Aerothermodynamics and Operation of Turbine
System under Unsteady Pulsating Flow
MASSACHUSETTS INSTITUTE
OF TECHNOLOLGY
by
Jinwook Lee
JUN 23 2015
B.S., Seoul National University (2013)
LIBRARIES
Submitted to the Department of Aeronautics and Astronautics
in partial fulfillment of the requirements for the degree of
Master of Science in Aeronautics and Astronautics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
® Massachusetts Institute of Technology 2015. All rights reserved.
Signature redacted
A u th o r ................................................................
Denartment of Aeronautics and Astronautics
Signature redacted
May 15, 2015
...................
Certified by
Signature redacted
C ertified by
Choon S. Tan
Senior Research Engineer
Thesis Supervisor
. ..........................
Borislav T. Sirakov
Manager, Aerodynamics Science, W&A COE
Honeywell Turbo Technologies
Signature redacted
Thesis Supervisor
Accepted by ..............
....
Paulo C. Lozano
Associate Professor of Aeronautics and Astronautics
Chair, Graduate Program Committee
2
Aerothermodynamics and Operation of Turbine System under
Unsteady Pulsating Flow
by
Jinwook Lee
Submitted to the Department of Aeronautics and Astronautics
on May 15, 2015, in partial fulfillment of the
requirements for the degree of
Master of Science in Aeronautics and Astronautics
Abstract
An assessment of a turbine system operating under highly pulsating flow environment
typically found in vehicular turbochargers is made to: identify the key operating
parameters, enable the formulation of a reduced order model, delineate the sources of
loss and suggest strategies for performance improvement. The turbine system consists
of a scroll-volute followed by a turbine wheel and then a diffuser. The assessment
includes calculating unsteady three-dimensional flow in the turbine system followed
by in-depth interrogation complemented with flow modeling. The key findings are
(1) The flow mechanisms behind the turbine wheel performance, the diffuser loss and
the wastegate port loss appear locally quasi-steady such that we can characterize the
performance of the components based on a series of steady calculations subjected
to varying inlet conditions reflecting the inlet flow pulsation; (2) the operation of
scroll-volute and the diffuser pressure recovery can be adequately determined using
a quasi-one-dimensional unsteady flow model; (3) A significant fraction of the loss
that is not from skin frictions occurs downstream of turbine wheel exit (18%pts out
of 34%pts in Peak Torque and 20%pts out of 56%pts in Turbo Initial Transient based
on cycle loss debit); (4) The condition of maximum power extraction on unsteady
pulsating environment can be approximated with a simple modeling of volute storage
effect. A physically consistent definition of ideal power that elucidates the role of
unsteadiness in an unsteady turbine system is derived; it informs one on what the
extractable power is compared to what it could be for an ideal system. Finally the
findings are used to define the required attributes of methodology for estimating
efficiency with a specified uncertainty bandwidth.
Thesis Supervisor: Choon S. Tan
Title: Senior Research Engineer
Thesis Supervisor: Borislav T. Sirakov
Title: Manager, Aerodynamics Science, W&A COE
3
Honeywell Turbo Technologies
4
Acknowledgments
First and foremost, I would like to sincerely thank my advisor, Dr. Choon S. Tan,
for all his patience, guidance, and enlightening insight throughout my research and
learning at MIT. I can assert, without any hesitance, that I would have achieved
literally nothing at MIT without him. I also would like to thank Professor Edward
M. Greitzer for being a friendly consultant from time to time through my experience
at Gas Turbine Laboratory.
And, I thank Samsung Foundation of Culture and Honeywell Turbo Technology
for their merciful support over my research. I especially thank Dr. Borislav T. Sirakov
and Dr. Hong-Sik Im from Honeywell Turbo Technology for their critical advice and
affection on my research.
Also, I will never forget all my GTL friends! Especially, I would like to thank,
once again, our forever-admin (eventually to be Dr.) Andras L. Kiss for his noble
sacrifice to resurrect GTL cluster from ashes from time to time. No one can dare to
dispute that GTL without him would have been definitely fruitless.
And, I cannot skip this person. Changhoon Oh. I thank him so much for being a
constant friend whom I can bother at any moment without worrying that the person
might kill me in return. I was fortunate enough to have him as a next-door neighbor
in building 31.
Actually, there is one more person. Hyosang Yoon. I am so glad that I have such
a great friend like him in AeroAstro. He was always the first one to come to me
whenever I was struggling with so many hardships. I really appreciate his help and
advice.
Finally, I deeply appreciate all my family - mom, dad, and my brother Sungwook
- for their ever lasting love and patience. I can hardly imagine that I could have ever
initiated this long journey to this foreign country without their endless support.
Thank you all.
5
6
Contents
1
Introduction
23
1.1
M otivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
1.2
Technical Background
. . . . . . . . . . . . . . . . . . . . . . . . . .
24
. . . . . . . . . . . . . . . . . . . . . . . . . . .
24
1.3
1.2.1
Turbocharger
1.2.2
Sources of Unsteadiness
1.2.3
Characterization of Unsteadiness
. . . . . . . . . . . . . . . .
27
1.2.4
Turbocharger versus Pulse Detonation Engine . . . . . . . . .
29
Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
1.3.1
Metric for Unsteady Turbine System Performance . . . . . . .
30
1.3.2
Timescale Analysis and Impact of Unsteadiness
31
1.3.3
Modeling of Turbine under Unsteady Pulsating Flow
1.3.4
. . . . . . . . . . . . . . . . . . . . .
. . . . . . . .
26
. . . . .
31
Flow Management Strategy
. . . . . . . . . . . . . . . . . . .
32
Research Questions and Objectives
. . . . . . . . . . . . . . . . . . .
32
1.4.1
Research Questions . . . . . . . . . . . . . . . . . . . . . . . .
32
1.4.2
Research Objectives
. . . . . . . . . . . . . . . . . . . . . . .
34
1.5
Summary of Key Results and Contributions . . . . . . . . . . . . . .
35
1.6
Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . .
36
1.4
2 Technical Approach
2.1
39
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
2.1.1
Temporal Discretization of Inlet Pulsation . . . . . . . . . . .
40
2.1.2
Categorization of Sub-Components . . . . . . . . . . . . . . .
41
2.1.3
Simplification: Characterization of Sub-Components . . . . . .
41
7
2.4
2.2.1
Integrating components into system . . .
. . . . . .
42
2.2.2
Flow Management Strategy
. . . . . . .
. . . . . .
43
2.2.3
Maximum Power Extraction Condition .
. . . . . .
43
Technical Details in Implementations . . . . . .
. . . . . .
43
2.3.1
CFD Simulation Specifications . . . . . .
. . . . . .
43
2.3.2
Metric for Unsteady System Performance
. . . . . .
47
. . . . . .
47
.
.
.
.
.
.
42
Sum m ary
. . . . . . . . . . . . . . . . . . . . .
49
3.1
Review of Steady Ideal Power . . . . . . . . . . . . . . . . . . . . .
49
3.2
Derivation of Quantitative Expression for Unsteady Ideal Power . .
51
3.2.1
Storage Rate Effect in Unsteady Flow System . . . . . . . .
53
3.2.2
Entropy Generation Rate and Loss . . . . . . . . . . . . . .
54
3.2.3
Approximation of Entropy Generation Term in the Expression
.
.
.
.
Metric for Unsteady System Performance
for Ideal Power . . . . . . . . . . . . . . . . . . . . . . . . .
56
A pplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.3.1
Metric for the Utility of Component Models . . . . . . . . .
57
3.3.2
E fficiency
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
3.3.3
Loss Categorization . . . . . . . . . . . . . . . . . . . . . . .
58
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
3.4
.
.
.
Component Models
61
Categorization of Component Models . . . . . . . . . . . . . . . . .
61
4.2
Quasi-steady Component Models
. . . . . . . . . . . . . . . . . . .
62
.
Wastegate Port Loss Model
. . . . . . . . . . . . . . . . . .
63
4.2.2
Turbine Wheel Performance Model . . . . . . . . . . . . . .
65
4.2.3
Diffuser Loss Model . . . . . . . . . . . . . . . . . . . . . . .
67
. . . . . . . . . . . . . . . . . . . . .
71
4.3.1
Volute M odel . . . . . . . . . . . . . . . . . . . . . . . . . .
72
4.3.2
D iffuser M odel
. . . . . . . . . . . . . . . . . . . . . . . . .
81
Unsteady Component Models
.
.
.
.
4.2.1
.
4.3
.
4.1
.
4
Sum m ary
.
3.3
.
.
3
. . . . . .
.
2.3
Synthesis . . . . . . . . . . . . . . . . . . . . . .
.
2.2
8
4.3.3
4.6
. . . . . . . . . . . . . . .
. . . . . . . . . . . . .
84
4.4.1
Volute to Turbine Interface Model . .
. . . . . . . . . . . . .
85
4.4.2
Turbine to Diffuser Interface Model .
. . . . . . . . . . . . .
86
Error from Locally Quasi-Steady Assumption
. . . . . . . . . . . . .
86
4.5.1
Assumption Error . . . . . . . . . . .
. . . . . . . . . . . . .
87
4.5.2
Interpolation Error . . . . . . . . . .
. . . . . . . . . . . . .
88
4.5.3
Normalized Interpolation Error . . .
. . . . . . . . . . . . .
89
Sum m ary . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . .
91
.
.
.
.
.
Interface Models
.
82
.
4.5
. . . . . . . . . . . . .
.
4.4
Radial Scroll Interaction Model
5 Loss Mechanisms and Potential for Improvement
..............................
93
Component Model Based Loss Mechanism Identification
94
5.1.2
Boundary Layer Loss Estimation
. . . . . . . . . . . .
95
5.1.3
Tip leakage flow estimation
. . . . . . . . . . . . . . .
95
.
5.1.1
Loss Categorization for Peak Torque and Turbo Initial Transient Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
5.2.1
Peak Torque . . . . . . . . . . . . . . . . . . . . . . . .
96
5.2.2
Turbo Initial Transient . . . . . . . . . . . . . . . . . .
96
.
Flow management for radial scroll interaction
. . . . . . . . .
97
5.4
Flow management for turbine wheel inflow angle mismatch . .
99
.
.
5.3
General Description . . . . . . . . . . . . . . . . . . . .
100
5.4.2
Ideal Variable Inlet Guide Vanes . . . . . . . . . . . . .
101
.
.
5.4.1
Sum m ary
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
5.5
6
.
.
5.2
Procedure .......
.
5.1
93
101
Maximum Power Extraction Condition and Proposed Multi-Tiered
CFD Approach
105
6.1
Maximum Power Extraction Condition . . . . . . . . . . . . . . . . .
105
6.2
Multi-Tiered CFD Approach . . . . . . . . . . . . . . . . . . . . . . .
108
6.2.1
Full Unsteady CFD . . . . . . . . . . . . . . . . . . . . . . . .
108
6.2.2
LQS (Locally Quasi-Steady) Approach . . . . . . . . . . . . .
108
9
. . . . . . . . . . . . . . . . .
109
6.2.4
Single Steady CFD at Maximum Power Extraction Condition
109
.
QS (Quasi-Steady) Approach
Limitations in Steady CFD Results . . . .
. . . . . . . . . . . . . .
112
6.4
Guideline for Selecting a Specific Approach
. . . . . . . . . . . . . .
113
6.5
Sum m ary
.
.
6.3
.
. . . . . . . . . . . . . . . . . .
Summary and Future Work
115
119
Summary
. . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
119
7.2
Key findings . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .
120
7.3
Recommendation for Future Work
.
7.1
.
7
6.2.3
121
A Frozen Rotor Interface
123
B Volute Inlet Mass Flow Fluctuation
127
10
List of Figures
1-1
2010 BMW 4.4 L Gasoline Wastegate Twinscroll Turbocharger . . . .
25
1-2
Twinscroll Type Turbocharger . . . . . . . . . . . . . . . . . . . . . .
26
2-1
Outline of the research . . . . . . . . . . . . . . . . . . . . . . . . . .
39
2-2
Inlet Pressure Ratio Boundary Condition . . . . . . . . . . . . . . . .
41
2-3
A Set of Steady Inlet Conditions Encompassing the Locus of Unsteady
Inlet Condition
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
2-4
Conceptual view
2-5
Turbine System Overview
. . . . . . . . . . . . . . . . . . . . . . . .
45
2-6
Turbine System Configuration . . . . . . . . . . . . . . . . . . . . . .
46
4-1
Categorization of Component Models . . . . . . . . . . . . . . . . . .
62
4-2
Wastegate port loss characterization . . . . . . . . . . . . . . . . . . .
64
4-3
Comparion of wastegate port loss model and unsteady CFD result . .
65
4-4
Turbine inflow angles . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
4-5
Inflow Angle Parameter Space . . . . . . . . . . . . . . . . . . . . . .
68
4-6
Comparion of turbine wheel performance model and unsteady CFD
resu lt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
4-7
System Instantaneous Efficiency . . . . . . . . . . . . . . . . . . . . .
70
4-8
Diffuser mixing loss modeling
. . . . . . . . . . . . . . . . . . . . . .
71
4-9
Comparion of diffuser loss model and unsteady CFD result . . . . . .
72
4-10 Volute modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
4-11 Quasi-1D Volute Model: Inlet 1 - Part 1/3 . . . . . . . . . . . . . . .
75
4-12 Quasi-1D Volute Model: Inlet 1 - Part 2/3 . . . . . . . . . . . . . . .
76
11
4-13 Quasi-1D Volute Model: Inlet 1 - Part 2/3 . . . . . . . . . . . . . . .
77
4-14 Quasi-iD Volute Model: Inlet 2 - Part 1/3 . . . . . . . . . . . . . . .
78
4-15 Quasi-iD Volute Model: Inlet 2 - Part 2/3 . . . . . . . . . . . . . . .
79
4-16 Quasi-1D Volute Model: Inlet 2 - Part 3/3 . . . . . . . . . . . . . . .
80
4-17 Diffuser mixing modeling . . . . . . . . . . . . . . . . . . . . . . . . .
81
4-18 Diffuser mixing modeling. Region of consideration . . . . . . . . . . .
83
4-19 Quasi-1D Diffuser Model . . . . . . . . . . . . . . . . . . . . . . . . .
84
4-20 Radial scroll interaction from inlet 1 side scroll to Inlet 2 side scroll .
85
-
4-21 Radial scroll interaction from inlet 1 side scroll to Inlet 2 side scroll
datum locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
4-22 Comparison of radial scroll interaction model and unsteady CFD result 87
4-23 Steady Cases Encompassing Unsteady Case
. . . . . . . . . . . . . .
89
. . . . . . . . . . . . . . . . . .
90
4-25 Reduced number of steady cases . . . . . . . . . . . . . . . . . . . . .
91
4-24 Normalized Interpolation Resolution
4-26 Comparion of turbine wheel performance model and unsteady CFD
resu lt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
4-27 Comparion of turbine wheel performance model and unsteady CFD
resu lt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
5-1
Boundary Layer Loss Model in Volute . . . . . . . . . . . . . . . . . .
95
5-2
Cycle Loss Breakdown - Peak Torque . . . . . . . . . . . . . . . . . .
97
5-3
Cycle Loss Breakdown - Turbo Initial Transient . . . . . . . . . . . .
98
5-4
Measurement of radial scroll interaction from unsteady CFD on Turbo
Initial Transient operation . . . . . . . . . . . . . . . . . . . . . . . .
5-5
Leakage flow from inlet 2 side to inlet 1 side driven by a higher static
pressure side due to the configuration of the radial scroll
5-6
99
. . . . . . .
100
A suggestion on the radial scroll configuration for the reduction of
radial scroll interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5-7
Velocity triangle at peak power extraction point on two different operation s
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
12
5-8
Locus of Power vs Turbine Instantaneous Efficiency on Two Scenarios
103
5-9
Conceptual Ideal IGV Implementation
103
6-1
Quasi-1D Diffuser Model . . . . . . . . . . . . . . . . . . . . . . . . . 106
6-2
Power scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-3
Comparison between Unsteady CFD and QS Approach based on Tur-
. . . . . . . . . . . . . . . . .
108
bine Perform ance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6-4
Comparison between Unsteady CFD and QS Approach at Volute Inlet 117
A-1 Turbine Inlet Interface Environment . . . . . . . . . . . . . . . . . . . 124
A-2 Comparison of Frozen Rotor Interface and Rotating Impeller Interface 125
A-3 FFT of the Difference between the Two Interfaces . . . . . . . . . . . 125
B-1 Volute Inlet Mass Flow Fluctuation, Peak Torque Operation . . . . . 128
B-2 Volute Inlet Mass Flow Fluctuation, Turbo Initial Transient Operation 129
B-3 Inlet Mass Flow Fluctuation . . . . . . . . . . . . . . . . . . . . . . . 130
B-4 Decoupled Volute Model . . . . . . . . . . . . . . . . . . . . . . . . . 131
B-5 Impact of Area Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
B-6 Impact of Length Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 132
13
14
List of Tables
6.1
Comparison of Turbine Flow Environment between Unsteady CFD and
Single Steady CFD - MPE on Inlet 1 side pulse, Peak Torque . . . . .
6.2
Comparison of Turbine Flow Environment between Unsteady CFD and
Single Steady CFD - MPE on Inlet 2 side pulse, Peak Torque. . . . .
6.3
111
111
Comparison of Turbine Flow Environment between Unsteady CFD and
Single Steady CFD - MPE on Inlet 1 side pulse, Turbo Initial Transient 112
6.4
Comparison of Turbine Flow Environment between Unsteady CFD and
Single Steady CFD - MPE on Inlet 2 side pulse, Turbo Initial Transient 112
6.5
Comparison of Loss Categorization Result between Unsteady CFD and
Single Steady CFD - Cycle Averaged Quantity, Peak Torque . . . . .
6.6
113
Comparison of Loss Categorization Result between Unsteady CFD and
Single Steady CFD - Cycle Averaged Quantity, Turbo Initial Transient 113
6.7
Comparison of Loss Categorization Result between Unsteady CFD and
Single Steady CFD - Ideal Work Weighted Cycle Average Quantity,
Peak Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8
114
Comparison of Loss Categorization Result between Unsteady CFD and
Single Steady CFD - Ideal Work Weighted Cycle Average Quantity,
Turbo Initial Transient . . . . . . . . . . . . . . . . . . . . . . . . . . 114
15
16
Nomenclature
/tub
Turbine inflow incidence angle
6m Rankine vortex core radius at mixed out state
rh Mass flow rate
g"e'
Ster
Volumetric entropy generation rate
Volumetric thermal entropy generation rate
S'iSC Volumetric viscous entropy generation rate
SBL
Entropy generation rate from boundary layer dissipation
Sge,i Entropy generation rate from
Sref
ith
mechanism
Reference entropy generation rate
SRSI,12
Entropy generation rate due to radial scroll interaction from inlet 1 side to
inlet 2 side
SRSI,21
Entropy generation rate due to radial scroll interaction from inlet 2 side to
inlet 1 side
W Power
r Isentropic efficiency
-y Specific heat ratio
Fm Rankine vortex core strength at mixed out state
17
'tturb Turbine inflow axial angle
E
Non-dimensional energy storage rate
I Non-dimensional mass storage rate
S Non-dimensional entropy storage rate
Qm
Rankine vortex core angular speed at mixed out state
()
Time averaged quantity
m Mass averaged quantity
)
(
Mixing averaged quantity
b Any flow variable
p Static density
pt Stagnation density
T
Shear stress tensor
0 Cylindrical circumferential coordinate
O Momentum thickness
(
) Vector quantity
u Velocity
A Area
a Acoustic speed
Am Diffuser mixed out state area
Cd
Boundary layer dissipation coefficient
cp Constant pressure specific heat constant
18
Dtrb
Turbine outer diameter
E Quasi-iD Euler equation component matrix
e Specific energy
et Specific stagnation energy
Ext Quasi-1D Euler equation extraction matrix
H Quasi-1D Euler equation component matrix
h Specific enthalpy
ht Specific stagnation enthalpy
in Inlet
inj Injection
K12 Proportional constant for radial scroll interaction from inlet 1 side to inlet 2 side
K 21 Proportional constant for radial scroll interaction from inlet 2 side to inlet 1 side
Keff Effective pressure recovery coefficient for diffuse model
keff Effective thermal conductivity
L Length scale
out Outlet
p Static pressure
pa Atmospheric pressure
pt Stagnation pressure
peff Effective static pressure on diffuser side wall
Q
Quasi-1D Euler equation component matrix
19
R Air specific gas constant
r Cylindrical radial coordinate
r1 Inlet 1 pressure ratio
r2 Inlet 2 pressure ratio
Rm Diffuser mixed out state effective radius
Re Reynolds number
ref Reference state
S Quasi-1D Euler equation area distribution
s Specific entropy
s Streamline coordinate
T Static temperature
t Time
T Stagnation temperature
Tperiod
Period of pulsation
tre, Flow residence time
Trise Pulse rise time
turbln Turbine inlet
turbOut Turbine outlet
U Velocity scale
U,
a
12
ith
Cartesian velocity component
Characteristic velocity for radial scroll interaction from inlet 1 side to inlet 2 side
20
u2 1 Characteristic velocity for radial scroll interaction from inlet 2 side to inlet 1 side
Uturb
Turbine blade tip speed
V Velocity in absolute frame
V Volume
W Velocity in relative frame
w Specific work
x 1-dimensional coordinate
xj
jth
Cartesian coordinate
z Axial coordinate
21
Nature does not hesitate.1
'From an everyday conversation with Changhoon Oh, a next-door neighbor in Sloan Automotive
Laboratory.
