Computational Fluid Flow Analysis of Cryogenic Turboexpander Master of Technology

Computational Fluid Flow Analysis of Cryogenic Turboexpander  Master of Technology
Computational Fluid Flow Analysis of
Cryogenic Turboexpander
A Thesis Submitted in Partial Fulfilment
of the Requirements for the Award of the Degree of
Master of Technology
in
Thermal Engineering
by
Hitesh Dimri
Department of Mechanical Engineering
National Institute of Technology, Rourkela
Rourkela-769008, Odisha, INDIA
May 2013
Computational Fluid Flow Analysis of
Cryogenic Turboexpander
A Thesis Submitted in Partial Fulfilment
of the Requirements for the Award of the Degree of
Master of Technology
in
Thermal Engineering
by
Hitesh Dimri
(Roll – 211ME3188)
Under the Guidance of
Prof. Ranjit Kumar Sahoo
Department of Mechanical Engineering
National Institute of Technology, Rourkela
Rourkela-769008, Odisha, INDIA
2011-2013
DEPARTMENT OF MECHANICAL ENGINEERING
NATIONAL INSTITUTE OF TECHNOLOGY
ROURKELA, ODISHA-769008
CERTIFICATE
This is to certify that the thesis entitled “Computational Fluid Flow Analysis of Cryogenic
Turboexpander” by Hitesh Dimri, submitted to the National Institute of Technology (NIT),
Rourkela for the award of Master of Technology in Thermal Engineering, is a record of bona
fide research work carried out by him in the Department of Mechanical Engineering, under my
supervision and guidance.
I believe that this thesis fulfills part of the requirements for the award of degree of Master of
Technology. The results embodied in the thesis have not been submitted for the award of any
other degree elsewhere.
Prof. Ranjit Kumar Sahoo
Place: Rourkela
Date:
Department of Mechanical Engineering
National Institute of Technology
Rourkela Odisha-769008
i
ACKNOWLEDGEMENT
I am extremely fortunate to be involved in an exciting and challenging research project like
“Computational Fluid Flow Analysis of Cryogenic Turboexpander”. It has enriched my life,
giving me an opportunity to work in a new environment of ANSYS CFX. This project increased
my thinking and understanding capability as I started the project from scratch.
I would like to express my gratitude and respect to my supervisor Prof. Ranjit Kumar Sahoo,
for his excellent guidance, valuable suggestions and endless support. He has not only been a
wonderful supervisor but also a genuine person. I consider myself extremely lucky to be able to
work under guidance of such a dynamic personality. Actually he is one of such genuine person
for whom my words will not be enough to express.
I would like to express my sincere thanks to Mr. Balaji and Mr. Sachindra for their precious
suggestions and encouragement to perform the project work. They were very patient to hear my
problems that I am facing during the project work and finding the solutions. I am very much
thankful to them for giving their valuable time for me.
I would like to express my thanks to all my classmates, all staffs and faculty members of
mechanical engineering department for making my stay in N.I.T. Rourkela a pleasant and
memorable experience and also giving me absolute working environment where I unlashed, my
potential.
Date:
Hitesh Dimri
Roll. No. 211ME3184
M.Tech. (Thermal Engineering)
ii
ABSTRACT
Cryogenic turboexpander is the most critical component of cryogenic plant to achieve low
temperature refrigeration. A cryogenic turboexpander has many components like expansion
turbine, compressor, heat exchanger, instrumentations etc. Expansion turbine is the component
where temperature of gases decreases due to expansion and produce the coldest level of
refrigeration in the plant.
This project deals with the computational fluid flow analysis of high speed expansion turbine.
This involves with the three dimensional analysis of flow through a radial expansion turbine
using nitrogen as flowing fluid. This analysis is done using cfd packages, bladegen, turbogrid
and CFX. Bladegen is used to create the model of turbine using available data of hub, shroud and
blade profile. Turbogrid is used to mesh the model. CFX-Pre is used to define and specify the
simulation settings and physical parameters required to describe the flow through turboexpander
at inlet and outlet. CFX-Post is used for examining and analyzing results. Using these results
variation of different thermodynamic properties inside the turbine can be seen.
Various graphs are potted indicating the variation of velocity, pressure, temperature, entropy
and Mach number along streamline and span wise to analyze the flow through cryogenic turbine.
Keywords: Radial turbine, Bladegen, Turbogrid, CFX.
iii
CONTENTS
CERTIFICATE
i
ACKNOWLEDGMENT
ii
ABSTRACT
iii
CONTENTS
iv
LIST OF TABLES
vi
LIST OF FIGURES
viii
NOMENCLATURE
x
CHAPTER 1: Introduction
1
1.1 Overview of Turboexpander...………………….……………….………………...
2
1.2 Anatomy of a Cryogenic Turboexpander…………….…….………………...…...
3
1.3 Objective of the present investigation………...……………….………………….
4
1.4 Organization of the thesis ……………..……………………….…………………
5
CHAPTER 2: Literature Review
6
2.1 History of development …………………………………………………………..
7
2.2 Design of turboexpander ………………………………………………………....
11
CHAPTER 3: Theory
15
3.1 Design of Turboexpander...……………………………………………………....
16
3.1.1 Fluid parameters and layout of components ………………..………….
16
3.1.2 Design of turbine wheel ………………………….…………………….
17
iv
3.1.3 Determination of Blade Profile………………………………………....
CHAPTER 4: Computational Fluid Flow Analysis
18
21
4.1 Designing of Turboexpander in Bladegen ……………………………………….
22
4.2 Meshing of Model………………………………………………………………...
25
4.3 Physics definition of Meshed Model in CFX-Pre...................................................
28
4.4 Obtaining a Solution Using CFX-Solver.…………….…………….……...….….
30
4.5 Obtaining Results in CFX CFD-Post...…………………………….……...….…..
32
CHAPTER 5: Results and Discussion
33
5.1 Pressure variation along streamwise inlet to outlet……………………...…….….
35
5.2 Temperature variation along streamwise inlet to outlet………………………......
36
5.3 Velocity variation along streamwise inlet to outlet….….….…………………....... 38
5.4 Variation of Mach number along streamwise……………………………………..
38
5.5 Variation of density along streamwise inlet to outlet……………………………..
39
5.6 Variation of Static Entropy along streamwise…………………………………….
40
5.7 Pressure variation along spanwise hub to shroud…………………………………
41
5.8 Temperature variation along spanwise hub to shroud…………………………….
42
5.9 Velocity variation along spanwise hub to shroud………………………………...
43
5.10 Blade to blade plots for different spans………………………………………….
45
5.11 Meridional Plots…………………………………………………………………
47
CHAPTER 6: Conclusions and Future Work
49
6.1 Conclusions...……………………………………………………………………..
50
6.2 Future work…………………………………….………………………………….
50
References
51
v
LIST OF TABLES
Table 3.1: Basic input parameters for the cryogenic expansion turbine system ….…….…….
