Development of design software for Cryogenic

Development of design software for Cryogenic
Development of design software for Cryogenic
Turbo Expander
A Thesis Submitted for Award of the Degree of B.Tech
Asutosh Nayak
Mechanical Engineering Department
National Institute of Technology
Rourkela 769008
National Institute of Technology, Rourkela.
This is to certify that the project work entitled “Development of Design software for Cryogenic
Turbo Expander” by Asutosh Nayak has been carried out under my supervision in partial
fulfillment of the requirements for the degree of Bachelor of Technology during session 200910 in the Department of Mechanical Engineering, National Institute of Technology,
Rourkela and this work has not been submitted elsewhere for a degree.
Place: Rourkela
Date: 10.05.2010
Prof. Sunil Kumar Sarangi
Dept of Mechanical Engg.
Director, N.I.T. Rourkela
I am extremely fortunate to be involved in an exciting and challenging research project like
EXPANDER”. It has enriched my life, giving me an opportunity to work in a new
environment of cryogenic liquification. This project increased my thinking and understanding
capability as I started the project from scratch.
I would like to express my greatest gratitude and respect to my supervisor Dr. Sunil Kumar
Sarangi, 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 also like to sincerely thank Prof K. P. Maity who with his valuable comments and
suggestions during the viva voce helped me immensely. I would like to thank them because they
were the ones who constantly evaluated me, corrected me and had been the guiding light for me.
I would like to express my sincere thanks to Mr. Balaji for his precious suggestions and
encouragement to perform the project work. He was very patient to hear my problems that I am
facing during the project work and finding the solutions. I am very much thankful to him for
giving his 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 .I want to convey my heartiest gratitude to my parents for their unfathomable
Asutosh Nayak
This thesis provides the complete designing procedures encapsulated in an object oriented
programming. The software is written in C++codes and gives the detail design of each
component of the cryogenic turbo expander. The design procedure is complied an a very
systematic manner due to the work of various person in this typical region. The thesis begins
with the introduction of a Turbo expander. It contains the literature review which states the
work done by various person with passage of time. The anatomy of turbo expander provides the
complete picture and the understanding basics of each parts which helps in knowing and
analyzing various parameters associated. A systematic approach of calculation is mentioned
with the draw of flowcharts and step wise algorithm.
The various chapters helps in designing codes for the design of cryogenic turbo-expander.The
codes are effective and isvery userfriendly.
Sl no:
Pg nos.
Expansion turbine
Turbo expander in INDIA
Literature Review
Historical perspective
Why develop in India
Anatomy of expansion turbine
Turbine wheel
Nozzle configuration
Brake compressor
Aerostatic thrust bearing
Tilting pad journal bearing
Design procedure
Turbine wheel
Design of diffuser
Nozzle design
Design of shaft
Blade Design
Design of brake compressor
Off design prediction
Algorithm and flow process
Structure of the software
Design codes
List of figures(fig.)
Cryogenic cycles
Anatomy of turboexpander
Ns-Ds Curve
Performance diagram
Blade Profile
Turbine wheel
Nozzle diffuser
Aerostatic thrust bearings.
Journal Bearing
1.1 Expansion Turbines in cryogenic process.
Iindustrial gases such as oxygen, nitrogen and argon plays an important part of our economy.
The production and its proper utilisation is considered to be an index of technological
advancement of a society. 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 should harness and store them for meaningful use. Oxygen is a basic input to many
industrial processes - steel making, ferrous non-ferrous metallurgy, welding sewage treatment,
rocket propulsion and medical applications etc. Nitrogen is used as a blanket gas in most
chemical processes and serves as basic raw material in production of fertilizers and ammonia
based chemicals. Nitrogen of high purity finds extensive use as carrier gas in the semiconductor
industry and the Liquid nitrogen provides the most effective media for many low temperature
processes from shrink fitting to cryosurgery. The main application of argon as an inert gas in
high temperature furnaces and TIG welding. Demand for these gases has been increasing
The only viable source of oxygen, nitrogen and argon is the atmosphere.
For producing
atmospheric gases like oxygen, nitrogen and argon in large scale, low temperature distillation
provides the most economical route from many point of view. In addition, many industrially
important physical processes – from superconducting magnets and SQUID magnetometers to
treatment of cutting tools and preservation of blood cells, require very low temperature. As
discussed earlier the gases oxygen, nitrogen and argon can be separated by Air Separation
method. While room temperature separation, processes based on adsorption and membrane
separation are finding increasing application, particularly for production of low purity products,
cryogenic distillation remains the predominant method of producing major industrial gases. The
cryogenic distillation process, operating at temperature close to 100K provides the following
advantages over its room temperature counterparts:
• It is Economical in large scale,
• It delivers both gaseous and liquid products,
• It helps in Production argon and other rare gases (in larger plants),
• It Produces flexible product mix.
The low temperature can be achieved in many ways. Earlier Helium and hydrogen liquefiers
were used using the linde and heyland cycles . Recently cryogenic process plants are mostly
preferred which are exclusively based on the low-pressure cycles. They use an expansion
turbine to generate refrigeration. These plants have the advantage of high thermodynamic
efficiency, high reliability and easier integration with other systems. The expansion turbine is the
vital component of a modern cryogenic refrigeration or separation system. Cryogenic process
plants may also use reciprocating expanders in place of turbines.But due to lesser in efficiency
and other factors it is not popular.
In addition to their role in producing liquid cryogens, turboexpanders provide refrigeration in a
variety of other applications, such as generating refrigeration to provide air conditioning in
aeroplanes. In petrochemical industries, expansion turbine is used in order to separate propane
and heavier hydrocarbons from natural gas streams. The low temperature generated necessary for
the recovery of ethane and does it with less expense than any other method. The plant cost is
less, and maintenance, downtime, and power services are low, particularly at small and medium
scales. Many LNG peak shaving plants use turbo expanders located at available pressure release
points in pipelines.
Cryogenic liquefaction cycles can be grouped under three broad categories :
throttle expansion cycles without an active device, e.g. Linde and Mixed
Refrigerant Cycles,
expander cycles, e.g., Claude, Brayton, Collins and Kapitza cycles, and
regenerative refrigeration cycles, e.g. Stirling, Gifford McMahon and Pulse
Tube systems.
Q& ref
Q& ref
Linde Cycle
Q& ref
Claude Cycle
Brayton Cycle
Q& ref
Expanders in Parallel
Collins Cycle
Q& ref
Expanders in series
plus wet expander
Steady flow cryogenic refrigeration cycles with and without active
expansion devices.
Some other utilities of turbine expander are:
Energy extraction applications such as refrigeration.
Power is recovered from high-pressure wellhead natural gas.
In power cycles using geothermal heat.
In Organic Rankine cycle (ORC) used in cryogenic process plants in order to achieve
overall utility consumption.
In paper and other industries for waste gas energy recovery.
Freezing or condensing of impurities in gas streams.
The importance of the expansion turbine as an industrial product is well established. Unlike their
counterparts in aircraft propulsion or power generation, cryogenic turboexpanders are generallyy
small in size and need to operate continuously for years. This is made possible by use of gas
lubricated bearings, having process gas as the lubricant. While larger machines use axial flow
geometry;mixed flow, radial inlet and axial discharge, configuration is adopted by universal
cryogenic system. Multistaging is difficult to achieve with radial or mixed flow geometry.
Therefore, cryogenic turbines always adopt single stage expansion, irrespective of the expansion
1.2 Development of turo-expander in India
In a modern cryogenic plants a turbo expander is one of the most vital components- be it an air
separation plant or a small cryocooler. Industrially advanced countries like the USA, European
countries, Japan, Russia etc. have already been advanced with this technology and attained state
of the art.
In India, the existing air separation plants do not have the capacity to meet ever-growing
demands of pure cryogenic gases. While many of the plants are equipped with facility for both
liquid and gas withdrawal, liquid withdrawal leads to severe drop in gas production and/or loss
of purity. At the root of this problem is limited refrigeration capacity of the basic LindeHampson system. A Plant based on expansion engine operates at higher pressure and needs
regular maintenance. The above difficulties can be overcome by using turbo expander based
plants which offers reduced energy cost, flexible product mix, higher purity and more reliable
operations. In the realm of higher technology such as in nuclear science, space, defense,
superconductivity-liquid helium and hydrogen are very essential commodities. An expansion
turbine is a key element for these plants.While most of the components of a cryogenic plant can
either be indigenously fabricated or can be bought from the open markets, an expansion turbine
can not be procured unless: we build our own technology.
10 | P a g e
The expansion turbine or the turboexpander is one of the important component of most
cryogenic system. Since the turboexpander plays the role of the main cold generator, its
properties – reliability and working efficiency, to a great extent, affect the cost effectiveness
parameters of the entire cryogenic plant. The concept that a turbine can be used as a
refrigerating machine was first introduced by Lord Rayleigh. In his letter of 26 June 1898 to
Nature, he suggested the use of turbine instead of a piston expander for air liquefaction
because of practical difficulties being encountered with the low temperature reciprocating
machines. In this letter, Rayleigh described the most important function of any cryogenic
expander, which is to production of the cold, rather than the power produced. This followed a
series of early patents on cryogenic expansion turbine.
Therefore the turboexpander has attracted the attention of a large number of researchers over the
years. Investigations involving applied as well as fundamental research, experimental as well as
theoretical studies, have been reported in this literature. Critical reviews and specialised technical
articles on the subject have been published in journals such as Cryogenics and Turbomachinery,
and in major conference proceedings such as Advances in Cryogenic Engineering and
Proceedings of the International Cryogenic Engineering Conference.
2.1 A Historical Perspective
Collins and Cannaday and Sixsmith
have presented detailed reviews of the history of
turboexpander development. A brief summary of their accounts is given below to help the
reader appreciate the full dimension of the subject.
The concept that a turbine can be used as a refrigerating machine was first introduced by Lord
Rayleigh in 1898 . He emphasized the most important function of a cryogenic expander, i.e.
the production of low temperature rather than mechanical power. Followed by this suggestion,
a series of early patents came out on cryogenic expansion turbine. In 1898, a British engineer
named Edgar C. Thrupp patented a simple liquefying machine using an expansion turbine.