22
Chapter 1
Introduction
1.1
Motivation
Unlike conventional turbomachineries, turbine stages for turbochargers and pulse detonation engines operate under time-varying inlet condition. The pulsating boundary
condition for both power extracting devices, originates from the inherent unsteadiness
of the energy source in the combustion stage: the reciprocating motion of cylinders
from the internal combustion engine for the turbocharger, and the periodically scheduled detonations in a cyclic array of tubes with explosives for the pulse detonation engine. Due to the unique unsteady boundary condition, the flow environment through
the turbine system - turbine wheel and the components in the immediate vicinity (i.e.
volute, wastegate, diffuser, etc.) - are changing with time continuously in a pulsating
manner. Therefore, the technical approach and the underlying philosophy for the
design of the turbine system can be distinctly different and thus must be adapted
accordingly.
However, a direct 3D unsteady computational approach targeted to understand
the aforementioned unsteady effect typically suffers from two major difficulties: (1)
high computational cost, (2) ineffective assessment of the result. 1 Firstly, the calculation time for unsteady simulation can easily surpass the steady case by a few
'The unsteady experiment also, of course, involves technical challenges such as the requirement
of high temporal resolution sensors, synchronization between apparatus and the corresponding additional expenditure. However, this thesis will focus on the computational aspects of the problem.
23
order of magnitude. Also, even if the numerical results are available, it may not be a
direct task to extract the essence of the flow physics underpinning the turbine system
unsteady operation.
The overall goal of the thesis is thus to formulate a simplified reduced-order framework to assess the turbine system performance /operation under pulsating environment. During the course of the work, physically consistent definition of ideal power
extractable from an unsteady system is derived and elaborated upon. By assessing the
difference between the ideal power and the real power, the potential for improvement
from the current system performance is quantified.
1.2
Technical Background
The focus of this thesis is on a representative turbine stage for vehicular turbochargers.
As such, we will first elaborate on the engineering and the technical aspects of a
representative turbocharger followed by a brief description of pulse detonation engine
for comparison (with vehicular turbocharger engine).
1.2.1
Turbocharger
In essence, the turbocharger (see Figure 1-1) is a gas turbine with a typical compressorcombustor-turbine configuration where combustion process is replaced by an internal
combustion engine. The role of turbocharger is to extract the otherwise wasted available energy from the main engine exhaust through a turbine and feed it back into the
combustion process in terms of the pressurized air via a compressor.
The benefit from the use of turbocharger is realized effectively through engine
downsizing. Compared to a naturally aspirated engine (without turbocharger) which
takes air from atmospheric pressure, a turbocharged engine can be smaller in size
since the intake air is pressurized (the air can accommodate the same mass of oxygen
required in a smaller volume). Pressurizing air leads to improved fuel economy via
reduced mechanical losses from engine downsizing. Further explanation with in-depth
24
. . .......
...
.....
......
..
...........
-'. _
:...
. .......
-- --
---___ -
....
....
....
.
.... ........
...
...
..............
..
..
.. ....
Figure 1-1: 2010 BMW 4.4 L Gasoline Wastegate Twinscroll Turbocharger [1] - Note
that the twinscroll turbine (left) is axially connected with the compressor (right). The
internal combustion engine (connected through volutes) is not shown on the figure
assessment of the matching of turbocharger to reciprocating internal combustion engine can be found in [2].
Specifically, twin scroll type turbine stage (see Figure 1-2) is considered in the
thesis. A twin scroll type turbine stage is a radial turbine stage with a volute that
keeps the inlet flow separated in two parallel channels until it reaches the volute
exit/discharge plane near the turbine wheel. The purpose of the volute is to take the
inlet flow from a pipe and distribute it circumferentially onto the turbine wheel. In
essence the twin scroll volute has two separate sub-volutes that discharge the flow into
a common flow path upstream of the radial turbine wheel. The flow coming from the
engine is kept separated in two channels for as far as possible downstream in order
to preserve the energy produced by the operating engine cylinders (so as to avoid
mixing between the high energy flow in the channels linked to the engine valves that
are opening, with the dead flow in the channels linked to the valves that are closed
at that moment of time). Each parallel sub-volute is connected directly to one half
of the engine cylinders (for example each sub-volute is connected to two cylinders on
a four cylinder engine).
25
A challenging aspect of the twin scroll type turbine is the twin scroll interaction.
Since one scroll is not operating (under low stagnation pressure) while the other
scroll is operating (under high stagnation pressure), the interaction of the two scrolls
cannot be avoided; that is, some of the high pressure side scroll flow leaks through
the other scroll with a negative impact on the turbine wheel performance. As such,
the natural questions to ask is whether there is a significant loss arising from twin
scroll interaction and, if there is, how we can mitigate it.
Figure 1-2: Twinscroll Type Turbocharger [1] - A cross section of the twin scroll is
shown with the turbine wheel. The compressor wheel is on the opposite side.
1.2.2
Sources of Unsteadiness
The sources of unsteadiness for turbocharger turbine stage can be categorized as
follows:
1. Engine operation change timescale (~0. 1 - 1Hz):
The timescale of the change in internal combustion engine operation due to any
changes in load or speed. It impacts the characteristics of the pulsation at inlet
(period, amplitude, pulse shape, etc.)
26
2. Inlet pulsation timescale (~10 - 100Hz):
The timescale associated with the inlet pulsation in stagnation pressure and
stagnation temperature
3. Blade pass timescale (~100 -1000Hz):
The timescale for a blade to travel through one blade pitch, the circumferential
distance between adjacent blades
Firstly, engine operation change can be treated on a quasi-steady basis without
any problem since it involves a sufficiently long timescale compared to the flow residence time through the turbine system. For the flow situations encountered here, the
unsteady effects associated with the rotating blade appears to be small compared to
that associated with the inlet pulsation; the rational for this is given in the analysis
presented in Appendix A.
By contrast, the level of impact of the unsteadiness from the inlet pulsation which
drives the system performance pulsation has to be assessed quantitatively. This assessment thus constitutes an important aspect of this thesis.
1.2.3
Characterization of Unsteadiness
Basic physical laws governing fluid flow (mass conservation, Newton's second law,
first/second law of thermodynamics) can generally be expressed as:
Ot
(1.1)
-
where b can be any of the flow variable (p, pa, pet, ps) pertaining to the corresponding
physical law. The physical laws as expressed in equation (1.1) allow one to know
what happens to the infinitesimal fluid particle that is convecting with the local flow
velocity. If the system of interest is approaching the steady state, the impact from
the first term in (1.1) reduces relative to the second term. As such, the ratio of the
first term (temporal term) to the second term (convective term) provides a measure
on the relative importance of unsteadiness. It is called reduced frequency
27
[3]:
Temporal term
Convective term
L/U
At
(1.2)
where L, U, and At correspond to characteristic length, characteristic velocity and
characteristic time respectively for the problem of interest. Thus, reduced frequency
can be interpreted as the flow residence time through the system over the unsteadiness
time scale. As it becomes larger compared to unity, the unsteadiness starts to play
an important role and vice versa.
For the case of turbocharger, the engine operation is such that it has a reduced
frequency of order of 0.1 or less and thus can be treated in a quasi-steady manner
as previously noted. However inlet pulsation has a reduced frequency of order of 1
or greater so that it is important to assess if the flow unsteadiness needs to be fully
accounted for. Here the characteristic time is chosen as the pulse rise time from the
given inlet pulsation since that is the time scale of significant change in the system
behavior.
A similar quantity is the compactness set by the time scale characterizing acoustic
propagation. For low Mach number flow (as is in the volute initial region, M < 0.3),
compactness scales as:
Compactness-
1
L/a
At
(1.3)
where L, a, and At correspond to characteristic length, characteristic acoustic speed
and characteristic time respectively for the problem of interest. As such, the compactness is the ratio of unsteady time scale (the inlet pulse rise time) to the time for
the acoustic wave to propagate through the device. For the turbocharger volute considered in the thesis, 1/compactness is around 0.5 implying that the acoustic speed
driven pressure wave effect would not be significant. As will be seen in Chapter 4,
the compactness effect is reflected as an almost quasi-steady behavior of stagnation
pressure through volute (spatially constant through volute on each time step).
28
1.2.4
Turbocharger versus Pulse Detonation Engine
The environment for turbine system operation on turbocharger is similar to the case
of pulse detonation engine (PDE). For both of the cases, the turbine wheel experiences unsteady pulsating flow; thus, the flow phenomenon through entire system is
inherently unsteady. In this section, we compare the two situations so as to determine
if the results from the current research on turbocharger are equally applicable to the
situation of pulse detonation engine.
Pulse Detonation Engine
PDE has long been investigated as a potential game-changer in air-breathing propulsion. There are two major traits: (1) Despite its simplicity, PDE can operate through
a broad range of flight speed from zero velocity to Mach 4; (2) PDE can have a higher
combustion efficiency as the detonation is effectively a constant-volume heat addition
process.
Compared to conventional gas turbine relying on deflagration (constant-
pressure heat addition), PDE can have higher thermodynamic efficiency.
There are various disciplines involved in the development of PDE. Some of the
typical topics are detonation science, structural endurance under extreme environment, and noise mitigation issues. An extensive review on the history, theory, and
design of PDE is provided in [4]. We will provide a brief discussion in a slightly
different topic; that is, the operation of turbine stage for Hybrid PDE [5].
Comparison of Flow Environment
Generally speaking, the situations for turbocharger and PDE are similar to each other
as both of them are under pulsating inlet condition. Also, for both of the cases, the
entire system should definitely be treated in an unsteady manner due to high reduced
frequency. However, there is a difference on the operation of turbine system. Unlike
the case of turbocharger, the flow phenomenon inside the turbine system might need to
be treated on an unsteady basis for PDE. This is because the pulsating environment
in PDE encounters a shock wave propagation through the system.
29
The traveling
shock wave between turbine blades might make it difficult to characterize the turbine
performance on a quasi-steady basis.
However, it is of interest to note that the leakage flow between each PDE combustor is also one of the loss mechanisms as in the twin scroll turbocharger [6]. Readers
interested in the interaction of turbine stage with PDE may refer to
([7],
[5], [81,
[9]). Specifically, experimental results on the hybrid radial turbine stage with PDE
is discussed in
1.3
[91.
Literature Review
A concise review of previous works on four specific topics (that are somewhat related) are given in this section: (1) Metric for unsteady turbine system performance;
(2) Timescale Analysis and Impact of Unsteadiness; (3) Modeling of Turbine under
Unsteady Pulsating Flow; (4) Flow Management Strategy.
1.3.1
Metric for Unsteady Turbine System Performance
There has been several publications that assessed the physical basis of computing the
performance of an unsteady turbine system based on the conventional metric for a
steady turbine system. Specifically, it is common to use the following expression to
estimate the ideal power from the turbine stage subjected to pulsating flow
([7],
[9],
[101, [11], [6]).
Wideal(t) -
in(t)CT,in(t)
I - (put)
(1.4)
\Pt, intM
Using the above expression can lead to an instantaneous efficiency above unity
or below zero ([12] and [10]). This calls into question on the utility and physical
consistency if turbine stage performance is estimated from equation (1.4) ([11] and
[6]).
Thus there is a need to formulate a physically consistent definition of ideal power
for highly unsteady turbine system where storage of mass, energy and entropy cannot
30
be neglected. Such a formulation is described in Chapter 3.
1.3.2
Timescale Analysis and Impact of Unsteadiness
There is a general consensus that volute constitutes an unsteady component where
filling and emptying effect cannot be neglected ([10], [13], [14], [15], [16]).
However, there is no consensus on whether the turbine wheel can be teated on a
quasi-steady basis. Although the turbine wheel is treated as a quasi-steady component
for the purpose of modeling ([10], [17], [12]), there have been research effort to trace
the source of unsteady effect in the turbine wheel [14]. It is noted that, however,
the reported discrepancy between unsteady turbine wheel and steady turbine wheel
situations can readily be corrected with phase lag adjustment.
1.3.3
Modeling of Turbine under Unsteady Pulsating Flow
One approach in Industry is to setup a steady CFD at a fictitious work-weighted average condition [18]. The ideal work is calculated based on the volute inlet stagnation
pressure and volute inlet stagnation temperature at each time step. And, the ideal
work weighted average of volute inlet stagnation pressure and volute inlet stagnation
temperature are utilized as boundary conditions for the steady CFD. The results from
steady CFD are then used to estimate the turbine system performance. However, the
utility of such a practice in Industry has not been rigorously assessed for its physical
consistency.
An alternative, still popular, approach to modeling of turbocharger turbine stage is
to treat volute as a mass capacitor and attach quasi-steady turbine wheel with turbine
wheel map lookup ([10], [17]). In this approach, the unsteady effect in the volute is
accounted for as a mass capacitor to provide time varying local boundary condition
to the turbine wheel. Once the turbine wheel boundary condition is identified, the
turbine wheel performance is estimated under quasi-steady assumption. Usually, the
pressure ratio across the turbine wheel is utilized as a variable parameter for the
quasi-steady performance lookup. The recent history on the modeling of turbine
31
wheel under pulsating flow is well summarized in [121.
1.3.4
Flow Management Strategy
The effectiveness of implementing guide vane at the inlet to the turbine wheel under
pulsation has been investigated in
[151.
They observed that the nozzles (guide vanes)
are effective in regulating the flow angle during pulsation. Also, the effect from the
cross-sectional shape of the volute (while maintaining the same area to radius ratio)
is assessed in [16]. It is observed that the smaller aspect ratio (more squarish crosssectional shape) case has higher efficiency during the cycle of pulsation. Lastly, The
effect of scroll interaction (leakage of flow from one scroll to the other scroll) and the
leakage flow mitigation strategy is reported in
1191,
but the report does not explain the
detailed procedure behind the redesign through which the leakage flow is effectively
alleviated.
1.4
Research Questions and Objectives
The overall goal of the current research is to determine the attributes of turbocharger
twin scroll turbine stage that would substantially improve efficient extraction of flow
energy by the turbine stage [1]. In that context, research questions and objectives
can be articulated as follows.
1.4.1
Research Questions
The research questions that need to be addressed are as follows:
Under unsteady pulsating flow,
1. What is the appropriate parameter to characterize the turbine wheel perforrriance?
Among many different ways of characterizing the steady turbine wheel performance (U/C, pressure ratio and corrected speed, corrected mass flow and pres32
sure ratio, etc.), it is not clear which one is the most effective way to quantify the
performance of turbine wheel extracting power from pulsating flow. Answering
this question will facilitate the procedure of turbine wheel characterization and
modeling.
2. What is the appropriatemetric for quantifying an unsteady turbine system performance?
The unsteady efficiency based on quasi-steady ideal power for a turbine system
operating in highly pulsating environment can be above unity or below zero
as reported in published literature ([12], [10]); thus one would infer such an
efficiency definition appears to yield confusing results. Therefore, we need a
definition of efficiency that is capable of informing us where we are compared
to where we could have been if things were ideal.
3. What is an effective way to address system level performance/operation where
the interactions between sub-components are fully accounted for?
We need not only the component by component performance but the system
performance where all the sub-components are interacting with each other by
sharing their time-resolved boundary conditions. As such, an effective way to
simulate system level performance behavior should be formulated apart from
using 3D unsteady computations at high cost.
4. What are the fundamental variables that incorporate twin scroll effect?
As reported in
[19],
twin scrolls are interacting with each other in a way that
is detrimental to turbine wheel performance. The turbine wheel inlet is not
presented with a typically simple uni-directional flow as is the case in a conventional turbine wheel. As such, we need to incorporate the non uni-directional
flow effect into the characterization of the turbine wheel performance.
33
1.4.2
Research Objectives
The key research objectives are:
Under unsteady pulsatingflow,
1. Identify loss mechanisms and potentialfor improvement
If all the losses except the loss from skin friction can be eliminated, this will
provide the potential for improvement that would be achievable from the current performance level. As such, the objective is to identify the potential for
improvement that exists in each individual sub-component.
2. Determine the maximum power extraction condition
For practical purpose, it is preferable to have one representative boundary condition which can be focused on during the early design phase. One rational
choice is the maximum power extraction condition. If this point can be determined prior to a detailed analysis involving 3D unsteady calculation, it can
serve as a preliminary design point.
3. Establish the required minimum level of modelling to obtain correct trends in
power extracted under given inlet pulsation
While high fidelity simulation that incorporates all tiers of complexity (fine
mesh for full geometry, time resolved calculation with sufficiently small time
step, accurate turbulence model, etc.) may yield accurate trend in unsteady
system performance, it is of interest to determine the minimum level of modeling that would reproduce the representative trend reflected in the high fidelity
simulation.
4. Formulate flow management strategy for performance improvement
Upon the successful accomplishment of the above objectives, a flow management
strategy can be developed to achieve a step improvement in the unsteady system
performance. Such a flow management strategy can either be passive or active.
34
1.5
Summary of Key Results and Contributions
The key findings from the research are summarized below:
1. Physical definition of unsteady efficiency
Unsteady turbine system performance is rigorously derived from basic physical principles of aerothermodynamics (mass conservation, first/second law of
thermodynamics). The newly derived metric shows that the hitherto used metric essentially neglects the mass, energy, and entropy storage and elucidates
the role of unsteadiness in ideal power. While both metrics are consistent for
steady system, the newly derived metric must be used under pulsating flow
environment.
2. Categorization of loss mechanisms
Loss mechanisms are categorized based on the impact on cycle loss debit. The
upper bound of system efficiency is obtained by asserting that the boundary
layer profile loss is the inherent loss mechanism (that cannot be eliminated
unless some treatment is made on the wall surface of the flow path). It is determined that the loss from the diffuser performance accounts for a significant
fraction of losses. Thus, the diffuser would be a focus for performance improvement. Also, the use of variable nozzle guide vane would yield an additional
performance enhancement of the turbine wheel by mitigating the inflow angle
mismatch.
3. Frameworkfor unsteady turbine system analysis and performance estimation
The turbine system is categorized into ID unsteady sub-components and 3D
quasi-steady sub-components depending on the reduced frequency of the corresponding component. While quasi-iD Euler equation is solved in ID unsteady
sub-components (volute/ diffuser), the quasi-steady sub-components (wastegate
port loss/turbine wheel performance/ diffuser loss) are characterized based on
steady CFD results: (1) Wastegate port loss scales with Mach number of the
main flow path with the proportional constant determined from steady CFD
35
results, (2) Turbine wheel performance is characterized by the inflow angles to
turbine blade using turbine efficiency map based on steady CFD results, and
(3) Diffuser loss is calculated based on a control volume analysis where the diffuser side wall static pressure is estimated based on steady CFD results. The
unsteady turbine system performance can be estimated if the sub-component
models are re-integrated into a system model.
1.6
Organization of Thesis
The central theme of this thesis is on the role of flow unsteadiness in the operation of
turbomachinery subjected to unsteady pulsating flow environment. With the physical
metric for unsteady turbine system performance rigorously defined, sub-component
characteristics are interrogated so as to setup a basis for a locally quasi-steady approach. The locally quasi-steady approach constitutes the second tier block among
the multi-tiered approach (full unsteady CFD, locally quasi-steady approach, quasisteady approach, and single steady CFD in the order of decreasing complexity) that
is summarized at the end of the thesis. Also, loss mechanisms are categorized based
on highest fidelity approach (full unsteady CFD) in order to quantify the potential
for improvement for each sub-component.