17
Table 3.2: Thermodynamic state at turbine outlet...………………………………………......
18
Table 3.3: Thermodynamic state at turbine inlet ……………………………………………..
18
Table 3.4: Coordinates for Generation of Blade Profile ……………………………………...
19
Table 3.5: Turbine blade profile co-ordinates of pressure and suction surfaces …..………….
20
Table 4.1: Physics definition for turbine rotor ……………………….……………………….. 29
Table 5.1: Variations of thermodynamic properties………….………………….……….……. 34
vi
LIST OF FIGURES
Figure 1.1: Division of cryogenic turboexpander …………………………………………………
3
Figure 3.1: State points of turboexpander………………….…………………………..……… 17
Figure 4.1: Meridional blade profile with different spans…………………………………….
23
Figure 4.2: Variation of Beta and Theta at different spans along radius ………………..……. 23
Figure 4.3: Variation of Beta and Theta ………………………………………….………....... 24
Figure 4.4: Wireframe model of turbine generated in bladegen ……………………………… 24
Figure 4.5: Solid model of turbine generated in bladegen ………………………….………… 25
Figure 4.6: Turbine rotor view after importing from Bladegen ………………………..……..
26
Figure 4.7: Turbine rotor view after setting topology ………………………………………… 27
Figure 4.8: Meshed 3D view of turbine rotor …………………….……….…………….……. 28
Figure 4.9: Flow direction at inlet and outlet ………………………………………………… 30
Figure 4.10: Wireframe and Meridional model of turbine rotor ……………….…………….
32
Figure 5.1: Pressure variation along streamwise inlet to outlet ……………………...………
35
Figure 5.2: Isometric 3D view of pressure variation …………………………………...…….
36
Figure 5.3: Temperature variation along streamwise inlet to outlet …………………….…...
37
Figure 5.4: Isometric 3D view of temperature variation ………………………………..……
37
Figure 5.5: Velocity variation along streamwise inlet to outlet …………………….……….
38
Figure 5.6: Variation of Mach number along streamwise ………………………….….…….
39
Figure 5.7: Variation of density along streamwise inlet to outlet ………….……………….
40
Figure 5.8: Variation of Static Entropy along streamwise ……………………...…………..
41
Figure 5.9: Pressure variation along spanwise hub to shroud ……………………………....
42
vii
Figure 5.10: Temperature variation along spanwise hub to shroud ……………………..…..
43
Figure 5.11: Velocity variation along spanwise hub to shroud ………………………..…….
44
Figure 5.12: Velocity Vectors at 20% Span ……………………………………………..….
45
Figure 5.13: Velocity Vectors at 50% Span …………………………………………………
45
Figure 5.14: Velocity Vectors at 80% Span ………………………………………………...
46
Figure 5.15: Mass Averaged Pressure on Meridional Surface …………………………..…..
47
Figure 5.16: Mass Averaged Relative Mach number on Meridional Surface ……………….
47
Figure 5.17: Velocity Streamlines at Blade Trailing Edge…………………………………..
48
viii
NOMENCLATURE
D
diameter (wheel)
(m)
d
diameter (shaft)
(m)
E
entropy
(J kg-1 K-1)
h
enthalpy
(J/kg)
Ke
free parameters
(dimensionless)
Kh
free parameters
(dimensionless)
M
mach number
(dimensionless)
N
rotational speed
(rev/min)
ns
specific speed
(dimensionless)
P
pressure
(N/m2)
Q
volumetric flow rate
(m3/s)
r
radius
(m)
SE
energy source
(kg m-1 s-3)
SM
momentum source
(kg m-2 s-2)
T
temperature
(K)
t
blade thickness
(m)
U
velocity magnitude
(m/s)
Z
number of vanes
(dimensionless)
ix
Greek symbols
ρ
density
(kg/m3)
τ
shear stress
(kg m-1 s-2)
ω
rotational speed
(rad/s)
θ
tangential coordinate
(dimensionless)
Subscripts
0
stagnation condition
in
inlet to the nozzles
1
exit from the nozzles
2
inlet to the turbine wheel
3
exit from the turbine wheel
x
M.Tech. Thesis
2013
Chapter 1
INTRODUCTION
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Chapter 1
1. INTRODUCTION:
1.1 Overview of Turboexpander:
Turboexpander are used in all areas of the gas and oil industries to produce cryogenic
refrigeration. A turboexpander, on other hand, is a pressure let-down device that produces
cryogenic temperature while simultaneously recovering energy from a plant stream in form of
shaft power that can be used to drive other machinery such as compressor.
Though nature has provided an abundant supply of gaseous raw materials in the
atmosphere (oxygen, nitrogen) and beneath the earth’s crust (natural gas, helium), we need to
harness and store them for meaningful use. In fact, the volume of consumption of these basic
materials is considered to be an index of technological advancement of a society. For largescale storage, transportation and for low temperature applications liquefaction of the gases is
necessary. The only viable source of nitrogen, oxygen and argon is the atmosphere. For
producing atmospheric gases like nitrogen, oxygen and argon in large scale, low temperature
distillation provides the most economical route. The low temperature required for liquefaction
of common gases can be obtained by several processes. While air separation plants, helium
and hydrogen liquefiers based on the high pressure Linde and Heylandt cycles were common
during the first half of the 20th century, cryogenic process plants in recent years are almost
exclusively based on the low-pressure cycles. They use an expansion turbine to generate
refrigeration.
Compared to the high and medium pressure systems, turbine based plants have the
advantage of high thermodynamic efficiency, high reliability and easier integration with
other systems. The expansion turbine is the heart of a modern cryogenic refrigeration or
separation system. Cryogenic process plants may also use reciprocating expanders in place of
turbines. But with the improvement of reliability and efficiency of small turbines, the use of
reciprocating expanders has largely been discontinued.
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1.2 Anatomy of a Cryogenic Turboexpander:
The turboexpander essentially consists of a turbine wheel and a brake compressor mounted
on a single shaft, supported by the required number of journal and thrust bearings. These
basic components are held in place by an appropriate housing, which also contains the
fluid inlet and exit ducts. The basic components are turbine wheel, brake compressor, shaft,
nozzle, bearing, diffuser, seals, etc.
Figure1.1 Division of cryogenic turboexpander
Most of the rotors for small and medium sized plants are vertically oriented for easy
installation and maintenance. It consists of a shaft with the turbine wheel fitted at one end
and the brake compressor at the other. The high-pressure process gas enters the turbine
through piping to the cold end housing and, from there, into the nozzle ring. The fluid
accelerates through the converging passages of the nozzles. Pressure energy is transformed
into kinetic energy, so t hat reduction in static temperature takes place. The high velocity gas
streams impinge on the rotor blades, imparting force to the rotor and creating torque. The
nozzles and the rotor blades are so aligned as to eliminate sudden changes in flow direction
and consequent loss of energy. The turbine wheel is of radial or mixed flow geometry, i.e. the
flow enters the wheel radially and exits axially. The blade passage has a profile of a three
dimensional converging duct, changing from purely radial to an axial-tangential direction.
