Research Journal of Applied Sciences, Engineering and Technology 3(5): 415-425, 2011
ISSN: 2040-7467
© Maxwell Scientific Organization, 2011
Received: March 12, 2011
Accepted: April 06, 2011
Published: May 25, 2011
Analysis of the Effect of Rotor-to-Casing Diameter Ratio on the Power Output
of a Vaned-Type Air Turbine-II
1
Bharat Raj Singh and 2Onkar Singh
Department of Mechanical Engineering, SMS Institute of Technology, Kashimpur Biruha,
Near Gosainganj, Lucknow-227125, Uttar Pradesh, India
2
Department of Mechanical Engineering, Harcourt Butler Technological Institute,
Nawabganj, Kanpur-208002, Uttar Pradesh, India
1
Abstract: This study describes new results of the performance evaluations of an air powered vane type rotary
novel air turbine/engine. The mathematical model with different parametric values such as; different rotor to
casing diameter (d/D) ratios at optimum vane angle of 45º and injection angle of 45º, have been considered and
analyzed. The optimum power output is obtained at some typical values of rotor/casing diameter ratios without
consumptions of excessive air. The study shows that the optimum power developed under such conditions
would be 4.3-5.5 kW (5.84-7.47 HP) at linear expansion (without excessive air consumption) when d/D ratios
are between 0.85 to 0.80 and casing diameter is kept 150 mm, injection pressure as 6 bar (90 psi) and speed of
rotation as 2500 rpm. This power output is enough to drive any motorbike or light vehicle.
Key words: Air turbine, compressed air, injection angle, motorbike, rotor/casing diameter ratios, zero pollution
In continuation to earlier analysis, this paper presents
new results on power output due to effect of rotor/casing
diameter ratios of the vaned-type turbine. The results of
earlier study show that the power output would be
optimum when injection angle is kept more than 30º. Thus
injection angle is kept 45º as constant throughout the
study. The effect of isobaric admission and adiabatic
expansion of high pressure air on different rotor/casing
diameter ratios have been considered and analyzed with
the help of the mathematical modeling shown in earlier
study. The results show that the optimum power would be
developed under linear expansion (without excessive air
consumptions) when d/D ratios are kept at 0.85 to 0.80
and casing diameter of 150 mm.
INTRODUCTION
Globally transport sector alone is consuming huge
quantity of hydrocarbon fuel (Hubbert, 1956), and
releasing about 77.8 percentage air pollutants in the
atmosphere (Aleklett and Campbell, 2003). Recent study
also indicates that in developing countries like India,
China, Taiwan etc., 80 percentage pollutants are
generated by the motorbikes. In order to reduce the air
pollution condition and eliminate 50-60% of the
pollutants exhausting, an air engine of small capacity is
proposed to be equipped on motorbikes. It was seen in the
author’s earlier study (Singh and Singh, 2010a) that the
compressed air driven prime movers are cost effective as
compared to fossil fuel driven engines and may become
the dominant technology in place of the electric, hydrogen
cell and other alternative fueled vehicles available in the
market (Fuglsang et al., 2004; Gorla and Reddy, 2005;
Honton, 2004; Knowlen et al., 1998; Rose et al., 2004;
Selig et al., 2004; Schreck and Robinson, 2004). Also the
pioneer work in the area of compressed air engine has
been carried out by Negre and Negre (2004) and SaintHilaire et al. (2005) and some of studies on performance
optimization of the low capacity of air turbines have also
been carried out in the author’s earlier publications (Singh
and Singh, 2010a, b, c).
HISTORY OF COMPRESSED AIR ENGINE
The compressed air as an energy is not a recent
technology. At the end of the 19th century the first
approximations to what could one day become a
compressed air driven vehicle already existed, through the
arrival of the first pneumatic locomotives. Yet even two
centuries before that Dennis Papin apparently came up
with the idea of using compressed air (Royal Society
London, 1687).
