HEAT DISTRIBUTION STUDY ON TURBOCHARGER TURBINE VOLUTE
MOHD IBTHISHAM BIN ARDANI
This thesis is submitted to the Faculty of Mechanical Engineering
in partial fulfillment of the requirements for the award of the
Master of Engineering (Mechanical)
Faculty of Mechanical Engineering
Universiti Teknologi Malaysia
JANUARY, 2012
iii
To my dearly mother, father, wife and all other family members …………….
iv
ACKNOWLEDGEMENT
First and foremost I would like to express my greatest gratitude to my two
supervisors of this project, which are Dr Srithar Rajoo and Prof. Amer Nordin Darus for
the guidance during conducting this study. The continuous support, supervision and
advice are highly appreciated. With the supervision, I gain abundance of knowledge that
hard to find by books.
Also not forget to mention my fellow colleagues who willing to share some ideas
which are related to this project. Also millions of thank you to Dr Khalid Saqr who
guide me on giving FLUENT tutorials and comments on my simulation works.
Las but not least, I would like to acknowledge the support given by my family
and those who contributed and involved directly or indirectly in this project.
v
ABSTRACT
The aimed of this project is to evaluate turbine’s performance based on its actual
condition. Holset H3B nozzles turbine geometry was used as simulation model.
Turbine’s actual working condition was simulated using common computational fluid
dynamics analysis software which is FLUENT. Initial analysis was done by onedimensional and two-dimensional analysis. Further investigation was done in threedimensional with heat loss via turbine volute by the mode of convection. All the
simulation results were compared with established data in order to confirm its validity.
The parameters studied are corrected mass flow, turbine’s efficiency at different heat
cases, temperature distribution along turbine’s volute and difference in temperature
between inner and outer wall temperature. Temperature difference within turbine’s
volute is the major factor that deteriorates turbine’s efficiency. Since turbine wall is thin,
small temperature difference will result to high heat loss.
vi
ABSTRAK
Analisis adalah bertujuan untuk menilai prestasi turbin berdasarkan keadaan
sebenar. Geometri turbin model Holset H3B telah digunakan sebagai model simulasi.
Keadaan kerja sebenar turbin disimulasi dengan menggunakan perisian analisis dinamik
yang biasa iaitu FLUENT. Analisis awal telah dilakukan dengan analisis satu dimensi
dan dua dimensi. Siasatan lanjut telah dilakukan dalam tiga dimensi dengan kehilangan
haba melalui volut turbin oleh mod olakan. Semua keputusan simulasi dibandingkan
dengan data simulasi dan ujikaji oleh penulis lain untuk mengesahkan kesahihannya.
Parameter yang dikaji ialah perbetulan aliran jisim, kecekapan turbin pada kes-kes haba
yang berbeza, suhu sepanjang volut dan perbezaan suhu turbin di antara suhu dinding
dalam dan luar. Perbezaan suhu di dalam volut turbin adalah faktor utama yang
menyebabkan kemerosotan kecekapan turbin. Disebabkan turbin mempunyai dinding
yang nipis, perbezaan suhu yang kecil akan menyebabkan kehilangan haba yang tinggi.
Pekali pemindahan haba juga memainkan peranan penting dalam menentukan kecekapan
turbin. Semakin tinggi nilai pekali, olakan yang lebih kuat akan berlaku seterusnya
menyebabkan kemerosotan kecekapan turbin.
vii
TABLE OF CONTENTS
CHAPTER
TITLE
TITLE PAGE
i
DECLARATION
ii
ACKNOWLEDGEMENT
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
ix
LIST OF FIGURES
x
LIST OF SYMBOLS
1
2
PAGE
xiv
INTRODUCTION
1
1.1 Background of study
1
1.2 Objectives
3
1.3 Problems Statement
3
1.4 Scope
4
1.5 Methodology
5
LITERATURE REVIEW
6
2.1
Introduction
6
2.2
Turbocharger Turbine Map
2.3 Heat Flow Path Analysis
10
17
viii
3
2.4 Non-Adiabatic Analysis For Turbocharger Turbine
20
2.5 Simulation On Turbine Side
22
ANALYSIS OF RESULTS
26
3.1 Model Simplification
26
3.1.1 One-Dimensional Model
27
3.1.2 Two-Dimensional Model
29
3.2 Three-Dimensional Analysis
33
3.2.1 Grid Independent Study and
Boundary Condition
4
36
3.3 Corrected Mass Flow Analysis
39
3.4 Efficiency Analysis
41
3.5 Efficiency Analysis With Heat Loss
46
3.5.1 Analysis of Case 1
49
3.5.2 Analysis of Case 2
53
3.5.3 Analysis of Case 3
56
DISCUSSION
57
4.1 Introduction
57
4.2 Discussion on Temperature Distributions At
Outer Wall of Turbine’s Volute
57
4.3 Discussion on Temperature Distribution At
Turbine’s Volute Centerline
59
4.4 Discussion on Temperature Difference Between
Inner and Outer Turbine’s Wall
5
60
4.5 Discussion on Turbine’s Efficiency
63
CONCLUSION AND RECOMMENDATION
65
5.1 Conclusion
65
5.2 Recommendation
66
REFERENCES
Appendices A - C
67
69-72
ix
LIST OF TABLES
FIGURE NO.
TITLE
PAGE
3.1
Holset H3B nozzleless volute dimensions
33
3.2
Data extracted from (J. R. Serrano, 2007)
42
3.3
o
Air properties at 370 C
48
3.4
Air properties at 248oC
48
3.5
Case number with value of heat transfer coefficient
48
3.6
Temperature distribution (vector and contour plot)
51
3.7
Temperature distribution (vector and contour plot)
54
4.1
Comparison of temperature distribution along outer wall
58
4.2
Comparison of turbine’s centerline temperature
59
4.3
Comparison of temperature difference between inner and outer
turbine’s volute wall
60
x
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
Operation of a turbocharger
2
1.2
Methodology for heat distribution study on turbocharger turbine volute
5
2.1
Variation of non-dimensional density, pressure and temperature
to sea level
7
2.2
Heat losses around turbine volute
8
2.3
Overdrive condition
8
2.4
Typical turbine performance maps
11
2.5
Turbine performance map
12
2.6
Turbine map with mass flow parameter and turbine efficiency
for several PR range
2.7
15
Turbine efficiency for several PR at different turbine inlet
temperature
15
2.8
Turbine efficiency at different turbine’s rotational speed
16
2.9
a) H-s diagram
b) Turbine volute, pressure inlet-outlet location
17
2.10
Mechanism of heat transfer within turbocharger components
18
2.11
Heat flow path in turbocharger
19
2.12
Heat flow path in turbocharger
19
2.13
Measured and simulated turbine inlet/outlet temperature
21
2.14
Difference between inner and outer wall temperature based on
xi
specified turbine inlet temperature
22
2.15
Extend of modelling for certain types of turbulent models
25
2.16
Turbine with domains extension
25
3.1
a) Actual turbine area
b) Simplified model of turbine volute
3.2
27
a) Simplified model of turbine volute
b) Boundary condition at volute wall for 1-D analysis
28
3.3
Temperature difference from 1-D analysis
29
3.4
Boundary condition of simplified converging nozzle for 2-D
analysis
30
3.5
Boundary condition for 2-D analysis
31
3.6
Temperature contour from 2-D analysis
32
3.7
Temperature difference between inner and outer of turbine
volute wall
32
3.8
Holset H3B nozzleless volute
33
3.9
Model deviation
34
3.10
a) Turbine volute model in SOLIDWORKS
b) Meshed model of turbine volute in GAMBIT
35
3.11
Flow chart of simulation work
36
3.12
Grid independent study of corrected mass flow
37
3.13
Grid independent study of Reynolds number
37
3.14
Types of boundary condition for simulation
38
3.15
Simulation of corrected mass flow rate
39
3.16
Comparison of non-dimensional corrected mass flow rate
40
3.17
Inlet and outlet temperature at certain pressure ratio
41
3.18
Deviation of turbine actual power with isentropic power
43
3.19
Turbine’s adiabatic efficiency
43
3.20
Comparison of adiabatic efficiency
44
3.21
Non-dimensional efficiency versus pressure ratio
44
3.22
Non-dimensional efficiency versus non-dimensional mass
flow rate
45
xii
3.23
Air flow around turbine’s volute
47
3.24
Azimuth angle around turbine’s volute
49
3.25
Temperature vector with actual grid
50
3.26
Temperature distribution at different pressure ratio
50
3.27
Temperature distributions along turbine volute centreline
52
3.28
Temperature difference between inner and outer wall
52
3.29
Turbine’s non-adiabatic efficiency
52
3.30
Temperature distribution at different pressure ratio
53
3.31
Temperature distributions along turbine’s volute
Centreline
55
3.32
Temperature difference between inner and outer wall
55
3.33
Turbine’s non-adiabatic efficiency
55
3.34
Turbine’s non-adiabatic efficiency
56
4.1
Difference of temperature between inner and outer turbine’s
volute wall with external ventilation and without external
4.2
ventilation
61
Comparison of efficiency for different cases
63
xiii
LIST OF APPENDIX
APPENDIX
TITLE
PAGE
A
Two-dimensional code in MATLAB
69
B
Simulation data for Case 1, 2 and 3
71
C
Sample calculation of heat transfer coefficient for Case 3
72
xiv
LIST OF SYMBOLS
A
-
turbine’s volute external area
Cp
-
air specific heat
hext
-
exhaust flow heat transfer coefficient
hamb
-
ambient heat transfer coefficent
k
-
ratio of specific heat
K
-
thermal conductivity
-
mass flow rate
•
m
•
m corr -
corrected mas flow rate
Pin
-
turbine inlet pressure
Pout
-
turbine outlet pressure
Pref
-
reference pressure
PR
-
pressure ratio
Qext
-
external heat loss
Qcond -
heat loss through conduction mode
Qconv -
heat loss through convection mode
Qrad
-
heat loss through radiation mode
Tin
-
turbine inlet temperature
Tout
-
turbine outlet temperature
Tinner
-
turbine inner wall temperature
Touter
-
turbine outer wall temperature
T∞
-
ambient temperature
xv
Tref
-
reference temperature
Vx
-
velocity in x-direction
Vy
-
velocity in y-direction
Vz
-
velocity in z-direction
Wact
-
actual turbine work
Wisen -
isentropic turbine work
ρ
-
air density
μ
-
air viscosity
η
-
turbine’s efficiency
CHAPTER
1
INTRODUCTION
1.1
Background of the study
Nowadays, demand on powerful engine has increased enormously due to the
ability of the engine to produce rapid acceleration. Power up engine is a method of
increasing engine power beyond the ability of normal stock engine. There are several
ways to power up engine such as, having bigger cylinder, which mean by increasing the
size of bore and stroke, supercharger and turbocharger. Some of these devices assist
engine to induce more air into intake manifold. Apparently, the least expensive, easy to
main yet producing good output to vehicle is by having a turbocharger.