Work is extracted as the process gas undergoes expansion with corresponding drop in static
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temperature.
The diffuser is a diverging passage that converts most of the kinetic energy of the gas
leaving the rotor to potential energy in the form of gain in pressure. Thus the pressure at
the outlet of the rotor is lower than the discharge pressure of the turbine system. The
expansion ratio in the rotor is thereby increased with a corresponding gain in cold production.
1.3 Objective of the present investigation:
Industrial gas manufactures in the technologically advanced countries have switched over
from the high-pressure Linde and medium pressure reciprocating engine based Claude
systems to the modern, expansion turbine based, low pressure cycles several decades ago.
Thus in modern cryogenic plants a turboexpander is one of the most vital components- be
it an air separation plant or a small reverse Brayton cryocooler.
For the development of computational fluid flow analysis of turboexpander system this
project has been initiated. The objectives include: (i) building comput at ional fluid
dynamic knowledge base on cryogenic turboexpanders (ii) construction of a computational
fluid flow model and study of its performance.
For the computational studies, a turboexpander system has been taken with the following
specifications:
Working fluid
:
Nitrogen
Turbine inlet temperature : 99.65 K
Turbine inlet pressure
: 3 bar
Turbine outlet pressure
: 1.28 bar
Mass flow rate
: 0.024kg/s
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1.4 Organization of the thesis:
The thesis has been divided into six chapters. The first chapter presents a brief introduction to
expansion turbines and their application in cryogenic process plants. Chapter–2 presents an
extensive survey of available literature on various aspects of cryogenic turbine development.
The chapter-3 delivers a systematic design procedure based on published works that has
been developed and documented for expansion turbine. In this chapter we discuss fluid
parameters and layout of the components, design of turbine wheel and determination of blade
profile from available research work.
Chapter-4 describes the computational set up to study the performance of the turbine.
This chapter represents the designing of turbine in bladegen, meshing in turbogrid and
simulation in CFX.
Simulated results for the expander have been included in this chapter-5. Various graphs
and contours have been plotted in this chapter. Finally Chapter–6 is confined to some
concluding remarks and for outlining the scope of future work.
*****
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Chapter 2
LITERATURE REVIEW
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Chapter 2
2. LITERATURE REVIEW
One of the main components of most cryogenic plants is the expansion turbine or the
turboexpander. Since the turboexpander plays the role of the main cold generator, its
properties– reliability and working efficiency, affect the cost effectiveness parameters of the
entire cryogenic plant.
Due to their extensive practical applications, the turboexpander has attracted the
attention of a large number of researchers over the years. Investigations involving
experimental as well as theoretical studies have been reported in literature.
Journals such as Cryogenics and Turbomachinery and major conference proceedings
such as Advances in Cryogenic Engineering and proceedings of the International Cryogenic
Engineering Conference devote a sizable portion of their contents to research findings on
turboexpander technology.
2.1 History of development
The concept that an expansion turbine might be used in a cycle for the liquefaction of gases
was first introduced by Lord Rayleigh in a letter to “Nature” dated June 1898. He discussed
the use of a turbine instead of a piston expander for the liquefaction of air. Rayleigh
emphasized that the most important function of the turbine would be the refrigeration
produced rather than the power recovered. In 1898, a British engineer named Edgar C.
Thrupp patented a liquefying machine using an expansion turbine [1]. Thrupp’s expander was
a double-flow device with cold air entering the centre and dividing into two oppositely
flowing streams. Joseph E. Johnson in USA patented an apparatus for liquefying gases.
Joseph’s expander was a De Laval or single stage impulse turbine. Other early patents include
expansion turbines by Davis (1922). In 1934, a report was published on the first successful
commercial application for cryogenic expansion turbine at the Linde works in Germany [2].
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The single stage axial flow machine was used in a low pressure air liquefaction and separation
cycle. It was replaced two years later by an inward radial flow impulse turbine.
The earliest published description of a low temperature turboexpander was by Kapitza
in 1939, in which he describes a turbine attaining 83% efficiency. It had an 8 cm Monel
wheel with straight blades and operated at 40,000 rpm [3]. In USA in 1942, under the
sponsorship of the National Defence Research Committee a turboexpander was developed
which operated without trouble for periods aggregating 2,500 hrs and attained an efficiency of
more than 80% [3].
Work on the small gas bearing turboexpander commenced in the early fifties by
Sixsmith at Reading University on a machine for a small air liquefaction plant [4]. In 1958,
the United Kingdom Atomic Energy Authority developed a radial inward flow turbine
for a nitrogen production plant [5]. During 1958 to 1961 Stratos Division of Fairchild
Aircraft built blower loaded turboexpanders, mostly for air separation service [6]. Voth et. al
developed a high speed turbine expander as a part of a cold moderator refrigerator for the
Argonne National Laboratory (ANL) [7]. The first commercial turbine using helium was
operated in 1964 in a refrigerator that produced 73 W at 3 K for the Rutherford helium bubble
chamber [4].
A high speed turboalternator was developed by G. E. Co., New York in 1968, which
ran on a practical gas bearing system capable of operating at cryogenic temperature with low
loss [8-9]. National Bureau of Standards at Boulder, Colorado [10] developed a turbine
with shaft diameter of 8 mm. This turbine operated at a speed of 600,000 rpm at 30 K inlet
temperature. In 1974, Sulzer Brothers, Switzerland developed a turboexpander for
cryogenic plants with self-acting gas bearings [11]. In 1981, Cryostar, Switzerland started a
development program together with a magnetic bearing manufacturer to develop a cryogenic
turboexpander incorporating active magnetic bearing in both radial and axial direction [12]. In
1984, the prototype turboexpander of medium size underwent extensive experimental testing
in a nitrogen liquefier. Izumi et. al [13] at Japan developed a micro turboexpander for a small
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helium refrigerator based on Claude cycle. This turboexpander consisted of a radial inward
flow reaction turbine and a centrifugal brake fan on the lower and upper ends of a shaft
supported by self-acting gas bearings. The turbine wheel diameter was 6mm and the shaft
diameter was 4 mm. The rotational speeds of the 1st and 2nd stage turboexpander were
816,000 and 519,000 rpm respectively.
A simple method sufficient for the design of a high efficiency expansion turbine
is outlined by Kun et. al [14-15]. Studies were initiated in 1979 to survey operating plants and
generate the cost factors relating to turbine by Kun & Sentz [16]. Sixsmith et. al. [17] in
collaboration with Goddard Space Centre of NASA, developed miniature turbines for
Brayton Cycle cryocoolers. They have developed of a turbine with diameter 1.5 mm, rotating
at a speed of approximately one million rpm [18].