Corresponding Author: Bharat Raj Singh, Department of Mechanical Engineering, SMS Institute of Technology, Kashimpur
Biruha, Near Gosainganj, Lucknow-227125, Uttar Pradesh, India. Tel: +91-522-2238116/+91-9415025825
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Res. J. Appl. Sci. Eng. Technol., 3(5): 415-425, 2011
The first recorded compressed-air vehicle in France
was built by the Frenchmen Andraud and Tessie of Motay
in 1838. A car ran on a test track at Chaillot on the 9th
July 1840, and worked well, but the idea was not pursued
further. In 1872 the Mekarski air engine was used for
street transit, consisting of a single-stage engine. It
represented an extremely important advance in terms of
pneumatic engines, due to its forward thinking use of
thermodynamics, ensuring that the air was heated, by
passing it through tanks of boiling water. Numerous
locomotives were manufactured and the first in Nantes in
1879. The H.K. Porter Company in Pittsburgh sold
hundreds of these locomotives to coal-mining companies
in the eastern U.S. With the hopeful days of air powered
street transit over, the compressed air locomotive became
a standard fixture in coal mines around the world because
it created no heat or spark and was therefore invaluable in
gassy mines where explosions were always a danger with
electric or gas engines.
Also in 1896, Porter supplied ten compressed air
motor cars for the Eckington System in Washington, D.C.
There was a tank on the front of the engine and it was
recharged at the station. Between 1890 and 1902 ten
compressed air trams circulated in Bern, Switzerland. In
1892, Robert Hardie introduced a new method of heating
that at the same time served to increase the range of the
engine. However, the first urban transport locomotive was
not introduced until 1898, by Hoadley and Knight, and
they introduced a two stage engine. Later on, in 1912 the
American’s method was improved by Europeans, adding
a further expansion stage to the engine (3 stages).
In 1926 Lee Barton Williams of Pittsburg USA
presented his invention: an automobile which he claims
run on air. The motor starts on gasoline, but after it has
reached a speed of ten miles an hour the gasoline supply
is shut off and the air starts to work. At the first test his
invention attained a speed of 62 miles an hour. In January
1932 what appears to be the first journalistic article ever
written about a car driven by compressed air was
published. In 1934, 21-year-old Johannes Wardenier
announced he developed the world’s first fuel-less
automobile. For weeks Dutch newspapers reported of an
incredible invention that would change the world for ever.
After the Second World War the term air engine was
never again used in textbooks referring to compressed air
or pneumatic locomotives and, whenever they were
mentioned the article would go on to state that these
engines were of little use or efficiency.
In the 1970’s Willard Truitt presented his invention
in McKees Rocks, USA. But because he did not have the
financial means to develop his compressed air car further
he gave the rights of his invention to NASA and the US
Army in 1982.
In 1979, Terry Miller decided that compressed air
was the perfect medium for storing energy. He developed
Air Car One, which he built for $ 1,500. Terry’s engines
showed that it was feasible to manufacture a car that
could run on compressed air. He patented his method in
1983 (US4370857).
In the 1980’s Carl Leissler developed a motor that
was able to function on air. The retired horticulturalist had
been working from his garage in Hollywood for over 15
years. He says that to use his motor in a car you might
have to use a small electric or gas energy source to help
drive the air compressor. ‘We might be able to get 2000
miles per gallon; air is a power in itself’ Leissler
comments. Until 1987 the German company Arnold Jung
Lokomotivenfabrik GmbH produced locomotives
functioning on compressed air to be used in mines. In the
1980’s they were still selling and renovating locomotives.
Currently the tram association in Bern Switzerland (BTG)
is developing a locomotive according to the original
plans.
At present (2008) various researchers and industries
are developing compressed air motors applicable to
transportation, apart from the many industries that
produce and commercialize compressed air motors for
industrial purposes.
Scope of compressed air engine: The per capita income
of a person in India, as a developing country, is very low
to meet livelihood requirements. On the basis of the recent
data 80% of the population of the country still lives in
rural and suburban areas where the means of transport is
either bicycle or motorbike. The continuous hikes of fossil
fuel prices at the rate of around 20-30% every year are
making the situation miserable. Extrapolation shows that
at this rate, by 2010-12, prices may be double as what
they were in 2005, and by 2030-40, may touch Rs. 1000
per L. A time will come when the common person will
not be able to purchase fuel to run motorcycles. This is
not only due to the high demand for vehicles or its
increasing numbers worldwide, but also due to the cost of
fossil fuel going high as 80% of the available fossil fuel
is presently being consumed in transport. Thus, it is
imperative to explore the possibility of alternatives to
fossil fuel to make the environment free from emission for
keeping the present and future generations healthy.