Thrupp’s expander was a double-flow device with cold air entering the centre and dividing
into two oppositely flowing streams. At about the same time, Joseph E. Johnson in USA
patented an apparatus for liquefying gases. His expander was a De Laval or single stage
11 | P a g e
impulse turbine. A fraction of the in-flowing air condensed in the turbine nozzle and then fell
to the bottom of the liquefaction chamber for collection and run off. Other early patents
include expansion turbines by Charles and Commett (1894) and Davis (1922).
Successful commercial application of an expansion turbine for gas liquefaction was done at the
Linde Works in Germany in early 1930s . The device was an axial flow single stage impulse
turbine, which was later replaced by an inward radial flow machine of impulse cantilever type
by an Italian inventor named Guido Zerkowitz. One feature of this new design was a reversing
chamber fitted inside the turbine wheel to give a second admission of gas to the moving
blades. In this way velocity compounding could be achieved with a consequent reduction in
the wheel speed. Zerkowitz’s patent gave many details of turbine construction to reduce
refrigerative and piping losses. For example, the shaft bearings were to be entirely outside the
turbine housing, well removed from the cold zone.
Following Kapitza’s recommendations, all subsequent developments in the field of cryogenic
turbines have used the radially inward flow arrangement. One of the first well documented air
liquefaction turbines was that designed by the Elliot company and constructed by the Sharples
company in USA. The turbine, described by Swearingen, was a radial inflow, reaction type
machine, having a design speed of 22,000 r/min.
The turbine was supported on ball
bearings.The radial inflow geometry thus became the standard configuration for small and
medium sized cryogenic turbines.
Working 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 [3]”as quoted by Ghosh S.K.
In 1958, the United Kingdom Atomic Energy Authority developed a radial inward flow turbine
for a nitrogen production plant [2] as quoted by Ghosh S.K. During 1958 to 1961 Stratos
Division of Fairchild Aircraft Co. built blower loaded turboexpanders, mostly for air separation
service [1] as quoted by Ghosh S.K. Voth et. al developed a high speed turbine expander as a
part of a cold moderator refrigerator for the Argonne National Laboratory (ANL) [4]. 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 [2] as quoted by Ghosh S.K.
A high speed turboalternator was developed by General Electric Company, New York in
1968, which ran on a practical gas bearing system capable of operating at cryogenic temperature
12 | P a g e
with low loss [5-6]. National Bureau of Standards at Boulder, Colorado [7] developed a turbine
of shaft diameter of 8 mm. The 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 [8]. 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 [9]. In 1984, the
prototype turboexpander of medium size underwent extensive experimental testing in a nitrogen
liquefier. Izumi et. al [10] at Hitachi, Ltd., Japan developed a micro turboexpander for a small
helium refrigerator based on Claude cycle. The 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 diameter of the turbine wheel 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 [11-13]. A study was initiated in 1979 to survey operating plants and
generate the cost factors relating to turbine by Kun & Sentz [12]. Sixsmith et. al. [14] in
collaboration with Goddard Space Flight Centre of NASA, developed miniature turbines for
Brayton Cycle cryocoolers. They have developed of a turbine, 1.5 mm in diameter rotating at a
speed of approximately one million rpm [15].
Yang et. al [16] developed a two stage miniature expansion turbine made for an 1.5 L/hr
helium liquefier at the Cryogenic Engineering Laboratory of the Chinese Academy of Sciences.
The turbines rotated at more than 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 [17]. The turboexpander developed by Kate
et. al [18] 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
[19–20]. The turboexpander consists of a 40 mm shaft, 59 mm impeller diameter and self acting
gas journal and thrust bearings [19]. Ino et. al [21-22] developed a high expansion ratio radial
13 | P a g e
inflow turbine for a helium liquefier of 100 L/hr capacity for use with a 70 MW superconductive
Davydenkov et. al [23] developed a new turboexpander with foil bearings for a cryogenic
helium plants in Moscow, Russia. The maximum rotational speed of the rotor was 240,000 rpm
with the shaft diameter of 16 mm. The turboexpander third stage was designed and manufactured
in 1991, for the gas expansion machine regime, by “Cryogenmash” [24]. Each stage of the
turboexpander design was similar, differing from each other by dimensions only produced by
“Heliummash” [24].
The ACD company incorporated gas lubricated hydrodynamic foil bearings into a TC–
3000 turboexpander [25]. Detailed specifications of the different modules of turboexpander
developed by the company have been given in tabular format in Reference [26].
Cryogenic Industries has been involved with this technology for many years including MafiTrench.
Agahi et. al. [27-28] have explained the design process of the turboexpander utilizing
modern technology, such as Computational Fluid Dynamic 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
favourable 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
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. [30] 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 4.76 mm turbine rotor at the cold end and a 12.7
mm brake compressor at the warm end. The expander had a design speed of 384,000 rpm and a
design cooling capacity of 444 Watts. Xiong et. al. [31] at the institute of cryogenic Engineering,
14 | P a g e
China developed a cryogenic turboexpander with a rotor of 103 mm long 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 liquid 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 [32-33]. These
turbines are characterized by the use of hydrostatic gas bearings, providing unique reliability
with a measured Mean Time between failures of 45,000 hours. Atlas Copco [34] has
manufactured turboexpanders with active magnetic bearings as an alternative to conventional oil
bearing system for many applications.
One of the more recent developments in the field of cryogenic turbines is the wet
turboexpander, where the expanded gas leaves the turbine in a mixed phase. This device, when
employed in a liquefier, increases liquid yield and improves plant efficiency by replacing the JT
Wet expanders used in hydrocarbon and petrochemical industries have been discussed by
Linhardt [37]. He explains that, in a wet expander, the presence of non-equilibrium expansion
(supersaturation) moves the condensation process downstream of the turbine. With large
expansion velocities, the resulting condensate droplets are of sub-micron size. These small
droplets follow the gas streamlines without slip and thus do not impinge on or erode the turbine
wheel. He further suggests that the radial turbine is not acceptable for high liquid content,
because the dense liquid droplets are centrifuged outwards resulting in significant flow
distortions and unacceptably low efficiency. However, Swearingen [36], an early exponent of the
wet expander, has shown that a cryogenic turboexpander of radial inflow configuration
discharging the fluid at its dew point has significantly higher efficiency than one discharging the
gas few degrees warmer. He further points out that if the blade lean angle is within 10~15° from
the radial direction, a radial turbine can act efficiently as a wet expander. Aghai et. al. [38-39]
have discussed the manufacturing steps for this expander. Obata et. al. [40] have recently
presented a theoretical study on the performance of a wet helium turbine. They have concluded
that the performance of a wet turbine is determined more by the outlet temperature than by the
presence of mixed phase inside the rotor. Timmerhaus and Flynn [35] have pointed out that the
15 | P a g e
use of wet expanders is generally restricted to systems using helium as the working fluid because
the latent heat of the liquid phase is less than the thermal capacity of the compressed gas.
Sixsmith et. al. [41] at Creare Inc., USA developed a small wet turbine for a helium
liquefier set up at the particle accelerator of Fermi National laboratory. The gas bearing based
turboexpander was designed to reliably withstand the pressure transients and resulting thrust
variations occurring in wet expanders. Kato et. al.developed a wet turbine for a large helium
liquefier. Their turboexpander was equipped with a relief device at the outlet of the turbine
which served as a JT valve to maintain the designed exit pressure. A wet turboexpander for
helium liquefier application, capable of producing 7% liquid in the outlet stream, has been
developed by the Rotoflow Corporation, USA.
2.2Why development of Turbo-expander in India.
In modern cryogenic plants a turbo-expander is one of the vital components : be it separation
plant or small cryocooler.Industrially advanced countries like USA , European countries ,Japan
,Russia etc have already perfected this technology and attained this art.In India the existing air
separation plant do not have the capacity to meet the everincreasing demands.
A plant based on expansion engine operates at higher pressure and needs regular
maintainence.The above difficulties can be overcome by using turbo-expander based plants
which involves reduced energy cost, increase in efficiency and more reliable operations .
16 | P a g e
The expansion turbine is a radial inflow configuration and axially outflow configuration.These
are suitable for moderately mass flow rate,high head and low power application.The advantage
of this type lie in extracting larger work in single step due to loss free centrifugal heads as the
gas leaves from larger to smaller radii.They are simple in construction and are very cmpact.The
main components are:
1. Nozzle ring.
2. Turbine wheel.
3. Diffuser.
4. Shaft.
5. Brake compressor.
6. Thrust bearing.
7. Journal Bearing.
The high-pressure process gas enters the turbine through piping into the plenum of the cold end
housing and enters radially into the nozzle ring. The flow accelerates through the converging
passage which abides continuity laws and half the adiabatic expansion takes place through
transformation of pressure energy into kinetic energy thereby reducing static temperature and
17 | P a g e
pressure. The nozzle exit angle is such that the flow is directed at the correct angle to the rotating
wheel to avoid the losses due to incidence, thus reducing incidence loss.
The turbine wheel is radial-axial type - i.e. the flow enters the wheel radially and exits axially.
The expansion occurs due to both momentum diffusion and acceleration. Work is extracted and
the process gas undergoes
expansion with corresponding drop in the temperature through
decrease in kinetic energy as well as centrifugal and Coriolis force.
The diffuser is a diverging passage and acts as a compressor that converts most of the kinetic
energy of the gas leaving the rotor to potential energy in the form of a gain in pressure. This
appears as a reduction in pressure at the outlet from the rotor. The expansion ratio in the rotor is
thereby increased with a corresponding gain in efficiency and this enables greater rate of cold
production to be achieved. A small temperature rise in an efficient diffuser does not offset the
increased cooling achieved by the wheel.