By the aid of turbocharger, engine can produce more power at the same speed of
Naturally Aspirated (NA) engine. Technically speaking, turbocharger forcing more air
into combustion chamber thus, this will increase and improve volumetric efficiency
(Crouse and Anglin, 1993).
2
Figure 1.1
Operation of a turbocharger (Source:
http://conceptengine.tripod.com)
In turbocharger system as illustrated in Figure 1.1, there are two main parts,
which are compressor and turbine. Turbine acts as centrifugal air pump, which is driven
by exhaust gas while compressor induced air, compressed it and forced the air to
combustion chamber. Both of the parts are connected via main shaft, which is turned by
turbine by the flow of exhaust gas that strike turbine’s blade. The rotation speed of
turbine depends on the speed of high temperature exhaust flow and normally it can
achieve to more than hundred thousands RPM. Heat is distributed throughout the whole
turbocharger components due to different of temperature between parts. Some of the
heat loss through convection to ambient and some of the heat are conducted through
components. Heat losses will deteriorate turbocharger performance and specifically on
turbine side. Since turbine volute has larger area exposed to ambient, thus it acts as a
main source of heat loss.
3
The main purpose of this research is to study of the temperature and heat
distribution at turbocharger turbine’s volute. This study will be focused on the
temperature variation at the turbine volute. The investigation on heat flow throughout
turbocharger components is well studied in this project. The author has made several
literature reviews in this topic, which will be discussed in great details after this.
Consequently, the author will develop simplified model of turbine volute in onedimensional and two-dimensional and verified with experimental works. Furthermore, a
three-dimensional model is made which mimics the real process that occurs at turbine
volute. The analysis will be conducted by MATLAB and FLUENT.
1.2
Objective
To identify the effect of heat distribution and heat transfer within a turbine volute
that influences a turbocharger performance.
1.3
Problems Statement
The problem statements for this thesis are
a) Heat loss can be portrayed as lost of energy that can be utilized.
b) Heat loss due to heat transfer should be reduced or minimized to
obtain optimum work transfer.
c) Investigation or study of heat distribution is deemed necessary to
capture the phenomenon of heat transfer that occurs.
4
1.4
Scopes
The scopes for this thesis are
a) Initial analysis will be based on numerical calculation in MATLAB
b) Three-dimensional model will be created in FLUENT
c) Volute modelling is based on HOLSET H3B nozzle less volute
d) Only steady state simulation will be conducted
5
1.5
Methodology
Methodology that have been created is applied throughout this research on the
simulation model as showed in Figure 1.2:
Figure 1.2
Methodology for heat distribution study on turbocharger turbine
volute
CHAPTER
2
LITERATURE REVIEW
2.1
Introduction
The ability of turbocharger to produce extra boost or energy to vehicle’s engine
is an added value for an engine that equip with turbocharger. Utilizing the unwanted gas
(exhaust gas) can be considered as brilliant work. Without doubt, with recirculation of
exhaust gas, engine will be able to gain some additional power. Power can be produced
more, if we tend to fill more the mixture of air-fuel into combustion chamber. This kind
of forced flow of mixture is assisted by exhaust gas. Vehicle with same weight will
possess different power to weight ratio if one of the vehicle equip with turbocharger.
The needs of turbocharger can be seen significantly on heavy vehicle that travel
up hills. Travelling through hills area (high altitude) requires engine than can overcome
vehicle rolling resistance and more importantly, gradient resistance. Gradient resistance
tend to create additional load based on hill gradient. This kind of load will burden
vehicle’s engine. Furthermore pressure, air density and temperature are decreased
inversely proportional with hill’s altitude as illustrated in Figure 2.1. With lack of air
7
density present during cruising along hill, its quite difficult for an engine to breathe.
However, at this point, one could see the importance of turbocharger when it could give
additional power by meant of forcing air into combustion cylinder thus, increasing air
density. With the aid of turbocharger, eventhough a vehicle is used under lack of air
density condition, the engine still can be running effectively as compared to naturally
aspirated engine.
Figure 2.1
Variation of non-dimensional density, pressure and temperature to sea
level (Source: www.wikipedia.com)
In turbocharger, heat is the main key factor that effect its performance since the
working fluid can hit up to thousand Kelvin (F. Westin, 2004). Turbine volute is the
biggest area exposed to high temperature however, the thickness of the volute is very
thin. As a result, heat is discharged through turbine volute thus affecting turbine’s
performance.
8
Heat is an energy that can be used which can be transformed in many ways. In
turbocharger turbine, heat loss can deteriorate its performance. Energy in turbine is
calculated based on the temperature of inlet and outlet of the turbine but within that,
there is heat loss occurring at turbine volute that creates massive reduction of turbine
efficiency.
Heat loss in turbocharger can be separated into two categories, namely internal
and external heat transfer (N. Baines et. al, 2009). Internal heat transfer can be describe
as heat loss through internal part of components such through bearing, shaft and through
compressor side while external heat transfer is heat loss through turbine volute. Heat
loss through turbine volute is more significant due to large area that is exposed to
ambient. Heat loss by convection and radiation are dominant around turbine volute and
heat loss by conduction is minimal. The heat loss via three medium of heat transfer
(convection, radiation and conduction) is illustrated in Figure 2.2.
Figure 2.2
Heat losses around turbine volute (Source: F. Westin, 2004)
Main heat loss occurs before exhaust gas strike turbine’s blade or upstream of
turbine rotor (J R Serrano et. al, 2010). The high temperature of exhaust gas that flows in
turbine volute will decrease until it reaches turbine’s outlet. Thus turbine inlet will be the
highest temperature at turbine volute. Moreover, the temperature of exhaust gas that
9
flows into turbine volute, is very high which ranging from 500-1200K as compared to
turbine outlet and with this range of temperature (at turbine inlet) more heat loss occurs
at inlet rather than the outlet of turbine. A turbine that operates at higher-pressure ratio
(PR) promotes influx of high speed of exhaust gas with high temperature. Severe heat
loss that occurs at turbine is something that is inevitable. Heat loss via convection
through turbine volute dominates the total heat loss of turbine system as illustrated in
Figure 2.3. It can be seen that, heat loss via convection mode depends on engine speed.
Thus, information of heat loss is vital during justification of turbine maps. Failure to
include heat loss will cause underestimation or overestimation of turbine isentropic
efficiency and inaccurate estimation of turbine power (J. R. Serrano et. al, 2010).