During last two decades, major work has been done
to tap the air freely available in the atmosphere and to
compress it for storage in cylinders for further use. Apart
from other uses of compressed air, this can also be used to
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Res. J. Appl. Sci. Eng. Technol., 3(5): 415-425, 2011
run combustion engines with the mixture of gas and air
getting Wred after the compression stroke at top dead
centre. The use of compressed air will eliminate the need
of having a separate compression stroke. Compressed air
helps in the attainment of the expansion stroke after
ignition takes place. Thus, the efficiency of the internal
combustion engine is improved, and without running all
four stroke cycles, it runs on two stroke cycles. The air
engines developed so far are basically running on hybrid
systems (Negre and Negre, 2004; Saint-Hilaire, 2005)
such as compressed air and gases, and are not 100%
pollution free.
Concept of multi vanes air turbine model: This study
proposes a multi-vanes type air turbine as shown in Fig.
1. Such air turbine is considered to work on the reverse
working principle of vane type compressor. In this
arrangement total shaft work is cumulative effect of
isobaric admission of compressed air jet on vanes and the
adiabatic expansion of high pressure air.
A prototype of air turbine was developed in an earlier
study (Singh and Singh, 2008d). At initial stage a cylinder
for minimum capacity of storing compressed air for the
requirement of 30 min running and maximum pressure of
20 bar is used as a source of storage energy. The
compressed air storage cylinder is designed to produce
constant pressure for the minimum variation of torque at
low volumes of compressed air and attached with filter,
regulator and lubricator which regulate and maintain the
constant pressure. The clean air then admits into air
turbine through inlet passage/nozzle. Vanes of novel air
turbine are placed under spring loading to maintain their
regular contact with the casing wall to minimize leakage
which is proposed as improvement over the currently
available vane turbine. A study on high efficiency energy
conversion system for liquid nitrogen (Honton, 2004),
design and verification of airfoil and its tests, influence of
tip speed ratios for small wind turbine and parabolic heat
transfer and structural analysis were also carried out for
conceptualizing the energy conversion system and design
of the air turbine (Fuglsang et al., 2004, Gorla and
Reddy, 2005; Honton, 2004; Knowlen, 1998;
Rose et al., 2004, Selig et al., 2004; Schreck and
Robinson, 2004), A detailed method of energy conversion
processes, development concept of utilization of air
turbine and optimization of its shaft work were made and
presented in various symposium, seminars and
conferences of international levels (Singh and Singh,
2006a, b, 2007a, b, 2008a, b, c, d, e, f, 2009a, b, c, d).
The objective of the earlier study was to investigate
the performance of an air turbine by varying vane angles
Fig. 1: Air turbine-model
with a particular injection angle, i.e., at which angle air
should admit into the turbine between first two
consecutive vanes. The air turbine considered has
capability to yield output of 4.0 to 5.5 kW at 4-6 bar air
pressure and for speed of 2000-2500 rpm, which is
suitable for a motorcycle.
MATHEMATICAL MODELING
The high pressure jet of air at ambient temperature
drives the rotor in novel air turbine due to both isobaric
admission and adiabatic expansion. Such high pressure air
when enters through the inlet passage, pushes the vane for
producing rotational movement through this vane and
thereafter air so collected between two consecutive vanes
of the rotor is gradually expanded up to exit passage. This
isobaric admission and adiabatic expansion of high
pressure air contribute in producing the shaft work from
air turbine. Compressed air leaving the air turbine after
expansion is sent out from the exit passage. It is assumed
that the scavenging of the rotor is perfect and the work
involved in recompression of the residual air is absent as
seen from Figure 1. Similar type mathematical modeling
is considered in earlier publications by authors and it is
being reproduced here for maintaining continuity and
benefits to the readers (Singh and Singh, 2009e, f, g,
2010a, b, c, d, e, f).