The organization of the thesis is as follows:
Chapter 1
Chapter 1 introduces the background of turbine stage operation under pulsating environment along with the present understanding from literature.
Chapter 2
Chapter 2 describes the approach to be implemented throughout the research. Technical details on the two unsteady operations (Peak Torque and Turbo Initial Transient)
and steady CFD formulations are presented.
36
Chapter 3
In chapter 3, we discuss the physical definition of unsteady turbine system performance from the basic physical laws (mass conservation, first/second law of thermodynamcis). This chapter resolves the lack of clarity and confusion arising from the
conventional definition of unsteady efficiency derived based on steady flow assumption used for unsteady turbine performance( 1.4).
Chapter 4
Chapter 4 delineates the detailed procedure of extracting characteristic flow physics
and incorporating them into models for cach sub-component. Unsteady components
and quasi-steady components are discussed separately.
Chapter 5
Chapter 5 describes the categorization of loss mechanisms in pulsating flow environment and the corresponding potential for improvement in each individual subcomponents. Specifically, the flow management strategies for radial scroll interaction
and turbine wheel inflow angle mismatch in Turbo Initial Transient operation are
suggested.
Chapter 6
Chapter 6 quantifies the conditions for maximum power extraction and the utility of
a steady CFD in conjunction with operation at maximum power extraction. Also, a
set of quantitative guidelines is presented as to how we can assess and interpret the
conditions for the applicability of each method from multi-tiered CFD approach.
Chapter 7
Chapter 7 summarizes the key findings from the research and propose recommendation for future work.
37
Appendix A
Appendix A explains what frozen rotor interface is. Also, the results from frozen
rotor interface and rotating impeller are compared and discussed for assessing the use
of frozen rotor interface on the current research.
Appendix B
Appendix B discusses the flow phenomena near the inlet of the volute: the mass flow
rate at inlet to the volute is fluctuating as the prescribed inlet stagnation pressure
decreases.
38
Chapter 2
Technical Approach
In this chapter, the formulation of the research framework is described. The idea is
conceptually visualized in Figure 2-1. We will analyze (decompose, simplify, characterize, and comprehend) the turbine system under unsteady pulsating flow and then
synthesize (reorganize, integrate, and manipulate) the system back again. The details
+
are discussed in the sections that follow.
Figure 2-1: Outline of the research - The full unsteady turbine system is conceptually and approximately decomposed into sub-components. Each sub-component is
characterized with either quasi-ID modeling or steady CFD.
39
2.1
Analysis
First, the system is divided into conceptual building-blocks. The decomposition process is conducted in two disparate dimensions. One is temporal dimension (separating
into different level of flow unsteadiness) and the other is spatial dimension (separating
into sub-components). The utility of such a framework is clarified in the followings.
Once the decomposition phase is completed, the building-blocks are simplified and
characterized. This will provide us with an in-depth comprehension of the role of each
conceptual block such that we can move forward toward the next step, or synthesis.
Lastly, we reorganize and reconstruct the system from the simplified blocks. The
procedure on this step will also provide an insight into formulating flow management
strategies.
2.1.1
Temporal Discretization of Inlet Pulsation
Let us consider the unsteady boundary condition to the system (Figure 2-2a). The
figure elucidates a representative pressure ratio boundary condition (stagnation pressure at volute inlet
/
static pressure at outlet) in an automotive turbocharger turbine
stage.
Since there are two inlets for twin scroll type turbine stage, two curves (blue and
red) are drawn on same plot to constitute the full boundary condition to the system.
And, the boundary condition is recast onto the 2D parameter space with inlet 1
pressure ratio on the abscissa and inlet 2 pressure ratio on the ordinate (Figure 2-2b).
On a conceptual basis, the steady flow cases can be determined corresponding to
each of the inlet pressure ratio (i.e. the discrete data on Figure 2-3); the set of discrete
points for steady flow can be chosen to populate the parameter space encompassing
the locus of unsteady inlet boundary condition (see Figure 2-3). This implies that the
inlet pulsation can be thought of as a decomposition of a set of steady inlet conditions
with corresponding pressure ratios.
40
4
-
3.6 -
Inlet I
r
r4
Inlet 2 . ....
3.6-.
0
0
0.2
0.4
0.6
TImeIPerIod
0.8
1
1
(a) Pressure Ratio vs. Time
-
126 -.
-.-.-.
2.5
1.6
26
Inlet I Pressure Ratio
36
4
(b) Inlet 1 and Inlet 2 Parameter Space
Figure 2-2: Inlet Pressure Ratio Boundary Condition - The pair of pressure ratios
(blue line and red line in Figure (a)) constitutes a locus (green line) on 2D parameter
space in Figure (b).
2.1.2
Categorization of Sub-Components
In this step, the turbine system is decomposed into individual subcomponents each
with a specific set of spatial and temporal characteristics. As such, it is mainly set by
the reduced frequency (1.2) as well as the functionality of each sub-component within
the context of the operation of turbine system. A way to do so is to seek out the
sub-components that can be characterized with a reduced order of complexity: either
in spatial dimension (from 3D to quasi-ID) or temporal dimension (from unsteady to
quasi-steady).
2.1.3
Simplification: Characterization of Sub-Components
Each sub-component is selected such that the choice can lead to a reduced order of
complexity. In this step of analysis, we characterize the performance of each subcomponent with key parameters on a physical basis. The characteristics of quasisteady sub-components will be extracted from a set of steady CFD whose inlet boundary condition correspond to each inlet pressure ratio on the locus of the temporal
variation in pulsation at inlet (see Figure 2-2a and 2-3)
41
. .....
........
4
0
3.6
000
0.-
00
.
Steady inlet Conditions
Unsteady Inlet Condition
-
*
0
-
00
12.6
*
0
0
1
---
0
0
1.6
3
2.5
2
Inlet I Pressure Ratio
3.6
4
Figure 2-3: A Set of Steady Inlet Conditions (discrete points) Encompassing the
Locus of Unsteady Inlet Condition (greent continuous line)
2.2
Synthesis
Section 2.1 describes the analysis of flow and performance aspects on individual subcomponents. In this section, the focus will be on synthesizing the results from the
analysis phase to accomplish the followings: (1) An effective modeling of the system;
(2) A suggestion on flow management strategy for performance improvement; (3) An
identification of maximum power extraction condition; and, (4) Guidelines for assessing turbine system operation based on a multi-tiered framework with the attended
simplifying approximations in each tier.
2.2.1
Integrating components into system
The components modeled in an appropriate manner are reintegrated for estimating
the full unsteady system performance without implementing the prohibitive full 3D
unsteady simulation. The result from this step will constitute the answer to the
question of required attributes for the minimum level of modeling of the turbine
system subjected to unsteady pulsating flow.
42
2.2.2
Flow Management Strategy
Ideally, the analysis on the characteristics of each sub-component would lead to means
of improving the system performance based on either active or passive flow management strategy. Suggestion on flow management strategy will be assessed in Chapter
5.
2.2.3
Maximum Power Extraction Condition
From the analysis and the synthesis of sub-components, a simplified condition for
maximum power extraction is identified. This in turn will allow one to implement
design assessments without the use of full unsteady 3D calculation.
2.3
Technical Details in Implementations
For the remainder of the chapter, the focus will be on implementing the proposed
framework of research. The approaches to the specifications of CFD simulation and
the metric for unsteady system performance are addressed.
2.3.1
CFD Simulation Specifications
Two types of numerical simulations, steady CFD and unsteady CFD, have been implemented to assess the characteristics of the entire turbine system as well as the
individual constituting sub-components.
General Setup of CFD
A conceptual view of the operation of turbine system within the context of vehicular
turbocharger engine is shown in Figure 2-4.
The pulsating source is the internal
combustion engine and the power utilization system is the compressor. The focus is
on the performance of Turbine System. Other blocks (Pulsating Source, Atmosphere,
and Power Utilization System) are treated as boundaries (inlet stagnation pressure,
inlet stagnation temperature, outlet static pressure, and power sink respectively).
43
...
....
.....
POWER
Figure 2-4: Conceptual view - The turbine system receives flow from a pulsating
source (internal combustion engine) and exhaust the flow to atmosphere. The extracted power from the turbine system is utilized in another system (compressor).
The mesh for the turbine system (Figure 2-5) is composed of 7.5 million finite
volume elements, on which RANS calculation is performed with commercial software
ANSYS CFX. Turbulence model to be used is k-w SST (Shear Stress Transport)
turbulence model with 5% initial turbulence intensity.
The turbine system consists of three sub-components (Figure 2-6): volute (where
the wastegate port is attached), turbine wheel, and diffuser. Flow passes through the
sub-components in sequence. The flow is taken either from inlet 1 or inlet 2 of the
volute and then accelerated to a state where it is circumferentially distributed into
turbine wheel. After the power is extracted, the flow is discharged to the diffuser
where the static pressure is recovered to match the given static pressure at outlet.
Also, it is noted that the length of the inlet pipes to the volute has been selected to
match the volume of a representative manifold and piping on the engine.
The location of the wastegate port is in the inset region denoted with purple rectangle in Figure 2-6. The purpose of the wastegate is to provide a direct path from the
volute to the diffuser for flow to bypass the turbine wheel so as to protect the turbine
wheel mechanically under over loading condition. Although the opening/closure of
wastegate will not be considered in the thesis (thus the wastegate will remain closed),
44
(a) Overview
(b) Mesh
Figure 2-5: Turbine System Overview - The geometric configuration in Figure (a) is
meshed as shown in Figure (b).
the existence of the extrude port impact the flow beneath it via local flow sudden
expansion.
It leads to local entropy generation and this will be modeled with an
appropriate wastegate port loss model to be described and presented in Chapter 4.
Setup of Unsteady CFD
Two different turbine system unsteady operations will be considered. One is "Peak
Torque" (Turbine Operating Point) and the other is "Turbo Initial Transient". Peak
Torque is the unsteady case where the speed of turbine wheel for turbocharger is
sufficiently accelerated to attain the operating speed. In contrast, Turbo Initial Transient is the unsteady case where the turbine wheel is still being accelerated toward
the operating point.
The delay (typically around the order of 10 pulsation periods) between Turbo
Initial Transient and Engine Rated Power is called turbo lag. And, it is desirable
to minimize the delay. As such, a good performance and the corresponding larger
torque and acceleration are the key design requirements on Turbo Initial Transient
operation. In Chapter 5, we will discuss the possibility of improvement via installing
variable inlet guide vanes on the Turbo Initial Transient operation.
For time-accurate unsteady computation, the time-resolved stagnation pressure
and stagnation temperature variation at volute inlet is enforced as inlet boundary
condition.
Also, atmospheric static pressure is imposed at diffuser exit as outlet
45
.......
....
VOLUTE
TURBINE
inlet 2
Outlet
Wastegate port 2
Inlet 1
Wastegate port 1
Figure 2-6: Turbine System Configuration - There are three components in the turbine
system: volute, turbine and diffuser. The flow passes through the components in
sequence. The flow is taken from inlet 1 or 2 of the volute and circumferentially
distributed into the turbine wheel. After power is extracted from the flow in the
turbine wheel, static pressure is recovered through the diffuser to match the ambient
pressure at the outlet.
boundary condition. However, the time-varying turbine wheel rotation speed will
not be considered since the variation is less than or order of 1% around the time
averaged value. Lastly the time step is chosen as 1/12 of blade passing time while
the interface model between the volute and the turbine wheel, and the turbine wheel
and the diffuser is of the frozen rotor type approximation.
Setup of Steady CFD
For each unsteady operations (Peak Torque and Turbo Initial Transient), a finite set
of steady CFD are implemented based on the boundary condition delineated in Figure
2-3.
'The ratio of the flow residence time through the turbine wheel to the turbine wheel rotation
period is smaller than unity (around 0.3). This suggests the use of frozen rotor type approximation.
Detailed argument about the utility of frozen rotor interface is discussed in Appendix A.
46
2.3.2
Metric for Unsteady System Performance
Once the numerical results are available from steady CFD and unsteady CFD, a
proper metric of unsteady system performance is needed to normalize the performance
of each sub-component or the system as a whole. Preferably, this step should be
conducted based on a physical basis in order to avoid non-physical results encountered
by previous researchers as described in subsection 1.3.1.
2.4
Summary
This chapter presents the technical approach that is to be applied to the problem of
interest: assessing the aerothermodynainics and operation of turbine wheel system
under unsteady pulsating flow. An in-depth analysis for the unsteady turbine system
is performed based on the framework presented in section 2.1. The flow characteristics
and performance of each sub-component is analyzed and modeled. The analysis step is
followed by integrating the sub-components for estimating the system performance.
The minimum level of modeling, flow management strategy, and maximum power
extraction condition will be addressed accordingly. Two unsteady operations will be
considered (Peak Torque and Turbo Initial Transient) and unsteady/steady CFD will
be implemented for each operation with representative boundary conditions. While
the boundary condition for unsteady CFD is straightforward, the boundary condition
for steady CFD has to be extracted from a given inlet pulsation.
47
48
Chapter 3
Metric for Unsteady System
Performance
There has been considerable confusion and controversy on defining and determining
the performance of a turbine system operating in a pulsating flow environment. In
this chapter, physical laws/principles are invoked to arrive at a physically consistent
framework for quantifying the turbine system performance under pulsating flow.
3.1
Review of Steady Ideal Power
Steady isentropic efficiency is first reviewed on a concise basis before extending its
utility to the unsteady flow situation. Most basic aerothermodynamics text would
provide the derivation of isentropic efficiency (for example,
[3]).
Three physical prin-
ciples for adiabatic system are used for the derivation:
Mass conservation:
min -
(3.1)
rout = 0
First Law of Thermodynamics:
outwhou =
(3.2)
hinhtin-
-
49
Second Law of Thermodynamics:
S"' dV = 0
minsin - moutsout +
(3.3)
Upon substituting the expression of entropy (in terms of temperature and pressure)
in equation (3.3), we obtain
-
RIn (Ptin
--
ou
In
TR
n
c
Pref ) )
(Tref
)
+
Tie
)
hn (cpln
(Pref ) ) +V
S"' dV
V'Ou
-
0
\
(3.4)
From Second Law of Thermodynamics (for adiabatic system),
V
Uin
- R
eIn
Tref }
+hout
\Pre5
(cP In (Teft
)
(cpin
'
'ndV =
)
J
- R In
t'Out
pref
(3.5)
By combining with the mass conservation (3.1),
-
hout
(cP In
T'""
- RIn
Tt,in
> 0
Ptin
Ptout )
(3.6)
)
)
IV
S'"ndV
Upon further manipulation,
t'Out
In
-routcp
yen
//V
\\ Tt,in"
Pt'out
(3.7)
Pt,in)
Therefore,
-Y-
1
(Pt
PtOut
(3.8)
in)
Tt,in}
Combining (3.1), (3.2), and (3.8) leads to,
(I
- T,
\
tti n
<;J nCT,in
<
I -
//\Pt,in
Pt'i
1
(3.9)
/
W = TiCpT,in
Finally, we obtain the familiar expression for ideal power as
Pt'Out
Pt,in
)
Wideal = 7hincpTt,in
50
^Y
(3.10)
;> 0
And, the familiar isentropic efficiency for steady system is recovered as,
W
I
t,i.t
1 -
___
(3.11)
77steady
Y
ptOut
Wideal
)
Pt,in
Note that the ideal power (or work) can also be determined using T-s diagram as
found in many texts (for example,
3.2
[3]).
Derivation of Quantitative Expression for Unsteady Ideal Power
Firstly, we need to clarify the utility of T-s diagram for unsteady system. The interpretation of unsteady flow process on the T-s diagram can be challenging. A T-s
diagram can be defined by tracing an arbitrary fluid particle from inlet to outlet for
steady system as the system does not change with time. However, in contrast, the
T-s diagram for each particle changes with time in unsteady system. Although the
entropy of each particle will still change in accordance with physical law, defining an
ideal work in an unsteady system is thus far more challenging on the T-s diagram.
Now, let's derive the expression for unsteady ideal power in an analogous way to
steady case. Again we start from basic physical principles.
Mass conservation:
Min - Mot -
(3.12)
pdV = 0
dtv
First Law of Thermodynamics:
-inhtin
-
+
petdV
(3.13)
=
Second Law of Thermodynamics:
psdV +
inSin - ToutSout -
51
$ jdV
0
(3.14)
Enforcing the definition of entropy on (3.14) yields
'__
c
out
n
)
\ref
-
-
( Tout
Tref
tout
- RIn
/
'___ - RIn
c pIn
r ii
SPre, ))
IpsdV +
"' dV = 0
(3.15)
From Second Law of Thermodynamics (for adiabatic system),
$",'dV
rin cp In Ti)
=-
R In
\Pref
Tref
)
Iv
-R In (
+ hout (cP In ( T refn
(3.16)
ret
+ d fpsdV > 0
dt jv
Upon further manipulations,
[
'in
oi t
t
TtOi"/(T
\ Tref/
Tref
min
Pt'out
Pref
- RIn
)
I
' dV =Th
gn
V
ln(
Pt in )
/ (Pref
+ +
J
mont
psdV > 0
(3.17)
In ((Ttut) /
iotc
",',dV =
vkTtin
(
-1
ront
\Tref
n
'"tout
1
\
Pt,in
(Pt/ n'
mot
\Pref
+
jpsdV
(3.18)
(Thont)~
Jv
" dV
=
rh0 tcin
Tt,2lmout
Pt,in
d
dt
Tef
T
J
psdV > 0
(3.19)
Pref
Thus,
Ptin
,
Tou >
Ting
,y-
Pt 'ou t
1
(Tt in/Trej)
I
-U
mt
-1
exp y
L(Pt,in /Pref)>
1
d
c dt
m0T-utcp
Iv
(3.20)
psdV)
Recognizing that
(Tt,in/Tref
exp
(Pt,in/Pref) ^' _
52
(Sin)
(3.21)
1
> 0
Upon substituting (3.21) into (3.20) gives,
Y- 1
Tt'aou
T,in--
epn
rxhout
Pt,Out
Pt,in
Sin
4
1
rnout c dt
cp
(3.22)
psdVl
IV
I
Combining (3.22) with mass conservation (3.12),
T'in
exp
(Pt,in
exp - .
IToutcp dt J y
Pt in,
S(PtOut
d
,)Utcp dt
r cI d jipdV
IV
psdV
(3.23)
-
1
s ad
p(s - sin)dVl
From (3.13), the inequality (3.23) leads to
(1
-
W =rhinCp,
n
Tout
\~i
<rhinCpTt,in (1
- +ipedV
pt
Tt
lout>
m4n)exp
a
+ j y p(s mhoutcp dt V
- .
d
sin)dV)
I
V
petdV
(3.24)
Finally, we obtain the expression for the ideal power in an unsteady system as
-y-
W'ideal = ThinCpT,in
1I
1
\ Ptiout
rht
Ptnin
)exp
1
rhoutcp
f P(s - sin)dV
]tV P
df
_it
(3.25)
3.2.1
Storage Rate Effect in Unsteady Flow System
The expression for ideal power (3.25) accounts for the mass /energy/ entropy storage
rate through the system. In essence, the storage rate is driven by the time lag between
the influx and outflux of mass/ energy/ entropy in an unsteady flow. Notice that the
time lag between inlet and outlet mass flux vanishes for incompressible flow. For
53
petdV
Jv
convenience of interpretation, let's define three non-dimensional numbers as follows:
S
d
1
out
1in
pdV
indt I
d
= I petdV
(3.26)
hinC Tindt i
exp
-I
It is noted that M,
mhoutcp
j p(s
dt fy
-
sin)dV
, and S indicate mass, energy, and entropy storage rate in
unsteady system respectively. Now the expression for unsteady system ideal power
can be rewritten as,
Wideal =
7i2 cnpT,in 1
-
- S)
-
('n
-
(3.27)
We will call (3.27) as the Storage Rate Form of ideal power. This form explicitly
shows the reason why and how we should take the storage effect into account when
defining what ideal power is when flow unsteadiness becomes significant. By using
the Storage Rate Form, the so called filling and emptying effect ([10]) does not reveal
itself on the efficiency as it should. Lastly, the expression for the unsteady ideal power
(3.27) reduces to that for steady ideal power (3.10), as the reduced frequency (1.2) of
the system shrinks to zero (then,
M a I,
-
1, and k
-
0).