Figure 2.3
Mode of heat loss at turbine (Source: F. Westin, 2004)
Turbocharger is designed in such a way that it can cope with heat transfer but,
the capability is only approximately 30% (internal heat transfer) of the total heat loss
(N. Baines, 2009). Approximately one third of the total heat loss is taken care by
lubrication oil, which is located between turbine and compressor. Eventhough internal
heat transfer is absorbed by lubrication oil, but there is still heat loss that reaches the
compressor. Heat from turbine that flows by the mean of conduction will deteriorate
10
compressor efficiency (A. Romagnoli et. al, 2009) and (D. Bohn et. al, 2005). The
remaining 70% of heat loss is lost through surroundings/ambient (M. Commerais et. al,
2009). Heat loss through surroundings by heat convection through turbine volute is
dominant and there is no device or system that compensate this heat loss.
Reduction of pressure and temperature along turbine’s volute is converted as an
output of turbine’s power. However, analysis made by turbocharger manufacturers only
take into account pressure and temperature drop along turbine volute without take into
consideration external heat loss via turbine volute for turbine’s energy properties (power
and efficiency). It is quite difficult to justify actual heat loss since there are many
parameters effecting turbochargers performance on actual condition. Contradiction of
turbine power possibly exists between data from turbine maps given by turbocharger
manufacturer and data from actual turbine operation on engine.
2.2
Turbocharger Turbine Map
Predicted output of turbine is given based on turbine map. Turbine maps contains
output of turbine based on throttle opening, mass flow rate and the value of parameters
are depends on the turbocharger manufacturer geometry. The performance
characteristics of turbine or turbine map typically are displayed in term of efficiency and
mass flow rate with varying pressure ratio on a steady flow rig (M Tancrez et. al, 2011).
The graph that illustrated in the turbine map is made based on adiabatic conditions as
portrayed in Figure 2.4 and Figure 2.5. Thus the results will slightly deviate from real
time situation because there is no heat transfer effect is taken into account (adiabatic
condition).
11
Turbine map gives the information about the pressure drop in turbine and
turbine’s efficiency. Pressure drop along turbine volute is namely as pressure ratio (PR)
in the turbine map and this parameter is strongly related to mass flow of air (exhaust
gas) that flow into turbine. At higher PR, more air flows into turbine and this shows
turbine possesses more power at higher PR due to high influx of exhaust gas. Mass flow
inside turbine volute depends on cross section area of volute. The smaller cross section,
the higher the mass flow will be thus, resulting to a higher boots pressure or higher PR.
Figure 2.4
Typical turbine performance maps (Source: Watson and Janoda, 1982)
12
Figure 2.5
Turbine performance map. Colour indicates constant speed (Source:
Fredrik Westin, 2005)
Parameter such as corrected mass flow is used in typical turbine characteristics to
demonstrate the strong relationship with PR furthermore it is a dimensionless parameter
to calculate swallowing capacity of turbine (A. Romagnoli et. al, 2011). Characteristics
or parameters should be independent from any variable, thus corrected mass flow is
introduced in turbine characteristics in order to avoid dependency of turbine map on
temperature and pressure upstream of turbine (M. Tancrez et. al,2011). The equation of
corrected mass flow is depicted in Equation (2.1) below:
PR =
•
•
m corr =
m
Pin
Pout
Tin
Tref
Pin
Pref
(2.1)
(2.2)
13
Equation (2.1) shows corrected mass flow for typical turbocharger characteristics which
•
m refers to actual turbine’s mass flow rate, while Tref and Pref are ambient temperature
and pressure which have value of 298K and 101.3kPa respectively.
Usually, turbine maps come along efficiency maps that plotted turbine’s
efficiency based on certain engine revolution per-minute (RPM) and certain PR.
Turbine’s acquire power from rapid flow of exhaust gas that turned turbine’s rotor.
Exhaust gas flow with high speed and high temperature thus, the high temperature of the
exhaust gas absorbed by turbine volute. Major heat loss occurs at turbine’s volute due to
high temperature gradient present between turbine volute and ambient and this results to
high heat transfer or heat loss from turbine volute to the environment. Turbine efficiency
will suffer and deviates from the actual performance as stated in turbine’s performance
map.
Typical turbine’s efficiency is calculated based on ratio of isentropic works that
assuming reversible process without friction and heat interaction within the control
volume with actual works calculated based on the difference of temperature between
turbine inlet and outlet temperature. The equations involve during calculation of
turbine’s efficiency are given as follows:
•
Wact = m c p (Tin − Tout )
Tout ⎛ Pout ⎞
=⎜
⎟
Tin ⎝ Pin ⎠
(2.3)
k−1
k
⎛P ⎞
Tout = Tin ⎜ out ⎟
⎝ Pin ⎠
k−1
k
(2.4)
•
Wact = m c p (Tin − Tout )
(2.5)
14
Substituting Equation (2.3) into Equation (2.4) gives:
Wisen
⎡P ⎤
= m c pTin (1− ⎢ out ⎥
⎣ Pin ⎦
•
k−1
k
)
(2.6)
By definition of efficiency :
ηturbine =
ηturbine =
ηturbine
Wact
Wisen
(Tin − Tout )
k −1
k
⎡P ⎤
Tin (1 − ⎢ out ⎥ )
⎣ Pin ⎦
(Tin − Tout )
=
k −1
⎡ 1 ⎤
Tin (1 − ⎢ ⎥ ) k
⎣ PR ⎦
(2.7)
Thus, the final equation for turbine efficiency is given by Equation (2.7). From
the derivation above, there is no heat interaction taken into account. The calculation is
based on adiabatic manner thus, actual turbine’s performance deviates from actual
condition. Turbine’s efficiency is plotted over certain range of PR, as illustrated in
Figure 2.6 and 2.7 (typical turbine efficiency map).
15
Figure 2.6
Turbine map with mass flow parameter and turbine efficiency for several
PR range (Source: H. Hiereth and P. Prenniger, 2007)
Figure 2.7
Turbine efficiency for several PR at different turbine inlet temperature
(Source: S. Shaaban, 2004)
16
At higher turbine’s rotational speed, turbine will achieve better efficiency since
more exhaust gas flow into turbine’s volute thus increasing mass flow and kinetic energy
however, heat loss also playing vital role in turbine’s efficiency. The higher turbine
rotational speed the higher the efficiency will be. However, at certain point heat loss is
dominant and will cause significant drop in efficiency as portrayed in Figure 2.8.
Turbine is tested at specified turbine inlet temperature while the turbine rotational speed
is varied and approximately 10% drop of efficiency can be seen on turbine’s efficiency
map (Figure 2.8).
Figure 2.8
Turbine efficiency at different turbine’s rotational speed (Source: S.
Shaaban, 2004)
The assumption that is not taken into account, the heat transfer can be clearly
shown by h-s (Entalphy Vs Entropy) diagram as depicts in Figure 2.9 (a). From the
figure, it is crystal clear that actual energy (Δhreal ) produce is less than energy produce
by the assumptions of adiabatic (Δhideal ) .
17
(a)
Figure 2.9
2.3
(b)
(a) H-s diagram, (b) Turbine volute, Pressure inlet-outlet location
Heat Flow Path Analysis
In turbocharger system, heat input is given by the flow of exhaust gas through
turbine and then it dissipates throughout the system. Heat flow path is essential in this
study because it gives the information how the heat is spread throughout the system
whether the heat is transferred by the mean of conduction, convection or radiation. Since
turbocharger has complex shape, it is quite difficult to justify heat transfer mechanism
that lies in the system. However, S. Shaaban (2004) has made classification of heat
transfer between components in turbocharger aided with diagram as illustrated in Figure
2.10 and written as follows:
i.
Heat transfer from turbine to the compressor
ii.
Heat transfer from turbine to the oil
iii.
Heat transfer from turbine to the ambient
iv.
Heat transfer from turbine to the cooling water (for water cooled
turbochargers)
v.
Heat transfer from compressor to the ambient
18
vi.
Heat transfer between the compressor and the oil
vii.
Heat transfer between the turbocharger and the engine block
Figure 2.10
Mechanism of heat transfer within turbocharger components (Source : S
Shaaban, 2004)
There are different types of heat loss experienced by turbine. The whole 3 modes
of heat loss, which are convection, conduction and radiation, involved in turbine’s heat
loss. These two types of loss that occur in turbine are heat loss via internal heat transfer
and external heat transfer. Both heat transfer contribute to deterioration of turbine’s
efficiency. However, heat transfer via external heat loss plays significant role on the
efficiency (S. Shaaban, 2004). External heat transfer is lumped together as made by (N.
Baines et al., 2009). They assume external heat transfer is the sum of heat transfer
through conduction, convection and radiation as written in Equation (2.8).
Qext = Qcond + Qconv + Qrad
T −T
Qext = KA s ∞ + hA(Ts − T∞ ) + εσ A(Ts4 − T∞4 )
dx
(2.8)
19
Two-dimensional heat flow path starting from turbine and ends at compressor is
made by (N. Baines et al., 2009) and (M. Commerais et. al, 2009). Both work show
general agreement as portrayed in Figure 2.11 and 2.12 respectively.