From Fig. 2, it is seen that work output is due to
isobaric admission from E to 1, and adiabatic expansion
from 1 to 4 and reference points 2, 3 in the figure shows
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Res. J. Appl. Sci. Eng. Technol., 3(5): 415-425, 2011
Fig. 2: Thermodynamic processes (Isobaric, adiabatic and
isochoric expansion)
the intermediate position of vanes. Thus, total work output
due to thermodynamic process may be written as:
Fig. 3: Variable length BG and IH and injection angle ø
[Area under (E145CE)] = [Area under (E1BOE)
+Area under (14AB1) - Area under (4AOD4)
+ Exit steady flow (45CD4)] or
Total work output = [Thermodynamic expansion work
(w1)] + [Exit steady flow work (w2)]
(1)
or
w = [(w1) + (w2)]
where
⎛ γ ⎞
⎟.
Wexp = n. N 60 . ⎜
⎝ γ − 1⎠
(
⎧
⎪ ⎛ p4 ⎞
⎟
p1 . v1 ⎨ 1 − ⎜
⎪ ⎝ p1 ⎠
⎩
The process of exit flow (4-5) takes place after the
expansion process (E- 4) as shown in Fig. 2 and air is
released to the atmosphere. In this process; till no over
expansion takes place pressure p4 can’t fall below
atmospheric pressure p5. Thus at constant volume when
pressure p4 drops to exit pressure p5 no physical work is
seen. Since turbine is functioning as positive
displacement machine and hence under steady fluid
flow at the exit of the turbine, the potential work is
absorbed by the rotor.
Thus, the total power output or work done per unit
time (Wtotal), for speed of rotation N rpm, will be
mentioned as (Singh, 2009):
γ −1
γ
)(
⎫
⎪
⎬
⎪
⎭
Wflow = n.( N 60).( p4 − p5 ) v4
Figure 1 shows that if vanes are at angular spacing of
2 degree, then total number of vanes will be n = (360/2).
The variation in volume during expansion from inlet to
exit (i.e., v1 to v4) can be derived by the variable extended
length of vane as shown in Fig. 3 at every point of
movement between two consecutive vanes.
From Fig. 3, it is seen that when two consecutive
vanes at OK and OL moves to position OH and OB, the
extended vane lengths varies from SK to IH and LM to
BG, thus the variable length BG at variable "i is assumed
as Xat’variable’" can be written from the geometry:
(2)
⎫
⎪
⎬ + n. N 60 . p 4 − p5 . v 4
⎪
⎭
(
γ −1
γ
and
⎛ γ ⎞
⎟ . p .v .
Wtotal = n. ( N / 60). ⎜
⎝ γ − 1⎠ 1 1
⎧
⎪ ⎛ p4 ⎞
⎟
⎨1 − ⎜
⎪ ⎝ p1 ⎠
⎩
)
)
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Res. J. Appl. Sci. Eng. Technol., 3(5): 415-425, 2011
BG = X at ,var iable'α '
where,
⎡
⎧⎛ R − r ⎞
⎫⎤
⎟ .sin α ⎬ ⎥
= R.cos⎢ sin −1 ⎨ ⎜
⎩⎝ R ⎠
⎭⎦
⎣
+ ( R − r ).cos α − r
⎧( X
+ X 2 min ) ⎫
v1 = vmin = L. ⎨ 1 min
⎬.sin θ ,
4
⎩
⎭
(3)
⎧( X
+ X 2 max ) ⎫
v4 = vmax = L. ⎨ 1 max
⎬.sin θ ,
4
⎩
⎭
where, 2R = D is diameter of casing and 2r = d is
diameter of rotor, " is angle ∠ BOF, $ is angle ∠ BAF
and 2 is angle ∠ HOB or ∠ H’OF or ∠ KOL, between
two consecutive vanes and N is angle ∠ KOJ at which
injection pressure admits to the air turbine.