The isentropic efficiency for an unsteady steady system can now be defined in an
analogous manner to steady case (3.11) as
1-
3.2.2
(Tt~out)
_1
_.
riunsteady
(3.28)
Entropy Generation Rate and Loss
Although Storage Rate Form (3.27) clarifies the impact of unsteadiness in defining
ideal power, it is not as practical as one would like for application. The expression for
ideal power can be simplified further. We replace the time derivative term on energy
54
storage in (3.25) with power via First Law of Thermodynamics (3.13).
-y- 1
Wideal = TinCpTtin
1
\(ptoin)
\Min /
n t,in
-
-
outt,out
-
d
exp - .1
o
Y
P(s - sin)dV
rMoutcp dtV
_
W
(3.29)
Upon manipulating,
ty- 1
ut
Pt,in}
Wideal -
(
W + rhoutc'TtOut
k
1
-
exp
.
d
I
f p(s - sin)dV
V
outcp
.
3
(3.30)
Recognizing that
(Tt,in/Tou )(sin
- Sout
(3.31)
Cp
(Pt,'in/ptout) ,
Thus,
Wideal
-W
+ hOutCPTtOut ( I
-
exp
s-s1
d
d
1
Sn-Su
T4outCp dt
I Cp
j
p(s - sin)dVl)
(3.32)
+ rhOutCPTtOut (I - exp
Lm0outCp
((7rn>t
d
dt j pdV I
d
Sin -
houtsout -
dt j
-
W
+
Wideal
.
With further manipulation, we obtain
(3.33)
Upon applying mass conservation (3.12) to (3.33),
W +
rOutCpTtOut ( I - exp [. outcp
(
si --
ri20
tsout
-
d
-
Wideal
jpsdV)])
(3.34)
Use of Second Law of Thermodynamics (3.14) in (3.34) finally yields
Wideal
W
+ routcTtout 1 - exp
(-
fvSn dV
Loutcp
(3.35)
Equation (3.35) will be called the Entropy Generation Rate Form for ideal power.
From the Entropy Generation Rate Form, it is clear what the loss is: the additional
55
psdV)])
power that could have been extracted from the system at the instantaneous moment.
The equation for the lost power is thus
WoSS = 7riutcpTt0out I - exp
-
(
I/ dV
V
(3.36)
ThoutCp
which directly points out entropy generation as the source of loss in unsteady system.
Finally, the isentropic efficiency can be defined for an unsteady flow system as
r7unsteady
3.2.3
fv
W-eal
Wideal
+ rutcpTt'out I - exp
W
dV)
1
(3-37)
(ls
Approximation of Entropy Generation Term in the Expression for Ideal Power
Now a remaining question is: How can we categorize and quantify the origins of the
losses? Or, what is the portion of each loss mechanism on the loss from the entire
system? This question can be answered by the Approximation Form - the approximated version of Entropy Generation Rate Form. The process is straightforward.
Firstly, we apply the Taylor expansion on the exponential part of (3.36) and neglect
the higher order terms.
Wiea1
~W + Tt,01
f$'"dV
(3.38)
This can be simplified further by taking the averaged outlet stagnation temperature (as the variation compared to averaged quantity is small typically),
Wide~
W +T ,
Widear""
fV geri
S'" dV
(3.39)
Equation (3.39) is an Approximation Form for ideal power. This will be the form
that we are going to use for assessments. The loss from each irreversible flow mechanism is proportional to the corresponding entropy generation. Note the familiar TAS
is readily recognized as lost work [3]. Also, the instantaneous isentropic efficiency can
56
--
now be rewritten as
(3.40)
?7unsteady
W
ieai
3.3
W + T,ontfy SgndV
Application
In this section, the utility of the expression for ideal power is elucidated.
Three
topics are discussed: (1) A metric for assessing the utility of component models; (2)
Efficiency; and (3) Loss categorization.
3.3.1
Metric for the Utility of Component Models
As will be discussed in Chapter 4, simplified models for each sub-component will
be established based on the key controlling parameters (such as Mach number and
inflow angles). In order to discern the utility of the model or in order to identify the
importance of each sub-component's performance, we need a proper metric. Cycle
averaged ideal power can be the reference for the purpose as the cycle averaged ideal
power sets the upper limit of system performance. With normalization based on cycle
averaged ideal power, it can be quantitatively determined if the model is adequate
or if the corresponding loss mechanism is important. Cycle averaged ideal power is
defined as
Average Ideal Power =
And the metric for the
ith
Teriaod
Widealdt
(3.41)
component or loss mechanism is either
Average Ideal Power
or
Average Ideal Power
(3.42)
depending on whether the power is extracted (turbine wheel) or not (components
other than the turbine wheel).
57
3.3.2
Efficiency
The definitions of two efficiencies are considered. One is instantaneous efficiency and
the other is cycle1 efficiency. Instantaneous efficiency shows the current performance
compared to ideal performance at the instantaneous moment considered. In contrast,
cycle efficiency indicates the performance of the system during the cycle. The instantaneous efficiency has been defined in various formats (3.28, 3.37, 3.40). Here
we define cycle efficiency as work extracted during the cycle (one period) compared
to the work that could have been extracted from the system during the same cycle
(one period). Based on the Approximation Form in (3.38), the cycle efficiency can be
written as
period
L
14dt
e
Ucycle =Tperiod W
L
3.3.3
r
Widealdt
fo period
VWdt
+
fo p-" (W + Tt,out,
(3.43)
fTeriod
,1,1,dV) dt
Loss Categorization
Once the numerical value of cycle efficiency is obtained, a relevant question is then
where the loss comes from. The procedure of linking the origin of loss to the individual
sub-component is referred to as loss categorization. We start from the cycle efficiency
definition.
S
TOcycle
pTeriod
Vdt
Tpro
L
Widealdt
fo
L period I
fTperiod Widealdt
Tpro
Widealdt
(3.44)
W47
108 dt
fTperiod
=fTperiod
ossdt
-
dealdt
With (3.39), it can be further manipulated as (assuming that there are total N loss
mechanisms throughout the system),
1
-
"cycle
N~
fTperiodSgnd
Tt,out Ej0
Tper od(3.45)
fo
Sgnid
3.5
Widealdt
'It is noted that cycle will always refer to inlet pulsation cycle (not to be confused with thermodynamic cycle) in the thesis.
58
Now the cycle efficiency loss debit from the ith mechanism can be given as
qioss i
3.4
(1
-
7lcycle)
[
f(
S"'en $dt
'
f[T
LE
(3.46)
fTperiod
Summary
In this chapter, a physically consistent definition for the ideal power in an unsteady
turbine system is derived based on physical principles. We do need to account for
the mass/ energy/ entropy storage rate (see equation 3.35) in the system in order
to define the unsteady ideal performance.
This essentially resolves the confusion
and controversy on defining ideal power for a device operating in an unsteady flow
environment. Lastly, the metric for the utility of component models as well as system
performance metrics (instantaneous efficiency and unsteady efficiency) are delineated.
59
60
Chapter 4
Component Models
In this chapter, the modeling of the turbine system is addressed. The basic idea is to
divide the entire system into two categories: quasi-steady components and unsteady
components. And, the guiding criterion is the reduced frequency (1.2). If the local
reduced frequency is small
(<<
1), the corresponding component (or flow mechanism)
can be modeled based on locally quasi-steady assumption. If not, the storage effect
of mass/ energy/entropy through the component should be appropriately accounted
for. Lastly, interface models should be established to connect the characteristics from
each modeled components.
4.1
Categorization of Component Models
The categorization of component models are summarized in Figure 4-1. Note that
reduced frequency between unsteady component and steady component are usually
different by factor of hundreds.
For example, the reduced frequency for volute is
around 3 while the reduced frequency for turbine wheel is order of 0.03. One might
seek for the reason why the diffuser is in both quasi-steady models and unsteady models. The characteristic length scale of diffuser loss mechanism (the length of mixing
region) is short enough such that it can be treated in a quasi-steady manner while the
diffuser as an entity for pressure recovery should be treated in an unsteady manner.
In other words, the loss generation is quasi-steady while the pressure recovery process
61
is unsteady. Lastly, radial scroll interaction consists of the phenomena covering the
leakage of flow from one side scroll in volute to the other side scroll in the radial scroll
region (the region of the volute where the flow is being distributed into the turbine
wheel).
Wastegate port loss model
Quasi-steady
Component Models
Turbine performance model
Diffuser loss model
Turbine
System
Models
Volute entrance region model
Unsteady
Diffuser region model
Component Models
Radial scroll interaction model
Figure 4-1: Categorization of Component Models - The turbine system model is
categorized in to two parts: quasi-steady component models and unsteady component
models. The figure shows the corresponding components in each category.
In addition, there will be two interface models. The role of the first interface model
is to connect the information between volute and turbine wheel while the second model
links the turbine wheel exit to the diffuser inlet. The modeling method of quasisteady component, unsteady component and interface treatment will be discussed in
the following sections.
4.2
Quasi-steady Component Models
The implied assumption of quasi-steady modeling is that the non-dimensionally short
(reduced frequency << 1) component will behave as if it is an instantaneous steady
flow state. For example, the flow beneath the wastegate port almost instantaneously
adapts to the boundary condition as the reduced frequency is much less than unity.
This effectively indicates that we can determine the unsteady performance of the
62
component based on steady state results corresponding to the instantaneous boundary
condition.
With the conceptual framework, the modeling for wastegate port loss, turbine
wheel performance and diffuser loss are established. The general approach is to: (1)
identify the key parameter that defines the characteristics of the component performance, (2) extract the correlation between the parameter(s) and characteristics from
steady CFD, and (3) assess the utility of the modeling technique using the result from
3D unsteady computed flow.
4.2.1
Wastegate Port Loss Model
As described in Chapter 2, the wastgate port induces entropy generation on the flow
beneath it due to local sudden expansion even though the wastegate is closed. For
such an increment in entropy, a simple loss scaling based on Mach number would be
adequate.
For small change in stagnation pressure,
Ass
R
- In
(t,Pt,2 \
(pti
p
Ap
Pt
(4.1)
The stagnation pressure change (Apt) can be scaled as dynamic pressure (jpu 2 ) with
the result that
As
-YM2
R
2
(4.2)
Now introducing a proportional constant kWG, the entropy increase per unit mass
can be expressed as
As
_1
IkWGYm2
R 2
(4.3)
Therefore,
Sgen/rh
e1
yR
= kWGM
2
44
We setup the wastegate port loss model by identifying the kWG from steady CFD.
However, the relation in (4.4) raises an issue involving small number (entropy generation rate) divided by small number (mass flow rate). In order to overcome this
63
.
..
.......
. .........
.....
....
.
........
..
issue, we recast equation (4.4) using the mass flow rate expression (rm = puA
=
p(MV'yRT)A) to give
= kWG M 3
Seen
(4.5)
(R)3/2Apv/T
The proportional constant can be estimated from steady CFD results based on
(4.5). Note that the proportional constant is equally applicable to both of the wastegate port (inlet 1 side wastegate port and inlet 2 side wastegate port) as shown in
Figure 4-2.
__
X10
o WG1 - Steady CFD
o WG2 - Steady CFD
Fitting line
4 -C
Forward flow
Reverse flOW*
N
-o
0
0
1-
0
0
0.1
0.3
0.2
0.4
0.5
M
Figure 4-2: Wastegate port loss characterization - WG1 indicates wastegate port loss
on inlet 1 side and WG2 indicates inlet 2 side loss. Note that reverse flow case has
higher proportional constant for entropy generation rate. The fitting line is generated
based on least square fit. Also, the array of steady data points above the fitting line
correspond to reverse flow (when the flow through the corresponding volute is in
reverse direction compared to normal forward flow direction) characteristics.
Now the wastegate port loss model is assessed against the loss estimated from
unsteady 3D computed flow. We apply equation (4.4) to unsteady flow situation
(computed in full unsteady CFD) with the same proportional constant but with
Mach number changing with time. The result is shown on Figure 4-3. As discussed
in Chapter 3, the metric for the model is lost power over average ideal power (3.42).
64
It shows the relative importance of the component performance compared to cycle
averaged ideal system performance.
In general, the model shows good agreement with the unsteady CFD result. This
indicates that the wastegate port induced loss mechanism generally behaves in a
locally quasi-steady manner except at certain points (for example, around normalized
time of 0.4) where it deviates from steady characteristics. The probable cause behind
the discrepancy is volute mass flow fluctuation (discussed in Appendix B) that leads
to a change in wastegate port loss characteristics.
0.1
-WG1
WG2
0
S0.08
WG
S
WG2
& 0.06
- Model
- Model
- Unsteady CFD
- Unsteady CFD
-.-.-.-.-.-.-
- ---
--
~0.04
0
0
0.2
0.4
0.6
Time/Period
0.8
1
Figure 4-3: Comparion of wastegate port loss model and unsteady CFD result - The
wastegate port loss model (blue and red) shows good agreement with unsteady CFD
results (green and magenta).
4.2.2
Turbine Wheel Performance Model
Turbine wheel is usually characterized by the pressure ratio across the turbine wheel.
And, the effect from stagnation temperature variation (or the corresponding variation
in corrected tip speed) is accounted for as a corrective effect. However, for the twin
scroll type turbine wheel, this approach requires an operation map based on four
65
. ....
.......
....
..
....
..
....
...
......
.
dimensional parameter space1
In view of this, the choice is made to parameterize the turbine wheel performance
(efficiency) in terms of relative incidence angle to the turbine wheel blade. For the
twin scroll type turbine wheel, the efficiency would have a functional dependence on
two inflow angles (#turb and
Thtb,
see Figure 4-4).
3
turb
is the conventional relative
incidence angle to turbine wheel blade in the direction of turbine wheel rotation.
And, Ytub is the angle from the plane of volute to the axis of rotation of the turbine
wheel. It is noted that both of the two angles are measured with mass averaged 2
velocity components on the surface at the inlet to the turbine wheel. This can effectively average out the non-uniformity from the unsteadiness in the radial scroll region
(the volute region where the flow is being distributed into the turbine wheel). The
definition of the two angles are
W
bYturb tana- --
/3
(4.6)
,b-
tan-ur,
M
M
,
Figure 4-4: Turbine inflow angles - Two inflow angles to turbine wheel is used to
characterize the turbine performance.
We identify the relation of
7turb
- Tturb(turb, Yturb) from the set of steady CFD
(Figure 4-5) and apply the same relation to unsteady case (Figure 4-6) based on the
locally quasi-steady assumption.
1
Two pressure ratios based on inlet 1 side scroll stagnation pressure and inlet 2 side scroll stagnation pressure. And two corrected tip speeds based on inlet 1 side scroll stagnation temperature
and inlet 2 side scroll stagnation temperature.
2
The idea behind the mass average as opposed to other method (i.e. area average) is to weight
more on the main flow than the boundary layer flow.
66
Once the efficiency on each time step is determined based on the characterization
in terms of the two angles, the power can be calculated from the definition of efficiency
as follows.
77turb(/3 turb,i
Yturb)
rnTturbln Cp Tturbln
-
-M
47
ttrln
Pt,turbln
Note that mass averaged stagnation pressure and stagnation temperature at turbine wheel inlet and mass averaged static pressure at turbine wheel outlet is utilized.
The purpose of using mass average is to average out the non-uniformity for estimating
the mean value while maintaining the flux of stagnation temperature and stagnation
pressure through the turbine inlet.
There are two implications from the results in Figure 4-6. First, turbine wheel
model based on the characterization using two angles works well; this can be inferred
from the comparison of the model (blue line) and unsteady CFD result (green line).
The second implication is on the instantaneous efficiency equation (3.40) - by calculating power (green line) over ideal power from the system (black line), we can readily
calculate system instantaneous efficiency shown in Figure 4-7.
However, the plot of instantaneous efficiency does not reveal what needs attention.
Figure 4-7 might give an impression that we need to focus on the low instantaneous
efficiency point (around normalized time of 0.2 or 0.7) to improve the system performance. However, it is not the case. Those regions with low instantaneous efficiencies
correspond to low ideal power regions in Figure 4-6. Even if the system performance
is improved to approach that for ideal flow situation, the gain is relatively small (order
of 1 %pts in cycle efficiency). Rather, we need to focus on maximum power extraction
point near normalized time of 0.3 or 0.9 (see Figure 4-6).
4.2.3
Diffuser Loss Model
The last quasi-steady model to assess is the diffuser loss model. Basically, the model
is nothing but a control volume analysis on flow sudden expansion
[3]
followed by
Rankine vortex growth. Figure 4-8 shows the general situation to be considered.
67
..
..
...
........
-
40
o Steady CFD points
-Unsteady
CFD locus
200
-40
0
40
-60
-40
-20
p [deg]
0
20
40
Figure 4-5: Inflow Angle Parameter Space - the blue discrete points are steady CFD
points while the green line is unsteady CFD locus. The unsteady turbine performance
(unknown) is estimated based on steady turbine performance (known) on the inflow
angle parameter space.
Also, for simplicity, the following approximations are made:
1. Incompressible flow (Note that Mach number in diffuser is less than 0.3)
2. Uniform temperature, density and axial velocity at mixed out state
3. Axisymmetric pressure and circumferential velocity at mixed out state
4. No radial velocity at inlet and outlet
5. Fully developed Rankine vortex (6m/Rm ~ 1)
Three conservation equations are solved simultaneously. The pressure distribution
at outlet is obtained from the radial equilibrium relation. Variables at inlet to the
diffuser and mixed out state are denoted with subscript 1 and m respectively. The
equations are manipulated such that unknowns are on the left hand side while the
right hand side can be readily calculated from known quantities.
Mass conservation:
PmUzm
Am
68
A
puzdA
(4.8)
.
..
. ......
.
.. ....
..
...........
3.5
0
3
A
...........--..
............--.-..
..........
..
..-...
.---..
......
-..
.......
1.5
.
..
.....
-...
----...
.....
......
..-.-..
.--..
...
..
....
.
1
.
2
.
2.5
.
0.
--T Turbine Model
Unsteady CFD
Ideal System
0.5
0
C
0.2
0.4
0.6
Time/Period
0.8
I
Figure 4-6: Comparion of turbine wheel performance model and unsteady CFD result
- Blue line is turbine wheel model, green line is unsteady CFD, and black line is ideal
system performance
Momentum conservation:
PmUZm
Am _
Pa)
(4.9)
pu dA]
Angular momentum conservation (mixed out state is for Rankine vortex type flow):
(Rm)
(1
1
(Rm,))
I
Tr muzm Am 1
p(ruo)uzdA
(4.10)
Rankine vortex radial equilibrium (p/&r = pu 2 /r):
(0 < r <
PpI + pmr2 Q2i
3m)
PM (r) =
1p'M6 M2Q
2 - (,)2)
(4.11)
(Jm <r < Rm)
Now here comes the role of steady CFD. Unlike the idealized sudden expansion
analysis, turbine wheel exit pressure (p1) is not the same as diffuser side wall pressure
(peff). This is mostly due to the streamline curvature near the diffuser inlet. Since the
69
0
70
C
0
j40
C
20
0
0.2
0.4
0.6
Time/Period
0.8
1
Figure 4-7: System Instantaneous Efficiency - The low instantaneous efficiency does
not necessarily indicate the point of interest. The region with instantaneous efficiency
around 30% actually corresponds to low ideal power region for this case.
pressure gradient associated with streamline curvature is proportional to the product
of dynamic pressure and the curvature, we can assume the following relation between
static pressure at turbine wheel exit (pi) and diffuser inlet side wall pressure (peff):
Peff - Pi = Keff (PiU)
(4.12)
Motivated by streamline curvature argument, the proportional constant Keff is
defined as a function of two angles pointing out from the turbine wheel exit. That is,
Keff = Keff(a,, -Y)
where,
-M
S= tan-
70
0, 1
VM
-
ai = tan-1
(4.13)
The remaining steps in the procedure is similar to the quasi-steady models for
wastegate port loss and turbine wheel performance. We identify the relation (4.13)
from the set of steady CFD and generalize the relation to unsteady flow situation.
And, at each time step, we solve the conservation laws (4.8), (4.9), and (4.10) to
calculate the entropy generation. The result is plotted based on component metric
given in equation (3.42) in Figure 4-9.