Yang et. al [19] developed a two stage miniature expansion turbine made for 1.5 L/hr
helium liquefier at the Cryogenic Engineering Laboratory of the Chinese Academy of
Sciences. The turbines rotated at more and equal 500,000 rpm. The design of a small high
speed turboexpander was taken up by the National Bureau of Standards (NBS) USA. The
first expander operated at 600,000 rpm in externally pressurized gas bearings [20]. The
turboexpander developed by Kate et. al [21] was with variable flow capacity mechanism (an
adjustable turbine), which had the capacity of controlling the refrigerating power by using the
variable nozzle vane height.
A wet type helium turboexpander with expected adiabatic efficiency of 70% was
developed by the Naka Fusion Research Centre affiliated to the Japan Atomic Energy
Institute [22-23]. The turboexpander consists of 59 mm impeller diameter, a 40 mm shaft, and
self-acting gas journal and thrust bearings [22]. Ino et. al [24-25] developed a high expansion
ratio radial inflow turbine for a helium liquefier of 100 L/hr capacity for use with a 70 MW
superconductive generator. The turboexpander third stage was designed and manufactured in
1991, for the gas expansion machine regime, by “Cryogenmash” [26]. Each stage of the
turboexpander design was similar, differing from one another by dimensions only produced
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by “Heliummash” [26].
The ACD Company incorporated gas lubricated hydrodynamic foil bearings into a TC–
3000 turboexpander [27]. Detailed specifications of the different modules of turboexpander
developed by the company have been given in tabular format in Reference [28].
Agahi et. al. [29-30] have explained the design process of the turboexpander utilizing
modern technology, such as CFD software, Computer Numerical Control Technology and
Holographic Techniques to further improve an already impressive turboexpander efficiency
performance. Improvements in analytical techniques, bearing technology and design features
have made turboexpanders to be designed and operated at more favorable conditions such as
higher rotational speeds. A Sulzer dry turboexpander, Creare wet turboexpander and IHI
centrifugal cold compressor were installed and operated for about 8000 hrs in the Fermi
National Accelerator Laboratory, USA [31]. This Accelerator Division/Cryogenics
department is responsible for the maintenance and operation of both the Central Helium
Liquefier (CHL) and the system of 24 satellite refrigerators which provide 4.5 K refrigeration
to the magnets of the Tevatron Synchrotron. Theses expanders have achieved 70% efficiency
and are well integrated with the existing system.
Sixsmith et. al. [32] at Creare Inc., USA developed a small wet turbine for a helium
liquefier set up at the particle accelerator of Fermi National laboratory. The expander shaft
was supported in pressurized gas bearings and had a turbine rotor of 4.76 mm at the cold
end and a 12.7 mm brake compressor at the warm end. The turboexpander had a design speed
of 384,000 rpm and a design cooling capacity of 444 Watts. Xiong et. al. [33] at the institute
of cryogenic Engineering, China developed a cryogenic turboexpander with a 103 mm long
rotor and weighing 0.9 N, which had a working speed up to 230,000 rpm. The turboexpander
was experimented with two types of gas lubricated foil journal bearings. The L’Air company
of France has been manufacturing cryogenic expansion turbines for 30 years and more than
350 turboexpanders are operating worldwide, installed on both industrial plants and
research institutes [34-35]. These turbines are recognised by the use of hydrostatic gas
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bearings, providing unique reliability with a measured Mean Time between failures of 45,000
hours.
India has been lagging behind the rest of the world in this field of research and
development. Still, significant and decent progress has been made during the past two
decades. In CMERI Durgapur, Jadeja et. al [36-37] developed an inward flow radial
expansion turbine supported on gas bearings for cryogenic plants. This device gave stable
rotation at about 40,000 rpm. This programme was, however, discontinued before any
significant progress could be achieved. Another programme at IIT Kharagpur developed a
turboexpander unit by using aerostatic thrust and journal bearings which had a working speed
up to 80,000 rpm. The detailed summary of technical features of the cryogenic
turboexpander developed in various laboratories has been given in the PhD dissertation of
Ghosh [38]. Recently Cryogenic Technology Division, BARC developed Helium refrigerator
capable of producing 1 kW at 20K temperature.
2.2 Design of turboexpander
The process of designing turbomachines is very seldom straightforward. The final design is
usually the result of several engineering disciplines: fluid dynamics, stress analysis,
mechanical vibration, tribology, controls, mechanical design and fabrication. The process
design parameters which specify a selection are the flow rate, gas compositions, inlet
pressure, inlet temperature and outlet pressure [39]. This section on design and development
of turboexpander intends to explore the basic components of a turboexpander.
Turbine wheel
During the past two decades, performance chart has become commonly accepted mode of
presenting characteristics of turbomachines [40]. Several characteristics values are used for
defining significant performance criteria of turbomachines such as turbine velocity ratio,
pressure ratio, flow coefficient factor and specific speed [40]. Balje has presented a simplified
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method for computing the efficiency of radial turbomachines and for calculating their
characteristics [41]. Similarity considerations offer a convenient and practical method to
recognize major characteristics of turbomachinery. Similarity principles state that two
parameters are adequate to determine major dimensions as well as the inlet and exit
velocity triangles of the turbine wheel. The specific speed and the specific diameter
completely define dynamic similarity.
Specific speed and specific diameter
The concept of specific speed was first introduced for classifying hydraulic machines.
Balje [42] introduced this parameter in design of gas turbines and compressors. Values of
specific speed and specific diameter may be selected for getting the highest possible
polytropic efficiency and to complete the optimum geometry [39]. Specific speed is a useful
single parameter description of the design point of a compressible flow rotodynamic machine
[43]. A design chart that has been used for a wide variety of turbomachinery has been given
by Balje [42, 44]. The diagram helps in computing the maximum obtainable efficiency
and the optimum design geometry in terms of specific speed and specific diameter for
constant Reynolds number and Laval number.
According to Rohlik [45], for radial flow geometry, maximum static and total
efficiencies occur at specific speed values of 0.58 and 0.93. Luybli and Filippi [46] state that
low specific speed wheels tend to have major losses in the nozzle and vaneless pace zones as
well as in the area of the rotating disc where as high specific speed wheels tend to have
more gas turning and exit velocity losses. The specific speed and specific diameter are often
referred to as shape parameters. They are also sometimes referred to as design parameters,
since the shape dictates the type of design to be selected. Corresponding approximately to the
optimum efficiency [15] a cryogenic expander may be designed with selected specific speed
is 0.5 and specific diameter is 3.75. Kun and Sentz [16] had taken specific speed of 0.54 and
specific diameter of 3.72. Sixsmith and Swift [20] have designed a pair of miniature
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expansion turbines for the two expansion stages with specific speeds 0.09 and 0.14
respectively for a helium refrigerator.