A loading device is necessary to extract the work output of the turbine. The rotor is
generally mounted in a vertical orientation to eliminate radial load on the bearings. A pair of
journal bearings, apart from serving the purpose of rotor alignment, takes up the load due to
residual imbalance. For horizontally oriented rotors, the journal bearings are assigned with the
additional duty of supporting the rotor weight. The shaft collar, along with the thrust plates, form
a pair of thrust bearings that take up the load due to the difference of pressure between the
turbine and the compressor ends.
The supporting structures mainly consist of the cold and the warm end housings with an
intermediate thermal isolation section. They support the static parts of the turbine assembly, such
as the bearings, the inlet and exit ducts and the speed and vibration probes. The cold end housing
is insulated to preserve the cold produced by the turbine.
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 . This section on design and development of turboexpander intends to explore
the basic components of a turboexpander.
18 | P a g e
A brief review of basic turbomachinery concepts is discussed in this section. These concepts are
useful in understanding the analytical studies presented in later chapters. They have been taken
from standard text books and reviews on turbomachinery and works of various persons[42-43].
3.1 Turbine wheel
The performance chart has become commonly accepted mode of presenting characteristics of
turbomachines . Several characteristic values are used for defining significant performance
criteria of turbomachines, such as turbine velocity ratio C 0 , pressure ratio, flow coefficient
factor and specific speed . Balje has presented a simplified method for computing the efficiency
of radial turbomachines and for calculating their characteristics The specific speed and the
specific diameter completely define dynamic similarity. The physical meaning of the parameter
pair n s , d s which is taken with consideration with the efficiency is that, fixed values of specific
speed n s and specific diameter d s define that combination of operating parameters which permit
similar flow conditions to exist in geometrically similar turbomachines .
Brake Compressor
Turbine wheel
Aluminum is the most ideal material for turbine impellers or blades because of its excellent low
temperature properties, high strength to weight ratio and adaptability to various fabrication
techniques. This material is widely used in expanders either in cast form or machined from
forgings. Expander and compressor wheels are usually constructed of high strength aluminum
19 | P a g e
alloy which provides better design. Low density and relatively high strength aluminum alloys are
ideally suited to these wheels as they operate at moderate temperature with relatively clean gas.
The weight of the wheels is reduced using low alloy which is desirable to avoid critical speed
problems [49] and centrifugal stresses.
A high strength aluminium alloy is used for manufacture of Rotors. A rotor integral with the
shaft would be simpler, but it was found difficult to end mill the rotor channels in high tensile
titanium alloy . With tip speeds up to 500 m/sec, titanium compressor wheels machined out of
solid forgings are standard industry practice [52]. Duralumin is ideal material for use in the rotor
disk, it has a high strength to weight ratio and is adaptable to various vibrating techniques.
The basic objective of a cryogenic turbine is to achieve the highest possible isentropic efficiency.
Unlike aircraft applications, where the turbines have to operate under widely varying conditions,
a cryogenic turboexpander operates with fixed inlet and exit conditions throughout its life. In
small and medium sized cryogenic plants, the throughput and head combinations lead to small
values of specific speed , where the radial inflow configuration provides the highest efficiency .
During operations there are many losses which decreases the efficiency .The three major losses
[43]are as follows:
1. Rotor passage loss.
2. Rotor incidence loss.
3. Rotor clearance loss.
The required inlet velocity and swirl can only be obtained by providing a set of static nozzles
around the turbine wheel. The flow is subsonic, the absolute Mach number being around 0.95.
Filippi [58] has derived the effect of nozzle geometry on stage efficiency by a comparative
discussion of three nozzle styles: fixed nozzles, adjustable nozzles with a centre pivot and
adjustable nozzles with a trailing edge pivot. At design point operation, fixed nozzles yield the
best overall efficiency. Nozzles should be located at the optimal radial location from the wheel to
minimize vaneless space loss and the effect of nozzle wakes on impeller performance. Fixed
nozzle shapes can be optimized by rounding the noses of nozzle vanes and are directionally
oriented for minimal incidence angle loss.
20 | P a g e
The throat of the nozzle has an important influence on turbine performance and must be sized to
pass the required mass flow rate at design conditions. The continuity equations determines the
exit flow angle and exit velocity from nozzle. The throat velocity should be similar to the stator
exit velocity and this determines the throat area by continuity [59]. Turbine nozzles designed for
subsonic and slightly supersonic flow are drilled and reamed for straight holes inclined at proper
nozzle outlet angle [60]. In small turbines, there is little space for drilling holes; therefore two
dimensional passages of appropriate geometry are milled on a nozzle ring. The nozzle inlet is
rounded off to reduce frictional losses.
Thomas used the inlet nozzle of adjustable type. In this design the nozzle area is adjusted by
widening the flow passages. The efficiency of a well designed nozzle ring should be about 95%
while the overall efficiency of the turbine may be about 80% .
Fig 1[43]: Nozzle diffuser
3.2.1Different Nozzle Configurations[42]
Several configurations of variable area nozzles have been studied by Kato et. al. [61]. They
classify the nozzles into three types. In a type A nozzle, the discharge angle is set by rotating the
vane about a pivot. The type B
nozzle is of partial admission type, where the region of
admission is controlled, while in Type C the flow cross section is manipulated by changing the
nozzle height by movement of the lower plate. Type B nozzles are used in turbochargers and in
large cryogenic plants. Leakage of process gas around anchor pins of the actuating mechanism is
substantial. Hence Type C nozzles are preferred in helium applications . Luybli and Phillipi have
shown that for fixed nozzle designs, very high nozzle efficiency can be attained at the design
point; but the efficiency drops sharply under off-design conditions. The nozzle ring with trailing
21 | P a g e
edge pivot provides the flattest curve for the efficiency with changing mass flow rate. The
Rotoflow Corporation uses variable nozzle design for their helium turbines. The plate covering
the nozzles uses special springs to provide clamping force and prevent “blow-by” over a wide
range of operating conditions [62]. The helium turbine developed by CCI Cryogenics also uses
an adjustable height type nozzle.
The space between the nozzle and the rotor, known as the vaneless space, has an important
bearing on turbine design. Watanabe et. al. empirically determined that the maximum efficiency
occurs at a value of the interspace parameter k given by the relation :
k = ∆r / bn cos α1 =2
where ∆r is the radial clearance between the nozzle exit and the rotor tip. Whitfield and Baines
have concluded from others’ observations that the design of vaneless space is a compromise
between fluid friction and nozzle-rotor interaction. They have recommended the assumption of
free vortex flow in the design of the vaneless space.
There is always a tendency of foreign particles to accumulate in the space between the nozzle
and the wheel which may cause surface damage by erosion. In severe cases, the trailing edges of
the nozzles have been completely worn away. The use of stainless steel nozzles reduces the rate
of deterioration but the only satisfactory cure is the prevention of particle entry by filtration .
3.3 Diffuser
The diffuser acting as a compresso r, converts most of the kinetic energy in the gas leaving the
rotor to potential energy in the form of pressure rise. The design of the exhaust diffuser is a
difficult task, because the velocity field at the inlet of the diffuser (discharge from the wheel) is
hardly known at the beginning.The expansion ratio in the rotor is thereby increased with a
corresponding gain in efficiency.
The efficiency of a diffuser may be defined as the fraction of the inlet kinetic energy that
gets converted to gain in static pressure. The Reynolds number based on the inlet diameter
normally remains around 105. The efficiency of a conical diffuser with regular inlet conditions is
about 90% and is obtained for a semi cone angle of around 5° to 6°. According to Shepherd, the
optimum semi cone angle lies in the range of 3°-5° [63]. A higher cone angle leads to a shorter
diffuser and hence lower frictional loss, but enhances the chance of flow separation. Whitefield
and Baines and Balje have given design charts showing the pressure recovery factor against
geometrical parameters of the diffuser.
22 | P a g e
Ino et. al. [64] have given the following recommendation for an effective design of the
Half cone angle should be 5° - 6°
and Aspect ratio : 1.4 – 3.3.
The inner radius is chosen to be 5% greater than the impeller tip radius and the exit radius of the
diffuser is chosen to be about 40% greater than the impeller tip radius this proportion is roughly
been the representative of what is acceptable in a small aero turbine application.
3.4 Shaft
The major inertia force is due to the force acting on the turbine shaft due to the revolution of its
mass center and around its geometrical center constitutes. A restoring force equivalent to a
spring force for small displacements, and viscous forces between the gas and the shaft surface,
act as spring and damper to the rotating system. The film stiffness depends on the relative
position of the shaft with respect to the bearing and is symmetrical with the center-to-center
In order to eliminate the need for a heavily loaded thrust bearing,Winterbone has suggested that
the diameter of the shaft be made the same as the diameter of the turbine wheel. Shaft speed is
limited by the first critical speed in bending . This limitation for a given diameter determines the
shaft length, and the overhang distance into the cold end, which strongly affects the conductive
heat leak penalty to the cold end. In practice, particularly in small and medium size turbines, the
bending critical speeds are for above the operating speeds. On the other hand, rigid body
vibrations lead to resonance at lower speeds, the frequencies being determined by bearing
stiffness and rotor inertia.
The important criteria in choosing the material for shaft are:
I.The critical frequency should be greater than the operating frequency so as to avoid damage.
II.The stress calculated over the surface should be less than the yield stress of the material
The material of the shaft is 410 stainless steel or K-monel. stainless steel 410 which was chosen
because of its desirable combination of low thermal conductivity and high tensile strength [66].
Prevention of contact damage between the journal and bearing at start up is very important while
23 | P a g e
designing the shaft. . The 18/8 stainless steel is also frequently used as a shaft material since its
low thermal conductivity is advantageous in limiting heat flow into the cold region of the
machine. To improve its bearing properties,it is necessary to treat the
3.5 Brake Compressor[43]
The power developed in the expanders may be absorbed by a geared generator, oil pump, viscous
oil brake or blower wheel . Where relatively large amounts of power are involved, the generator
provides the most effective means of recovery. Induction motors running at slightly above their
synchronous speed have been successfully used for this service. This does not permit speed
variation which may be desirable during plant start up or part load operation.