Note the diffuser loss model shows good
agreement with the trend of loss estimated from unsteady CFD. This implies that
the loss mechanism can be considered as quasi-steady as initially assumed.
Mixed, Am - R-m
Irrotational
outside field,.
Turbine exit, Ai
r
-4
-4
' Core radius 6M
Strength I'm = 27r Inm
-:
=
z
I
--
4
Forced vortex
inside core
Va riablesat inlet
......
uz,l(r,
uOi(r, 0)
Ur,1I ",
Variables at exit
pr(r) uz,m = const
ue,M(r)
3m _
)
p1 (r,9)
Peff
0
U r,m
4 Unknowns:
Pm
Uz,m UO,m
0
Qm
Figure 4-8: Diffuser mixing loss modeling - Control volume analysis is applied on
sudden expansion with Rankine vortex type flow. Also, the diffuser side wall static
pressure is modeled adequately.
4.3
Unsteady Component Models
Unlike the quasi-steady component models, there are components where the unsteadiness cannot be neglected (high reduced frequency). Three sub-components the performance of which may involve loss mechanism of pressure recovery will be addressed;
71
........
. .......
1.2
Diffuser Loss Model
S
............ .........iien
Unsteady CFD: S
Vlsc
S
p0.6 ...
- --.-.-
0.4
0
0
0
0.2
0.4
0.6
Time/Period
0.8
1
Figure 4-9: Comparion of diffuser loss model and unsteady CFD result - Blue line is
diffuser loss model, green line is unsteady CFD. Notice the good agreement between
the two.
the volute, the diffuser and the radial scroll interaction in the order of consideration.
It is noted that the radial scroll interaction is not yet fully identified as an unsteady
mechanism. It is hypothesized as an unsteady mechanism since any estimation based
on quasi-steady assumption could not capture the computed trend from an unsteady
CFD.
4.3.1
Volute Model
As described in the first Chapter, the volute is an unsteady component (reduced
frequency
-
3). Since the area change along the volute can be approximated as 1D
along the center, it can reasonably be inferred that quasi-1D Euler equation would
enable adequate estimation of effects associated with the unsteady phenomena in the
volute. The quasi-iD Euler equation to be solved is
- (SQ) + Ox -- H = 0
72
(4.14)
............
..
.......
.
... .............
. ...
......
where
Q
pu
pet
0
pu
p
dS
E=S
,
H=
Pet + P) U_
p
S = Area(x)
(4.15)
0
For assessing the utility of quasi-1D Euler equation in the context here, basic solution technique suffices (i.e. high accuracy shock capturing schemes are not needed).
The applied scheme is 4th order modified Runge-Kutta with Davis-Yee Symmetric
TVD in temporal dimension and 2nd order accurate finite difference in spatial dimension. Almost any basic CFD text explains the aforementioned schemes (see [20]).
The situation to be considered is described in Figure 4-10. We will solve quasiID Euler equation bounded by two boundary conditions (inlet stagnation pressure
and outlet static pressure) starting from the initial flow condition. And, the flow
variable from the quasi-1D model will be compared with the flow variable from full
3D unsteady simulation. Note that only the volute entrance section (from s=0 to
s=0.6) will be considered. The radial scroll section (beyond s=0.6) is discussed in a
separate section on interface models (section 4.4).
t
Given
1D Euler?
pt, Tt L
1
Given
IPsttice
.
S
0.6
77777
0.0
Given I.C.
S= 0.0
Figure 4-10: Volute modeling - The blue crosses and red crosses are numerical probes
to extract the flow variable from the unsteady CFD. s is normalized coordinate such
that s=0 is inlet and s=1.0 is the end of volute. Note that s=0.6 is end of volute
entrance section.
73
The results are presented in Figure 4-11, 4-12, 4-13, 4-14, 4-15, 4-16. The figures
are the time evolution of pulsating flow on each scroll. The top left plot shows the
relative location of the time step based on the pulsation at inlet and the other three
plots present the distribution of flow variable in the spatial domain. The variables
are chosen based on their significance to the turbine wheel operation. Pressure ratio indicate the stagnation pressure over static pressure at diffuser outlet (Pt/Pexit),
corrected temperature is the reciprocal of corrected tip speed squared (yRT/U P),
and the normalized mass flow is mass flow on each cross section normalized by the
volute inlet maximum mass flow rate (rh/max(rhniet)). The quasi-iD model (solid
line) shows good agreement with the full 3D unsteady CFD (discrete points) over the
pulsating period.
74
Peak Torque
Time/Period=0.24
4
0
.
i
--.-.
.-..
-....
..- .... --..
S2
Ix
.
-.
.......
-.....
-..-.-0.3
3
2
1
0.6
0.4
0.6
Time/Period
Model
CFD
06
0.4
0.2
Normalized Coordinate
...
...
...
..
-..
..
.
-.
-..
......
....
..
.-
1
0
.
0 3
-Inlet 1I
...
.... ....
....-.
.-...
.-.. -Inlet 2
-
-.
...........-.
......
.....
-..
-.-..-..-.-.--
E
0.51
- ..................-..--..-.-.....-
O.d
0
0
0
U
0
Z
0
0.6
0.2
0.4
Normalized Coordinate
0
Peak Torque
i
4
-Inlet 1I
Inlet 2
3
0
3
1
0.3
0.4
0.6
Time/Period
1I
0.6
0.2
0.4
0.6
Normalized Coordinate
1.6
0
11
-.-
_...
-_.
...
- _._.....
&
LL
- ......
I-
-. . . .. . . . ..- . . -. ..-. . . .. . . -..
. .. . . . ... ..
0.5
.......
-..
-.
.. -.
..... ..
.-..
-.
.
ES
0.6
S
3
Model
CFD
2
2L 2
'I
0.6
Time/Period=0.27
4
0
0.2
0.4
Normalized Coordinate
...
...
....
.....
....
...
.
..-
0
0
l~1I
0
0.2
0.4
Normalized Coordinate
0.6
0
0.2
0.4
Normalized Coordinate
Figure 4-11: Quasi-ID Volute Model: Inlet 1 - Part 1/3
75
0.6
..
.. ..
..
..
...
..... ....
..
...... . .....
....
.....
..
..
..
......
.....
..
. -_ I
. .-... ------
Peak Torque
Time/Perlod=0.31
4
4
Ilt1
3
.....
....
2
IL
...
.. .. ....-..
........-...
2
1
.
0.3
CFD
3
- - ..
..
-.
.
--...
a.
Model
0
--....
... In e 22
--......
.
0
0.6
0.4
0.6
Time[Period
0.4
0.2
Normalized Coordinate
0
0.6
0
IL
xx
.....- ....-.
..
.-...-.
.-.
..-..
...
..
1
..........-..--.---..
.-..-
0.5
-
E
x
...............................
0.5
-.
....
-..
--.
.-...
..
....
0
.
0
0
z
U0
0
0.6
0.2
0.4
Normalized Coordinate
0
0.2
0.4
Normalized Coordinate
Peak Torque
Time/Perlod=0.35
4
4
1.
- ............
..........
..
..
0.3
0.4
0.6
Time/Period
3
I
CFD
2.................. ....... ..........
....................
0.6
X
A
0
............
....... ---..
... -..
0. 6
-.
..............
-.....
-..-..
0.5
z.
...
...
.....
.... .....
--..
......
.
0
L.
0.4
Coordinate
.
E
S0.2
Normalized
..-.
..
-..
-..
...
...
---...
.....
1
-..
..... -.
..
..
-..
i
...
..
...
----..
-..
- -...
...
.
-........
2
-Model
0
.
..
.-.
-..
j3
-Inlet 1
-Inlet 2
.
0
I1
0.6
-..
-
0
U
o
0.2
0.4
0.6
0
Normalized Coordinate
0.2
Figure 4-12: Quasi-1D Volute Model: Inlet 1 - Part 2/3
76
0.4
Normalized Coordinate
0.6
.. ......
...............
.....
.....
............
............
.....
....
.. .................
.........
...
...
.........
......
Peak Torque
TImelPeriod=0.39
A
0
4
-...-.
...2
-..
..
. ..
j3
-Inlet
1
.. -. Inlet 2
.-
-
0 3
-. --..
w2
-
Model
CFD
-
0
2
.
.-.
...
-..
...
-..
..
0
0.3
0.6
0
0. 6
0.2
0.4
Normalized Coordinate
"
0.4
0.5
Time/Period
01
IL
Ow. 0
S--
E
E0.5
....
.....-..-.-..
.
-
-.--.-.-.-.-.-
0
N
0.5
'2
E0
0
U
I
0
0.6
0.2
0.4
Normalized Coordinate
0
0.6
0.4
Time/Period=0.42
Peak Torque
4
4
- ....
2
-.
-
0
j3
...-.. ...
..
-
.......
-....-..--..-.
0.3
0.4
0.5
Time/Period
Model
CFD
2
.
3
Inlet 1I
-Inlet
2
..........-..
.
0
0.2
Normalized Coordinate
1
0.6
0
0.2
0.4
Normalized Coordinate
0. 6
I A
-.
.......
.......
....
...-.
...
........
...-.
.
.... - ....-........
.
- -.
......
-
E
............
-.......-..
-.
-..
0.5 -.
110
-..
......
... .
-.
........
.......
.
.6
0
S0.5
U
.
01
0
....
...
...
...
....
...
...
...
...
....
...
...
....
...
...
..-
z
a
0.2
0.4
0.6
0
0.2
0.4
Normalized Coordinate
Normalized Coordinate
Figure 4-13: Quasi-1D Volute Model: Inlet 1 - Part 2/3
77
0.6
..............
Time/Period=0.74
Peak Torque
A.
4
.2
-Inlet 1I
- - --- -Inlet 2
3
-
0
j3
-t
......--n---i-.-..
.--..
.-..
2
-
2
-odel
SCFD
0
-.. -.-..
A
-- . . . . . . . -... . . . . . . . - -...
1I
0.8
0.9
I
0.4
Normalized Coordinate
S0.2
TimelPerlod
0. 6
Ii
IL
...-....-.
...-.....
-..
.
--..
-.
.
-....-.-
.....---..---..--..-.-..--.-..----..-..
S. 1I-.............-.
E
S.
.
-.
.....
-....-......
-.
....
-.
... .E
0
U
II
"0
0.2
0.4
Normalized Coordinate
0
0
0.6
0.2
0.4
Normalized Coordinate
0.6
0
Peak Torque
Time/Perlod=0.78
A.
4
- . ...
. ...--..
...
.....
2
.
........-..
-
0
g3
.
3
-Inlet 1I
-Inlet 2
Model
CFD
2
.
0
..--.. ..-.
-- ..-..
..
.....
-.
0.8
0.9
I
0.2
0.4
Normalized Coordinate
0
TimelPeriod
0. 6
01
-.
0.5
-.
3
............---....-..
....-.
.
.
20.5
E
.
..
.......
.
..
.
-..
---..
...
...-..
.n
...
-..
.
..-...
..
..-..
.-..
0
0
0
U
o
0.2
0.4
0.6
0
Normalized Coordinate
0.2
0.4
Normalized Coordinate
Figure 4-14: Quasi-1D Volute Model: Inlet 2 - Part 1/3
78
0.6
-. . . .
...
...........
....
....
. . ..
......
.........
.........
......
.....
.
.....
.
Peak Torque
Time/Period=0.82
4
4
-
--Inlet1 I
-Inlet 2
0 3
I
...
.......
0
j3
2
Model
CFD
2
1
0.9
Time/Perlod
0.8
1
0
0. 6
0.4
0.2
Normalized Coordinate
1.5
I
E
0.5
20.5
.....--.
....-......-
-.
---..
....
....
..
-.....-..--.
.-...-.
..
-...
.
0
..
..
..
0
.
0.
. ...
-. .
1.
.
IL
E
0
0
U
Z
"I
0
0.2
0.4
Normalized Coordinate
0.6
0
0.6
0.2
0.4
Normalized Coordinate
Peak Torque
Time/Period=0.85
4
4
-
-Inlet 1
-Inlet 2
. ---...
..........
..---..
..
0
.
;3
0
-....-..
...- ........
-.
-..
...-.
..
02 .. . ..
..
.... .
0.8
2
-..
..
Ii
..
-...
....
.......
........
--..
.....
........... ..................
.
0.9
Tlme/Perlod
31
0
I
Model
SCFD
............
0.4
0.2
Normalized Coordinate
0.6
1.5
.
..
..
.
...
..
.
...
.....
....
....
.....
....
....
..
Ii
-
......
..........
...
...
.....
.. .......
..
*
....
..
20.5
.
..... .... ..... ... .... . . . .. . . . .
.....
....
-..
.-.
...-..
........
.
0
0.
0
n
z
0.2
0.4
0
0.6
Normalized Coordinate
0.2
0.4
Normalized Coordinate
Figure 4-15: Quasi-1D Volute Model: Inlet 2 - Part 2/3
79
0.6
..........
. ......
-
..........
Peak Torque
Time/Period=0.89
4
-Inlet
1I
-Inlet
2
..
--...
....
.........-..
Model
CFD
.
3
0
3
2
-.
--...
-...... -.....
-..
...
.....
0.9
Time/Perlod
1.4I. I
- _____________
I
0.2
0
0.4
Normalized Coordinate
0. 6
- _____________
-.-.---
-.-
01
-
0.8
2I
U.
I
1 0.5
.........-- .-..
.
0.5
cc0
0
- .--
-..
...
.....- ...
0
U
r
z
hi
0
0.2
0.4
Normalized Coordinate
0
0.6
0.2
0.4
Normalized Coordinate
Peak Torque
0.6
Time/Perlod=0.93
4
0
3
-- Inlet 1
-Inlet
2
-Model
CFD
0
-.--....-.... -.-
j3
- -*----
- .
.
.-...
..
. -.....
... .......--..
..-...
..
..
..
.... - -.
0.8
-I
1.5
E
1
0 .9
TImefPerlod
CL
...
....
.
.
1
-i -o
------
2
.
2
---
1
D
0.2
0.4
Normalized Coordinate
0
1
..... .......-...
..
0.5
.
.... ...
..-...
-..
......
..-..
...
0. 6
0
U
0.5
0
0
Z
Al
0
0.2
0.4
0
0.6
Normalized Coordinate
0.2
0.4
Normalized Coordinate
Figure 4-16: Quasi-1D Volute Model: Inlet 2 - Part 3/3
80
0.6
4.3.2
Diffuser Model
In general, diffuser modeling is based on the same idea as in volute entrance region
modeling (see Figure 4-17). However, there are two specific aspects that need further
elaboration.
s =1.0
t
Given
pt, Tt
0.0
1D Euler?
Given
pstutle
7
S
Given I.C.
s= 0.0
Figure 4-17: Diffuser mixing modeling - s is normalized coordinate such that s=O is
inlet and s=1.0 is the end of diffuser.
First, the flow in the diffuser is highly non-uniform unlike the flow in volute
entrance region.
In the volute region, the flow variable on each cross-section can
be represented in a consistent manner regardless of the averaging method (or even
using the values along the centerline of the volute) as the flow is quite uniform on
each cross-section. However, in the diffuser, we would need to select an appropriate
averaging method for the variables.
The choice is constant area mixed-out averaging. This method is chosen since it
provides representative variables that maintains the conservation laws on each crosssection along the diffuser (Note the diffuser loss generation is separately accounted
for by the diffuser mixing loss model (subsection 4.2.3)). We solve the conservation
laws and equation of state (4.16), and assume all the flow non-uniformity is effectively
mixed-out on each cross-section. The set of conservation equations for this process
81
is presented below. They are mass conservation, momentum conservation, energy
conservation and equation of state in that order.
puzdA = PXUX
(p+pu) dA
A
d
= ix + x()
(4.16)
1f phtuz) dA = jpx (cpu
+ I(;U )2
<
,x = pRTX
Second, the flow around the inlet of diffuser is highly three dimensional in its
nature.
The flow near the diffuser wall is separated and forms a relatively large
(comparable to turbine wheel diameter) recirculating zone'. Even after the mixing
out process the flow phenomena in the region cannot be represented by a single
variable on each cross section. Thus, we assess the utility of quasi-iD Euler equation
and the constant area mixing in the section beyond the highly three dimensional flow
region involving flow separation (see Figure 4-18). The unsteady mass flow fluctuation
associated with static pressure recovery in the diffuser is reasonably well estimated
based on diffuser ID model (see Figure 4-19). The result indicates the adequacy of
quasi-ID Euler equation description.
4.3.3
Radial Scroll Interaction Model
The impact from the interaction between scrolls is reported to be detrimental to
turbine wheel performance
[19].
Here, only the idea behind the modeling is presented.
It seems that the current quasi-steady based model does not explain the radial scroll
interaction effect quantitatively.
Based on the interrogation of the CFD result, the flow behavior is simplified as
in Figure 4-20. Some part of the high stagnation pressure side flow is leaked to the
lower stagnation pressure side while generating loss through mixing. Due to large
stagnation pressure difference (as the interaction happens only at large stagnation
3Note that the flow is not axis-symmetric since
the diffuser shape is not. It is due to issues of
integration with wastegate port and packaging with other components in the engine room.
82
..........
--. .- - . ... ......
......
...
..
....
..
..
.....
ID model outlet
tatic
1D model inlet
pt, Tt
Figure 4-18: Diffuser mixing modeling. Region of consideration - The quasi-ID diffuser model is assessed beyond the three dimensional flow region.
pressure difference), the lower stagnation pressure side has reverse flow.
Motivated by the aforementioned flow behavior during the interaction, the loss
can be scaled based on dimensional analysis (assuming constant K 12 and K21 ) as
follows. It is noted that 12 indicates leakage flow from inlet 1 side to inlet 2 side and
vice versa. Also, the location of "1" and "2" is described in Figure 4-21.
SRSI,12 =K
1turb
12
i 4.1 ()
SRSI,21
=
K
where,
U12 =
U21 =
2cT,1
2cTt,2
tub
2 1 P2U21
E IY
[1 I
l -
-
P2
Pt,1
P
2z11
(4.18)
Note that the two velocities are characteristic velocities based on isentropic ex83
.
......
........
..
....................
1.6
1.6
-Diffuser
ID model
Unsteady CFD
-Diffuser
ID model
Unsteady CFD
0.8--.
0.3
0.4
0.5
0.6
0.8
Time/Period
(a) Inlet 1 side pulse
0.9
TimelPeriod
1
1.1
(b) Inlet 2 side pulse
Figure 4-19: Quasi-1D Diffuser Model - The mass flow fluctuation associated with
static pressure recovery in the diffuser is estimated with diffuser 1D model. Notice
the good agreement between diffuser model (blue and red) with 3D unsteady CFD
result (green and magenta).
pansion between two locations.
The comparison between steady CFD data pools and unsteady CFD is plotted
in Figure 4-22.
The steady CFD based model appears to capture the qualitative
trend although it underestimates the radial scroll interaction effect. Note the entropy
generation rate is normalized by a reference entropy generation rate defined below.
The reference density and the reference temperature is from the time averaged volute
inlet boundary condition.
5
4.4
Pef trb
= PrefU
(4.19)
DturbTref
Interface Models
Two interface models must be added to the component models for integration into the
entire system. The first interface is located between the volute radial section (where
the flow is circumferentially distributed to the turbine wheel) and the turbine wheel.
And, the second interface is connecting the turbine wheel outlet to the diffuser inlet.
84
.
.. .........
...
........
-......
........
.-
......
..
..
Cross sectional flow
Axial flow
Forward flow
Figure 4-20: Radial scroll interaction from inlet 1 side scroll to Inlet 2 side scroll
4.4.1
Volute to Turbine Interface Model
On the interface from volute to turbine wheel, the flow is circumferentially distributed
into the turbine wheel. However, the flow can be considered as quasi-iD since the
cross-sectional area distribution can be well approximated as one dimensional along
the circumference.
Thus, the idea is to adjust the quasi-iD Euler equation such
that the result represents the inflow to the turbine wheel from the volute. It can
be accomplished by incorporating a sink term on the right hand side. The equation
that could be utilized is suggested as below. The utility of the equation has not been
explored yet.
-SQ+
ot
M- H = -Ext
9x
(4.20)
where
0
PU
Q=
pu
pet
,E=S
2+
p
(pp
(pet + p)u
H
dS
p
mk,ext
k
Ext =[
t
Lk
0o
S = Area(x)
Mkexht
U
Lk
(4.21)
85
Mass averaged on
Mass averaged on
circumference: pi, pt,1, T1, pi
cross section: p2
-
Figure 4-21: Radial scroll interaction from inlet 1 side scroll to Inlet 2 side scroll
datum locations
4.4.2
Turbine to Diffuser Interface Model
The key question on the interface between turbine wheel and diffuser is how to link the
diffuser inflow angle needed for diffuser loss model with turbine wheel performance.