One major difficulty in applying specific speed criteria to gas turbines exists because
of dependent on the Mach and Reynolds numbers that occur. For this reason the specific
speed is not a parameter that satisfies the laws of dynamic similarity if the compressibility of
the operating fluid cannot be ignored. Endeavors to relate the losses exclusively to specific
speed, and using it as the sole criterion for evaluating a design are not only improper from a
fundamental point of view but may also create a false opinion about the state of the
art, thereby hindering or preventing research work that establishes sound design criteria.
Vabra [47] has suggested improvement of these charts by incorporating new data obtained
through experiments. He has shown that optimum turbine performance can be expected at
values of specific speed between 0.6 and 0.7 and the operating range for radial turbines may
lie between specific speed values of 0.4 to 1.2.
Parameters
The ratio of exit tip to rotor inlet diameter should be limited to a maximum value of 0.7 to
avoid excessive shroud curvature. Similarly, the exit hub to the tip diameter ratio should
have a minimum value of 0.4 to avoid excessive hub blade blockage and loss [43, 45]. Kun
and Sentz [16] have taken ε = 0.68. Balje [41] has taken the ratio of exit meridian
diameter to inlet diameter of a radial impeller as 0.625. The inlet blade height to inlet
blade diameter of the turbine wheel would lie between values of 0.02 to 0.6 [43]. The
detailed design parameters for a 90° inward radial flow turbine is shown in Table 2.2 of the
PhD dissertation of Ghosh [38].
The peripheral component of absolute velocity at the inlet of turbine wheel is mainly
dependent upon the nozzle angle. The peripheral component of absolute velocity at the exit of
turbine wheel is a function of the exit blade angle and the peripheral speed at the outlet
[41]. Balje [41] shows that the desirable ratio of meridional component of absolute velocity at
Mechanical Engineering Department, N. I. T. Rourkela
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the inlet and exit of the turbine wheel is a function of the flow factor and Mach number. He
has taken the value of the ratio of Meridional components of absolute velocity at exit and
inlet for a radial turbine as 1.0. Whitfield [48] has shown that for any given incidence angle,
the absolute flow angle can be selected to minimize the absolute Mach number. The general
view is that the optimum incidence angle is a function of the number of blades and lies
between -20° and -30°.
Number of blades
Assuming a simplified blade loading distribution, Balje has derived an equation for the
minimum rotor blade number as a function of specific speed. Denton [49] has given guidance
on the choice of number of blades. By using his theory it can be ensured that the flow does
not stagnate on the pressure surface. He suggests that a number of 12 blades is typical for
cryogenic turbine wheels. Wallace [50] has given some useful information on best number
of blades to avoid excessive frictional loss on the one hand and excessive variation of flow
conditions between adjacent blades on the other.
Rohlik [45] recommends a procedure to estimate the required number of blades
considering the criterion of flow separation in the rotor passage. In his formula, the number of
blades is chosen so as to inhibit boundary layer growth in the flow passage. Sixsmith [10]
used twelve complete blades and twelve partial blades in his turbine designed for medium size
helium liquefiers. The blade number is calculated from the value of slip factor [36]. The
number of blades must be so adjusted that the blade width and thickness can be manufactured
with the available machine tools.
*****
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Chapter 3
THEORY
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Chapter3
3. THEORY
3.1 Design of Turboexpander
In this chapter the process of designing the experimental turboexpander and associated units
for cryogenic process have been analyzed. The design procedure of the cryogenic
turboexpander depends on working fluid, flow rate, inlet conditions and expansion ratio. The
procedure created in this chapter allows any arbitrary combination of fluid species, inlet
conditions and expansion ratio, since the fluid properties are adequately taken care in the
relevant equations. The computational process is illustrated with examples. The present
design procedure is available in literature [55].
The design methodology of the
turboexpander system consists of the following units, which are described in the subsequent
sections.
 Fluid parameters and layout of the components
 Design of turbine wheel
 Determination of blade profile
3.1.1 Fluid parameters and layout of components
The fluid specifications have been dictated by the requirements of a small refrigerator
producing less than 1 KW of refrigeration. The inlet temperature has been specified
rather arbitrarily, chosen in such a way that even with ideal (isentropic) expansion; the exit
state should not fall in the two-phase region. The basic input parameters for the system are
given in Table 3.1.
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Table 3.1: Basic input parameters for the cryogenic expansion turbine system
Working fluid
:
Nitrogen
Discharge pressure
:
Turbine inlet temperature:
99.65K
Mass flow rate
: 0.025 kg/s
Turbine inlet pressure
3bar
:
1.27 bar
3.1.2 Design of turbine wheel
The design of turbine wheel has been done following the method outlined by Balje [8] and
Kun & Sentz [29], which are based on the well-known “ similarity principles”. The similarity
laws state that for given Reynolds number, Mach number and Specific heat ratio of the
working fluid, to achieve optimized geometry for maximum efficiency, two dimensionless
parameters: specific speed and specific diameter uniquely determine the major dimensions
of the wheel and its inlet and exit velocity triangles. Specific speed ( n s ) and specific
diameter ( d s ) are defined as:
ns 
Specific speed
  Q3
(3.1)
hin3s 3 / 4
D2  hin3s 
Q3
1/ 4
ds 
Specific diameter
(3.2)
in
Vane less Space
1
2
3
Turbine Wheel
State points
In Nozzle inlet
1
Nozzle outlet
2
Turbine inlet
3
Turbine outlet
Nozzle
Diffuser
Figure3.1 State points of turboexpander
In summary, the major dimensions for prototype turbine have been computed by S.K. Ghosh
[52] as follows:
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Rotational speed:
N = 22910rad/sec = 218790rpm
Wheel diameter:
D2 = 16.0 mm
Eye tip diameter:
Dtip = 10.8mm
Eye hub diameter:
Dhub = 4.6mm
Numbers of blades: Ztr = 10
Thickness of blades: t tr = 0.6mm
Thermodynamic state at wheel discharge (state 3):Thermodynamic state at turbine wheel outlet calculated by S. K. Ghosh [52] is in table3.2.
Table 3.2 Thermodynamic state at turbine outlet
Stagnation value
Static value
Pressure (bar)
1.505
1.29
Entropy (kJ/kg.K)
5.452
5.452
Temperature (K)
90.02
85.96
Density (kg/m3)
5.89
5.26
Mass Flow Rate (kg/s)
0.02326
0.02326
Thermodynamic state at wheel inlet (state 2)
Table 3.3 Thermodynamic state at turbine inlet
Stagnation value
Static value
Pressure (bar)
2.872
2.453
Entropy (kJ/kg.K)
5.335
5.335
Temperature (K)
99.65
90.45
Density (kg/m3)
10.312
9.728
Mass Flow Rate (kg/s)
0.02326
0.02326
3.1.3 Determination of Blade Profile:
The detailed procedure describes computation of the three dimensional contours of the blades
and simultaneously determines the velocity, pressure and temperature profiles in the turbine
wheel. The computational procedure suggested by Hasselgruber [51] and extended by Kun &
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Sentz [16] has been adopted. The fluid pressure loss in a turbine blade passage depends on the
length and curvature of the flow path. Thus two parameters Ke and Kh defined by
Hasselgruber [51] control the flow path and its curvature. The magnitude of the velocity and
change in its direction determine the optimum blade profile of the turbine. For the turbine
blade design Ke varies between 0.75 and Kh 1 varies between 1 and 20.