A popular loading device at lower power levels is the centrifugal compressor . The centrifugal
compressor is ideally suited for the loading of small turbines because of its simplicity and ease of
control. It has the additional advantage that it can operate at high speeds. An electrical brake can
be used for small turbines whose work output exceeds the capacity of a centrifugal gas
compressor.. The compression ratio ranges between 1.2 and 2.5 depending upon the speed.
3.6 Bearings[43]
3.6.1 Aerostatic thrust bearings
The gas bearing is mostly suited for supporting the rotors of these machines. Kun, Amman and
Scofield [69] have both described the development of a cryogenic expansion turbine supported
on gas bearings at the Linde division of the Union Carbide Corporation, USA during the mid and
late 1960’s. They used aerostatic bearings to support the shaft.
L’Air Liquide of France began its developmental efforts on cryogenic turboexpander from the
late 1960’s . The high speed rotors were supported by Gas lubricated journal and thrust bearings.
This bearing system assured an unlimited life to the rotating system, due to total elimination of
contact between the parts in relative motion.
24 | P a g e
In recent times, Thomas [70] reported the development of a helium turbine with flow rate of 190
g/s, working within the pressure limits of 15 and 4.5 bar. Both the journal as well as the thrust
bearings used process gas for external pressurisation. The journal bearings with L/D ratio of 1.5
were designed for a shaft of diameter 25.4 mm. The bearing clearance was kept within 20 and 25
µm. The bearing stiffness was measured to be 1.75 N/µm.
3.6.2 Tilting pad journal bearings
In this design, a converging film forms between the pads and the shaft and generates the
required pressure for supporting the radial load. A fraction of the bearing gas from each
converging film is fed to the back of the pad, thus forming a film between the pad and the
25 | P a g e
The pad floats on this film of gas. This tilting pad bearing is characterised by the absence of
pivots in any form.
Gas lubricated tilting pad journal bearings were also used to support the rotor of a large helium
turboexpander developed by the Japan Atomic Energy Research Institute and the Kobe Steel
Limited [72]..
Contact damage between the journal and the bearing should be prevented at start up which is
very important. No flaws should be found in the contact surface of the bearing and the shaft. Ino
et. al. found no flaws on the heat treated surface of the journal combined with the ceramic tilting
pads after 200 start/stop cycles and then it was confirmed that the combination of shaft and
ceramic bearing provides significant improvement in their contact damage and thus design is
The materials of Bearings are of nickel silver, which are used largely for ease of accurate
machining and compatibility with respect to its coefficient of contraction in cooling. The
material is selected for its anti friction properties which reduces scoring during initial testing .
3.7 Seals
In a small turboexpander, Proper sealing of process gas, is a very important factor in improving
machine performance. For lightweight, high speed turbomachinery, requirements are somewhat
different from heavy stationary steam turbines [73]. The most common sealing systems are
labyrinth type, floating carbon rings, and dynamic dry face seals. Due to extreme cold
temperature, commercial dry face seal materials are not suitable for helium and hydrogen
expanders and a special design is needed.
Effective shaft sealing is extremely important in turboexpanders since the power expended on
the refrigerant generally makes it quite valuable. Simple labyrinths can be used with relatively
good results where the differential pressure across the seal is low. More elaborate seals are
required where relatively high differential pressures must be handled. In larger machines, static
type oil seals have been used for these applications in which the oil pressure is controlled by and
balanced against the refrigerant pressure .
26 | P a g e
The development of an expansion turbine system consist of the design of wheel, nozzles, diffuser
and the brake compressor,then the prediction of performance under varying operating conditions.
It has been well presented by many authors like Kun ,Hasselgruber, Katsanis, Ghosh .
In this chapter we will see the various calculations involved in the design of:
i. Turbine Wheel: calculation of rotational speed and gross dimension like major
diameter,hub diameter,tip diameter etc.
ii. Design of diffuser.
iii. Design of nozzle.
iv. Design of blade profile.
v. Design of brake compressor and shaft.
vi. Off design performance prediction.
m Mass flow rate in (Kg/s)
η Efficiency
V Volume flow rate (m3/s)
H Available head (J/Kg)
P Pressure (Pa)
T Temperature (K)
h Enthalpy (J/Kg)
Entropy (J/(Kg K))
ρ Density (Kg/ m3)
ω Rotational speed (rad/s)
R Gas constant (J/(Kg K))
Cp Gas property (J/(Kg K))
27 | P a g e
ξ Loss coefficient
Function e.g. h=f (P, T) implies h is a known function of P and T
m Meridional component
θ Circumferential component.
Radial component.
in Inlet
Nozzle exit
Impeller inlet
Impeller exit
ex Diffuser exit
Isentropic process
α Absolute flow angle (angle between C and U)
β Relative flow angle (angle between W and U)
δ Blade lean angle (angle between Wm and axis of rotation)
θ Angular coordinate of cylindrical coordinate system
A Area
D Diameter
b Blade height
28 | P a g e
Blade thickness
C Absolute velocity
W Relative velocity
U Circumferential velocity
4.2 Turbine Wheel
Input Parameters:
Inlet Pressure: Pin
Inlet Temperature:Pout
Exit Pressure: Pout.
Expected efficiency: n. ,and mass rate flow Mr and exit velocity Cex.
From inlet pressure and temperature, other state properties at the inlet can be evaluated.
[hin,sin,ρin]= f (Pin, Tin)
For an isentropic process, the exit entropy is equal to the inlet entropy
sexs= sin
Exit state properties for an isentropic process are calculated from exit pressure and exit entropy.
[Texs,hexs,ρexs]= f (Pexs, sexs)
Expected efficiency is used to evaluate actual exit enthalpy from isentropic exit enthalpy and
inlet enthalpy.
hex = hin + η × (hexs −hin)
In order to determine the gross dimensions of the turbine wheel we need to take the help of NsDs curve as obtained by Balje.
29 | P a g e
Major diameter
Figure d[a].
Ns-Ds Curve
The Balje’s ns-ds diagram, shows lines of optimum geometry along with contours of constant
efficiency. The following observations may be noted:
1. The validity of maximum efficiency occurs only when the Reynolds number exceeds a
certain value and the Laval number is less than a certain quantity.
2. Efficiency penalties are considered for stress-limited wheels, wet turboexpanders and
sub-optimum installations.
3. The diagram are based on certain values of clearance ratio, trailing edge ratio and surface
roughness ratio.
30 | P a g e
4. A major advantage of Balje’s representation is that the efficiency is shown as a function
of parameters which helps in calculating the rotor frequency and its diameter.
Corresponding to expected efficiency the value of Ns and Ds is determined from the above
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
ω × Q3
( ∆hin−3s )
Specific diameter ds =
D2 × ( ∆hin −3s )
Take k1,k2 which accounts for the difference between state 3,ex caused by pressure recovery and
consequent rise in temperature and density in the diffuser.
The specific volume (v) can be found from the chart at initial conditions. So the volumetric flow
rate Qex is determined by the formula Qex=Mtr*v.
H01, Hex is found out from chart with gIven initial and final conditions.
The isentropic enthalpic drop from inlet to turbine exit = ∆hin −3 s = k 2 (h0 in − hexs )
Dt= Inner diameter of turine wheel is calculated by the formula 1.[43] and the angular velocity
“w”is calculated by 2[43].
The blade velocity at inlet of turbine U2= w*Dt/2;
Velocity Triangle at inlet
Velocity triangle at outlet
31 | P a g e
The ratio of eye tip diameter to inlet diameter should be limited to a minimum of .7[43] to avoid
excessive shroud curvature.
Dtip= .6*Dt;……………………………………3[43]
The exit hub diameter to tip diameter ratio should be maintained above a value of 0.4 to avoid
excessive hub blade blockage and energy loss.
Mean outlet diameter=(Dhub+Dtip)/2;
The Number of blades and the blade thickness is chosen to be 10,.6mm respectively.[43]
From geometrical considerations:
A3 =
Z tr t tr Dtip − Dhub
Dtip − Dhub −
2 sin β mean
Z tr = number of blades,
t tr = thickness of the blades, and
β = exit blade angle
Now by writing equation (3.12) in the form Q3 results:
Q 3 = A3C 3 = C 3 
Q3 = C 3
− D hub
)− Z
Z tr t tr Dtip − Dhub
Dtip − Dhub −
× W3
32 | P a g e
(D tip
− D hub 
2 sin β mean
tr t tr
Recommended Source
Parameter Recommended Source
W3 / W2
U 3 / U2
< 0.4
D3 tip/D2
< 0.7
D 3 m/ D 2
0.6 – 0.67
b2 / D2
0.09 – 0.07
U2 / C0
area ratio
D3h/D3 tip
The Velocity triangle at turbine inlet
Assuming the incidence angle α2=26;
C2= 1000(h02-h03)+ u3*c3*cos(α3).
C02= C2 cos(α2).
Cm2= C2 sin(α2);
Tan β2= Cm2/( U2-C02).
Velocity triangle at turbine outlet
Assuming the incidence angle, α2=26
Absolute velocity at the turbine outlet,
C03=C3 cos(α3)
33 | P a g e
Thermodynamic state at wheel discharge (state 3)
At the exit of the diffuser,Qex,Aex
The exit velocity is defined as :
C ex = Qex/Aex.
This velocity is below 20 m/s as suggested by Balje [8].
Exit stagnation enthalpy:
+ ex
h 0ex = h ex
Exit stagnation pressure:
ρ ex C 2 ex ≈ p
(because velocity C ex is small)
p 0ex = p +
From the stagnation enthalpy, h03 , and stagnation pressure p 0 ex , the entropy s 3 is estimated .
And static enthalpy:
h3 = h03 −
Tip circumferential velocity
U 3tip =
ω Dtip
Relative velocity at eye tip
W3tip = U 3tip + C 3
Highest Mach No
C s3
β 3tip = tan −1
34 | P a g e
4.3 Design of Diffuser
Kinetic energy at rotor outlet should be recovered using a diffuser.Generally a diffusing angle of
5-5 degrees is used which minimizes the loss in pressure recovery .The aspect ratio is 1.43.3.The diameter of the diffuser at inlet is equal to the diameter of the turbine wheel at inlet with
recommended clearance of 2%of the exit radius.Diffuser outlet diameter is equal to the outlet
piping diameter which gives the length of the diverging section.