Variable volume of cuboids’ B-G-I-H-B can be
written as:
vcuboids
X 1 min =
⎡
⎫⎤
⎧⎛ R − r ⎞
⎟ .sin 180 − θ − φ ⎬ ⎥
R.cos⎢ sin −1 ⎨ ⎜
⎭⎦
⎩⎝ R ⎠
⎣
(
[
X 2 min =
⎡
⎧⎛ R − r ⎞
⎫⎤
R.cos⎢sin −1 ⎨⎜
⎟ .sin(180 − φ ) ⎬⎥
⎩⎝ R ⎠
⎭⎦
⎣
where, BG = X1i and IH = X2i variable length of vanes
when rotate into turbine as shown in Fig. 3. The lengths
(IG, HB and LK, SM), are considered linear whereas all
are chords of circles. This approximation is done in
mathematical model which has least effect on the overall
values.
The volume at inlet v1 or vmin will fall between angle
∠ LOF= "1min = (180-2-N) and angle ∠ KOF= "2min =
("1min + 2) = (180 - N) as seen in Fig. 3, when air is admits
into turbine at angle N.
The Volume at exit v4 or vmax will fall between angle
∠ BOF = "1max = " = 0 and angle ∠ HOF = "2max =
("1max + 2) = 2.
Applying values of v1 and v4 to Eq. (2), the total
power output available Wtotal can be written as:
Wtotal
(
)
γ −1
γ
) ]
+ ( R − r ).cos 180 − θ − φ − r
⎧ ( X + X 2i )( 2r + X 1i ) ⎫
= L. ⎨ 1i
⎬.sin θ (4)
4
⎩
⎭
⎧
⎛ γ ⎞ ⎪ ⎛ p4 ⎞
⎟
⎟ . ⎨1 − ⎜
= n. N 60 . ⎜
⎝ γ − 1⎠ ⎪ ⎝ p1 ⎠
⎩
(
)
[
+ ( R − r ).cos(180 − φ ) − r
]
X 1 max = ( D − d ) = 2( R − r )
and
X 2 max =
⎡
⎧⎛ R − r ⎞
⎫⎤
R.cos⎢sin −1 ⎨⎜
⎟ .sin θ ⎬⎥
⎩⎝ R ⎠
⎭⎦
⎣
+
⎫
⎪
⎬ p1
⎪
⎭
{( R − r ).cosθ } − r
Input parameters and assumptions: Various input
parameters are considered and listed in Table 1 for
investigation of effect of rotor/casing diameter ratio and
its optimization. It is assumed that rotor will have 8
numbers of vanes and hence angle between two
consecutive vanes would be 45º. It is also considered that
high pressure air (2-6 bar) will enter into two consecutive
rotor vanes at an injection angle 45º. Rotor to casing
diameter ratios for study was considered from 0.95, 0.90,
0.85 to 0.55 for different set of casing diameters 150 mm.
Exit air pressure is considered as atmospheric pressure
(1.0132 bar) and rotor length also assumed as 45 mm for
this study.
⎡ ⎧ ( X 1 min + X 2 min ).( 2r + X 1 min ) ⎫
⎤
⎢ L. ⎨
⎬.sin θ ⎥
4
⎢⎣ ⎩
⎥⎦
⎭
+ n. ( N 60). ( p4 − p5 ).