Analysis of results done by S. K. Ghosh [53] reveal that an optimum combination of
parameters Ke= 0.75 and Kh= 5.0 leads to a batter blade profile for turboexpander. The blade
profile co-ordinate of mean surface, pressure surface and suction surface are shown in the
Table 4.3 and Table 4.4 respectively.
Table 3.4 Coordinates for Generation of Blade Profile
z(mm)
-0.24
0.24
0.71
1.18
1.63
2.08
2.52
2.95
3.37
3.79
4.19
4.58
4.97
5.34
5.69
6.02
6.33
6.62
6.87
7.09
7.28
Tip Camber line
r(mm)
5.38
5.29
5.22
5.19
5.18
5.19
5.22
5.27
5.33
5.41
5.51
5.63
5.78
5.95
6.16
6.4
6.68
6.99
7.33
7.7
8.1
θ (deg)
0
6.71
12.39
17.19
21.22
24.58
27.37
29.65
31.49
32.96
34.1
34.96
35.61
36.06
36.38
36.58
36.7
36.77
36.8
36.81
36.81
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z(mm)
0.24
0.67
1.11
1.55
2
2.46
2.93
3.39
3.86
4.33
4.79
5.24
5.68
6.09
6.47
6.81
7.11
7.37
7.59
7.76
7.9
Hub Camber line
r(mm)
2.32
2.56
2.76
2.94
3.1
3.25
3.4
3.56
3.72
3.91
4.13
4.37
4.65
4.97
5.32
5.7
6.11
6.54
6.99
7.45
7.92
θ (deg)
0
6.71
12.39
17.19
21.22
24.58
27.37
29.65
31.49
32.96
34.1
34.96
35.61
36.06
36.38
36.58
36.7
36.77
36.8
36.81
36.81
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Table 3.5 Turbine blade profile co-ordinates of pressure and suction surfaces
z pressure(mm)
r pressure(mm) θ pressure(rad) z suction (mm) r suction(mm)
θ suction(rad)
0
3.85
0.055
0
3.85
-0.055
0.45
3.92
0.166
0.45
3.92
0.068
0.91
3.99
0.26
0.91
3.99
0.172
1.36
4.07
0.339
1.36
4.07
0.261
1.82
4.14
0.404
1.82
4.14
0.336
2.27
4.22
0.458
2.27
4.22
0.4
2.72
4.31
0.502
2.72
4.31
0.453
3.17
4.41
0.537
3.17
4.41
0.497
3.62
4.53
0.566
3.62
4.53
0.533
4.06
4.66
0.588
4.06
4.66
0.562
4.49
4.82
0.605
4.49
4.82
0.585
4.91
5
0.617
4.91
5
0.603
5.32
5.21
0.627
5.32
5.21
0.616
5.71
5.46
0.633
5.71
5.46
0.626
6.08
5.74
0.637
6.08
5.74
0.633
6.42
6.05
0.64
6.42
6.05
0.637
6.72
6.39
0.641
6.72
6.39
0.64
6.99
6.77
0.642
6.99
6.77
0.641
7.23
7.16
0.642
7.23
7.16
0.642
7.43
7.58
0.642
7.43
7.58
0.642
7.59
8.01
0.642
7.59
8.01
0.642
******
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Chapter 4
COMPUTATIONAL FLUID FLOW
ANALYSIS
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Chapter 4
4. COMPUTATIONAL FLUID FLOW ANALYSIS
Computational fluid flow analysis of turboexpander can be done in three steps. Bladegen is
used to create the model of turbine using available data of hub, shroud and blade profile.
Turbogrid is used to mesh the model. CFX-Pre is used to define and specify the simulation
settings and physical parameters required to describe the flow through turboexpander at inlet
and outlet. CFX-Post is used for examining and analyzing results.
4.1. Designing of Turboexpander in Bladegen
ANSYS BladeGen is a geometry creation tool that is specialized for turbomachinery blades.
Bladegen designing of model is done by using available hub, shroud and blade profile
coordinates. The hub and the tip streamlines are available in the previous chapter. A surface is
created by joining the hub and tip streamlines with a set of tie lines. BladeEditor will loft the
blade surfaces in the streamwise direction through curves that run from hub to shroud. The
surface so generated is considered as the mean surface within a blade. Non Uniform Rational
B Splines are used to develop the solid surface. The suction and pressure surfaces of two
adjacent channels are computed by translating the mean surface in the positive and negative
theta direction through half the blade thickness.
After making all the surfaces when blade merge topology property is used, then blade
faces will be merged where they are tangent to one another. Create fluid zone property is
selected, to create a stage fluid zone body for the flow passage, and an enclosure feature to
subtract the blade body. This resulting enclosure can be used for a CFD analysis of the blade
passage. Create all blades this property is used to create all the blades using the number of
blades specified in the Bladegen model. Here we are using ten numbers of blades.
Different views and curves of radial expansion turbine in bladegen are as following.
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Figure 4.1: Meridional blade profile with different spans
Figure 4.2: Variation of Beta and Theta at different spans along radius
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Figure 4.3: Variation of Beta and Theta
Figure 4.4: Wireframe model of turbine generated in bladegen
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Figure 4.5: Solid model of turbine generated in bladegen
4.2. Meshing of Model:
Meshing of model is done in turbogrid. It creates high quality hexahedral meshes that are
tuned to the demands of fluid dynamic analysis in turbine rotor. Turbine rotor geometry
information is imported from bladegen. Turbogrid uses this bladegen file to set the axis of
rotation, the number of blades, and a length unit that characterizes the scale of the machine.
Machine data gives the basic information about the geometry. Here units specified for base
units represent the scale of the geometry being meshed, these units are not used for importing
geometric data nor do they govern the units written to a mesh file, they are used for the
internal representation of the geometry to minimize computer round-off errors. To complete
the geometry a small gap of 1 mm is created between the blade and the shroud.
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Figure 4.6: Turbine rotor view after importing from Bladegen
Next step is to create the topology that guides the mesh. Topology definition, placement to
traditional with control points provides access to the legacy topology methods. Here H/J/C/LGrid method is used to create mesh. The H/J/C/L-Grid method causes ANSYS Turbogrid to
choose an H-Grid, J-Grid, C-Grid, L-Grid, or a combination of these, based on heuristics. In
this case, the H/J/C/L-Grid method causes ANSYS Turbogrid to choose an H-Grid topology
for the upstream end of the passage, and an H-Grid topology for the downstream end. Include
O-Grid with 0.5 width factor is selected to add an O-Grid (thickness equal to half the average
blade thickness) around the blade to increase mesh orthogonality in that region.