One suggestion is to make use of Euler turbine equation that can connect the absolute
flow angle change to power extraction. Further elaboration stemming from this idea
is suggested as a future work.
4.5
Error from Locally Quasi-Steady Assumption
In this section, we assess the error from the modeling based on locally quasi-steady
assumption. The error is defined as the difference between unsteady flow and locally
quasi-steady based interpolated quantity. Note that an interpolation is needed since
we have finite number of steady CFD results. The variable of interest can be any flow
quantities and performance metrics such as efficiency. For the sake of simplicity, we
will consider the case of the turbine wheel efficiency. We begin with
LQS (Locally Quasi-Steady) error
= Unsteady - LQSiterp
86
1.2
R lto
-* RSlito2 - Steady CFD
* RSl2to1 - Steady CFD
0.8 RS11to2 - Unsteady CFD
a
RS12toi - Unsteady CFD
L..0.82U 0 .6
--..-...---
-.....-..--.........
0
0
50
100
150
Norm RSI - Scaling
200
250
Figure 4-22: Comparison of radial scroll interaction model and unsteady CFD result
- Crosses and thin solid line is steady CFD. And, the thick solid line is unsteady CFD
=
(Unsteady -LQSexact) + (LQSexact -LQSinterp)
The first part, Unsteady -LQSexact, will be called Assumption Error. And, the
second part, LQSexact -LQSinterp will be called Interpolation Error. Each of them is
discussed in the following subsections.
4.5.1
Assumption Error
Suppose we have infinite number of steady CFD results that can match any unsteady
flow situation. Even so, the unsteady flow will still be different from the steady CFD
result.
For example, even if we have exact matching of inflow angles, the steady
turbine wheel performance will still be slightly different from unsteady performance
due to the impact of flow unsteadiness. This difference constitutes the Assumption
Error.
It is an inherent error and cannot be eliminated.
It is simply due to the
assumption itself. As such, it can be thought of as the upper limit of the resolution
attainable based on quasi-steady approach. The Assumption Error can be estimated
87
from
|lunsteady(t)
(4.22)
drqunsteady A
77LQS(t)
-
From the above equation, the efficiency changing rate can be scaled as the efficiency change divided by the pulse rise time. And for the time scale, we can pick the
flow residence time through the turbine wheel. It is a conservative choice since, on a
conceptual basis, the flow environment in the turbine wheel is washed away after one
flow residence time.
Therefore, Assumption Error can be estimated as
Assumption Error = |unsteady (t)
-
77LQS
(t)
npeak
ibottom tres
-
(4.23)
Trise
4.5.2
Interpolation Error
Unlike the Assumption Error, Interpolation Error can be made vanishingly small by
having infinite number of steady CFD such that we can exactly match every time
step of unsteady CFD with corresponding steady case. Here, Interpolation Error is
estimated to be the order of second order terms from Taylor series. Recall that we
have steady cases (blue dots) shown in Figure 4-23. The error from Interpolation
Error for turbine wheel performance can be estimated as (r1 and r 2 indicate inlet 1
pressure ratio and inlet 2 pressure ratio respectively),
Interpolation Error ~max
(
Ar
1,ry1
,
ArAri
r18r2
88
2
,2,,Ar
1
'
r
2
(4.24)
4
3.6
.--.
-......
00
0
--
Steady Inlet Conditions
Unsteady inlet Condition
.
00
0
Goe
00
I
1
1
o o
1.5
0
0
00 o9
0*
2
2.5
3
Inlet I Pressure Ratio
0
3.5
4
Figure 4-23: Steady Cases Encompassing Unsteady Case
4.5.3
Normalized Interpolation Error
Useful observations can be made based on Normalized Interpolation Resolution (NIR)
defined as follows.
Normalized Interpolation Resolution
Assumption Error - Interpolation Error
Assumption Error
(4.25)
The idea of NIR is to show the resolution of steady cases compared to Assumption
Error. For example, suppose that NIR is positive in a specific region on 2D pressure
ratio parameter space. This indicates that Assumption Error is larger than Interpolation Error. Thus, the local steady cases are too dense. Conversely, if NIR is negative,
it means the local steady case density is too sparse.
For the current case, NIR is calculated and plotted in Figure 4-24. The red cells
indicates locally dense steady case region on 2D pressure ratio parameter space while
the blue cells denotes locally sparse steady case region on 2D pressure ratio parameter
space. If we want to minimize the number of steady cases, we might want to decrease
the number of cases in the red cells while maintaining the blue cells.
From the
original 68 steady cases, the case for interpolation is reduced to 12 cases in Figure
4-25. Still the turbine wheel model appears to be appropriate as shown in Figure
89
. ..
...
..
.......
.......
................
...
.......
...
.......
. ............
...
. .......
.....
4-26. The difference between the turbine wheel model and unsteady CFD is 2%pts
based on cycle efficiency (see Figure 4-27) The result implies that the turbine wheel
characteristics on pressure ratio parameter space is relatively linear.
.
I
-- --.......
I
.
4r
Steady CFD points
. --..
...-..
...
......
-...
--..
.----..
..-
3.5[
.
0
0
..........
~~
~~-..
.......-..
--...
-.
---...
--..
2.5-
04
Z.
-1
Dili
2F............
............
..........-..
...
...
---..
. -.
.
C
-2
1.5 ..
.1'
1
2
3
Inlet I Pressure Ratio
4
-'
3
Figure 4-24: Normalized Interpolation Resolution - Blue and red cells indicate locally
sparse and dense regions respectively on 2D pressure ratio parameter space
90
......................
......................
....
- ........
..
...
........................
.....
....
....
. ..
......
. .....
. ...........
4
.
3.5
0 Steady Inlet Conditions
..........-- Unsteady inlet Condition
..
0
1
1.5
2
2.5
3
Inlet I Pressure Ratio
3.5
4
Figure 4-25: Reduced number of steady cases - The number of steady cases is reduced
from 68 to 12 guided by NIR. Note the good agreement between the model and the
unsteady CFD even after reduction of steady cases by more than a factor of 5
4.6
Summary
This chapter presented the modeling methods for the sub-components as well as the
system and the analysis on the error from the modeling.
In general, three types
of modeling are required: quasi-steady component modeling, unsteady component
modeling, and interface modeling. Under the category of quasi-steady component
models are wastegate port loss, turbine wheel performance, and diffuser loss. The
flow characterization in a volute is such that it has to be treated as an unsteady
component. Similarly, the pressure recovery characterization in the diffuser has to
be analyzed on an unsteady basis, in contrast to the loss generation in the diffuser.
Lastly, two interface models (from volute to turbine wheel and from turbine wheel
to diffuser) are suggested. The error from locally quasi-steady approach is assessed.
With adequate understanding on the source of the error, we can reduce the number of
steady CFD cases while reasonably maintaining the technical adequacy of the result.
91
.
.
.......
.............
.. - __ -
__ .
....
.......
..
.. ..........
....
-
........
.....
4
Turbine Model
-- Unsteady CFD
-
3 .
0
........... -
Ideal System
3I .....
A.
0
0.2
.............................
.
..
....
2
0.4
0.6
Time/Period
0.8
I
Figure 4-26: Comparion of turbine wheel performance model and unsteady CFD
result - Blue line is turbine wheel model, green line is unsteady CFD, and black line
is ideal system performance
I
-Turbine Model
-UUnsteady CFD
0- 0.8
- Ideal System
........
-..--..-.-..-.
.-...
-..
......
0.6
0
..-...
..
.
..
.............
0.4
.
Ut
-..
..
..
..
..
..
.--...
.-..
......
-..
....----...
..
..
.
-
0.2
0
0.2
0.6
OA
0.8
I
Time/Perlod
Figure 4-27: Comparion of turbine wheel performance model and unsteady CFD
result - Blue line is turbine wheel model, green line is unsteady CFD, and black line
is ideal system performance. The work is calculated by integrating the power with
respect to the time.
92
Chapter 5
Loss Mechanisms and Potential for
Improvement
In this chapter, we identify the loss mechanisms of the turbine system under unsteady
pulsating flow. The performance metric derived in Chapter 3 and the component
modeling from Chapter 4 will be applied to estimate the loss and to assess the potential for improvement. The categorization and the quantification of loss sources
will be presented for both the Peak Torque and the Turbo Initial Transient operations. Lastly, a flow management strategy is suggested based on the identified loss
mechanism in turbine wheel. A conceptual framework is suggested for assessing the
proposed strategy.
5.1
Procedure
The identification and quantitative assessment of loss mechanisms is based on volumetric entropy generation rate. The volumetric entropy generation rate consists of
computing the viscous entropy generation rate (velocity gradient) and the thermal
93
entropy generation rate (temperature gradient) in the turbine system flow path.
gen
ther
V1sc
1
&ui
keff
OT
T j
Ox
T2
ag,
2
(5.1)
We identify the loss mechanisms and assess the importance from each mechanism with
the help of equation (3.46). Lastly, component models from Chapter 4 are utilized to
categorize the loss mechanisms.
5.1.1
Component Model Based Loss Mechanism Identification
In this section, we assess the sources of loss in the turbine wheel and in the diffuser.
Turbine Performance Model Based Loss Estimation
There are two types of loss in the turbine wheel. One is the loss induced by the
mismatch in the inflow angles to the turbine wheel blades. Therefore, conceptually,
the loss from the mismatched inflow angles can be eliminated by adjusting the angles
to match the flow angles. And the other type of loss is the inherent loss which exists
even if the inflow angle is optimally matched. With the help of turbine wheel model,
we can determine what would have been the loss if the angles were optimally matched
on each time step along pulsation cycle. This will quantitatively answer the upper
limit of the benefit from incorporating the variable inlet guide vanes.
Diffuser Loss Model Based Loss Estimation
With component models, we can turn on and off the effect from the each source
of losses. The effect from the turbine wheel exit non-uniformity can be eliminated
through averaging out the turbine wheel exit condition to assess its impact on diffuser
loss model. It can bring out the importance of diffuser performance on the system
performance during a pulsation cycle (excluding the non-uniformity effect linked with
the turbine wheel design). Also, the averaging technique for the turbine wheel exit
94
- _ _ - ".4-__
. .. ...........
-1 ...
..
..
......
..
..
..........
........
stagnation pressure and stagnation temperature is mass flow weighted average. Mass
flow weighted averaged maintains the flux of stagnation pressure and stagnation temperature.
5.1.2
Boundary Layer Loss Estimation
The portion from boundary layer dissipation (profile loss) can be factored out with
profile loss model [211.
SBL
Cd TdA
=
(5.2)
Cd = 0.0056Re0-1/
6
~ 0.002
The utility of the boundary layer loss model can be assessed using the entropy
generation rate computed for the volute. The boundary layer loss model shows good
agreement with the unsteady CFD result (Figure 5-1).
0.014
-
0.012
--
UU1
BL Model
Unsteady CFD
i
-
BL Model
Un
& 0.008
.-..
...... ..
-..
..
-.........
- ....
.
.
0.01
0.008
0.006
.. ........
.....
..
..
-.
.
... ......
-..
.
0.004
.
0.006
.
.-.
..... ..
.........
0.004
0.002
0.002
-0
0.2
0.4
0.6
0.8
1
"O
0.2
TimelPerlod
0.4
0.6
0.8
1
TimelPeriod
(a) Inlet 1 Side
(b) Inlet 2 Side
-
Figure 5-1: Boundary Layer Loss Model in Volute The boundary layer loss model
(blue and red) is in accordance with the computed values from 3D unsteady CFD
(green and magenta).
5.1.3
Tip leakage flow estimation
In the turbine wheel, the loss originated from tip-leakage flow can be estimated from
a control volume analysis based on small leakage flow over nearly unchanged main
95
flow [22].
5.2
Sirrev
drh
~(ux - U,in)2 + (uyinj)21
C
rm
_
[f]+
LT
2cpT
(1
T
->
T
dT
(5.3)
Loss Categorization for Peak Torque and Turbo
Initial Transient Operation
The loss categorization from the two unsteady operations, Peak Torque and Turbo
Initial Transient, are assessed.
5.2.1
Peak Torque
The loss categorization at Peak Torque operation is delineated in Figure 5-2. The loss
from boundary layer dissipation (profile loss) accounts for 1/5 of entire loss. It is noted
that large portion of non-profile loss (around 1/3 of non-profile loss) originated from
the sudden expansion of flow at diffuser inlet. Thus, it is suggested that we should
focus on the diffuser performance as well as the turbine wheel design (on which most
of the effort has been invested) for improvement under Peak Torque operation. It
is noted again that diffuser loss can be understood based on quasi-steady modeling
(Chapter 4).
5.2.2
Turbo Initial Transient
The loss categorization on Turbo Initial Transient operation is summarized in Figure
5-3. The impact from the diffuser performance (sudden expansion) in Turbo Initial
Transient is still important (1/5 of non-profile loss). However, there are two interesting traits in this operation. First, unlike the Peak Torque operation, the impact
from radial scroll interaction is significant (1/5 of non-profile loss) for Turbo Initial
Transient operation. This indicates the need of redesigning the configuration of the
two scrolls such that the leakage flow from one scroll to the other is mitigated. Second, the losses linked to the angle mismatch is roughly 1/6 of the entire non-profile
96
..........
11..
.....
.........
................................
...
......
Volute
5%pts
K
...
...
Wastegate Z%pts
Radial scroll
Interaction 3%pts
Angle mismatch 2%pts
System
42%pts
Turbine
11%pts<
Main flow 9%pts
Tip leakage 2%pts
Others 7%pts
Viscous mixing
Non-uniformity from
turbine exit 4%pts
14%pts
Profile
8%pts
Sudden expansion
10%pts
Diffuser
18%pts
Thermal mixing
4%pts
Figure 5-2: Cycle Loss Breakdown - Peak Torque: The cycle efficiency is 58% for
Peak Torque. The red numbers indicate the origin of the 42% (=100%-58%).
loss. This naturally raises the question if the use of variable inlet guide vanes would
eliminate/mitigate the loss induced by the angle mismatch.
With all the sources of loss mechanisms identified, now we would like to know
to what extent the system can be improved further. In essence, the losses that are
not from the boundary layer loss can be mitigated (or even eliminated) by having an
improved design of the corresponding component. The flow management strategies
for radial scroll interaction and turbine wheel inflow angle mismatch are discussed in
the following sections respectively.
5.3
Flow management for radial scroll interaction
As discussed in subsection 4.3.3, some of the high stagnation pressure side volute flow
might leak through to the lower stagnation pressure side volute. And, the impact from
97
Volute
14%pts
...
.....
........
-- -. :::::
..............
......
.....
Wastegate 3%pts
Radial scroll
Interaction 11%pts
Angle mismatch 9%pts
System
68%pts
Turbine
22%pts <
Main flow 17%pts
Tip leakage 5%pts
Viscous mixing
16%pts
Profile
12%pts
Others 8%pts
Non-uniformity from
turbine exit 7%pts
Sudden expansion
9%pts
Diffuser
20%pts
Thermal mixing
4%pts
Figure 5-3: Cycle Loss Breakdown - Turbo Initial Transient: The cycle efficiency is
32% for Turbo Initial Transient operation. The red numbers indicate the origin of
the 68% (=100%-32%).
the interaction is the unintended irreversible mixing process.
In this section, we suggest an adjusted radial scroll configuration in order to reduce
the leakage flow in the radial scroll interaction. Let us focus on the difference between
the characteristics of radial scroll interaction from inlet 1 side to inlet 2 side and the
characteristics of radial scroll interaction from inlet 2 side to inlet 1 side. Figure 4-22
is copied again in Figure 5-4. It is noted that the impact from RSI21 (the leakage flow
from inlet 2 side to inlet 1 side) is larger than RSI12 (the opposite case to RSI21).
The reason behind the difference RSI12 and RSI21 is hypothesized to be the
configuration of radial scroll shape and the corresponding streamline curvature. For
example, in the case of RSI21, higher static pressure is driving the leakage flow due
to streamline curvature as shown schematically in Figure 5-5. This can be the reason
behind the higher loss on RSI21 compared to RSI12.
98
.........
. .........
..
.....
.-....
-
...
....... ........
................
.............
...............
....
..
...
........
. ....-: -.::-.
............
- :............
..................- ... ..................,: .. _':__Z: ................. . ..
1.2
-1
-
RS1lto2 - Unsteady CFD
RSl2tol - Unsteady CFD
u. 0.8
-.-.-.-.
U
0 0.4 .....
z
0
0
50
100
150
Norm RSI - Scaling
200
Figure 5-4: Measurement of radial scroll interaction from unsteady CFD on Turbo
Initial Transient operation - Note that the loss from inlet 2 side to inlet 1 side leakage
flow (RSI21, magenta) is higher than the one from the opposite case (RSI12, green).
Motivated by the argument based on streamline curvature, an adjusted radial
scroll configuration is suggested as shown in Figure 5-6. The idea is to parallelize
both the scrolls to be aligned with the turbine wheel inlet such that we can minimize
the impact from the radial scroll configuration. The assessment of the benefit from
the new configuration would constitute future research.
5.4
Flow management for turbine wheel inflow angle
mismatch
In this section, we assess the potential gain from installing variable inlet guide vanes
for the mitigation of wheel inflow angle mismatch.
99
.
.. .. . . . . . . .
Inlet
2 side
Low
pressure
Inlet
1 side
Leakage flow
High
pressure
Figure 5-5: Leakage flow from inlet 2 side to inlet 1 side driven by a higher static
pressure side due to the configuration of the radial scroll
5.4.1
General Description
The inherent problem on the Turbo Initial Transient operation is as follows. The
turbine wheel struggles with the velocity triangle mismatch especially at maximum
power extraction point (Figure 5-7). The blade suffers from suction side separation
at maximum power extraction point for the Turbo Initial Transient operation. The
consequence is the poor turbine wheel efficiency at the maximum power extraction
point (Figure 5-8). Notice the conspicuous difference in the trend of power vs efficiency
curve between the two unsteady operations. The turbine wheel efficiency becomes
worse as it approaches the maximum power extraction point in the Turbo Initial
Transient operation.
Let us compare the two operations quantitatively based on the loss categorization
charts (Figure 5-2, Figure 5-3). In the Peak Torque operation, the loss from angle
mismatch is only 2%pts out of the entire non-profile loss (34%pts).
In contrast,
the Turbo Initial Transient suffers from a huge loss due to angle mismatch (9%pts)
out of the entire non-profile loss (56%pts). As such, there exists the motivation for
incorporating variable inlet guide vanes especially during the Turbo Initial Transient
operation.
100
..............
...
...........
.
... . .......
..
...................
. ..
......
...................
...
.....
......
.
. . ..............................
....
........
.............
Pt,2
Suggested configuration
for reduced RSl
Pt,
1)1,2
Current configuration
Figure 5-6: A suggestion on the radial scroll configuration for the reduction of radial
scroll interaction - The two scrolls are parallelized to each other so as to mitigate the
loss from leakage flow.
5.4.2
Ideal Variable Inlet Guide Vanes
In this section, we present an idea that can mimic the effect from the use of variable
inlet guide vanes.
The conceptual process is described in Figure 5-9.
Basically,
the inflow angles are manipulated while maintaining the stagnation pressure and
stagnation temperature pulsation at the turbine wheel inlet. The newly prescribed
inflow angle (changing with time) is chosen such that the relative inflow angle is
aligned with the turbine blade.
Through this process, we expect to simulate the
effect from ideal inlet guide vanes that actively align the inflow angle to the turbine
blade without any additional loss.
Admittedly, the actual implementation of variable inlet guide vanes for automotive
applications appears very unlikely in the near term future. However, it will be a topic
of interest due to the large potential for improvement in mitigating the inflow angle
mismatch.