⎡ ⎧⎪ ( X 1 max + X 2 max ). ( 2r + X 1 max ) ⎫⎪
⎤ (5)
⎢ L. ⎨
⎬.sin θ ⎥
4
⎪⎭
⎢⎣ ⎪⎩
⎥⎦
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Res. J. Appl. Sci. Eng. Technol., 3(5): 415-425, 2011
Table 1: Input parameters
Symbols
Parameters
Rotor to casing
0.95, 0.9, 0.85, 0.80, 0.75 , 0.70, 0.65, 0.60 and
(d/D) ratio
0.55 when casing diameters are kept D = 150 mm
p1
2 bar (.30 psi), 3 bar (.45psi), 4bar (.60psi),
5 bar (.75psi), 6bar (.90psi) - inlet pressures
= (v1 / v4)y. p1 assuming adiabatic expansion
p4
1 atm = 1.0132 bar
p5
N
2500 rpm
L
35mm length of rotor
(
1.4 for air
n
(360 / 2) Number of vanes
2
45º angle between 2-vanes, (i.e., rotor contains
correspondingly 8 number of vanes)
M
45º angle at which compressed air through nozzle
enters into rotor
RESULTS AND DISCUSSION
Using the mathematical model the effect of
rotor/casing diameter ratio and different injection
pressures 2-6 bar on the expansion power output, flow
work output and total power output from air turbine is
studied. Here the vane angle 2, injection angle N and
speed of rotation N of the air turbine are considered to be
constant for whole of the study. The results obtained have
been plotted in Fig. 4-8, for the rotor/casing diameter ratio
(d/D), varied as 0.95, 0.90, 0.85, 0.80, 0.75, 0.65, 0.60
and 0.55 at vane angle of 45º, injection angle of 45º, at
different injection pressures of 2, 3, 4, 5 and 6 bar (i.e.,
Fig. 4: Expansion power vs. Rotor /casing diameter (d/D) ratio when D = 150 mm
Fig. 5: Exit flow power vs. Rotor/casing diameter (d/D) ratio when D = 150 mm
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Res. J. Appl. Sci. Eng. Technol., 3(5): 415-425, 2011
Fig. 6: Percentage contribution of expansion power vs. rotor / casing diameter (d/D) ratio when D = 150 mm
Fig. 7: Percentage contribution of exit flow power vs. rotor/casing diameter (d/D) ratio when D = 150 mm
Fig. 8: Total power output vs. rotor/casing diameter (d/D) ratio when D = 150 mm
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Res. J. Appl. Sci. Eng. Technol., 3(5): 415-425, 2011
different injection pressure 2-6 bar is shown in Fig. 8.
Total power at 2-6 bar is seen increasing linearly from
rotor/casing diameter ratio 0.95 to 0.80 and gradually
further increases parabolically to highest when
rotor/casing diameter ratio reaches to 0.55. This shows the
behavior of higher air consumption. Thus for moderate air
consumption maximum value of shaft power output is
obtained as 4.29-5.50 kW at rotor/casing diameter ratio
0.85 to 0.80.
Thus it is observed that in the rotary vane type air
turbine total shaft power output is combined effect of the
component of expansion power and exit flow power. The
contribution of exit flow power due to steady flow in
respect to total power output varies from 4.60 to 7.84%
only for all injection pressure 2-6 bar at constant injection
angle 45º, constant vane angle 45º, at speed of rotation
2500 rpm. Thus it is obvious that the expansion power
output as well as total power output is found optimum as
4.29 and 5.50 kW, respectively for moderate air
consumption when rotor/casing diameter ratio lies
between 0.85 to 0.80 at casing diameter 200 mm and is a
deciding factor for desired shaft power output.
30, 45, 60, 75 and 90 psi), speed of rotation of 2500 rpm,
and casing diameter 150 mm.
Figure 4 shows the variation of expansion power at
different rotor/casing diameter ratios with respect to
different injection pressure. It is evident that the shaft
power due to expansion at 2 bar is lower at higher
rotor/casing diameter ratio of 0.95, thereafter gradually
increases linearly upto 0.85 to 0.80 and, largest when
rotor/casing diameter ratio is kept 0.55. For higher
injection pressure 4 to 6 bar, this is attributed to the large
work output per time unit in similar pattern. It is evident
that there exists maximum rotor/casing diameter for every
injection pressure which offers the linear expansion power
at moderate air consumption and beyond 0.75 to 0.55
rotor/casing (d/D) ratios, the value of maximum
expansion power is more but expansion is parabolic which
shows the higher air consumption for higher shaft output.
The higher injection pressures produces higher shaft
power in similar manner as compared to lower injection
pressures.
Figure 5 shows the variation of exit flow power at
different rotor/casing diameter ratios with respect to
different injection pressure. It is evident that the shaft
power due to exit flow work is lowest at 2 bar and
parabolically increases up to rotor/casing diameter ratio of
0.55. It is quite evident that the shaft power due to exit
flow work gradually increases with reducing value of
rotor/casing diameter ratio in view of the gap between the
rotor and casing as increases gradually. On these ground,
the exit flow power is nearly insignificant for rotor/casing
diameter ratio of 0.95 and would be absent when this ratio
value is unity.