Figure 2.11
Figure 2.12
Heat flow path in tuborcharger (Source : N. Baines et. al, 2009)
Heat flow path in tuborcharger (Source : M. Commerais et. al, 2009)
From both diagrams, general conclusion of heat flow can be made which is heat
flow through turbine and lost through conduction via volute and convection to
surroundings. Hence, heat is loss through conduction between turbine and compressor
and some of the heat is absorbed by lubrication oil and some of it flows through
compressor. By apprehending the method of heat transfer, thus accurate model that is
20
suitable in modelling heat loss or temperature distribution within turbine volute can be
made.
2.4
Non-Adiabatic Analysis For Turbocharger Turbine
As discussed earlier, predicted power or work given by turbine map is based on
turbocharger manufacturer and adiabatic analysis, which deviates from real turbocharger
operation. Heat transfer effect that excludes in the analysis had made the predicted result
far beyond actual data set.
Experimental and simulation work carried by (F. Westin et. al, 2004) to
determine heat loss within turbocharger turbine. The authors made a one-dimensional
model using GT Power to predict the condition of turbine inlet and outlet temperature.
However, the model cannot take into account the effect of heat loss from turbine volute.
As a result the turbine exit temperature deviates far beyond experimental analysis as
illustrated in Figure 2.13. Based on the figure below, the deviation is around 50K. This
analysis shows that there is a need to investigate the heat loss and incorporated the effect
to the current turbine map to obtain the true value of power output or efficiency of
turbocharger turbine.
21
Figure 2.13
Measured and simulated turbine inlet/outlet temperature (Source : F.
Westin et. al, 2004)
Since heat loss through turbine volute (external heat transfer) taken up 70% of
total heat transfer, experimental analysis is made by (N. Baines et. al, 2009) to study the
temperature distribution of turbine volute. The author investigates the difference of
temperature between inner and outer wall of turbine volute based on several value of
turbine inlet temperature (TIT). Based on the analysis, it can be seen that turbine inlet
temperature is the main parameters that will affect the heat loss. The higher turbine inlet
temperature will cause large difference between inlet and outlet turbine wall temperature
as illustrated in Figure 2.14.
22
Figure 2.14
Difference between inner and outer wall temperature based on specified
turbine inlet temperature (Source: N. Baines et. al, 2009)
Scatter data obtain by N. Baines is difficult to interpret. Due to there are some
negative values for difference in temperature. However the data obtained can be used to
calculate heat flux rejected from turbine volute to ambient. Given difference in
temperature, by using heat conduction equation, heat rejected can be calculated. Due to
the thin volute thickness, small changes in temperature will result to high heat loss.
2.5
Simulation on Turbine Side
Simulation was carried out to evaluate and mimic the real condition with the aid
of several assumptions to ease the simulation. Assumptions made are based on capability
of computing and degree of accuracy of the answer. The higher the degree of accuracy,
the longer the simulation time will be taken. However, simulation is just a tool gives
23
answer or result based on model that user creates. It is strongly recommended that
simulation results must be compared with established data or experimental works for its
validity.
CFD or Computational Fluid Dynamic is numerical analysis that solves fluid
flow and heat physics. CFD solve partial differential equation (PDE) and ordinary
differential equation (ODE) that represent the nature of flow physics. Physics of flow are
illustrated in the form of equation, which are in terms of conservation of mass Equation
(2.9), conservation of momentum Equation (2.10) and conservation of energy Equation
(2.11) respectively.
∂ρ ∂
∂
∂
+ ( ρ v x ) + ( ρ v y ) + ( ρ vz ) = 0
∂t ∂x
∂y
∂z
⎛ ∂2 v x ∂2 v x ∂2 v x ⎞
∂vx
∂vx
∂vx
∂vx
1 ∂P
+ vx
+ vy
+ vz
=−
+υ⎜ 2 + 2 + 2 ⎟
∂t
∂x
∂y
∂z
ρ ∂x
∂y ∂z⎠
⎝ ∂x
⎛ ∂2T ∂2T ∂2T ⎞
⎛ ∂T
∂T
∂T
∂T ⎞
ρC p ⎜ + v x
+ vy
+ vz
⎟ = k⎜ 2 + 2 + 2 ⎟+φ
∂x
∂y
∂z ⎠
∂y
∂z ⎠
⎝ ∂t
⎝ ∂x
(2.9)
(2.10)
(2.11)
All the three equations stated above are the basic equation that involved in CFD
analysis. Additional terms are included such as turbulent dissipation, if turbulent mode is
taken into account in the simulation. Turbulence takes place in flow with high Reynolds
number which above 4000 (www.pipeflow.co.uk).
Solving turbulence problems is more than difficult. However, with appropriate
assumptions made in turbulent model, turbulence phenomenon can be simulated.
24
Turbulence appears to be dominant over all flow phenomena and with successful
modeling technique of turbulence, numerical quality of the simulation will significantly
increase (J. Sodja, 2007).
Solving flow phenomenon numerically, involved problems geometry and grid
generation, physical model boundary condition, solver (simulation model) and post
processing the analyzed data. Selection of solver is crucial since different solver or
model suitable for certain condition and geometry. J. Sodja, 2007 has listed several
model for turbulent which are Direct Numerical Simulation (DNS), Large Eddy
Simulations (LES) and Reynolds Averaged Navier Stokes (RANS). DNS is the most
accurate method to use since it resolved all the turbulent equation as illustrated in Fig.
2.15. However, it emerged to be the most difficult method while LES model is time
consuming. RANS model such as k-ε is less demanding than LES. Furthermore, k-ε
model has computing time approximately only 5% of LES model (J. Sodja, 2007).
Simulation of turbocharger turbine is done at turbulent mode, due to the high
flow of exhaust gases into turbine’s volute (R. Cavalcanti, 2011) and (G. Descombes et
al., 2002). Appropriate turbulent model selection is deemed necessary since the working
geometry is complicated and k-ε model is chosen for simulation due to its traditional
choice of the automotive industry (R. Cavalcanti, 2011). During evaluating turbine’s
characteristics, the turbine model need to be modified to obtain more stabilize numerical
solution as illustrated in Figure 2.16.
25
Figure 2.15
Extend of modeling for certain types of turbulent models (Source: J.
Sodja, 2007)
Figure 2.16
Turbine with domains extensions (Source: R. Cavalcanti, 2011)
CHAPTER
3
ANALYSIS OF RESULTS
3.1
Model Simplification
To simplify the problems, several assumptions are made regarding volute
modelling. Area inside volute is assumed as converging nozzle. The nozzle area will
mimic the area of actual turbine from inlet through its outlet. Outlet area of turbine is the
area around inner circumference of turbine volute or the region at maximum radius of
turbine’s rotor as illustrated in Figure 3.1 (a) while Figure 3.1 (b) shows simplified
model of turbine volute.
In actual turbine volute, flow inside is discharged along inner circumference
from initial start of turbine inlet. However, in turbine volute simplification model, the
flow discharged at the end exit of converging nozzle. To make the simplification model
to be more realistic, the exit area of nozzle is made to be equivalence to outlet area of
turbine.
27
(a)
Figure 3.1
(b)
(a) Actual turbine area,
(b) Simplified model of turbine volute
(Converging nozzle)
3.1.1
One-Dimensional Model
From the simplified model of turbine volute, by considering wall of converging
nozzle, temperature of inner wall and outer wall can be calculated. Furthermore the
difference between inner and outer wall also can be justified and compared with
experimental works by (N. Baines et. al, 2009).
Given the boundary condition, which is convection for both inner and outer wall,
with convection of exhaust gas flow at inner wall and convection of ambient air at outer
wall as illustrated in Figure 3.2 (b). The governing equation are given as follow:
Qext = hext A(Text − Tinlet ) =
kA
(Tinlet − Touter ) = hamb A(Touter − T∞ )
Δx
hext A(Text − Tinlet ) =
kA
(Tinlet − Touter )
Δx
kA
(Tinlet − Touter ) = hamb A(Touter − T∞ )
Δx
(3.1)
(3.2)
(3.3)
28
With two equations, which are Equation (3.1) and (3.2) having two unknowns,
temperature of inner wall (Tinlet) and temperature of outer wall (Touter) can be calculated.
By forming 2 by 2 matrix in MATLAB, and difference between Tinlet and Touter are
calculated. In this analysis, assuming heat convection coefficient hext (h1) which is heat
transfer coefficient for exhaust flow and hamb (h2) which is heat transfer coefficient for
ambient condition which are 250 W/m2 K and 25 W/m2 K (Typical value of convection
heat transfer coefficient for free convection of gasses and forced convection of gasses)
respectively. While thermal conductivity of turbine volute is equal to 45 W/m K.
(a)
Figure 3.2
(b)
(a) Simplified model of turbine volute, (b) Boundary condition at volute
wall for 1-D analysis
The results from the analysis are compared with experimental works by (N.