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Figure 4.7: Turbine rotor view after setting topology
After setting topology definition, mesh data setting is used to control the number and
distribution of mesh elements. Here we set the target number of nodes to 250000 to produce a
fine mesh. Before generating the 3D mesh, mash quality should check on the layers,
especially the hub and shroud tip layers. After correcting mash quality on layers, we generate
the mesh with 228640 nodes and 206368 elements.
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Figure 4.8: Meshed 3D view of turbine rotor
4.3. Physics definition of Meshed Model in CFX-Pre:
CFX-Pre is known as physics-definition pre-processor for ANSYS CFX. In cfx, turbo mode is
used to define physic of meshed turbine rotor. Under basic setting in turbo mode, we set the
machine type as radial turbine and rotation axis to z. In component definition we set
component type rotating and set rotation value 218780 rev/min. Turbo mode will
automatically select a list of regions that correspond to certain boundary types. This
information should be reviewed in the Region Information section to ensure that all is correct.
This information is used to set up boundary conditions and interfaces. In wall configuration
option we set tip clearance at shroud.
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Physics definition tab is used to set fluid type, analysis type, model data, inflow and outflow
boundary templates and solver parameters. Physics definition used for turbine rotor is given in
the table below.
Table 4.1: Physics definition for turbine rotor
Tab
Setting
Values
Physics
Fluid
Nitrogen
Definition
Analysis Type
Steady state
Modal Data
Reference pressure
0 (Pa)
Heat Transfer
Total Energy
Turbulence
k-Epsilon
Inflow/Outflow Boundary Templates
Mass
Flow
Inlet
P-Static
Outlet
T-Total
99.65k
Mass Flow
Per Component
Mass Flow Rate
0.002326 kg/sec
Flow Direction
Normal to Boundary
Outflow
P-Static
1.29 bar
Solver
Advection Scheme
High Resolution
Parameters
Convergence control
Physical Timescale
Physical Timescale
0.000004 s
Inflow
After setting physics definition Cfx-Pre will try to create appropriate interfaces and boundary
conditions using the region names presented previously in the region information.
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Figure 4.9: Flow direction at inlet and outlet
4.4. Obtaining a Solution Using CFX-Solver:
This chapter describes the mathematical equations used to model fluid flow, heat, and mass
transfer in ANSYS CFX for single-phase, single and multi-component flow without
combustion or radiation.
ANSYS CFX solves for the relative static pressure in the flow field, and is related to Absolute
pressure.
Pabs = Pref + Pstat
(4.1)
Specific static enthalpy is a measure of the energy contained in a fluid per unit mass. Static
enthalpy is defined in terms of the internal energy of a fluid and the fluid state:
hstat = ustat +
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Pstat
stat
(4.2)
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When we use the thermal energy model, the ANSYS CFX-Solver directly computes the static
enthalpy.
The set of equations solved by ANSYS CFX are the unsteady Navier-Stokes equations
in their conservation form. The instantaneous equations of mass, momentum and energy
conservation can be written as follows in a stationary frame:
Continuity equation

   ( U )  0
t
Momentum equations
( U )
 U  ( U  U )   p      S M
t
(4.3)
(4.4)
Where the stress tensor,  , is related to the strain rate by


2
3


    U  (U ) T    U 
Total energy eqn.
( htot ) P

   ( Uhtot )    (T )    (U   )  U  S M  S E (4.5)
t
t
Where htot is the total enthalpy, related to the static enthalpy h (T, P) by:
1
htot  h  U 2
2
(4.6)
The term   (U  ) represents the work due to viscous stresses and is called the viscous
work term. The term U  S M represents the work due to external momentum sources and is
currently neglected.
CFX-Solver is used to launch both solvers and monitor the output. ANSYS Workbench
generates the CFX-Solver input file and passes it to ANSYS CFX-Solver Manager. In CFXSolver first we set the solution units as SI system. Under solution control we set maximum
iterations to 10000 and residual type to RMS. Convergence criteria, residual targeted to 1.E-4.
In output control, extra output variable set as temperature.
On the Define Run dialog box, Solver Input File is set automatically by ANSYS Workbench.
Now we can start the solver run. When the solver run has finished, a completion message
appears in a dialog box.
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4.5. Obtaining Results in CFX CFD-Post:
CFD-Post is a flexible, state of art post-processor. It is used to allow easy visualization and
quantitative analysis of results of CFD simulations. Turbo workspace is used to improve and
speed up post-processing for turbomachinery simulation. It includes all the expected plotting
objects like, plans, isosurfaces, vectors, streamlines, contours, animations, etc. It allows
precise quantitative analysis as, weighted average, forces, results, comparisons, built in and
user defined macros. It can create user defined scalar and vector variables. CFD-Post includes
automatic reports, charts, and tables.
Figure 4.10: Wireframe and Meridional model of turbine rotor
In CFD-Post general workflow, first we prepare locations where data will be extracted from
or plots generated. Variables and expression is created to extract data at particular location.
Generate qualitative and quantitative data at that location and on the basis of it generate
reports to present results.
******
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Chapter 5
RESULTS AND DISCUSSION
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Chapter 5
5. RESULTS AND DISCUSSION:
The computational fluid flow analysis is done in CFD post after completion of cfx simulation.
A tabulated result can be seen in generated report. This report gives the variation of different
properties from inlet to outlet and hub to shroud, by graphs and counters.
Variations of thermodynamic properties, at different locations of turbine rotor are as
following.
Table 5.1: Variations of thermodynamic properties
Quantity
Inlet
LE Cut
TE Cut
Outlet
TE/LE
Units
Density
8.5944
8.4588
4.7636
4.5933
0.5631
[kg m-3]
Pstatic
244299
241899
125866
127695
0.5203
[Pa]
Ptotal
300332
295012
173430
166980
0.5879
[Pa]
Ptotal (rot)
300241
292385
194824
187423
0.6663
[Pa]
Tstatic
95.8298
95.1123
89.6811
88.6704
0.9875
[K]
Ttotal
99.6526
98.5519
96.7926
96.8437
0.9684
[K]
Ttotal (rot)
99.6435
99.6405
99.6466
99.7047
1.0001
[K]
Entropy
5377.19
5385.71
5512.42
5524.16
1.0235
[J kg-1 K-1]
Mach (abs)
0.784
0.7449
0.6667
0.6011
0.8949
Mach (rel)
1.2649
1.1969
0.9175
0.8663
0.7665
U
186.972
182.671
94.5048
92.5352
0.5173
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From tabulated results we can see that inside the turbine, pressure, temperature, density,
velocity and Mach number are decreasing from inlet to outlet while entropy is increasing a
little bit from inlet to outlet.
Static temperature of nitrogen available at outlet is 88.67K which is nearly equal to the
temperature obtained by S.K. Ghosh [52] during experimental work on turboexpander. Now
our output result is validated to experimental results obtained by S.K. Ghosh [52].