Figure 6 shows the percentage contribution of
expansion power against total work output at different
rotor/casing diameter ratios with respect to different
injection pressure. It is evident that percentage
contribution of expansion power is low at (d/D) ratio =
0.95 and highest at (d/D) = 0.55 for all injection pressure
2-6 bar. At rotor/casing ratio 0.95 the contribution of
expansion power against total power is lowest and
gradually increases from 92.16 to 95.40% as rotor/casing
diameter ratio decreases from 0.95 to 0.55.
Figure 7 shows the percentage contribution of exit
flow power in total power output at different rotor/casing
diameter ratios with respect to different injection pressure.
It is evident that percentage contribution of exit flow
power is higher, when rotor/casing diameter ratio is 0.95
and gradually decreases from 7.84 to 4.60% as this
diameter ratio drops up to 0.55 when casing diameter is
kept 200 mm at all injection pressure from 2-6 bar.
Variation of total power output with respect to
different rotor/casing diameter ratios with respect to
CONCLUSION
The results obtained from above investigations based
on input parameters such as injection angle, vane angle
and speed of rotation are kept 45º, 45º and 2500 rpm,
respectively, following conclusions are drawn:
There exists an linear value of shaft power output at
rotor/casing diameter ratio (approx. 0.85 to 0.80) and
between 0.75 to 0.55, though the shaft output increases in
parabolic form that indicates higher air consumption for
the considered air turbine for all air injection pressures.
Thus the rotor/casing diameter ratio 0.80 offers the
optimum expansion power to 5.14 kW at injection air
pressures 6 bar for the moderate air consumption.
The exit flow power due to steady flow is seen to increase
parabolically for the rotor/casing diameter ratio varying
from 0.95 to 0.55 and is found maximum 0.12 to 0.43 at
6 bar injection pressure.
Total output power from the air turbine is seen to be
optimum for the higher injection air pressure and there
exists an optimum value of rotor/casing diameter ratio for
all injection pressure 2-6 bar at linear increase (moderate
air consumptions). The optimum power output is seen to
be 5.50 kW at 0.80 rotor/casing ratio for injection
pressure of 6 bar.
Thus the optimum shaft power output of a rotary
novel vane type air turbine having casing diameter 150
mm and other design parameters such as: rotor to casing
diameter (d/D) ratios between 0.85 to 0.80 and at
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Res. J. Appl. Sci. Eng. Technol., 3(5): 415-425, 2011
optimum value of vane angle 45º (8 vanes) and pressure
injection angle 45º, offers 4.29-5.50 kW (5.84-7.47 HP)
power output. Here air consumption has also an important
role for optimizing the power output.
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ACKNOWLEDGMENT
The Authors are indebted to express thanks to the
CEO, SMS Group of Institutions, Lucknow and
Mechanical Engineering Department, Harcourt Butler
Technological Institute, Kanpur for their support to
provide facilities of the library and laboratories.
NOMENCLATURE
d
D
L
n
N
p
p1, v1
:
:
:
:
:
:
:
p4, v4
:
p5
:
v
w
W
X1i
X2i
:
:
:
:
:
Diameter of rotor (2r) in meter
Diameter of outer (2R) cylinder in meter
Length of rotor having vanes in meter
No. of vanes = (360/2)
No. of revolution per minute
Pressure in bar
Pressure and volume respectively at which air
strike the Turbine,
Pressure and volume respectively at which
maximum expansion of air takes place,
Pressure at which turbine releases the air to
atmosphere.
Volume in cum
Theoretical work output in (J) Joules
Theoretical power output (W) Watts
Variable extended lengths of vane at point 1
Variable extended lengths of vane at point 2
Subscripts:
: Subscripts-indicates the positions of vanes in
1, 2...4, 5
casing
exp
: Expansion
min
: Minimum
max
: Maximum
Greek symbols:
"
: Angle BOF (Fig. 3)
"1
: Angle LOF (=180 - N) (Fig. 3)
"1
: Angle KOF (=180 - 2 - N) (Fig. 3)
$
: Angle BAF (Fig. 3)
(
: 1.4 for air
2
: Angle between 2-vanes (BOH) (Fig. 3)
N
: Angle at which compressed air enters into
rotor through nozzle
>d
: Eccentricity (R-r)
423
Res. J. Appl. Sci. Eng. Technol., 3(5): 415-425, 2011
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