5.5
Summary
In this chapter, the loss mechanisms of the turbine system under unsteady pulsating
flow are identified and assessed. The sources of the loss are categorized and estimated
101
u
Peak
Torque
0W
V
Turbo
Initial
Transient
U
W
high
7
4
Figure 5-7: Velocity triangle at peak power extraction point on two different operations - The blade suffers from the suction side separation during the Turbo Initial
Transient operation.
using flow modeling and computed results presented in Chapter 3 and Chapter 4. The
potential for performance improvement in each sub-component in the turbine system
are identified and quantified. The diffuser performance is the main source of loss for
both unsteady operations considered (1/2 and 1/3 of the entire non-profile loss for the
Peak Torque operation and the Turbo Initial Transient operation respectively). On
the Turbo Initial Transient operation, the potential for improvement from variable
inlet guide vanes (that match the flow angle to turbine wheel) and the elimination of
radial scroll interaction are 9%pts and 11%pts respectively based on cycle efficiency
(out of the entire non-profile loss, 56%pts).
102
2.6
-UnstedyCFDl
-Unsteady
2
.......
a. 1.6 -.
.
0
I
- 2 -
1.5
40
-0
-
-
*1
8
-.......
....
..............
-.....
........ -
......
-...
....... .......
-
................
CFD
06
0.6
a.
0
0
so
so
40
Turbine Local Efficiency [%]
20
0
100
(a) Peak Torque Scenario
20
40
60
80
Turbine Local Efficiency [%]
100
(b) Turbo Initial Transient Scenario
-
Figure 5-8: Locus of Power vs Turbine Instantaneous Efficiency on Two Scenarios
Turbine has relatively low instantaneous efficiency in the Turbo Initial Transient case
due to suction side separation near maximum power extraction point.
Full unsteady CFD
Extract turbine inlet information (t)
Re-run unsteady CFD
Such that
0 = 0* no
Ideal IGV
Mass averaged inlet
m,1. Abs. angles shifted
2. Tt, pt maintained
Figure 5-9: Conceptual Ideal IGV Implementation - The inflow angle is artificially
realigned to turbine blade while the stagnation temperature and stagnation pressure
at the turbine wheel inlet is maintained. This will constitute the fictitious inlet
boundary condition for the new unsteady CFD with ideal IGV.
103
104
Chapter 6
Maximum Power Extraction
Condition and Proposed Multi-Tiered
CFD Approach
In Industry, the turbine system performance is often estimated using a single (or a
few) steady CFD points; this would be the practice during the preliminary phase of
a design process where frequent design changes are anticipated. However, it is not
clear how reliable the process is to extrapolate the steady CFD based result to the
unsteady pulsating flow situation. For example, if one design shows 1% increment
in total-to-static efficiency at a chosen steady point, will that design be better in a
pulsating environment? The answer to the question is crucial for assessing the utility
of common practice in Industry. In this chapter, we propose multi-tiered approach
(from full unsteady CFD to single steady CFD) with quantitative guidelines such that
an appropriate approach can be chosen depending on the goal of analysis and design.
6.1
Maximum Power Extraction Condition
The maximum power extraction point can be a representative point not only because
it is the point where the turbine wheel is extracting most of the power but also
because it is the operating point that provides huge potential for improvement. Note
105
the large gap between the power extraction from the current design (green line) and
the power from the ideal system (black line) near the maximum power extraction
point in Figure 6-1. As such, it becomes obvious that the early design phase should
anchor on the maximum power extraction point. Then, the issue is how one could
set up the maximum power extraction point without any prior unsteady CFD results.
In other words, we firstly need to explore what condition constitutes the maximum
power extraction.
ft .
i
--deal
..
..
..
.-.
....
.
3
022.5
Unsteady CFD
System
-UUnsteady CFD
Ideal System
-
9.
................-..
........
-..
....
0
-...-.
.-.
......
.
-.
...-.
..
-....
...
C.L
-.
...... .....
--..
-..
...
..
.....
......
-..
....
...
.....-
p3
.......
................................
-.....
2
..... ..
.
2
0
-- ..
......--.
..
...
.. ..
..
0
0.2
..
.-.
...
......
...
...
...
0.4
0.6
Time/Period
0.
0.8
1
W0
0.2
0.4
0.6
TImeIPerIod
0.8
1
(b) Turbo Initial Transient Scenario
(a) Peak Torque
Figure 6-1: Quasi-1D Diffuser Model
Since, the only power generating mechanism is through the turbine wheel, the
power is thus given by
=
7turbrnturbCpTt,turbln (1
PturbOut
-
W
(6.1)
Pt,turbIn
The stagnation pressure and temperature at turbine wheel inlet and outlet are
mass averaged quantity. Now isentropic velocity Cien is given as
a~i
2
cpTt,turbln
(I
PturbOut
-
Cisen =
Pt,turbIn
(6.2)
From the observation based on computed results, the ratio of static pressure at
turbine wheel outlet to stagnation pressure at turbine wheel inlet (PturbOut/Pt,turbln)
106
can be approximated to the ratio of atmospheric pressure at diffuser outlet to stagnation pressure at turbine wheel inlet (Pa/Pt,turbin)l. Therefore, the isentropic velocity
can be approximated as,
'Y-1
Cisen ~
2
(6.3)
Pa
1
CpTt,turbIn
\Pt,turbln/
Now, we can scale various terms in equation (6.1).
'tturb -1
mturb
~ PturbInUr,turbInAturbIn
PtturbIn
RT,turb1,
CisenAturbIn
(6.4)
-1
CP
tturbn
I
PturbOut
2
(PtturbIn
isC
Therefore,
W
1l_( Pt,turbln
2 RTt
CN
Aub
CenAturbIn
~
65
(6.5)
The results on Figure 6-2 shows that the scaling equation (6.5) provides an adequate estimation of power. The implication is that the maximum power extraction
condition can be identified from the turbine wheel inlet stagnation pressure and stagnation temperature regardless of the turbine wheel performance
(Tturb).
This is be-
cause the impact from small variation in turbine wheel efficiency (around factor of 2)
is effectively overwhelmed by dramatic change in isentropic velocity cubed (around
factor of 10).
The maximum power extraction condition will provide the boundary condition
for the to be discussed single steady CFD. The single steady CFD constitutes the
simplest of the multi-tiered approach. Each approach is discussed in detail in the
following section.
'It is noted that the static pressure rise (Pa - PturbOut) compared to dynamic pressure at turbine
wheel exit cannot be negligible. However, the difference between the two static pressures is small
compared to turbine wheel inlet stagnation pressure (Pa - PturbOut << Pt,turbln).
107
...
..........
1
-
0.8
-PowerS
-
-
I
Power
-- Power
-
ale.
0.6
00.6
-
E
Powersa
-.
E
0.4 .......
N0.4
E
.... ....
...
..
..... ...
... ....
....
E
0.2
0.2
0
0.2
0.4
0.6
Time/Period
0.8
1
10
(a) Peak Torque
0.2
0.4
0.6
TimePeriod
0.8
1
(b) Turbo Initial Transient Scenario
Figure 6-2: Power scaling
6.2
Multi-Tiered CFD Approach
In general, four tiers of CFD approach (in the order of decreasing complexity and
fidelity) is discussed: (1) Full unsteady CFD; (2) LQS (Locally Quasi-Steady) approach; (3) QS (Quasi-Steady) approach; (4) Single CFD at maximum power extraction. Each method is discussed and assessed in the following subsections.
6.2.1
Full Unsteady CFD
A full unsteady CFD is the approach where all the time-resolved flow phenomenon
is simulated with highest-fidelity within the confine of the selected CFD solver.
However, this approach is usually not a feasible option in practice due to its demand/requirements in computational resources. As such, it is preferred to reserve
the full unsteady CFD as the final check near the end of design phase.
6.2.2
LQS (Locally Quasi-Steady) Approach
In LQS approach, we reconstruct the full unsteady system behavior from sub-component
modelings where each of modeling reduces the order of complexity either in tempo-
ral dimension or in spatial dimension.
The key trait of the approach is that the
mass/energy/entropy storage effect in unsteady sub-components are accounted for.
108
This approach is discussed in-depth in Chapter 4.
6.2.3
QS (Quasi-Steady) Approach
This is another simple approach to the problem of interest: turbine system performance under unsteady pulsating flow. In QS approach, we neglect the mass/ energy/ entropy
storage throughout the system. Thus, we effectively assume that the system adapts
to the inlet boundary condition instantaneously.
Interestingly, the approach still provides a useful estimate of the system performance implying that the storage effect of mass/ energy/ entropy throughout the system
can be neglected for estimating the general trend of mass flow rate and power extrac)
tion 2 . The turbine system performance is qualitatively (although not quantitatively 3
determined based on QS approach (see Figure 6-3). However, as can be expected,
the consequence in neglecting the volute storage effect can be inferred in Figure 6-4.
A brief discussion on the mass flow fluctuation at the volute inlet is presented in
Appendix B.
6.2.4
Single Steady CFD at Maximum Power Extraction Condition
Lastly, the simplest among the multi-tiered approach is the single steady CFD. As
discussed in section 6.1, we focus on the MPE (Maximum Power Extraction) condition. As seen from Figure 6-2, the power scaling equation (6.5) can be utilized to
identify the MPE condition. However, all we have is the stagnation pressure and
the stagnation temperature at the volute inlet but not at the turbine wheel inlet. In
steady flow environment, both the stagnation temperature and the stagnation pressure at the turbine wheel inlet is identical to variables at the volute inlet if the loss
in stagnation pressure is neglected. However, this cannot be the case in unsteady
flow situation. We need to account for the mass/energy/ entropy storage effect in the
2
Recall that reduced frequency for volute is slightly larger than unity (see subsection 1.2.3)
The difference between QS approach and unsteady approach is around 10%pts based on cycle
efficiency.
3
109
volute to estimate the stagnation pressure and stagnation temperature at the turbine
wheel inlet.
A simple estimation technique is suggested based on observations.
Near MPE
point, the rise in stagnation temperature at the volute inlet is not delivered to the
turbine wheel inlet yet. However, the stagnation pressure rise is almost synchronized
between the volute inlet and the turbine wheel inlet as static pressure propagation
is mainly driven by acoustic speed4 . Therefore, we can assume that the stagnation
pressure at the volute inlet is effectively the same as the stagnation pressure at the
turbine wheel inlet with respect to characterizing turbine wheel performance.
In contrast, the stagnation temperature propagation is set by the mean convection
speed. The range of Mach number (the ratio of the convection speed to the acoustic
speed) in the volute is from 0.1 to 0.5; therefore, the convection of the stagnation
temperature is slower than the static pressure propagation. However, the stagnation
temperature at the turbine wheel inlet is increasing due to the rise of the stagnation
pressure even before a convection time is passed. To sum up, the convection of the
stagnation temperature (driven by mean convection speed) can be neglected compared
to the increase of the stagnation temperature due to the rise of the stagnation pressure
(driven by acoustic speed) at least at MPE point 5 since the Mach number in the volute
is low. This process can be modeled with an isentropic relation. Note the reference
value is chosen as time averaged quantity.
Pt,turbIn
(tturbln
I
(Pt, turbln
,6
(6.6)
)
TIturbln
This can be approximated further based on the near instantaneous stagnation pressure
4 The portion from dynamic pressure is negligible compared to the turbine wheel outlet static
pressure. Note that the pressure ratio across the turbine wheel (stagnation pressure at turbine
wheel inlet over static pressure at turbine wheel outlet) is the quantity of interest for turbine wheel
characterization.
5 0f course, the convection of the stagnation temperature will impact the turbine wheel performance afterwards.
110
propagation assumption discussed above.
(
tturbIn
(Pt,voluteIn
Tt ,voluterIn
(6.7)
PtvoluteIn
Now, the turbine wheel inlet temperature is readily available from the boundary
condition. The results in Table 6.1 to 6.4 indicate that the simulated turbine wheel
flow environment at MPE point based on aforementioned approximation is nearly the
same as that from full unsteady CFD result.
The success of single steady CFD is based on the quasi-steady behavior of turbine
wheel. As long as the turbine wheel inlet boundary condition can be estimated as
described above, the turbine wheel performance estimated using single steady CFD
should be reasonably close to unsteady flow situation.
Table 6.1: Comparison of Turbine Flow Environment between Unsteady CFD and
Single Steady CFD - MPE on Inlet 1 side pulse, Peak Torque: Notice that the single
steady CFD provides accurate estimation on turbine wheel efficiency, turbine pressure
ratio, corrected temperature and inflow angles at maximum power extraction point.
Case
Unsteady CFD
Single Steady CFD
Effciency []Pressure Ratio
67
67
3.6
3.4
Corrected Temperature
0 [0]
[0]
0.6
0.8
30
34
19
20
Table 6.2: Comparison of Turbine Flow Environment between Unsteady CFD and
Single Steady CFD - MPE on Inlet 2 side pulse, Peak Torque: Notice that the single
steady CFD provides accurate estimation on turbine wheel efficiency, turbine pressure
ratio, corrected temperature and inflow angles at maximum power extraction point.
Case
Unsteady CFD
Single Steady CFD
Effeiency []Pressure Ratio
67
3.4
67
3.2
111
Corrected Temperature
0.7
#3[0]
31
[01
-46
0.8
31
-46
Table 6.3: Comparison of Turbine Flow Environment between Unsteady CFD and
Single Steady CFD - MPE on Inlet 1 side pulse, Turbo Initial Transient: Notice
that the single steady CFD provides accurate estimation on turbine wheel efficiency,
turbine pressure ratio, corrected temperature and inflow angles at maximum power
extraction point.
Case
Unsteady CFD
Single Steady CFD
Effciency %]Pressure Ratio
35
2.1
38
2.1
Corrected Temperature
6.0
5.8
[0]
57
58
[0]
18
20
Table 6.4: Comparison of Turbine Flow Environment between Unsteady CFD and
Single Steady CFD - MPE on Inlet 2 side pulse, Turbo Initial Transient: Notice
that the single steady CFD provides accurate estimation on turbine wheel efficiency,
turbine pressure ratio, corrected temperature and inflow angles at maximum power
extraction point.
Case
Unsteady CFD
Single Steady CFD
6.3
Effeiency []Pressure Ratio
37
39
2.0
2.0
Corrected Temperature
5.5
5.6
#[0]
54
53
[*]
-43
-46
Limitations in Steady CFD Results
Large discrepancy between steady CFD based estimation and unsteady CFD result
can occur for the entire system performance.
For example, if a fictitious steady
boundary condition is formulated by selecting the time averaged inlet stagnation
pressure and stagnation temperature, the system efficiency from the steady CFD can
differ from the unsteady CFD result by 9%pts (Table 6.5) to 21%pts (Table 6.6).
Moreover, even if the fictitious steady boundary condition is weighted by the ideal
work in time averaging procedure, the system performance estimated based on the
steady CFD can be misleading. Note that the categorization of losses are not aligned
correctly in Table 6.7 and Table 6.8. For example, in Table 6.5, the distribution of
-
the origin of loss based on steady CFD (volute - 1%, turbine wheel - 7%, diffuser
25%, boundary layer - 7%) is not aligned with that based on unsteady CFD (volute
- 3%, turbine wheel - 12%, diffuser - 19%, boundary layer - 7%).
112
This is because
the performance of each sub-component depends on the local boundary condition
subjected to storage effect through the system. Although useful information can be
extracted for the turbine wheel at MPE point, a caution is warranted when assessing
cycle performance for the entire system.
Table 6.5: Comparison of Loss Categorization Result between Unsteady CFD and
Single Steady CFD - Cycle Averaged Quantity, Peak Torque: The cycle loss estimated
in steady CFD differs from unsteady CFD by 9%pts. Also, the distribution of the
origin of loss based on steady CFD (1%, 8%, 14%, 9%) is not aligned with that based
on unsteady CFD (3%, 12%, 19%, 7%).
Case
Loss []Volute []Turbine []Diffuser [%]
Boundary Layer[%
Unsteady CFD
41
3
12
19
7
Cycle Averaged
Single Steady CFD
32
1
8
14
9
Table 6.6: Comparison of Loss Categorization Result between Unsteady CFD and
Single Steady CFD - Cycle Averaged Quantity, Turbo Initial Transient: The cycle loss
estimated in steady CFD differs from unsteady CFD by 21%pts. Also, the distribution
of the origin of loss based on steady CFD (3%, 11%, 19%, 10%) is not aligned with
that based on unsteady CFD (6%, 25%, 23%, 11%).
Case
Unsteady CFD
Loss []Volute [%]
Turbine []Diffuser []Boundary Layer [%]
64
6
25
23
11
43
3
11
19
10
Cycle Averaged
Single Steady CFD
6.4
Guideline for Selecting a Specific Approach
Based on the observations up to now, a quantitative guideline on multi-tiered approach is suggested.
1. Full unsteady CFD: Efficiency resolution < 1%pt
It is recommended to use full unsteady 3D CFD only at the final phase of design
113
Table 6.7: Comparison of Loss Categorization Result between Unsteady CFD and
Single Steady CFD - Ideal Work Weighted Cycle Average Quantity, Peak Torque:
The distribution of the origin of loss based on steady CFD (1%, 7%, 25%, 7%) is not
aligned with that based on unsteady CFD (3%, 12%, 19%, 7%).
Case
Unsteady CFD
Ideal Work Weighted
Single Steady CFD
Loss []Volute []Turbine []Diffuser []Boundary Layer[%
41
3
12
19
7
40
1
7
25
7
Table 6.8: Comparison of Loss Categorization Result between Unsteady CFD and
Single Steady CFD - Ideal Work Weighted Cycle Average Quantity, Turbo Initial
Transient: The distribution of the origin of loss based on steady CFD (1%, 18%,
36%, 10%) is not aligned with that based on unsteady CFD (6%, 25%, 23%, 11%).
Case
Unsteady CFD
Ideal Work Weighted
Single Steady CFD
Loss []Volute []Turbine []Diffuser []Boundary Layer[%
64
6
25
23
11
65
1
18
36
10
refinements. The full unsteady CFD will provide the highest fidelity result with
instantaneous efficiency resolution of less than 1%pt.
2. LQS (Locally-Quasi Steady Approach): Efficiency resolution ~ 1%pt
LQS will be the most reasonable approach during design process. Once steady
data pool is constructed (still within reasonable computational cost), the performance of the turbine system can be estimated (with storage effect appropriately
modeled) to provide an adequate values of instantaneous efficiency resolution
during a pulsation cycle.
3. QS (Quasi Steady Approach): Efficiency resolution ~ 10%pts
The resolution of instantaneous efficiency calculated from QS approach will
provide a general trend of the turbine system performance (mass flow and power)
over a pulsation cycle.
However, this approach cannot provide an adequate
estimation of the turbine wheel performance for design purpose.
114
4. Single Steady CFD at MPE condition: Efficiency resolution ~ 3%pts
During the design phase, this approach is recommended due to its practical
utility despite its simplicity. The turbine wheel performance can be easily estimated based on simple procedure delineated in this chapter. However, it is
pointed out that the cycle performance estimated based on single steady CFD
should be interpreted with caution.
6.5
Summary
In this chapter, a simple technique to estimate the performance of the turbine wheel
at MPE condition is proposed. Also, a guideline is put forward on the utility and
interpretation of the four tiers of CFD approaches: (1) Full unsteady CFD, (2) LQS
(Locally Quasi-Steady) Approach, (3) QS (Quasi-Steady) Approach, (4) Single Steady
CFD. Lastly, it is argued that a caution must be accompanied while extracting cycle
performance from a single steady CFD.
115
..
-
I
i
I
'WJ
Unsteady CFD
Quasi-Steady Assumption
...
..
.- ...
0.8[
CFD
-Unsteady
6Qua-Steady Assumption
-...
..
.............
.
1.2
.. .......
....
..
--.....
....-............... 100Time..
..
r"
i
0.6
.3
~~.....~..~~~
....~
.
0.4
0.21
U0
0.2
0.4
0.6
Time/Period
0.8
00
1
0.2
0.4
0.6
0.8
1
Time/Pedod
6
Unsteady CFD
I
-
I
0
r
Unsteady CFD
Quasi-Steady Assumption
100
Quasi-Steady Assumption
Ideal System
20
..
....
-...-...40
.............. -..
.
I
s0
.
-
-
I-
0
0.2
0.4
0.6
Time/Period
0.8
20F
0
1
0.2
0.4
0.6
Time/Period
0.8
1
IUUb
-Unsteady
CFD
-- Quasi-Steady Assumption
.0--T-power
......
40
...
...
System
.......
-...
2 0 ......
0.2
.
... ....-.. -.. -..
.. ..
T0
0.4
.
...
..
..
...
0.
Time/Period
..
.
SO
.