Various graphs and contours available from generated results are as following.
5.1 Pressure variation along streamwise inlet to outlet:
Static and total pressure variation can be seen from the graph below. Total pressure at inlet
and static pressure at outlet is nearly equal to the pressure obtained by S.K. Ghosh [52]
experimentally. Total pressure varies from 3bar to 1.6 bar while static pressure varies from
2.4 bar to 1.27 bar along streamline from inlet to outlet of turbine rotor.
Figure5.1: Pressure variation along streamwise inlet to outlet
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Figure5.2: Isometric 3D view of pressure variation
5.2 Temperature variation along streamwise inlet to outlet:Static and total temperature variation can be seen from the graph below. Total temperature at
inlet and static temperature at outlet is nearly equal to the temperature obtained by S.K. Ghosh
[52] experimentally. Total temperature varies from 99.6K to 96.7K, while static temperature
varies from 95.82K to 88.67K along streamline from inlet to outlet of turbine rotor.
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Figure5.3: Temperature variation along streamwise inlet to outlet
Figure5.4: Isometric 3D view of temperature variation
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5.3 Velocity variation along streamwise inlet to outlet:
Velocity variation can be seen from the graph below. Velocity is decreasing inside the turbine
from inlet to outlet, 186.90 m/s to 130.146m/s respectively.
Figure5.5: Velocity variation along streamwise inlet to outlet
5.4 Variation of Mach number along streamwise:
Absolute and relative Mach number variation can be seen from the graph below. Absolute
Mach number varies from 0.7 to 0.89, while relative Mach number varies from 1.2 to 0.45
along streamline from inlet to outlet, inside the turbine rotor.
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Figure5.6: Variation of Mach number along streamwise
5.5 Variation of density along streamwise inlet to outlet:
Density variation can be seen from the graph below. Density is decreasing inside the turbine
from inlet to outlet, 8.59 kg/m3 to 4.59 kg/m3 respectively.
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Figure5.7: Variation of density along streamwise inlet to outlet
5.6 Variation of Static Entropy along streamwise:
Static Entropy variation can be seen from the graph below. Static Entropy varies from 5377 J
kg^-1 K^-1 to 5524 J kg^-1 K^-1 along streamline from inlet to outlet, inside the turbine
rotor, which shows that expansion process is not isentropic. A small increment in entropy can
be seen from inlet to outlet, inside the turbine.
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Figure5.8: Variation of Static Entropy along streamwise
5.7 Pressure variation along spanwise hub to shroud:
Pressure variation at different span, hub to shroud can be seen from graph below. At inlet
span, hub to shroud variation of pressure is around 2.48 bar to 2.67 bar, while at mid and
outlet span pressure is varying around 1.7 bar to 1.8 bar and 1.26 bar to1.27 bar respectively.
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Figure5.9: Pressure variation along spanwise hub to shroud
5.8 Temperature variation along spanwise hub to shroud:
Temperature variation at different span, hub to shroud can be seen from graph below. At inlet
span, hub to shroud variation of temperature is around 102 K to 99 K, while at mid and outlet
span temperature is varying around 92 K to 94 K and 91 K to86 K respectively.
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Figure5.10: Temperature variation along spanwise hub to shroud
5.9 Velocity variation along spanwise hub to shroud:
Velocity variation at different span, hub to shroud can be seen from graph below. At inlet
span, hub to shroud variation of velocity is around 186 m/s to 188 m/s, while at mid and outlet
span velocity is varying around 160 m/s to 130 m/s and 90 m/s to100 m/s respectively.
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Figure5.11: Velocity variation along spanwise hub to shroud
Observation:The gas flows radially inward, is accelerated through inlet guide vanes, and turned. The
swirling, high velocity gas enters the expander impeller with relatively low incidence, because
the blade tip velocity at the impeller outside diameter approximately matches the gas velocity.
Work is extracted from the gas by removing this momentum: as the gas moves inward, it is
forced to slow down because the blade rotational velocity decreases with the decreasing
radius. The blades also turn the gas to reduce the gas velocity even further. As a result, the gas
exits the impeller with low tangential velocity relative to the outside world. In this way, the
angular momentum of the gas is efficiently removed. Dew to this reason, different
thermodynamic properties decrease from inlet to outlet.
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5.10 Blade to blade plots for different spans:
Contour of velocity vector at different Spans:
Figure5.12: Velocity Vectors at 20% Span
Figure5.13: Velocity Vectors at 50% Span
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Figure5.14: Velocity Vectors at 80% Span
Observation:Above figures are showing the variation of velocity vectors at 20%, 50% and 80% spans from
hub to shroud. Here we can see that velocity of fluid is decreasing from inlet to outlet and
variation in velocity vectors are more complicate from hub to shroud. At 20% and 50% spans
there is less space to move velocity vectors; while at 80% span (near to shroud) variation is
more because of gap between blade tip and shroud.
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5.11 Meridional Plots:
Contour of Mass Averaged Pressure on Meridional Surface
Figure5.15: Mass Averaged Pressure on Meridional Surface
Contour of Mass Averaged Relative Mach number on Meridional Surface:-
Figure5.16: Mass Averaged Relative Mach number on Meridional Surface
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Streamline Plot:Velocity Streamlines at Blade Trailing Edge:-
Figure5.17: Velocity Streamlines at Blade Trailing Edge
Observation:Meridional plots are showing the variation of pressure and relative Mach number from inlet to
outlet. Here we can see that pressure and relative match number are continuously decreasing
due to transfer of fluid energy to impeller. As a result, the gas exits the impeller with low
pressure and velocity. In fig 5.17 we see that at trailing edge color of streamline is turning to
blue, which shows decrease in fluid velocity.
*****
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Chapter 6
CONCLUSIONS AND FUTURE
WORK
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Chapter6
CONCLUSIONS AND FUTURE WORK
6.1. CONCLUSIONS
This work is a modest attempt at flow analyzing inside a cryogenic turboexpander through
computational fluid dynamic. A prototype expander has been designed, meshed and simulated
using this recipe. The design procedure covers the designing of hub, shroud and blade
profile of turboexpander in Bladegen. A cfx model has been developed for flow
analysis inside the turbine rotor. The modeling of the various parts of the turbine is
done in Bladegen and the computational fluid flow analysis is done using CFX. After
validation of output results with experimental results, various graphs and contours
indicating the variations of temperature, pressure, velocity, Mach number and
entropy inside the turbine along the streamline and spanwise are drawn.
6.2. FUTURE WORK
Future work in this direction will be aimed at computational fluid flow analysis of the
remaining parts of turboexpander like nozzle, diffuser, etc. It is expected that a complete
model of turboexpander can be computationally analyzed by using proper designing and
simulation tools. In this regard, work is planned on the application of CFX tool in mixing
plane selection. Once it will be done then computational simulation of different types of
turboexpander can be analyzed.
*****
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*****
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