The different geometric parameters to be computed are:
i. Diffuser exit diameter.
ii. Diffuser inlet diameter.
iii. Diffuser profile for 1st and 2nd section.
iv. Total diffuser length.
The Datas entered by the user are:
Mass rate flow:Mtr.
Discharge velocity: Cex As calculated.
Discharge Density:ρex.
35 | P a g e
Performance diagram for diffusers( reproduced from balje[8])
In order to assess the validity of the above dimensions of the diffuser, the Fig. 3.5 is reproduced
from Ref [8]. From the figure, in the divergent section, the length to throat radius ratio of 8.31
and exit area to throat area ratio 2.98 give a stable operation of recovery factor of 0.7. This
confirms the design of the diffuser.
1. D ex =
4 × Vex
; diffuser exit diameter………………………………d[1]
π × C ex
2. Inlet Diamter Din =Dt+ 2*radial clearance………………d[2]
Area at inlet of diffuser =π/4 * Din*Din.
3. Diameter at throat =Dtd=Dtip+2*radial clearance………d[3]
4. Let taper angle=5degree= ¥
Length of the diverging section of diffuser:
Ld= (Dex-Dtd)/ (2*Tan ¥)……………………………….d[4]
4.4 Nozzle Design[42]
In order to avoid incidenc loss ,the flow form the nozzle should come on to the wheels at correct
angle α2.Hence, a well-designed nozzle is very necessary for an efficient turbine.
One of the important forcing mechanisms in evaluating the fatigue conditions at the wheel is the
nozzle excitation frequency. As the wheel blades pass under the jets emanating from the
stationary inlet blades, there will be periodic excitation proportional to the inlet nozzles and the
speed of the wheel. To reduce the effect due to this periodic excitation a thumb rule is that the
number of nozzles should not be integral multiple of the number of turbine blades.
Following [] the nozzle cascade height is taken as:
b1 = 0.9 × b2
This is in order to leave some margin for expansion in annular space above the wheel and for
axial misalignment. Providing 4% vane less space the throat diameter (Dt):
Dt = 1.08 × D
The above values (0.9 and 1.08) are commonly used but the designer is free to change them. Let
Cmt be the meridional component at the throat of the nozzle. From the continuity equation:
36 | P a g e
C mt = C 2 ×
ρ2 D b2
ρt Dt bt
From the conservation of angular momentum, the tangential component of velocity at throat:
C θt = r2 × ω ×
From conservation of energy:
= h
C 22
C θ2 t
C 2mt
st = s2
[Tt, ht, ρt] = f (Pt, s2)
The absolute velocity at the nozzle throat:
C t = C 2mt + C θ2t
Using continuity throat width (Wt) and angle (αt) are calculated as:
Wt =
b t × Zn × ρt × Ct
From the conservation of angular momentum we get the radius of the
r22 × ω
rt =
C t × cos(α t )
 C mt
 C θt
α t = tan −1 
From the cosine rule of triangles the radius of cascade discharge is given by:
r1 = rt2 +
Wt2 Wt × r22 × ω
Blade loading δu is defined as:
δu = cot(αt) −cot(α0)
Let the mean velocity angle be β∝, then:
cot (α t ) + cot (α 0 )
cot β ∞ =
( )
37 | P a g e
Then the stagger angle β s:
βs = β ∝ − 4o
Chord length of the nozzle vane
4 × π × δ u × r1
 
δ u  
Ψ z × Z n × 1 +  cot (β ∞ ) +   × sin (β s )
2  
 
4.4 Design of shaft[43]
It is believed that the strength of materials improves at low temperature and thus stress
consideration are taken as unimportant. In reality, cryogenic turbines, because of the moderate
to high-pressure ratio and low flow rates operate at high rotational speeds, leading to significant
centrifugal stresses in the shaft. The shaft transmits the torque produced by the turbine to the
brake compressor.. Also the turboexpander is vertically oriented and bending load is neglected
due to the absence of any radial load. Important considerations in the design of the shaft are:
number and size of components linked with the shaft,
tangential speed on bearing surfaces,
stress at the root of the collar
critical speed in shaft bending mode,
The major dimensions of the shaft include:
• diameter of the shaft,
• diameter of the collar and
• length of the shaft
Ino et. al [82] have chosen a shaft diameter of 16 mm for their helium turbine rotating at
2,30,000 r/min, while Yang et al have chosen 18 mm for their air turbine rotating at 180,000
r/min. A shaft of diameter 16 mm and length 88.1 mm with a thrust collar of diameter 30 mm has
been selected in the present case.
VSurf=w*d/2 m/s.
and that on the tip of the collar is 2*Vsurf. ................s[2]
A preliminary calculation considering the collar as a solid disk gives [83]
σ = 1/3*ρss*Vsurf2 Ma
38 | P a g e
This value is more than recommended design stress of 230 MPa for stainless steel SS 304 ,
justifying the need for other material. Hence K-Monel-500 for the shaft material is chosen
having design stress of 790 Mpa. By using K-Monel-500 as a shaft material the possibility of
yielding of the shaft is very less.
Shaft speed is generally limited by the first critical speed in bending. This limitation for a given
diameter determines the shaft length. The overhang distance into the cold end, strongly affects
the conductive heat leak penalty to the cold end .
The first bending critical speed for a uniform shaft is given by the formula
f = 0.9 d l 2
where d is the diameter of the shaft, l is the length, E is the Young’s modulus and
ρ is the
density of the material. Considering the shaft to be a K-Monel-500 cylinder of diameter 16.0 mm
and length 88.1 mm, the bending critical speed is
 0.016  18 × 1010
= 8544 Hz = 5,12, 640
 0.08812 
f = 0.9 
This is well above the operating speed of 2,18,775 r/min.
The gas lubricated bearings of a cryogenic turbine need to be maintained at room temperature to
get the necessary viscosity. This requires a strong temperature gradient over the shaft overhang
between the lower journal bearing and the turbine wheel. The rate of heat flow can be reduced by
(a) using material of lower thermal conductivity (b) reducing the shaft diameter below the lower
journal bearing and (c) by using a hollow shaft in that section.
4.5 Blade design
In the design of a turbo expander, the vital part is the turbine wheel, because losses mainly occur
in the flow passage due to improper blade design. Therefore, design of the blade should be such
that it will produce the flow angles and velocities required by the velocity diagrams. An
analytical procedure has been outlined by Hasselgruber . This procedure requires the major
dimensions of the wheel and the relative flow angle at the wheel inlet and exit. Then the blade
profile is calculated.
Flow direction
39 | P a g e
In the figure:
Direction and arc length of relative streamline
Direction and arc length of meridian streamline
⊥ to t and s
⊥ to t and n
The profile is determined based on the theory of frictionless flow in a rotating wheel and the
basic boundary conditions. The equations of motion in a moving coordinate frame have been
derived equating pressure forces and the inertial forces acting on the fluid element.
The pressure forces:
 ∂P ∂P ∂P 
,− 
 ∂t ∂b ∂n 
The inertial forces consist of
1. Forces due to relative motion with respect to the impeller.
2. Centrifugal force.
3. Coriolis force.
The governing equations come out to be:
∂W U 2
+ ρ ×  − W ×
× sin (δ )× sin (β ) = 0
 W2 U2
+ ρ ×  −
× sin (δ )× cos(β ) + 2 × ω × W × sin (δ ) = 0
Three characteristic functions used by Hasselgruber for calculation of the profile:
1. The first function depicts the variation of relative acceleration of the fluid from turbine
wheel inlet to the wheel exit
 C2
+ ρ ×  u × cos(δ ) − m
 r
 s
f 1 
 s2
 = (cosec(β 3m ))2 + (cosec(β 2 ))2 − (cosec(β 3m ))2 × A
 s
 
 × (k h + 1) × cosec(β 2 ) + (cosec(β 3m ) − cosec(β 2 ))× 1 − 1 −
 s2
  s 2
k h × cosec(β 2 ) + cosec(β 3m )
40 | P a g e
k h +1
 
 
2. This function gives the relative flow angle along the flow path.
 s
f 2 
 s2
 =
 s
cosec(β 2 ) + {cosec(β 3m ) − cosec(β 2 )}× 1  s2
3. This function is a combination of the first two.
 s
f 3 
 s2
 s
 = f 1 
 s2
 s
 × 1 − f 22 
 s2
4.6 Design of brake compressor
The shaft power generated by the turbine must be transferred to a braking device mounted on the
shaft.For relatively large amount of power ,an electrical generator is mostly used as a raking
device.A brake compressor is the most common device for small turbo-expander.
Design Input Parameters
a. Process Gas.
b. Power to be dissipated.(P)
c. Angular speed.(w)
d. Inlet total pressure.(p01)
e. Inlet total temperature( T01)
f. Expected efficiency( Nb)Assume isentropic enthalpin drop as
Specific speed n s =
ω Q4
Specific diameter
ds =
D5 ∆hs
Balje has pointed out that mixed geometry is necessary to obtain the highest efficiency
at these Values Ns,DS.
From above equations , Q4 and D5 is determined.
Where D5 is the diameter of the impeller at the exit.
41 | P a g e
From input parameters, P01,Mn,R,T01
Density ρ4=.94*ρ04………………………………………………B[1]
Where ρ04= (P01*Mn)/(R*T01)………………….B[2]
Mass rate flow Mb= ρ4 *Q4.
Peripheral Speed at exit=U5= w*D5/2
Assuming zero swirl at inlet , Power Input P;
where, φ = power input factor = 1.02
σ sf = slip factor =
Cθ 5
= 0.78
C θ5 = Tangential component of the absolute velocity at exit
U 5 = peripheral speed at exit = ωD5 2
Assuming exit to inlet diameter ratio as 2.25 and blade height to diameter ratio at inlet as .2.