Baines et. al, 2009). From the analysis, temperature difference between inner and outer
wall is increased when turbine inlet temperature is increased as portrayed in Figure 3.3.
Work by (N. Baines et. al, 2009) shows that the temperature difference is within the
range of 1-7 K, which portrayed in Figure 2.14 while in this one –dimensional analysis,
the temperature difference is 1.25-1.33 K.
29
Figure 3.3
3.1.2
Temperature difference from one-dimensional analysis
Two-Dimensional Model
Given the converging nozzle model as simplification model, this model can be
further extended for two-dimensional analysis with several assumptions. The nozzle
circumference is ‘open’ thus, it can be assumed as 2-D flat plate. With Dirichlet and
Neumann (at side and up/below surface respectively) boundary conditions, the
temperature variation within the flat plate (Nozzle) can be determined. Due to thickness
of the nozzle is thin, it can be assume that, turbine inlet temperature and turbine outlet
temperature that obtained from experimental value, to be the temperature (Dirichlet B.C)
for the flat surface at right and left side respectively as illustrated in Figure 3.4.
30
Figure 3.4
Boundary conditions of simplified converging nozzle for twodimensional analysis
By using heat conduction equation, temperature of inner and outer wall can be
calculated. However, to model the two-dimensional plate, the general heat conduction
equation is discretized to be able for the equation to be code in MATLAB environment.
The general heat conduction for two-dimensional are:
•
d 2T d 2T q 1 dT
+
+ =
dx 2 dy 2 k α dt
(3.4)
Assuming no heat generation and steady state condition, Equation (3.4) can be
simplified to:
d 2T d 2T
+
=0
dx 2 dy 2
(3.5)
31
By Equation (3.5), discretization is made for coding purposes as depicts as below:
Ti+1, j − 2Ti,i + Ti−1, j Ti, j+1 − 2Ti, j + Ti, j−1
+
=0
Δx 2
Δy 2
(Δy)2
(Ti+1, j + Ti−1, j ) + (Ti, j+1 + Ti, j−1 )
(Δx)2
(Δy)2
2
+2
(Δx)2
(3.6)
(3.7)
Equation (3.7) is used for modeling of nozzle in two-dimensional analysis. Fifty
nodes are made along X-direction while 15 nodes are made along Y-direction. Figure
3.5 shows boundary condition for two-dimensional analysis.
y
x
Figure 3.5
Boundary condition for two-dimensional analysis
With two-dimensional analysis, temperature contour of volute plate (by
thickness) can be seen. From the analysis, turbine inlet temperature is 1175oC, turbine
outlet temperature is 1027.5oC and flow temperature (exhaust gas temperature) is taken
32
by taking the average value of turbine inlet and turbine outlet temperature, which is
1101oC. The contour of temperature is illustrated in Figure 3.6, note that the temperature
is in oC (degree Celsius). From the analysis, difference of temperature between inner and
outer wall can be calculated. Figure 3.7 shows temperature difference between inner and
outer wall and from the figure it can be seen that the difference is ranging from 1-3oC
which still within the range of experimental data from (N. Baines et. al, 2009).
Figure 3.6
Figure 3.7
Temperature contour from 2-D analysis
Temperature difference between inner and outer of turbine volute wall
33
3.2
Three Dimensional Analysis
Actual flow physics can be model more accurately in 3D since the working fluid
can flow in x, y and z direction in Cartesian grid. Turbine’s volute model is drawn based
on the given geometry for Holset H3B turbocharger as illustrated in Figure 3.8. Table
3.1 shows the dimension of the turbine geometry at every turbine Azimuth angle and
every section.
Figure 3.8
Holset H3B nozzleless volute (Source: S. Rajoo, 2007)
34
Holset H3B nozzleless volute dimensions (Source: S. Rajoo, 2007)
Table 3.1
Section
Azimuth Angle
Radius (mm)
Area (mm2)
D
0
73.94
2568.65
E
30
71.59
2284.91
F
60
70.24
2094.54
G
90
68.79
1896.55
H
120
67.44
1711.36
J
150
65.89
1517.81
K
180
64.29
1328.28
L
210
62.49
1126.56
M
240
60.54
923.51
N
270
58.39
718.91
P
300
55.84
502.91
Q
330
52.79
284.68
R
360
49.04
86.47
Based on the dimension given, turbine volute is drawn using SOLIDWORKS.
Minor modification has been made to suit meshing criteria in GAMBIT. The model
creates using SOLIDWORKS slightly deviates from actual model, which the deviation
shows in Figure 3.9. Model drawn in SOLIDWORKS and meshed in GAMBIT is
illustrated in Figure 3.10 (a) and (b) respectively.
35
Figure 3.9
Model deviation
(a)
Figure 3.10
(b)
(a) Turbine volute model in SOLIDWORKS, (b) Meshed model of
turbine volute in GAMBIT
Simulation works in CFD require user to verify few parameters such as grid
study, convergence of equation and the validity of the results from simulation. To
achieve good results of simulation, one should know the physical or the flow geometry
of the problem in order to select appropriate model (laminar or turbulent). Figure 3.11
shows the flow work in simulation.
36
Figure 3.11
3.2.1
Flow chart of simulation work
Grid Independent Study and Boundary Conditions
The main purpose of grid independence study is to evaluate simulation results
from being dependent with number of node. Corrected mass flow parameters and
Reynolds number are calculated and plotted over range of number of nodes from sixty
two thousands nodes to two hundred and thirty thousands nodes as illustrated in Figure
3.12 and 3.13. From the analysis, 199’517 nodes are chosen for further simulation
analysis, which is based from grid independent study.
37
By referring to Figure 3.12 and 3.13, the parameters stabilize at two different
regions of nodes. Selecting higher region of node, and taking the average of the higher
region, is the node that is selected for further analysis. Utilizing more nodes will cause
longer computation time due to computer needs to resolve more grids. Time for
completing computation, depends on computing power.
Figure 3.12
Figure 3.13
Grid independent study of corrected mass flow
Grid independent study of Reynolds number
38
Since the value of pressure inlet and outlet of turbine’s volute in known from
pressure ratio, pressure inlet and pressure outlet boundary condition are used at inlet area
and outlet area respectively for simulation in FLUENT. Both boundaries carried inlet
and outlet temperature and pressure value with their respective pressure ratio. Boundary
condition for inlet and outlet temperature is obtained by experimental data from (F.
Westin et al., 2004) for analysis of corrected mass flow while for efficiency analysis,
experimental data from (J. R. Serrano, 2007) is utilized. To investigate the heat loss
along external turbine’s volute surface, convection boundary condition is applied
throughout the external surface as illustrated in Figure 3.14. During the simulation,
working fluid (gas) is assumed to be perfect gas (ideal gas), turbulent and in steady state
condition (G. Descombes et al., 2002).
Figure 3.14
Types of boundary condition for simulation
39
3.3
Corrected Mass Flow Analysis
Corrected mass flow is one of turbine parameters that reflect turbine
performance. It is a parameter that calculates the capability of turbine in swallowing
exhaust gas (A. Romagnoli et al., 2011). Different turbine geometry will have different
limit of swallowing capacity thus, corrected mass flow parameter will gives the limit of
exhaust gas swallowing capability.
•
•
m corr =
m
Tin
Tref
Pin
Pref
(3.7)
The parameter is calculated using Equation (3.7) and plotted over range of
pressure ratio. Tin and Pin refer to inlet temperature and inlet pressure of turbine volute
whilst Tref and Pref refer to 298K and 101.3kPa respectively. By keeping fixed value of
Tin which is 1175K data from (F. Westin et al., 2004) and by varying Pin based on
pressure ratio range (1.1 to 2.0), corrected mass flow is plotted against PR as portrayed
in Figure 3.15. Actual mass flow rate at certain pressure ratio is obtained by FLUENT
analysis, is used for calculating corrected mass flow.
Figure 3.15
Simulation of corrected mass flow rate
40
There are several papers that discussed with plotted graph of turbine corrected
mass flow rate. However the value of the mass flow is totally unidentical, because the
turbine model, geometry and test condition is different. Resolving on this issue, nondimensional corrected mass flow rate is introduced for every paper including simulation
model for comparing the trend of the result as portrayed in Figure 3.16.
Figure 3.16
Comparison of non-dimensional corrected mass flow rate
Figure 3.16 shows that simulation model act well by following the trend of
established data. Theoretically, at higher pressure ratio or higher pressure difference
between inlet and outlet, influx rate of exhaust gas is high. Thus, this promotes high
corrected mass flow at higher PR. Mass flow analysis does not take into account the
effect of heat loss, since the analysis only depending on inlet pressure, inlet temperature
and actual mass flow. In this analysis, only inlet pressure is varied accord with PR range.
