μt
⎢⎜ μ +
σε
⎢⎣⎝
⎞ ∂k ⎤
ε
ε2
C
G
C
+
−
ρ
⎥
⎟
k
1
2
k
k
⎠ ∂x j ⎥⎦
(2-18)
where Gk represents the generation of turbulent kinetic energy due to mean velocity
gradients, defined by
Gk = Rij
∂u j
∂xi
(2-19)
When utilizing the Boussinesq hypothesis for Rij , this expression becomes
Gk = 2μt Sij Sij
(2-20)
The definition of Sij is the same as Sij ' but with u j ' replaced with u j . The turbulent
viscosity, μt is found to
μ t = ρ Cμ
k2
ε
(2-21)
The σ k and σ ε 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 k − ε Model
Cμ C1 C2 σ k σ ε 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
∂
∂
∂
( ρ E ) + (v j ( ρ E + P )) =
∂t
∂x j
∂x j
⎛
⎞
∂T
+ (τ ji ) vi ⎟
⎜⎜ κ eff
eff
⎟
∂x j
⎝
⎠
(2-22)
where
κ eff = κ +
and
(τ )
ji eff
c p μt
Prt
(2-23)
is τ ji with μ replaced with μeff = μ + μt , the effective viscosity. The
default value for the turbulent Prandtl number, Prt is 0.85.
The standard k − ε 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 k − ε model has in some cases, several other
turbulence models have been developed. Some are still two-equations models based on
the standard k − ε model, such as Realizable k − ε model, Re-Normalization Group
(RNG) k − ε model, Lam-Bremhorst (LB) k − ε model, Launder-Sharma (LS)
k − ε 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 k − ε 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 rate ω . 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 k − ε 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 k − ε 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 “nearwall modeling” approach, the turbulence models are modified to enable the viscosityaffected 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.
⎧ y∗
, y ∗ < 11.225
⎪
U∗ = ⎨ 1
[21]
∗
∗
ln
Ey
,
y
11.225
>
(
)
⎪
⎩ κ
(2-24)
17 where U * ≡
U P Cμ1/4 k P1/2
τw / ρ
, and y * ≡
ρ Cμ1/4 k P1/ 2 yP
μ
and κ = von Kármán constant ( = 0.4187 )
E = empirical constant ( = 9.793)
U P = mean velocity of the fluid at point P , P is a point in the near wall region
k P = turbulence kinetic energy at point P
yP = distance from point P to the wall
μ = dynamic viscosity of the fluid
τ w = wall shear stress
2.5.3 Turbulence
In the k − ε models, the k equation is solved in the whole domain including the walladjacent cells. The boundary condition for k imposed at the wall is [17]
∂k
=0
∂n
(2-25)
where n is the local coordinate normal to the wall.
The production of kinetic energy, Gk is computed from
Gk ≈ τ w
τw
∂u
=τw
1
1
∂y
κρC 4 k 2 y
μ
P
P
(2-26)
and the rate of dissipated turbulent energy ε is computed from
3
ε=
3
Cμ 4 k P 2
κy P
(2-27)
The production of kinetic energy, Gk , and its dissipation rate, ε , at the wall-adjacent
cells are the source terms in the k equation.
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,
T* ≡
(Tw − TP ) ρ c pC
q
1/4 1/2
P
μ
k
⎧ Prt y ∗
,
⎪
= ⎨ ⎡1
⎤
∗
⎪Prt ⎢ κ ln ( Ey ) + P ⎥ ,
⎦
⎩ ⎣
y ∗ < y T*
y ∗ > yT*
(2-28)
⎡⎛ Pr ⎞3/ 4 ⎤
−0.007Pr/Prt
⎤⎦ [21], y*T is the dimensionless thermal
where P = 9.24 ⎢⎜
⎟ − 1⎥ ⎡⎣1 + 0.28e
⎢⎣⎝ Prt ⎠
⎥⎦
sublayer thickness, and computed as the y ∗ value at which the linear law and the
logarithmic law intersect [17].
k P = turbulent kinetic energy at point P
ρ = density of fluid
c p = specific heat of fluid
q = wall heat flux
TP = temperature at the cell adjacent to wall
Tw = temperature at the wall
Pr = molecular Prandtl number ( μ c p / k f
)
Prt = turbulent Prandtl number ( 0.85 at the wall )
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
heff =
q
Tw − Tref
which, after utilizing the logarithmic law for mean temperature, yields
(2-29)
19 (Tw − TP ) ρ c pCμ1/4 kP1/2
q
heff =
=
Tw − Tref
(Tw − Tref ) T *
(2-30)
where Tref ≠ TP , and T * depends on the value of y ∗ .