Inlet Diameter D4=D5/2.25
Inlet blade height B4= .2*D5
Blade thickness of .75mm and number of blade ZB=12 recommended.
Inlet velocities
Assuming number of blades, Z b = 12 and a uniform thickness t b = 0.075 mm, the radial absolute
velocity C r 4 (which is also equal to the absolute velocity C 4 in the absence of inlet swirl) is given as:
C r 4 = C 4 = Q4 /((πD4 − Z b t b ) × b4 )
The peripheral velocity at inlet is computed to be:
U 4 = D4ω 2
42 | P a g e
The inlet blade angle β 4 and the inlet relative velocity W4 are computed from the inlet velocity triangle
β 4 = tan −1
Cr 4
W4 = U 42 + C 42
The relative Mach number at inlet
This value indicates that the flow is subsonic in nature.
Exit velocities
The absolute exit velocity:
C 5 = 2(h05 s − h5 s )
Using the value of 0.82 for the slip factor, the tangential velocity:
Cθ 5 = 0.82 U 5
Cr 5 =
C52 − Cθ25
The exit blade angle:
and the absolute exit angle :
 Cr5
 Cθ 5
α 5 = tan −1 
43 | P a g e
The relative velocity at exit:
W5 = C r 5 cos ecβ 5
Exit temperature
T5 = T04 +
and exit pressure:
p5 = p 04  5
 T04
Density at exit:
ρ5 =
 γ −1
The required blade height at exit:
b5 =
m& b
(πD5 − Z b t b )ρ 5 C r 5
4.7 Off Design Predictions
It is also important for the designer to predict the complete performance map of a machine so
that alternative designs can be compared, assessed and implemented.A turbo expander is one of
the key components of cryogenic process plants, which run under varying operating conditions.
This necessitates the study of the performance of the turbine at conditions different from the
designed ones such as to examine the start transients.
44 | P a g e
A systematic procedure is followed to calculate the various parameters associated with the
design of Turbo exapander. The help is taken from previous discussed design procedures.Help
has been taken from various works of Shri S.K.Ghosh and Shri Partho Sarathi to compile them in
a systematic manner.
Turbine profile
Taper angle
Design of diffuser
Nozzle design
stress,dia, length
Design of Shaft
Design of brake compressor
Off design performance prediction
45 | P a g e
Diameter, length of
diverging section
Gross dimensions,
Velocity triangle
T0,in ; p 0 ,in ; p ex ; m; η T − st
Thermodynamic properties
ρ in ; hin ; s in at the inlet and
ρ ex ; hex ; s ex ; Tex at the Exit are computed from chart
using the input parameters.(The entropy remain constant )
The initial value of k 1 and k 2 are assumed.
Q3 , ρ 3 and ∆hin −3 s is determined.
Ns ,Ds is determined wrt efficiency
ω and Dtr is computed.from 1[43],2[43].
Dtip and Dhub is computed. 3[43],4[43].
β mean and C m 3
is calculated.
The major dimensions and the velocities at inlet and outlet is finally
46 | P a g e
Design of diffuser
Input: taper angle.
The diffuser exit diameter is determined
from d[1].
The diffuser inlet diameter is determined
from d[2].
The Diameter at throat is determined
from d[3].
The length of diverging section is
determined from d[4].
From fig D[a] , h3 and s3 is computed at
the state point and ρ3 is calculated.
Is initial ρ3 and
calculated ρ
are equal
47 | P a g e
T 04 ; p 04 ; P ; ω; ηcomp
and working fluid
The compressor discharge pressure and flow rate assuming
ρ 4 = 0.95ρ 04 and determine ρ 4 from equation B[1]
Solving equations (b[i],b[ii]) simultaneously with approximate
value of ρ 4 , D 5 , Q 4 and ∆h adst is determined
Determine the compressor discharge thermodynamic
variablesT 5 , p 5 and ρ 5
Determine ∆h 0ad and U 5 from equations
Determine D 4 and b 4 from equation B[6],B[7]
Determine the Inlet and exit velocities using equations B[8]B[15].
48 | P a g e
Design of shaft
Choose a material with
recommended design stress
Select the diameter and
rpm using Yang et al work
Calculate the peripheral velocity and
velocity at tip using equations s[1],s[2]
Determine the stress on the rotating
shaft using equation s[3].
Is recommended
stress greater than
calculated stress
Calculate the critical frequency.
Is critical frequency
is greater than
operating speed
Safe design
49 | P a g e
The software has been designed using Turbo C++.This is a object oriented programming
language which is preferred approach for most software projects.It offers a new and powerful
way to cope with complexity.Instead of viewing a program as a series of steps to be carried out
,it views it as a group of objects that have certain properties and can take certain actions.
Major Elements Of C++
A. Objects.
B. Classes.
C. Inherintence
D. Reusability.
E. Polymorphism
F. Overloading.
The design codes have been written to develop each components of a turbo expander.Help has
been taken from various recent thesis to perform the systematic design procedure for the
development of Turbo-Expander.The output can be potrayed in a visual screen with the help of
visual C++.The designer is asked to enter the parameters and the output is displayed at every
design of the component. This software is easily upgradable and can be used for newer versions.
50 | P a g e
void main()
{ clrscr();
cout<<" design of turbo expander"<<endl;
cout<<"entr working fluid"<<endl;
char a[10];
cout<<"entr constants k1, k2"<<endl;
double k1,k2;
cout<<"entr turbine inlet temperature,inlet pressure,discharge pressure,efficiency"<<endl;
double t1,p1,p2,e;
cout<<" find the corresponding ns and ds wrt efficiency"<<endl;
double ns, ds;
cout<<" from mollier chart entr the inlet enthalpy and exit enthalpyin KJ/Kg"<<endl;
double h01,h02;
cout<< "entr exit volume rate as m3/sec" <<endl;
51 | P a g e
double q02;
double h,q ;
q= k1*q02;
double dt;//inner diameter of turbine wheel
dt= ds*pow(q,.5)/ pow(h,.25);
//determination of angular velocity
double w= ns* pow(h,.75)/pow(q,.5);
double u2= w*dt/2; // blade velocity.
double dtip=0.6*dt;
double dhub= .425*dtip;
double dmean=(dhub+dtip)/2;
cout<<"-----------------design results--------------"<<endl<<endl;
cout<<"enthalpy drop--"<<h<<endl<<endl;
cout<<"inner diameter--"<<dt<<"m"<<endl<<endl;
cout<<"angular speed---"<<w<<"rpm"<<endl<<endl;
cout<<"blade velocity at inlet of turbine----"<<(int(u2*100))/100<<"m/sec"<<endl<<endl;
cout<<"tip dia taking shi as .6---"<<dtip<<"m"<<endl<<endl;
cout<<"hub dia meter taking lamda as 0.425--- "<<dhub<<"m"<<endl<<endl;
cout<<"mean diameter---- "<<dmean<<endl<<endl;
// mean exit angle blade =b;
double b=45.922*3.14/180;
double c3;
double a3=95*3.14/180; //assumed.
52 | P a g e
//c3= q/(sin(a3)*(3.14*(pow(dtip,2)-pow(dhub,2))/4- 10*.006*(dtip-dhub)/(2* sin(b))));
cout<<" exhaust velocity"<<c3<<endl<<endl;
double u3= w*dmean/2;
cout<<" mean blade velocity"<<u3<<"m/sec"<<endl<<endl;
// the velocity triangle at turbine inlet.
cout<<" discharge velocity from diffuser as cex as m/sec"<<endl;
double cex;
double h0ex;//exit stagnation enthalpy
h0ex= h02+ pow(cex,2)/2000;
double c2;
double a2=26*3.14/180;
c2= (1000*(118.92-h0ex)+ u3*c3*cos(a3))/(u2*cos(a2));
double c02,cm2;
c02= c2*cos(a2);
cm2= c2*sin(a2);
double w2=pow( cm2*cm2+ pow(( u2-c02),2),.5);
double tanb2= cm2/(u2-c02);
cout<<" data for velocity triangle at inlet of turbine"<<endl;
cout<<" w2----"<<w2<<"m/sec"<<endl<<endl;
53 | P a g e
cout<<" tan of blade angle"<<tanb2<<endl<<endl;
// velocity triangle at turbine outlet.
double cm3= c3*sin(a3);
double c03=c3*cos(a3);
double w3= pow(( u3*u3 + c3*c3 - 2*u3*c3*cos(a3)),.5);
cout<<" data for velocity traiangle at outlet "<<endl;
cout<<" cm3----"<<(int(100*cm3))/100<<"m/sec"<<endl<<endl;
cout<<" c03----"<<(int(100*c03))/100<<"m/sec"<<endl<<endl;
cout<<" w3-----"<<(int(100*w3))/100<<"m/sec"<<endl<<endl;
// thermodynamic state at wheel discharge.
cout<<" entr mass flow through turbo expander as kg/sec"<<endl;
double m;
double h03=h0ex;
double h3= h03 - pow(c3,2)/2000;
double d3= m/q;
cout<<" stagnation enthalpy "<<h03<<endl<<endl;
cout<<" static entalhpy "<<h3<<endl<<endl;
cout<<" density "<<d3<<endl<<endl;
cout<<" find properties using above from charts"<<endl<<endl;
//design of diffuser
cout<<" design of diffuser"<<endl<<endl;
cout<<" taper angle"<<endl;
54 | P a g e
double t;
double dex,din,dtd,ld;
double aex;
dex= pow((4*aex/3.14),.5);
double ain;
dtd=dtip+ 2*.001;
ld= (dex-dtd)/(2*tan(t*3.14/180));
cout<<”---------design result--------“<<endl;
cout<<" inlet diameter--"<<din<<"m"<<endl<<endl;
cout<<" area at inlet of diffuser--"<<ain<<"m2"<<endl<<endl;
cout<<" diameter at throat ---"<<dtd<<"m"<<endl<<endl;
cout<<" exit diameter"<<dex<<"m"<<endl<<endl;
cout<<" exit area"<<aex<<"m2"<<endl<<endl;
cout<<" length of diverging section---"<<ld<<"m"<<endl<<endl;
//design of shaft.