-Ideal
0.8
1
Figure 6-3: Comparison between Unsteady CFD and QS Approach based on Turbine
Performance - Normalized mass flow is the mass flow normalized by the maximum
mass flow rate through turbine wheel inlet from unsteady CFD. Also, MFR is mass
flow rate ratio defined at the turbine wheel inlet as the ratio of mass flow through
inlet 1 side scroll to the total mass flow rate into the turbine wheel inlet. Note the
MFR is sometimes above unity or below zero due to reverse flow. Lastly, the work is
calculated by integrating the power with respect to the time for each case.
116
2
---
Unsteady CFD
Quasi-Steady Assumption
0.5
--
-
-
0
E
-0.5
0
0.2
0.4
0.6
Time/Perlod
0.8
1
-
Figure 6-4: Comparison between Unsteady CFD and QS Approach at Volute Inlet
Normalized mass flow is the mass flow normalized by the maximum mass flow rate
through turbine wheel inlet from unsteady CFD.
117
118
Chapter 7
Summary and Future Work
This chapter will provide a summary of the thesis followed by a delineation of the
key findings. The chapter concludes with a recommendation for future works.
7.1
Summary
In this thesis, a representative vehicular turbocharger turbine system performance
under unsteady pulsating flow environment is assessed. First, a rigorous definition
of unsteady system performance is derived from physical principles to quantitatively
elucidate the role of mass/energy/entropy storage rate on the ideal performance. Second, Locally Quasi-Steady (LQS) flow models for characterizing the performance of
subcomponents constituting the turbine system are formulated and assessed. Third,
the origin of the losses from unsteady pulsating environment are traced in order to
identify the potential for improvement of the turbine system performance. Fourth,
the condition of MPE (Maximum Power Extraction) is formulated based on the isentropic velocity determined by the turbine wheel boundary condition. Finally, guidelines on multi-tiered CFD approach consists of full unsteady CFD, LQS (Locally
Quasi-Steady) approach, QS (Quasi-Steady) approach, and single steady CFD are
suggested for selecting an appropriate tier based on a criterion on the required efficiency uncertainty bandwidth.
119
7.2
Key findings
1. The turbine system under unsteady pulsating flow representative of that for a
vehicular turbocharger can be decomposed into simpler sub-components. Each
sub-component has a reduced order of complexity either in temporal dimension
(from unsteady to steady) or in spatial dimension (from three dimension to
one dimension) based on the flow characteristics representative of each subcomponent to a specified flow pulsation. Wastegate port loss, diffuser loss, and
turbine wheel performance are adequately described as quasi-steady; thus the
characteristics of each can be determined based on a set of steady CFD. The
volute storage effect and the diffuser pressure recovery can be determined on an
unsteady basis and using quasi-1D Euler equation.
2. Loss categorization based on each loss mechanism is presented so as to provide a
quantitative guideline on what needs attention for further improvement on the
system performance. Diffuser is identified as an important sub-component that
accounts for major fraction of losses (more than one third of losses) for both Peak
Torque and Turbo Initial Transient operations. And, the importance of radial
scroll interaction (1/5 of the entire non-profile loss) on Turbo Initial Transient
operation raises the need of redesigning the radial scroll interaction. Also, an
active flow management strategy with variable inlet guide vane appears to be
reasonable (although practically not applicable for automobile turbochargers)
for Turbo Initial Transient operation since significant fraction (1/6 of the entire
non-profile loss) of loss occurs due to inflow angle mismatch at turbine wheel
inlet.
3. The condition of MPE (Maximum Power Extraction) is determined as the moment where the power scaling equation (6.5) becomes maximum.
It corre-
sponds to the condition of maximum isentropic velocity which is defined with
the pressure ratio across the turbine wheel and the stagnation temperature at
the turbine wheel. A single steady CFD based on MPE condition constitutes
the simplest implementation of the multi-tiered CFD approach. The antici120
pated resolution for each tier is - based on cycle efficiency - below 1%pt, around
1%pt, 10%pts, and around 3%pts for full unsteady CFD, LQS (Locally QuasiSteady) approach, QS (Quasi-Steady) approach, and single steady CFD at MPE
(Maxiumum Power Extraction) point respectively.
7.3
Recommendation for Future Work
1. There are still a few incomplete blocks needed to put the LQS (Locally QuasiSteady) approach on a complete implementable basis. Firstly, the model for
radial scroll region where the flow is distributed into the turbine wheel has not
been completed. The modeling of the radial scroll region should provide an
appropriate interface model between the radial scroll region and the turbine
wheel inlet. Also, we have not yet constructed the interface model for turbine
wheel outlet to the diffuser inlet.
2. The realization of the improvement suggested from loss categorization has not
been accomplished. Especially, flow management strategy (either active or passive) for diffuser loss, turbine inflow angle mismatch and radial scroll interaction
are suggested to be assessed due to their significance.
121
122
Appendix A
Frozen Rotor Interface
In this chapter, we discuss the meaning of frozen rotor interface and the impact from
applying this approximated interface. The frozen rotor interface is an approximated
interface treatment assuming that the unsteadiness due to the rotating motion of the
turbine wheel has negligible impact on turbine wheel performance. The use of the
frozen rotor interface on the current research is appropriate as the discrepancy from
the higher fidelity interface (rotating impeller) is small compared to the resolution of
our interest.
Let us define the reduce frequency to be the ratio of the flow residence time through
the turbine wheel to the blade pass time. On the physical situation experienced by
the turbine wheel (see Figure A-1), the reduced frequency can be interpreted as
the number of inlet locations felt by a passage in the turbine wheel during the flow
residence time through it.
Two extremes are considered to appreciate the meaning of the reduced frequency.
If the reduced frequency is much less than 11 (total number of locations), this implies
the turbine wheel is effectively frozen during the time a fluid particle passes through
a passage. It is what is assumed in the frozen rotor interface. On the other limit, the
reduced frequency can be much larger than 11. It indicates the situation where each
passage takes the flow from all inlet locations effectively mixing out the turbine wheel
inlet non-uniformities. This is the motivation behind the mixing-plane. For our case,
the reduced frequency is order of 3, less than 11. Therefore, the choice of the frozen
123
.........
.
. ...
....
-
...
..
. .. .....................
rotor interface is more favorable than the mixing plane.
Figure A-1: Turbine Inlet Interface Environment - The turbine wheel rotates in clockwise direction and the flow enters the interface through 11 passages
However, there is a difference between the frozen rotor interface based result and
the rotating impeller based calculation where the rotating motion of the turbine wheel
is fully accounted for on each time step. The comparison between the results from the
two interface models is presented in Figure A-2. Although rotating impeller case has
small fluctuations, the general trends of the turbine wheel performance for the two
cases are practically identical. The FFT analysis on the difference between the two
interfaces (Figure A-3) identifies the fluctuation to be a small perturbation induced
by the periodic blade passing motion on the turbine wheel inlet flow.
124
..
.... ..
....
............
. ......
.........
..
..
......
...
...
..
...
.....
2.6
-
21
* Frozen Rotor
Rotating impeller
-
--
CL
1.65
I
0.6
I
0
SC
0.06
0.1
0.16
0.2
TimelPeriod
0.26
0.3
Figure A-2: Comparison of Frozen Rotor Interface and Rotating Impeller Interface
- The result from frozen rotor interface (green) is practically identical to the result
from rotating impeller interface.
0.06
0.04
Blade pas
..
..
.................
S0.02
0.
.
1.0.03
frequency
I
......
....-
0.01
0
0
600
1000
1600
Frequency X Period
- -...........
2000
Figure A-3: FFT of the Difference between the Two Interfaces - A strong peak is
identified at the blade pass frequency. This indicates the difference between the two
interfaces is originated from the blade passing motion.
125
126
Appendix B
Volute Inlet Mass Flow Fluctuation
The mass flow rate at inlet to the volute is fluctuating as the prescribed inlet stagnation pressure drops (but not fluctuating). In this chapter, this phenomena is discussed.
Figure B-1 and Figure B-2 is the unsteady calculation result from the series of
numerical probes along the volute. Mass flow rate is normalized by the maximum
mass flow at the inlet. It is noted that the colors of the probes are matched with
the measured mass flow rate curves. There are two observations: (1) The mass flow
fluctuation is a general phenomenon. It happens for both operations (Peak Torque
and Turbo Initial Transient). (2) The fluctuation decays as the flow travels along the
volute. Thus, the phenomenon itself is not of severe concern for the performance of
the turbine wheel.
The phenomenon can be explained as a quasi-1D unsteady storage effect: the
quasi-iD volute model (Chapter 4) can assess the inlet fluctuation as validated in
Figure B-3.
As we are convinced that the quasi-iD model is sufficient to capture the fluctuation
at the inlet, we can perform simple manipulation on the quasi-1D model thus to assess
the flow mechanism. We will hypothesize mechanisms and analyze each of them.
The first hypothesis is that the fluctuation is purely due to the volute storage effect
not due to the interactions with the downstream components. In order to validate the
hypothesis, we cancel out the downstream component effect (outlet static pressure
perturbation) and see if the fluctuation still exists. Quasi-iD Euler equation is solved
127
...
..
......
..
....
-Probe
-Probe
1.2
-Probe
1
-Probe
-Probe
-Probe
I.
I
4
7
10
13
17
8
-
O.
Probe I
Probe 4
-Probe7
Probe 10
13
-Probe
-- Probe 17
-
a6
*1
O0A
0.2
0
0.2
0.4
0.6
0.8
0.2
1
TimelPeriod
0.4
0.6
TimelPeriod
0o
1
Figure B-1: Volute Inlet Mass Flow Fluctuation, Peak Torque Operation - Normalized
mass flow rate from numerical probes are overlaid. The color of the line matches the
color of the corresponding probe location. Notice the sever mass flow fluctuation near
the volute inlet (blue and red).
with a constant outlet static pressure instead of the time-accurate static pressure
variation from the unsteady 3D CFD. Since the mass flow magnitude itself is not of
interest, the mass flow rate is normalized such that it starts from zero and has the
maximum of unity. The ID volute model still shows the fluctuation behavior implying
that the inlet mass flow fluctuation is originated from the volute storage effect not
from the downstream static pressure coupling (Figure B-4).
Now, the geometrical configuration of the volute is assessed. Since we only focus
on the trend of the mass flow fluctuation behavior, the geometry is simplified to a
cylindrical duct with linear area distribution along the flow direction. Area ratio (AR)
is defined as the ratio of the outlet area to the inlet area. The original configuration
is AR of 0.25. Also, length ratio (LR) is defined as the normalized length based on
the original length of the volute. Thus, the original configuration is LR of 1.00.
128
1.4
Probe 1
4
1.2
It
.1
-Probe
-Probe?7
Probe 10
Probe 13
I
0.8
--
1 0.8
10.6
Probe 17
-Probe1
-- Probe 4
- Probe?7
-Probe
10
-Probe
-Probe
18
17
0.6
IOA L
_
_
_
0.4
0.2-20.
0
0.2
0.4
0.6
TimelPeriod
0.8
1
00
0.2
0
0.6
TimeIPerod
0.8
1
-
Figure B-2: Volute Inlet Mass Flow Fluctuation, Turbo Initial Transient Operation
Normalized mass flow rate from numerical probes are overlaid. The color of the line
matches the color of the corresponding probe location. Notice the sever mass flow
fluctuation near the volute inlet (blue and red).
Firstly, a parameter study is performed on area ratio (AR). The result is plotted
in Figure B-5. There are two observations: (1) For AR less than unity, the fluctuation
is alleviated as AR increases. (2) There is no fluctuation beyond AR greater or equal
to unity. Therefore, it appears that mass flow fluctuation is from the geometrical
blockage from the volute configuration connected with the volute mass storage effect.
The second parameter study is on length ratio (LR). It is noted that the first
bounce off time of mass flow fluctuation is delayed as LR is increased. The bounce
off time is matched with the acoustic wave travel time from the inlet to the outlet
and then back to the inlet. Thus, it can be inferred that the mass flow rebounds as
the pressure wave (leaved at maximum stagnation pressure) comes back to the inlet.
In summary, the volute inlet mass flow fluctuation can be explained by the volute
mass storage effect and the geometric blockage effect where the volute configura129
1. A I
1.
Inlet 1: Volute ID model
Inlet 1: Unsteady CFD
I-
I
_______
-
Inlet 2: Volute 1D model
Inlet 2: Unsteady CFD
I
1
.
..
.---.-....
..
.............
-- .......
.
.....
-..---
.
- -..-..
..-
-..
0.6
-
..- . --...
..........
..........
z 0
z
0.3
0.4
0.6
Tlme/Perlod
0
0.8
0.6
-..
....... -..
.....
.
0.6
0.9
1
Time/Period
1.1
(a) Inlet 1 Side Inlet Mass Flow Fluctuation (b) Inlet 2 Side Inlet Mass Flow Fluctuation
Figure B-3: Inlet Mass Flow Fluctuation - Volute 1D model (blue and red) are in
good agreement with unsteady 3D CFD (green and magenta). This implies that the
inlet mass flow fluctuation can be understood in a quasi-1D basis.
tion has a decreasing cross sectional area distribution along the flow direction. It is
noted that the acoustic wave traveling between the inlet and the outlet of the volute
determines the first bounce off time of mass flow fluctuation.
130
0.8 --........
--
Inlet 1: Volute ID model
-.Inlet 1: Unsteady CFD
0.2
Cr 0.4
---..
. --- ---...
...
- ---..
.....
....
- --...
----..
..
-- ... -.. ..
-..
- . - -.-
~0.2
0
-0.2
2
0.3
0.4
0.5
Time/Perlod
0.6
0.7
Figure B-4: Decoupled Volute Model - Constant outlet static pressure case (blue)
shows qualitative agreement with unsteady 3D CFD result (green). It implies that
the mass flow fluctuation is not originated from the static pressure coupling from the
downstream components.
I
-AR
II0.8 ...---.
-0r
13%
-- --.-AR
25%
0.6
-
0.4
-
0.2 - . ....
-. ........
..
AR
AR
AR
AR
50%
100%
150%
200%
.. .... ....
0
U~0
-0.2
0.2
0.3
0.4
0.5
0.6
0.7
Time/Period
Figure B-5: Impact of Area Ratio - Notice the strong correlation between the area
ratio and the degree of fluctuation. The fluctuation becomes severe as AR (the ratio
of the outlet area to the inlet area) decreases.
131
..
.. .. ....
..
0.8
---
-
I
-LR 13%
-- ------ - - LR 25%
-LR 50%
-----.-.---- --- --- - -L
100%
0.6
0r
Y~--11R150%
0.4
-
-
LR 200%
---
-
0.2
--
0
a~ 0
-0.2
0.2
0.3
0.4
0.5
Time/Period
0.6
0.7
Figure B-6: Impact of Length Ratio - Notice the strong correlation between the length
ratio (LR) and the time delay on the first bounce off time. It is noted that the bounce
off time can be explained by the acoustic wave travel time.
132
Bibliography
[1]
C. S. Tan and B. Sirakov. Statement of Agreement: Performance Improvement
of a Turbocharger Twin Scroll Type Turbine Stage, 2013.
[2] Richard Stone. Introduction to Internal Combustion Engines. Society of Automotive Engineers, Inc., third edition, 1999.
[3]
E. M. Greitzer, C. S. Tan, and M. B. Graf. Internal Flow. Cambridge University
Press, Cambridge, 2004.
[4]
G. D. Roy, S. M. Frolov, a. a. Borisov, and D. W. Netzer. Pulse detonation
propulsion: Challenges, current status, and future perspective. Progress in Energy and Combustion Science, 30:545-672, 2004.
[5]
A. Rasheed, V. E. Tangirala, C. L. Vadervort, and a. J. Dean. Interactions of a
Pulsed Detonation Engine with a 2D Blade Cascade. In 42nd Aerospace Sciences
Meeting and Exhibit, AIAA 2004-1207, number January, 2004.
[6] Ron Ho Ni, William Humber, Michael Ni, Rolf Sondergaard, and Mike Ooten.
Performance Estimation of a Turbine under Partial-Admission and Flow Pulsation Conditions at Inlet, GT2013-94811. In Proceedings of Proceedings of ASME
Turbo Expo 2013, San Antonio, Texas, USA, 2013.
[7] Takayuki Kojima, Nobuyuki Tsuboi, Hideyuki Taguchi, Hiroaki Kobayashi, Tetsuya Sato, Yu Daimon, and Kazuaki Inaba. Design Study of Turbine for Pulse
Detonation Combustor. In 43rd AIAA/ASME/SAE/ASEE Joint Propulsion
Conference & Exhibit, AIAA 2007-5081, number July, Cincinnati, OH, 2007.
[8]
Ayaka Nango, Kazuaki Inaba, Takayuki Kojima, and Makoto Yamamoto. Numerical Study on Single-Stage Axial Turbine with Pulse Detonation Combustor.
In 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum
and Aerospace Exposition, AIAA 2009-294, number January, Orlando, Florida,
2009.
[9] Kurt P. Rouser, Paul I. King, Frederick R Schauer, Rolf Sondergaard, and John L
Hoke. Unsteady Performance of a Turbine Driven by a Pulse Detonation Engine.
In 48th AIAA Aerospace Sciences Meeting Including The New Horizons Forum
and Aerospace Exposition, AIAA 2010-1116, number January, Orlando, Florida,
2007.
133
[10] R. Aymanns, J. Scharf, T. Uhlmann, and D. Liickmann. A Revision of Quasi
Steady Modelling of Turbocharger Turbines in the Simulation of Pulse Charged
Engines. In 16th Supercharging Conference, 2011.
[11] Ambady Suresh, Douglas C. Hofer, and Venkat E. Tangirala. Turbine Efficiency for Unsteady, Periodic Flows. Journal of Turbomachinery, 134(May
2012):034501, 2012.
[12] Nicholas C Baines. Turbocharger turbine pulse flow performance and modelling25 years on. Proc IMechE Turbochargers and Turbocharging Congress 2010,
(7):347-362, 2010.
[13] C D Copeland, P Newton, R F Martinez-Botas, and M Seiler. A Comparison of
Timescales within a Pulsed Flow Turbocharger Turbine. In 10th International
Conference on Turbochargers and Turbocharging, pages 389-404, 2012.
[14] Teng Cao, Liping Xu, Mingyang Yang, and Ricardo F Martinez-botas. Radial
Turbine Rotor Response to Pulsating Inlet Flows, GT2013-95182. In Proceedings
of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition, San
Antonio, Texas, USA, 2013.
[15] M H Padzillah, M Yang, W Zhuge, and R F Martinez-Botas. Numerical and
Experimental Investigation of Pulsating Flow Effect on a Nozzled and Nozzleless Mixed Flow Turbine for an Automotive Turbocharger, GT2014-26152. In
Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Dnsseldorf, Germany, 2014.
[16] Mingyang Yang, Ricardo Martinez-botas, and Srithar Rajoo. Influence of Volute
Cross-Sectional Shape of a Nozzleless Turbocharger Turbine under Pulsating
Flow Conditions, GT2014-26150. In Proceedings of ASME Turbo Expo 2014:
Turbine Technical Conference and Exposition Technical Conference and Exposition, Dusseldorf, Germany, 2014.
[17] Aaron W. Costall, Robert M. McDavid, Ricardo F. Martinez-Botas, and
Nicholas C. Baines. Pulse Performance Modeling of a Twin Entry Turbocharger
Turbine Under Full and Unequal Admission. Journal of Turbomachinery,
133(April 2011):021005, 2011.
[18] Borislav T. Sirakov. Personal communication, 2015.
[19]
Katsuyuki Osako, Takao Yokoyama, Toyotaka Yoshida, Toru Hoshi, Motoki
Ebisu, and Takashi Shiraishi. Development of Twinscroll Turbine for Automotive Turbochargers using Unsteady Numerical Simulation. Technical Report 1,
Mitsubishi Heavy Industries Technical Review, 2013.
[20] Klaus A. Hoffmann and Steve T. Chiang. Computational Fluid Dynamics. Engineering Education System, Wichita, KS 67208-1078, 2000.
134
[21] J. D. Denton. The 1993 IGTI Scholar Lecture: Loss Mechanisms in Turbomachines. Journal of Turbomachinery, 115(October 1993):621, 1993.
[22] J. B. Young and R. C. Wilcock. Modeling the Air-Cooled Gas Turbine: Part
2-Coolant Flows and Losses. Journal of Turbomachinery, 124(2):214, 2002.
135