Assume Tref = TP and y ∗ > y *T , then Equation (2-30) is reduced to
heff =
ρ C p Cμ1/4 k 1/2
p
T*
=
ρ C p Cμ1/4 k 1/2
p
⎡1
⎤
Prt ⎢ ln ( Ey ∗ ) + P ⎥
⎣κ
⎦
=
ρ C p Cμ1/4 k 1/2
p
Prt ⎣⎡U ∗ + P ⎦⎤
(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
Cylinders
Bore
Stroke
Displacement
Compression Ratio
Rated Power
Rated Engine Speed
Diesel TC
8V
132mm
145mm
16L
17
440kW
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 k − ε 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 of105 , which suggests the
flow is fully turbulent far away from the wall. The standard k − ε 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)
Inlet Flow Rate (kg/s)
2. Outlet Boundary
Type: Pressure outlet
Pressure: 1.2 bar
440
1.0508
700
1.4449
800
1.5587
1000
1.8383
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 kW , see reference[22].
2) Fixed temperature
The value used for the temperature at the wall surface is 418 K , which is the empirical
data often used for the heating surface of the cylinder head.
3) Convection
The values used for heat transfer coefficient 3000 W / ( m 2 ⋅ 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 kg / m3
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 400600 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 kg / s if they were not specified.
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 ( W / ( m 2 ⋅ K ) )
The area-averaged surface HTC is calculated to be 836.52 W / ( m 2 ⋅ K ) .
2) Specific regions
32 Figure 10 Surface HTC ( W / ( m 2 ⋅ 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 mm . Data at different locations and on different height planes was
collected and summarized in the table below.
Table 4 Surface HTC at Different Locations
HTC
Exhaust
Intake and
Intake valves
Fuel injector
Section
valves
exhaust valves
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 ( W / ( m 2 ⋅ K ) )
The area-averaged surface HTC at the wall is 1287.0704 W / ( m 2 ⋅ 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 ( W / ( m 2 ⋅ K ) )
36 The area-averaged surface HTC at the wall is 2142.2268 W / ( m 2 ⋅ K ) , which is greater
than the results of convection and fixed heat flux thermal boundaries. Moreover, the areaaveraged total surface heat flux reaches 277706.5 W / m2 , which is almost twice the
referenced [22] heat flux of 150 kW / m 2 . 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.
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 ( W / ( m 2 ⋅ 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 kPa , the resistance of the cooling system will be large, and loss of the power
will be considered to be high.
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 10 4 W / ( m 2 ⋅ K ) , which
deviated from the experimental data. The main causes of the disparity may lie on two
aspects:
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 k − ε 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 k − ε 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
[1] M. Diviš, R. Tichánek, M. Španiel, Heat Transfer Analysis of a Diesel Engine Head.
Acta Polytechnica, 2003 Vol. 43, No. 5 : 34-39.
[2] Malcolm H.Sandford,Lan Postlemthwaite. Engine Coolant Flow Simulation-A
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 PowertrainSupercharged Supercar. SAE TECHNICAL PAPER SERIES, 2004-0101252.
[7] Xunjun Liu, Qun Chen, Ju Li, Kang Li, Haie Chen, Automotive Diesel Engine Water
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).
[9] Qun Chen, Xunjun Chen, CFD Analysis of Cooling Water Jacket of Vehicle Diesel
Engine CA498 [J]. Design Computation Research, 1000-3703(2003)11-0008-04:8-11.
[10] Numerical Simulation on Flow and Heat Transfer of Cooling System in a SixCylinder Diesel Engine [J]. Transaction of CSICE, 2004, Vol.22, No.6: 525-531.
[11] Shengguan Qu, Wei Xia, Numerical Simulation and Experimental Research on
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
45 [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.
[17] Fluent Documentation 6.3
[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
Cylinder [J]. Int J Flow Turbulence and Combustion, 2000, 63:293-313.
[21] C. L. V. Jayatilleke, The influence of Prandtl number and surface roughness on the
resistance of the laminar sub-layer to momentum and heat transfer, Progress in Heat
and Mass Transfer, vol. 1, p. 193, 1969.
[22] Pamela Marie Norris, An experimental investigation of heat transfer in a diesel
engine cylinder head. Thesis of GIT. May, 1989.
[23] Kreith, F., Black, W.: Basic Heat Transfer. New York:
Harper and Row, 1980.