cout<<"design of shaft"<<endl;
cout<<" diamter of the shaft and operating speed"<<endl;
double d,w1;
55 | P a g e
double vs,vt;
vs= w1*d/2;
cout<<" choose the material and mention the recomended design stressin MPa"<<endl;
char n[10];
double s,den;
cout<<" entr the density of chosen material"<<endl;
double str;
str= den*vt*vt/(3*1000000);
if ( str>s) { cout<< "change the material"<<endl;
goto start;
cout<<"entr length of shaft,youngs modulus"<<endl;
double ln,el;
double f;
f= .9*( d/pow(ln,2))*pow((el/s),.5);
if (f<w1) { cout<<" design not safe entr values again"<<endl;
goto start;
cout<<”---------design result--------“<<endl;
56 | P a g e
cout<<" surface velocity"<<vs<<endl<<endl;
cout<<" velocity at tip of the collar"<<vt<<endl<<endl;
cout<<" calculated stress"<<str<<endl<<endl;
cout<<" critical frequency"<<f<<endl<<endl;
cout<<"design is safe with "<<n<<" material having design stress as"<<s<<" and having
diameter and length as "<<d<<" m "<< ln<<" m respectively"<<endl;
//design of brake compressor.
cout<<" design of brake compressor"<<endl<<endl;
cout<<" input parameters"<<endl;
cout<<" process gas"<<endl;
char pr[10];
cout<<" power required"<<endl;
double pw,ip,it,w4,n2;
cout<<" entr inlet total pressure in N/m2,inlet Temperature in kelvin ,angilar speed,expected
double d8;
cout<<" molecular weight of the gas"<<endl;
double mw;
d8= .94*ip*mw/(8314*it);
cout<<" asumption ofdrop in enthalpy"<<endl;
57 | P a g e
double h8;
cout<<" corresponding to expected efficiency find Ns and Ds"<<endl;
double ns1,ds1;
double q4,d4,d5,mb,b4;
double pw1;
cout<<" entr power factor, slip factor"<<endl;
double z,y,pv;
pv= w4*d5/2;
pw1= z*y*mb*pow(pv,2);
if(pw1<pw) { goto start1;
double zb,tb;
cout<<" entr number of blades and blade thickness in m"<<endl;
//inlet velocities.
double cm4,u5,w6;
58 | P a g e
w6=pow( ((u5*u5)+(cm4*cm4)),.5);
cout<<” ------design result------“<<endl;
cout<<" diameter of impeller at exit "<<d5<<"m"<<endl<<endl;
cout<<" mass flow"<<mb<<"kg"<<endl<<endl;
cout<<" power input"<<pw1<<" watt"<<endl<<endl;
cout<<" inlet diamter"<<d4<<" m"<<endl<<endl;
cout<<" blade height"<<b4<<" m"<<endl<<endl;
cout<<" radial velocity"<<cm4<<" m/sec"<<endl<<endl;
cout<<" peripheral velocity"<<u5<<" m/sec"<<endl<<endl;
cout<<" inlet relative velocity"<<w6<<" m/sec"<<endl<<endl;
cout<<" number of blades"<<zb<<endl<<endl;
cout<<" blade thickness"<<tb<<" m"<<endl<<endl;
59 | P a g e
Design of Turbo-Expander
Enter working fluid:
Enter Constants k1,k2:
Enter turbine inlet temperature,inlet pressure, discharge pressure,efficiency.
Find the corresponding Ns and Ds wrt efficiency:
From chart enter the inlet enthalpy and exit enthalpy as kJ/kg:
Enter exit volume rate as m3/sec:
-------Design Results------------Enthalpy Drop-------------------51227.05 J/kg
Inner diameter------------------0.02956 m
Angular speed--------------------14531.80 rad/sec
Blade velocity at inlet of turbine--------214 m/sec.
Tip diameter -----------------------0.0177 m
60 | P a g e
Hub diameter---------------------0.00753 m
Mean diameter------------------ 0.01263 m
Exhaust velocity-----------------110.32 m/sec
Mean blade velocity------------91.827 m/sec.
Enter discharge velocity as m/sec:
Data for velocity triangle at inlet of turbine.
C2-------187.93 m/sec
C02------ 168.92 m/sec
Cm2-------82.34 m/sec
W 2------ 94.25 m/sec
Tan of blade angle----1.795
Data for velocity triangle at outlet.
Cm3------- 109 m/sec
C03-------9 m/sec
W 3-------149 m/sec
Enter mass flow through turbo expander as kg:
Stagnation enthalpy-----------------81.7595 KJ/kg
Static enthalpy------------------------75.67 KJ/Kg
Density at exit ------------------------4.65 kg/m3
61 | P a g e
Design of diffuser
Enter taper angle in degree:
-------------design result-----------------Inlet diameter -----------------0.03156 m
Area at inlet of diffuser------0.00078 m2
Diameter at throat
---------0.019738 m
Exit diameter-------------------0.0333 m
Exit area-------------------------0.000871 m2
Length of diverging section-------0.07756 m
Design of shaft
Enter diameter of shaft and operating speed:
Choose the material and mention the recommended design stress as MPa:
Enter the density of chosen material as Kg/m3:
Enter the length of shaft ,young modulus
-------------design result------------Surface velocity------------143.45 m/sec
Velocity at tip of collar-----286.9 m/sec
62 | P a g e
Calculated stress---------------293.57 N/m2
Critical frequency--------------28640 rad/sec
Design is safe.
Design of brake compressor.
Process gas:
Power required in Watt:
Enter inlet total pressure in N/m2, inlet temperature in Kelvin, angular speed,expected
Enter molecular weight of process gas:
Assumption of drop in enthalpy in J/kg:
Corresponding to expected efficiency find Ns,Ds
Enter power factor,slip factor.
Enter number of blades and blade thickness
63 | P a g e
----------design result------------Diameter of impeller at exit-------------0.04574 m
Mass flow----------------------------------0.034 Kg/sec
Power input------------------------------2921.86 watt
Inlet diameter --------------------------0.02033 m
Blade height----------------------------0.009148 m
Radial velocity------------------------ 56.013 m/sec
Peripheral velocity-------------------145.815 m/sec
Inlet relative velocity----------------156.203 m/sec
64 | P a g e
The Software has been built for the designing the components of a turbo expander : turbine
wheel, nozzle, diffuser,brake compressor,shaft design, off design prediction.Care has been taken
to produce the data in a systematic manner. Still the work is left to give it a visual form to insert
graphs . This may be performed using the visual C++ codes.
Future Scopes
.Future work can be done to validate the design with respect to manufacturing point of view.The
nozzle design can be perforemed using the complied algorithm and the design procedures
mentioned.Further work can be made to design the bearings and seal of the product.
65 | P a g e
Swearingen, J. S. Engineers' guide to turboexpanders RotoFlow Corp, USA, (1970),
Gulf Publishing Company
Clarke, M. E. A decade of involvement with small gas lubricated turbine & Advances in
Cryogenic Engineering (1974), V19, 200-208
Beasley, S. A. and Halford, P. Development of a High Purity Nitrogen Plant using
Expansion Turbine with Gas Bearing Advances in Cryogenic Engineering (1965), V10B,
Voth, R. O., Norton, M. T. and Wilson, W. A. A cold modulator refrigerator
incorporating a high speed turbine expander Advances in Cryogenic Engineering (1966),
V11, 127-138
Colyer, D. B. Miniature cryogenic refrigerator alternators Advances in Cryogenic
Engineering (1968), V13, 405-415
Colyer, D. B. and Gessner, R. L. Miniature cryogenic refrigerator Turbomachinary
Advances in Cryogenic Engineering (1968), V13, 484-493
Sixsmith, H. Miniature expansion turbines, C A Bailey (Ed), Advanced Cryogenics
Plenum Press (1971), 225-243
Schmid, C. Gas bearing turboexpanders for cryogenic plant 6th International Gas
Bearing Symposium University of Southampton England (March 1974) Paper 131 B1: 1-8
Reuter K. and Keenan B. A. Cryogenic turboexpanders with magnetic bearings AICHE
Symposium Series, Cryogenic Processes and Machinery 89 (294), 35-45
Izumi, H., Harada, S. and Matsubara, K. Development of small size Claude cycle
helium refrigerator with micro turbo-expander Advances in Cryogenic Engineering
(1986), V31, 811-818
Kun, L. C. and Hanson, T. C. High efficiency turboexpander in a N2 liquefier AIChE
Spring meeting, Houston, Texas (1985)
Kun, L .C. and Sentz, R. N. High efficiency expansion turbines in air separation and
liquefaction plants International Conference on Production and Purification of Coal Gas
& Separation of Air, Beijing, China (1985), 1-21
Kun, L. C. Expansion turbines and refrigeration for gas separation and liquefaction
Advances in Cryogenic Engineering (1987), V33, 963-973
Sixsmith, H., Valenjuela, J. and Swift, W. L. Small Turbo-Brayton cryocoolers
Advances in Cryogenic Engineering (1988), V34, 827-836
66 | P a g e
Creare Inc, USA
Yang, K. J., He, H. B., Ke, G. and Li, G. Y. Application and test of miniature gas
bearing turbines Advances in Cryogenic Engineering (1990), V35, 997-1003
Sixsmith, H. and Swift, W. A pair of miniature helium expansion turbines Advances in
Cryogenic Engineering (1982), V27, 649-655
Kato, T., Kamiyauchi, Y., Tada, E., Hiyama, T., Kawano, K., Sugimoto, M.,
Kawageo, E., Ishida, H., Yoshida, J., Tsuji, H., Sato, S., Xakayama, Y., Kawashima,
I., Development of a large helium turbo-expander with variable capacity Advances in
Cryogenic Engineering (1992), V37B, 827
Kato, T., Yamaura, H., Kawno, K., Hiyama, T., Tada, E., Kakayama,
Y.,Kawashima, I., Sato, M., Yoshida, J., Ito, N., Sato, S. and Shimamato, S. A. Large
scale turboexpander development and its performance test result Advances in Cryogenic
Engineering (1990), V35, 1005–1012
Kato, T., Miyake, A., Kawno, K., Hamada, K., Hiyama, T., Iwamoto, S., Ebisu, H.,
Tsuji, H., Saji, N., Kaneko, Y., Asakura, H., Kuboto, M. and Nagai, S. Design and
test of wet type turbo-expander with an alternator as a brake Advances in Cryogenic
Engineering (1994), V39, 917-92
Ino, N., Machida, A. and Ttsugawa, K. Development of high expansion ratio He
turboexpander Advances in Cryogenic Engineering (1992), V37B, 835-844
Ino, N., Machida, A. and Ttsugawa, K. Development of externally pressurized thrust
bearing for high expansion ratio expander Advances in Cryogenic Engineering (1992),
V37B, 817-825
Davydenkov, I. A., Ravikorichy, Yu A., Davydov, A. B., Ermilov, Yu. I., Zakharova,
N. E., Adler, Yu. R and Schedukhin Development of cryogenic turboexpanders with
gas dynamic foil bearings Cryogenics (1992) 32 (Supplement) 80
Baranov, A., Duzev, V., Kashirskikh, G., Mikhailov, A., Ugrovatov, A. and Zhulkin,
V. An experience in the maintenance of a liquefier from the T-15 cryogenic system,
results of its reliability and capacity enhancement Advances in Cryogenic Engineering
(1996), V41A, 737-743
Cryogenic Industries FrostByte - newsletter (Dec 1995)
ACD Inc., USA,
Aghai, R. R., Lin, M.C. and Ershaghi, B. High Performance cryogenic turboexpanders
Advances in Cryogenic Engineering (1996), V41, 941-947
67 | P a g e
Aghai, R. R., Lin, M.C. and Ershaghi, B. Improvements of the efficiency of the
turboexpanders in cryogenic applications Advances in Cryogenic Engineering (1996),
V41, 933-940
Fuerest, J. D. Experience with small turbomachinery in a 400 W refrigerator Advances
in Cryogenic Engineering (1996), V41, 949-955
Sixsmith, H., Hasenbin, R. and Valenjuela, J. A. A miniature wet turboexpander
Advances in Cryogenic Engineering (1990), V35, 989-995
Xiong Lian-You Hou, Y., Wang, J., Lin, M. F., Wu, G., Wang, B. C. and Chen, C. Z.