41
3.4
Efficiency Analysis
For thermal analysis, different experimental data set is used. To obtain realistic
simulation for thermal analysis and furthermore will be translated in efficiency analysis,
data of turbine inlet temperature and outlet temperature at certain pressure ratio is
essential. (J. R. Serrano, 2007) gives the best data that can feed into simulation. In this
paper it has experimental data for turbine inlet/outlet temperature at certain PR.
However, the analysis is based on VGT with 10% opening. Table 3.1 shows the
extracted data from Figure 3.17 (J. R. Serrano experimental data). The grey dotted
represents inlet temperature while the white dotted represents outlet temperature.
Figure 3.17
Inlet and outlet temperature at certain pressure ratio (Source: J. R.
Serrano, 2007)
42
Table 3.2
Pressure
Data extracted from (J. R. Serrano, 2007)
Inlet temperature (K)
Ratio
Outlet temperature
∆T
(K)
1.9
845
758
87
2.0
850
751
99
2.1
851
742
109
2.2
855
738
117
2.3
850
734
116
2.5
849
730
119
2.7
849
728
121
Calculations of turbine power derive in the Equation (2.3) to (2.7) in Chapter 2.
Turbine’s actual work and isentropic work was first analyzed before translating it into
turbine’s efficiency. Figure 3.18 shows the difference between actual work and
isentropic work. Turbine’s efficiency is ratio of turbine’s actual power over isentropic
power, which is, depicts in Figure 3.19. Equation (2.5) is used to calculate turbine’s
actual power while Equation (2.6) is used to calculate turbine’s isentropic power. Both
powers are calculated based on data from Table 3.1 and mass flow value are obtained
from simulation.
43
Figure 3.18
Deviation of turbine actual power with isentropic power
Figure 3.19
Turbine’s adiabatic efficiency
The calculated efficiency is compared with establish data in order to verify the
results of simulation. However, established data have different value of efficiency. This
is due to different turbine’s geometry that is tested and different test condition used in
evaluating turbine’s efficiency. Figure 3.20 shows efficiency from simulation and
efficiency from several established data at certain range of pressure ratio.
44
Figure 3.20
Comparison of adiabatic efficiency
In order to investigate similarity between simulation work with established data,
non-dimensional efficiency and non-dimensional PR are used as portrayed in Figure
3.21. Different established data has different set of pressure ratio. They tested turbine at
different range of pressure ratio, however with the aid of non-dimensional efficiency and
non-dimensional pressure ratio, some degree of similarity can be found.
Figure 3.21
Non-dimensional efficiency versus non-dimensional pressure ratio
45
The peak of efficiency emerges to be at the middle of pressure ratio range.
Moving more or shifted towards higher pressure ratio, the efficiency lowered as compare
with efficiency at middle range of PR. Mass flow rate can also be used to plot efficiency
curve as shows in Figure 3.22. The peak of efficiency emerges to be at the center point
of the non-dimensional mass flow rate for both simulation work and efficiency given by
(J. Piers, 2008).
Figure 3.22
Non-dimensional efficiency versus non-dimensional mass flow rate
46
3.5
Efficiency Analysis With Heat Loss
Turbine is simulated with heat loss to mimic the real case condition. Heat
transfer through convection to ambient is dominant in turbine heat loss. Since there are
no concrete value or serious analysis carried out in determining appropriate heat transfer
coefficient for calculating heat loss through ambient, the heat transfer coefficient will be
choose based on range given by (Y. A. Cengel, 2011). In this analysis, 3 different values
of heat transfer coefficients are chosen for simulation and to observe the effect towards
turbine’s efficiency.
The range for air forced convection heat transfer coefficient is given in the range
of 25 - 250 W/m2 K. The worst case scenario is chosen from the range which is 250
W/m2 K (Case 1). In order to achieve heat loss through convection to ambient accounts
70% of total heat loss, the simulation model requires heat transfer coefficient of 2500
W/m2 K (Case 2). Since radiation made an appreciable contribution heat loss to ambient,
it is assumed that heat transfer coefficient for case 2, is the sum of heat transfer
coefficient for convection and radiation. This value is assumed to be the lumped value of
heat transfer coefficient for convection and radiation. Furthermore, with this value, total
heat loss obtained from simulation model approximately 68.7% on average.
For case 3, assuming air flowing through turbine’s volute at vehicle speed of 150
km/h as illustrated in Figure 3.23. From that speed, heat transfer coefficient is calculated
using Nusselt number correlation as shows in Equation (3.8). From the calculation, heat
transfer coefficient is found to be 105.486 W/m2 K.
Nu =
1
hL
= 0.037Re 0.8 Pr 3
k
(3.8)
47
Air flow around turbine’s volute
Figure 3.23
Ambient air condition is important because it will determine the air properties
that will be taken in calculating speed of air flow that flows along turbine volute. The
calculation based on Equation (3.8). For case of heat transfer coefficient of 250 W/m2 K
(Case 1), assuming Tamb (ambient temperature) is equal to 600C and average temperature
of turbine volute is 6800C while for the case of heat transfer coefficient of 2500 W/m2 K
(Case 2), the average turbine volute temperature is 4360C. Air properties that include in
convection heat transfer coefficient are based on average temperature between Tamb and
average temperature of turbine volute. The sample of calculation (for case 1) to
determine the appropriate temperature for air properties is given as follows:
Tamb + Tave _ vol
2
=
60 + 680
= 370o C
2
From the calculation above, air properties that are used for calculating heat
transfer coefficients is based on temperature of 370oC for heat transfer coefficient of 250
W/m2 K (Case 1) while for 2500 W/m2 K (Case 2), the temperature is 248oC. With that
temperature value, appropriate value air properties such as air density, specific heat,
thermal conductivity, dynamic viscosity and Prandtl number are calculated by mean of
interpolation using air table properties. Table 3.2 and 3.3 show air properties at 370oC
and 248oC respectively.
48
Table 3.3
Air properties at 370oC
Density
0.54956 (kg/m3)
Specific heat
1.0612 (kJ/kg K)
Thermal conductivity
0.048386 (W/m K)
Viscosity
3.165x10-5 (kg/m s)
Prandtl Number
0.69414
Table 3.4
Air properties at 248oC
Density
0.6746 (kg/m3)
Specific heat
1.033 (kJ/kg K)
Thermal conductivity
0.04104 (W/m K)
Viscosity
2.760x10-5 (kg/m s)
Prandtl Number
0.6946
In order for the region near turbine volute (ambient area) to possess heat transfer
coefficient of 250 W/m2 K (Case 1), forced air that flow across turbine volute must
possess speed around 390 km/h while for heat transfer coefficient of 2500 W/m2 K (Case
2) the speed of air flow must be around 3900 km/h. The forced air flow is calculated
using Equation 3.8. For case 3, assuming air flow along turbine’s volute at vehicle speed
of 150 km/h and with air properties of case 1, heat transfer coefficient of 105.486 W/m2
K is obtained by using Equation (3.8). Table 3.4 shows case number with their
respective value of heat transfer coefficient.
Table 3.5
Case number with value of heat transfer coefficient
Case 1
250 W/m2 K
Case 2
2500 W/m2 K
Case 3
105.486 W/m2 K
49
3.5.1
Analysis of Case 1
Temperature along outside surface of turbine volute is plotted over azimuth angle
o
from 0 to 300o by increment of 30o as illustrated in Figure 3.24. Temperature is plotted
based on certain PR to investigate the effect of PR towards heat loss. Figure 3.25 shows
temperature vector with its grid for a clear view of the flow direction. The black surface
in Figure 3.25 demonstrates the actual gird of the turbine volute while the red-orange
contour represents the temperature value. Figure 3.26 illustrated temperature distribution
along turbine volute for PR 1.9, 2.3 and 2.7. Distribution of temperature in three
dimensional (temperature vector and temperature contour) is illustrated in Table 3.6.
Figure 3.24
Azimuth angle around turbine’s volute
50
Figure 3.25
Temperature vector with actual grid (Grid in black colour)
Figure 3.26
Temperature distribution at different pressure ratio
51
Table 3.6
PR
Temperature distribution (vector and contour plot)
Temperature Vector
Temperature Contour
1.9
2.3
2.7
Temperature drop along turbine’s centerline is plotted over pressure ratio range.
It can bee seen that moving away from 0o of Azimuth angle, the drop of temperature is
steeper as illustrated in Figure 3.27.
Difference between inner and outer wall
temperature are plotted over range of pressure ratio as depicts in Figure 3.28.
Furthermore, turbine’s efficiency for Case 1 is plotted which is portrayed in Figure 3.29.
52
Figure 3.27
Figure 3.28
Temperature distributions along turbine’s volute centerline
Temperature difference between inner and outer wall
Figure 3.29
Turbine’s non-adiabatic efficiency for Case 1
53
3.5.2
Analysis of Case 2
Temperature along outside surface of turbine volute is plotted over azimuth angle
o
from 0 to 300o by increment of 30o. Temperature is plotted based on certain PR to
investigate the effect of PR towards heat loss. Figure 3.30 illustrated temperature
distribution along turbine volute for PR 1.9, 2.3 and 2.7. Distribution of temperature in
three dimensional (temperature vector and temperature contour) illustrated in Table 3.5.
Figure 3.30
Temperature distribution at different pressure ratio
Temperature drop along turbine’s centerline is plotted over pressure ratio range.
It can bee seen that moving away from 0o of Azimuth angle, the drop of temperature is
more steep as illustrated in Figure 3.31. Difference between inner and outer wall
temperature are plotted over range of pressure ratio as depicts in Figure 3.32.
Furthermore, turbine’s efficiency for case 1 is plotted which is portrayed in Figure 3.33.
54
Table 3.7
PR
1.9
2.3
2.7
Temperature distribution (vector and contour plot)
Temperature Vector
Temperature Contour
55
Figure 3.31
Temperature distributions along turbine’s volute centerline
Figure 3.32
Temperature difference between inner and outer wall
Figure 3.33
Turbine’s non-adiabatic efficiency for Case 2
56
3.5.3
Analysis of Case 3
Heat loss analysis with heat transfer coefficient of 105.486 W/m2 K is more
focused on turbine’s efficiency only, since the other temperature parameter trends are
same with Case 1 and Case 2. Figure 3.34 depicts turbine’s non-adiabatic efficiency
plot.
Figure 3.34
Turbine’s non-adiabatic efficiency for Case 3
CHAPTER 4
DISCUSSION
4.1
Introduction
This chapter mainly discussed the results of simulation that are carried out in
previous section. The results discussed mainly in thermal aspect based on the turbine
simulation.
4.2
Discussion on Temperature Distributions At Outer Wall of Turbine’s
Volute
Temperature at turbine’s outer wall is simulated based on Case 1 and Case 2.
Maximum temperature obtained from Case 1 and Case 2 are 700oC and 459oC
respectively and the comparisons of the temperature distribution between two cases are
illustrated in Table 4.1. From Table 4.1, it can bee seen that the higher the value of heat
transfer coefficient, the lower will be the volute wall temperature. This is due to high
58
forced convection that flows around turbine volute if the coefficient is higher and
resulted to more heat been carried away.
The higher the value of pressure ratio, the higher will be the value of temperature
distributions. At higher pressure ratio, influx of air to turbine’s volute is high, thus will
lead to high heat convection from the inside turbine’s surface to turbine wall. More heat
is absorbed by turbine’s wall at high pressure ratio. This is the reason why turbine volute
is hot at high pressure ratio as compared to lower pressure ratio.
Table 4.1
Comparison of temperature distribution along outer wall
Case 1
Case 2
59
4.3
Discussion on Temperature Distributions At Turbine’s Volute Centerline
Turbine’s centerline temperature is simulated based on Case 1 and Case 2.
Moving away from 0o of Azimuth angle, the temperature drop is steeper due to loss of
heat. Temperature drop represents energy is taken out from the control volume
(converting heat to power) or energy is lost. Table 4.2 shows comparison of temperature
drop along volute centerline at range azimuth angle (0o – 300o).
The temperature drop for both cases is almost similar. However, the final value
of temperature drop (at Azimuth angle of 300o) is different. The final temperature value
for Case 2 is slightly less than Case 1. This is due to more heat is rejected to ambient due
to high forced convection (high heat transfer coefficient).
Table 4.2
Case 1
Comparison of turbine’s centerline temperature
Case 2
60
4.4
Discussion on Temperature Difference Between Inner and Outer Turbine’s
Wall
Difference of temperature is calculated by subtracting inner wall temperature
with outer wall temperature. The difference of temperature for Case 2 is higher than
Case 1, which is within the range of 10 – 14oC while for Case 1, 4 – 5oC. Table 4.3
shows the comparison of difference between inner and outer turbine’s wall temperature.
Table 4.3
Comparison of temperature difference between inner and outer turbine’s
volute wall
Case 1
Case 2
From the analysis taken for case heat transfer coefficients equal to 250 W/m2 K
(Case 1), it can be can seen that increasing pressure ratio, will increase the temperature
of outer wall. When turbine volute sustains high temperature at high pressure ratio,
while ambient temperature remains the same, this will creates high gradient of
temperature region thus the rate of heat transfer will increase and reduce turbine’s
efficiency. This is the reason why turbine efficiency is lower at high pressure ratio. The
61
temperature difference is compared with experimental works by (N. Baines, 2009). The
experimental work shows that, difference of temperature between inner and outer wall is
increased if there is external forced convection flow around turbine volute, which is
illustrated in Figure 4.1. The higher the mass flow rate, the higher will be the
temperature difference and external ventilation (forced convection) is another factor that
caused significant increase in temperature difference.
Figure 4.1
Difference of temperature between inner and outer turbine ‘s volute wall
with external ventilation and without external ventilation (Source: N. Baines, 2009)
High pressure ratio gives high difference between inner and outer wall
temperature. Turbine’s efficiency will deteriorate at high pressure ratio due to high
temperature gradient as shows in Table 4.3. Heat conducted through turbine’s wall
increased due to increasing of turbine’s wall temperature difference and the heat loss can
be represented by Equation (4.1), which is a heat conduction equation.
qloss _ condc = −kA
dT
dx
(4.1)
62
From Equation (4.1), it can be seen that since turbine volute thickness is thin (dx),
difference in temperature (dT) plays significant role in turbine’s heat loss.
Based on Table 4.3, the lower Azimuth angle the higher will be the temperature
difference. At lower Azimuth angle, flow of gas inside turbine’s volute posses high
temperature due to less heat loss and less energy taken out from the flow. Since the flow
having high temperature at early stage of Azimuth angle while the ambient temperature
is still the same, this will creates high temperature gradient. Good agreement was found
based on the results which is main heat loss occur before exhaust gas strike turbine’s
blade or upstream of turbine rotor (J R Serrano et. al, 2010).
63
4.5
Discussion on Turbine’s Efficiency
Turbine effectiveness is calculated by dividing actual power with isentropic
power. The actual powers are analyzed with heat loss effect based on Case 1, 2 and 3.
Different cases have different value of efficiency. Figure 4.2 compares the efficiency for
different cases.
Figure 4.2
Comparison of efficiency for different cases
Adiabatic efficiency is the highest efficiency due to no heat loss or heat
interaction takes into account during its calculation and it served as benchmark for
turbine characteristics, which included in manufacturer turbine’s map. However the
efficiency is differ based on tested condition. Turbine operates at hostile environment
which is to be its actual operating condition, thus adiabatic efficiency will gives
information with certain degree of error.
64
The higher the value of heat convection coefficient, the lower will be the
efficiency. This is due to, the coefficient that represent how strong is the forced
convection occur along turbine volute. Stronger forced convection, will caused high
temperature gradient and since the volute thickness is thin, high temperature gradient
will cause more heat loss furthermore deteriorate turbine’s efficiency.
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
5.1
Conclusions
Conclusion is made based on several topics that are discussed in Chapter 4. The
analyses are made separately based on cases to observe the effect of heat transfer
towards turbine’s efficiency. Simulation is carried out using FLUENT which is to be the
commercial software for computational fluid dynamic problems.
Heat transfer that occurs in actual turbine’s operation is something that cannot be
neglected since it gives significant effect towards turbine’s efficiency. Turbine maps
given by turbocharger manufacturer is made by running the turbocharger in laboratory
condition or in turbocharger test benches (M. Tancrez et al., 2011).
External heat transfer or heat loss through turbine volute via convection and
radiation accounts 70% of the total heat loss is agreed by several authors. Simulation
from Case 2 predicts the heat loss approximately 68.7% on average. It was a good result.
66
However to come out with such value of coefficient it is quite generic assumption.
Convection heat transfer coefficient for forced air ranging from 25 – 250 W/m2 K, while
convection heat transfer coefficient for forced liquid, the value is above 2000 W/m2 K.
Thus, the coefficient for Case 2 only valid for forced liquid. However, since radiation
also plays significant role in turbine external heat loss, by assuming Case 2 coefficient is
a lumped value for both convection and radiation, the model still can be used to evaluate
the condition of 70% of total heat loss, is the heat loss through turbine’s volute that was
mentioned by several authors. The model made for Case 2 is for further investigation on
how heat transfer coefficient affecting turbine’s efficiency.
The key attribute that affecting turbine’s efficiency is temperature difference
between inner wall and outer turbine’s wall. Since turbine thickness is only few
millimeters (in the model is 5mm), small value of temperature difference would tend to
deteriorate turbine’s efficiency.
5.2
Recommendations
Proper investigation or experiment must be carried out in order to obtain
appropriate heat transfer coefficient that suit with actual operation condition of turbine.
Effect of radiation towards turbine’s heat loss must be include since that mode of heat
transfer also plays significant impact on turbine’s heat loss.
Carry out simulation in unsteady manner to investigate temperature distribution
along turbine’s volute with respect to time.
67
REFERENCES
A. Hajilouy, M. Rad and M. R. Sahhoseinni, (2009), Modelling of Twin-Entry Radial
Turbine Performance Charateristics Based on Experimental Investigation Under Full and
Partial Admission Conditions, Transaction B : Mechanical Engineering, Scientia Iranica
A.Romagnoli, Ricardo Martinez-Botas, (2009), Heat Transfer On A Turbocharger Under
Constant Load Points, Proceedings of ASME Turbo Expo 2009: Power for Land, Sea
and Air
A. Romagnoli, Ricardo Martinex-Botas and S. Rajoo, (2011), Steady state performance
evaluation of variable geometry twin-entry turbine, International Journal of Heat and
Fluid Flow.
Bohn D, Tom Heuer and Karsten Kusterer, (2005), Conjugate Flow and Heat Transfer
Investigation of a Turbo Charger, Journal of Engineering for Gas Turbines and Power
Copyright © 2005 by ASME
Crouse, Anglin, (1993), Automotive Mechanics, McGraw-Hill International Editions
Fredrik Westin, (2005), Simulation of turbocharged SI engines with focus on turbine, PhD
thesis, KTH
Fredrik Westin, Jorgen Rosenqvist and Hane-Erik Angstrom, (2004), Heat Losses From the
Turbine of a Turbocharged SI-Engine – Measurement and Simulation, SAE Technical
Paper Series
G. Descombes, J. F. Pichouron, F. Maroteaux, N. Moreno and J. Jullien, (2002), Simulation
of the Performance of a Variable Geometry Turbocharger for Diesel Engine Road
Propulsion, Int. J. Applied Thermodynamics
Hermann Hiereth and Peter Prenniger, (2007), Charging the Internal Combustion Engine,
Springer Verlag, Wien
J. Piers, T. Waumans, K. Liu and D. Reynaerts, (2008), Measurement of compressor and
turbine maps for an ultra-miniature gas turbine, Proceedings of PowerMEMS 2008 +
microEMS 2008, Sendai, Japan
J. R. Serrano, P. Olmeda, A. P´aez and F Vidal, (2010), An experimental procedure to
determine heat transfer properties of turbochargers, IOP PUBLISHING
MEASUREMENT SCIENCE AND TECHNOLOGY
Jurij Sodja, (2007), Turbulence models in CFD, University of Ljubljana, faculty for
mathematics and physics.
M. Tancrez, J. Galindo, C. Guardiaola, P. Fajardo and O. Varnier, (2011), Turbine adapted
maps for turbocharger engine matching, Experimental Thermal and Fluid Science 35
(146-153)
Mickaël Cormerais, Pascal Chesse, Jean-François Hetet, (2009), Turbocharger Heat Transfer
Modeling Under Steady and Transient Conditions”, International Journal of
Thermodynamics
Nick Baines, Karl D. Wygant and Antonis Dris, (2009), The Analysis Of Heat Transfer In
Automotive Turbocharger, Proceedings of ASME Turbo Expo 2009: Power for Land,
Sea and Air
N. Watson and M. S. Janota, (1982), Turbocharging the internal combustion engine, Wiley
Rafael Cavalcanti de Souza and Guenther Carlos Kriger Filho, (2011), Automotive
Turbocharger Radial Turbine CFD and Comparisonn to Gas Stand Data, SAE Technical
Paper Series, SAE BRASIL International Congress and Exhibition, Sao Paolo, Brasil
Srithar Rajoo, (2007), Variable Geometry-Active Control Turbocharge, PhD thesis, Imperial
College London
S. Kakac and Y. Yener, (1993), HEAT CONDUCTION – Third Edition, Taylor & Francis
Sameh Shaaban, (2004), Experimental investigation and extended simulation of turbocharger
non-adiabatic performance, PhD thesis, University Hannover
Yunus A. Cengel and Afshin J. Ghafar, (2011), Heat and Mass transfer Fundamentals and
Applications – Fourth Edition in SI units, McGraw Hill Higher Education
www.pipeflow.com.uk
69
APPENDIX A
TWO-DIMENSIONAL CODE IN MATLAB
clear all,clc
Length=0.6;
Height=5e-3;
maxX=50;
maxY=15;
x=maxX-1;
y=maxY-1;
Dy=Height/y;
Dx=Length/x;
h1=25;
h2=250;
k=45;
Tamb=85;
Tex=1101;
P=Dy/Dx;
xlength=[0:Dx:Length];
ylength=[0:Dy:Height];
T=zeros(maxY,maxX);
%Boundary Condition For Left Wall
for j=1:maxY
T(j,1)=1175;
end
%Boundary Condtion For Right Wall
for j=1:maxY
T(j,maxX)=1027.5;
end
Error=1;
while Error>=0.00001
To=T;
for j=2:y
for i=2:x
T(j,i)=(T(j+1,i)+T(j-1,i)+(P^2)*(T(j,i+1)+T(j,i1)))./(2*(P^2)+2);
end
end
%For Top Surface
for i=2:x
Tup=T(y,i)-((2*Dy*h1)./(k))*(T(maxY,i)-Tamb);
T(maxY,i)=(Tup+T(y,i)+(P^2)*(T(maxY,i+1)+T(maxY,i1)))./(2*(P^2)+2);
end
%For Lower Surface
for i=2:x
Tdown=T(2,i)+((2*Dy*h2)./(k))*(Tex-T(1,i));
70
T(1,i)=(T(2,i)+Tdown+(P^2)*(T(1,i+1)+T(1,i-1)))./(2*(P^2)+2);
end
%Error
Res=T-To;
Error=max(max(Res))
end
T
figure
contourf(xlength,ylength,T,20)
%plot(xlength,T(m
71
APPENDIX B
SIMULATION DATA FOR CASE 1,2 AND 3
Actual
Heat
loss
(Total
heat
loss)
16.511
16.710
17.122
18.413
22.834
30.494
38.493
PR
Tin
Tout
∆T
Actual
Power
Isentropic
Power
Power
at
case 1
Power
at
case 2
1.9
2.0
2.1
2.2
2.3
2.5
2.7
845
850
851
855
850
849
849
758
751
742
738
734
730
728
87
99
109
117
116
119
121
33.866
40.663
46.919
52.639
54.125
60.118
65.074
50.377
57.373
64.041
71.052
76.959
90.612
103.567
28.643
35.338
41.523
47.134
48.632
54.556
59.440
20.633
26.978
32.798
37.931
39.266
44.697
49.085
PR
Tin
Tout
∆T
Actual
Power
Isentropic
Power
Power
at
case 3
1.9
2.0
2.1
2.2
2.3
2.5
2.7
845
850
851
855
850
849
849
758
751
742
738
734
730
728
87
99
109
117
116
119
121
33.866
40.663
46.919
52.639
54.125
60.118
65.074
50.377
57.373
64.041
71.052
76.959
90.612
103.567
28.643
35.338
41.523
47.134
48.632
54.556
59.440
Heat
loss
for
case
1
Heat
loss
for
case 2
%
loss
case
1
%
loss
case
2
5.223
5.325
5.396
5.505
5.493
5.562
5.634
13.233
13.685
14.121
14.708
14.859
15.421
15.989
31.6
31.9
31.5
29.9
42.8
18.2
14.6
80.1
81.9
82.5
79.8
65.1
50.6
41.5
Actual
Heat
loss
(Total
heat
loss)
16.511
16.710
17.122
18.413
22.834
30.494
38.493
Heat
loss
for
case 3
%
loss
case
3
2.721
2.761
2.783
2.822
2.806
2.821
2.841
16.5
16.5
16.3
15.3
12.3
9.3
7.4
72
APPENDIX C
SAMPLE CALCULATION OF HEAT TRANSFER COEFFICEINT FOR CASE 3
Assuming air properties is same as Case 1, which is:
Table 3.2
Air properties at 370oC
Density
0.54956 (kg/m3)
Specific heat
1.0612 (kJ/kg K)
Thermal conductivity
0.048386 (W/m K)
Viscosity
3.165x10-5 (kg/m s)
Prandtl Number
0.69414
Vehicle is travelling at the speed of 150 km/h and assuming speed of air that flowing
along turbine volute is the same as vehicle speed which 150 km/h or 41.67 m/s. Using
Equation (3.8)
Nu =
Re =
1
hL
= 0.037Re 0.8 Pr 3
k
ρ vD (0.54986)(41.67)(0.21)
=
= 151944.22
(3.165×10 −5 )
μ
1
h(0.21)
= 0.037(151944.22)0.8 (0.69414) 3
(0.048386)
h = 105.486W / m 2 K