A feasibility study on the use of new gas foil bearings in cryogenic turboexpander
Advances in Cryogenic Engineering (1998), V43, 662-666
L'Air Liquide, France
Marot, G. and Villard, J. C. Recent developments of air liquide cryogenic expanders
Advances in Cryogenic Engineering (2000), V45, 1493-1500
Atlas Copco Corp,
Timmerhaus, K. D. and Flynn T. M. Cryogenic Process Engineering Plenum Press
Swearingen, J. S. Turbo-expanders Trans AIChE (1947)
Linhardt, H. D. Cryogenic turboexpanders in Vance, R. W. (Ed), Application of
cryogenic technology
Aghai, R. R., Lin, M.C. and Ershaghi, B. High Performance cryogenic turboexpanders
Adv Cryo Eng (1996)
Aghai, R. R., Lin, M.C. and Ershaghi, B. Improvements of the efficiency of the
turboexpanders in cryogenic applications Adv Cryo Eng (1996)
Obata, M., Sayi. N., Asakura, H., Yoshinagar, S., Ishizawa, T. Theoretical study of
the performance of a wet turbine for Helium refrigerators Adv Cryo Engg. (2000)
Sixsmith, H., Hasenbin, R. and Valenjuela, J. A. A miniature wet turboexpander Adv
Cryo Eng (1990) .
Partha Sarathi Ghosh,
Analytical and Experimental Studies on Cryogenic
Ghosh S.K.,Sarangi S.K,Sahoo R.K . Experimental and Computational Studies
on Cryogenic Turboexpander.
Balje, O. E. A study on design criteria and matching of turbomachines: Part-A-similarity relations and design criteria of turbines Trans ASME J Eng Power (1972)
68 | P a g e
Akhtar M. S. Selection and Optimisation of Centrifugal Compressors for oil and gas
applications. Using computers in the design and selection of fluid machinery I.Mech.E
Trepp, C. Refrigeration system for temperatures below 25 K with turboexpanders Adv
Cryo Eng (1962)
von der Nuell , W. T. Single - stage radial turbine for gaseous substances with high
rotative and low specific speed Trans ASME (1952)
Land, M. L. Expansion turbines and engines for low temperature processes Advances in
Cryogenic Engineering (1957), V2
Mafi -Trench Corporation USA Product Profile
Blackford, J. E., Halford P. and Tantam, D. H. Expander and pumps in G G
Haselden (Ed) Cryogenic Fundamentals Academic Press London (1971)
Akhtar M. S. Selection and Optimisation of Centrifugal Compressors for oil and gas
applications. Using computers in the design and selection of fluid machinery I.Mech.E
Linhardt, H. D. Cryogenic turboexpanders in Vance, R. W. (Ed), Application of
cryogenic technology V4,
Futral, S. M., Wasserbauer, C. A. Off-design performance prediction with
experimental verification for a radial-inflow turbine NASA TN D-2621
Wasserbauer, C. A. and Glassman A. J. FORTRAN program for predicting off-design
performance of radial-inflow turbine NASA TN D-8063 (1967)
Benson, R. S. A review of method for assessing loss coefficients in radial gas turbine Int
J Mech Sci (1970), V12
Baines, N. C. A Meanline Prediction Method for Radial Turbine Efficiency Inst Mech
Eng Conference on Turbochargers I Mech E (UK) Publications(1998)
Colyer, D. B. Miniature cryogenic refrigerator alternators Advances in Cryogenic
Engineering (1968), V13
Luybli, R. E. and Filippi, R. E. Performance options for cryogenic turboexpander
AIChE symposium on Creyogenic properties, processes and applications (1986) V82
Denton, J. D. The turboexpander - a design, make and test student project ASME-96-GT191 (1996)
Jekat, W. K. An Impulse Type Expansion Turbine, Advances in Cryogenic Engineering
(1957), V2
69 | P a g e
Kato, T., Miyake, A., Kawno, K., Hamada, K., Hiyama, T., Iwamoto, S., Ebisu, H.,
Tsuji, H., Saji, N., Kaneko, Y., Asakura, H., Kuboto, M. and Nagai, S. Design and
test of wet type turbo-expander with an alternator as a brake Adv Cryo Eng (1994)
Iannello, V. and Sixsmith, H. Magnetic bearing for cryogenic turbomachines Adv Cryo
Eng (1987)
RohliK, Harold E. Analytical determination of radial inflow turbine geometry for
maximum efficiency NASA TN D-4384
Ino, N., Machida, A. and Ttsugawa, K. Development of high expansion ratio He
turboexpander Advances in Cryogenic Engineering (1992), V37B,
Kun, L .C. and Sentz, R. N. High efficiency expansion turbines in air separation and
liquefaction plants International Conference on Production and Purification of Coal Gas
& Separation of Air, Beijing, China (1985)
Birmingham, B. W., Sixsmith, J. H. and Wilson, W. A. The application of gas
lubricated bearings to a miniature helium expansion turbine Advances in Cryogenic
Engineering (1962), V7,
Land, M. L. Expansion turbines and engines for low temperature processes Advances in
Cryogenic Engineering.
Jekat, W. K. An Impulse Type Expansion Turbine, Advances in Cryogenic Engineering
(1957), V2
Kun, L. C., Ammann, H. H. and Scofield, H. M. Development of novel gas bearing
supported cryogenic expansion turbine Advances in Cryogenic Engineering (1969) V14,
Mafi -Trench Corporation USA Product Profile
Izumi, H., Harada, S. and Matsubara, K. Development of small size Claude cycle
helium refrigerator with micro turbo-expander Advances in Cryogenic Engineering
(1986), V31,
Kato, T., Kamiyauchi, Y., Tada, E., Hiyama, T., Kawano, K., Sugimoto, M.,
Kawageo, E., Ishida, H., Yoshida, J., Tsuji, H., Sato, S., Xakayama, Y., Kawashima,
I., Development of a large helium turbo-expander with variable capacity Advances in
Cryogenic Engineering (1992), V37B
von der Nuell , W. T. Single - stage radial turbine for gaseous substances with high
rotative and low specific speed Trans ASME (1952), V74,
Sixsmith, H., Hasenbin, R. and Valenjuela, J. A. A miniature wet turboexpander
Advances in Cryogenic Engineering (1990), V35,
70 | P a g e
Jekat, W. K. An Impulse Type Expansion Turbine, Advances in Cryogenic Engineering
(1957), V2,
Polishchuk, E. L., Shanklankin V. I. and Lyapin V. I. Self-contained microcryogenic
system with a turboexpander Khimicheskoe I Neftyanoe Mashinostroenie (Trans:
Chemical & Petroleum Engineering) (1991) V 27 (3/4)
Vavra, M. H. The applicability of similarity parameters to the compressible flow in
radial turbomachines Proc Ins Mech Eng Internal Thermodynamics (Turbomachine,
RohliK, Harold E. Analytical determination of radial inflow turbine geometry for
maximum efficiency NASA TN D-4384 (1968)
Whitfield, A. and Baines, N. C. Design of Radial Turbomachines Longman Scientific &
Technical (1990)
Watanabe, I. Ariga, I. and Mashimo, T. Effect of dimensional parameters of impellers
on performance characteristics of a radial-flow turbine Trans ASME J Eng Power (1971)
Sixsmith, H. and Swift, W. L. Cryogenic turbines and pumps in Hands, B. A. (Ed.)
Cryogenic Engineering Academic Press (1986),
Ino, N., Machida, A. and Ttsugawa, K. Development of high expansion ratio He
turboexpander Advances in Cryogenic Engineering (1992), V37B
Ryder, G. H. Strength of materials ELBS/Macmillan (1988),
71 | P a g e
72 | P a g e
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF