A numerical model for the design of a mixed flow cryogenic turbine
ABSTRACT Present day cryogenic gas turbines are in more popular as they meet the growing need for low pressure cycles. This calls for improved methods of turbine wheel design. The present study is aimed at the design of the turbine wheel of mixed flow impellers with radial entry and axial discharge. In this paper, a computer code in detail has been developed for designing such turbine wheel. To determine the principal dimensions of the turbine wheel, optimum operating speed has been taken from design charts based on Similarity principles. The algorithm developed, allows any arbitrary combination of fluid properties, inlet conditions and expansion ratio, since the fluid properties are properly taken care of in the relevant equations. The computational process is illustrated with an example. The main dimensions, thermodynamic properties at different states, velocity and angles at entry and exit of the turbine wheel were worked out. The work may help the researchers for further design and development of cryogenic turboexpander depending on their operating parameters.
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 01/1965; Vol: 10.
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ABSTRACT: Radial and mixed flow turbines which are an important component of a turbocharger consist essentially of a volute, a rotor and a diffuser. Vaneless volute turbines, which have reasonable performance and low cost, are the most used in turbochargers for automotive engines. Care has to be done in the design of the volute, whose function is to convert a part of the engine exhaust gas energy into kinetic energy and direct the flow towards the rotor inlet at an appropriate flow angle with reduced losses. Turbulent compressible flow analysis and performance prediction using the finite volume method implemented in the ANSYSCFX software, are carried out on two different volute types. Four volute, with different cross section areas used for radial turbines, are studied and the computed results such as the computed averaged volute exit flow angles, the volute overall loss coefficients and the exit radial velocity component distributions are compared with the available experimental data. The second volute studied is the one used for a mixed flow turbine in the turbocharger test rig at Imperial College. In this part of the study, the interest is focused on the influence of the volute inlet flow conditions on its performance (efficiency, exit flow angle, etc).
Page 1
MultiCraft
International Journal of Engineering, Science and Technology
Vol. 2, No. 1, 2010, pp. 175191
INTERNATIONAL
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TECHNOLOGY
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A numerical model for the design of a mixed flow cryogenic turbine
Subrata Kr. Ghosh
Department of ME & MME, Indian School of Mines, Dhanbad, Jharkhand, INDIA
Email: subratarec@yahoo.co.in
Abstract
Present day cryogenic gas turbines are in more popular as they meet the growing need for low pressure cycles. This calls for
improved methods of turbine wheel design. The present study is aimed at the design of the turbine wheel of mixed flow
impellers with radial entry and axial discharge. In this paper, a computer code in detail has been developed for designing such
turbine wheel. To determine the principal dimensions of the turbine wheel, optimum operating speed has been taken from design
charts based on Similarity principles. The algorithm developed, allows any arbitrary combination of fluid properties, inlet
conditions and expansion ratio, since the fluid properties are properly taken care of in the relevant equations. The computational
process is illustrated with an example. The main dimensions, thermodynamic properties at different states, velocity and angles at
entry and exit of the turbine wheel were worked out. The work may help the researchers for further design and development of
cryogenic turboexpander depending on their operating parameters.
Keywords: Cryogenic, turboexpander, mixed flow turbine, flow angle, flow velocity
1. Introduction
Compressor, heat exchanger, expansion turbine, and vacuum vessel are the main components to establish any cryogenic liquid
plant. To establish the set up, different companies are indigenously available in India for compressor, heat exchanger and vacuum
vessel. But the turboexpander is not readily available in market. As the technology is not yet developed indigenously, we are
forced to import the whole liquid plant. A simple method sufficient for the design of a high efficiency expansion turbine is outlined
by Kun (1987) and Kun et al. (1985). A study was initiated in 1979 to survey operating plants and generates the cost factors
relating to turbine by Kun & Sentz (1985). They are also sometimes referred to as design parameters, since the shape dictates the
type of design to be selected. Corresponding approximately to the optimum efficiency a cryogenic expander may be designed with
selected specific speed and specific diameter. Sixsmith et al. (1988) in collaboration with Goddard Space Flight Centre of NASA,
developed miniature turbines for Brayton Cycle cryocoolers. Another programme at IIT Kharagpur developed a turboexpander
unit by using aerostatic thrust and journal bearings which had a working speed up to 80,000 rpm. The detailed summary of
technical features of the cryogenic turboexpander developed in various laboratories has been given in the PhD dissertation of
Ghosh (2002). The detailed design parameters for a 90° inward radial flow turbine is shown in the PhD dissertation of Ghosh.
Bruce (Bruce, 1998) described the aerodynamic and structural analysis for the complete design of turbomachinery rotor. The
major elements of the turboexpander are briefly discussed in the paper published by Ghosh et al. (2005). Baines (2002) has shown
that mixed flow turbine concepts can achieve stage loadings that are about 20% greater than those of a conventional radial turbine,
without any increase in blade speed and maintaining structural integrity. Descombes (2003) has highlighted the variability of the
local distribution of velocities and pressures within the rotor and gives a real image of energy transformation for nearly ideal zero
incidence conditions at the rotor inlet. Abidat (2006) has taken care in the design of the volute essential component of a radial and
mixed flow turbines and interest was focused on the influence of the volute inlet flow conditions on its performance. A method of
computing blade profiles has been worked out by Hasselgruber (1958), which has been employed by Kun & Sentz (1985) and by
Balje (1970, 1981). Effect of some of the turbine operating and design parameters on the flow path and its curvature have been
analyzed and presented by Ghosh et al. (2009). The computational procedure developed describes the threedimensional contours
of the blades for the turbine wheel.
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176
2. Fluid parameters and layout of components
The fluid specifications have been dictated by the requirements of a small refrigerator producing less than 1 KW of refrigeration.
Turbine efficiency of 75% has been assumed following the experience of the workers (Beasley et al., 1965; Yang et al., 1990;
Denton, 1996; Jekat, 1957). The inlet temperature has been specified rather arbitrarily, chosen in such a way that even with ideal
(isentropic) expansion; the exit state should not fall in the twophase region. The basic input parameters for the system are given in
Table 1. Figure 1 shows the longitudinal section of a typical cryogenic turboexpander displaying the layout of the components
within the system. The major components of the turboexpander are shown in Table 2.
Table 1: Basic input parameters for the cryogenic expansion turbine system
Working fluid : Nitrogen
Turbine inlet temperature : 122 K
Turbine inlet pressure : 6.0 bar
Discharge pressure
Throughput
Expected efficiency
: 1.5 bar
: 67.5 nm3/hr
: 75%
Table 2: Basic unit of a turboexpander assembly
Diffuser
Journal bearings Thrust bearings
Turbine wheel
Brake compressor
Nozzle Shaft
Housing
Figure 1: Longitudinal section of the expansion turbine displaying the layout of the components
3. Design of turbine wheel
The design of turbine wheel has been done following the method outlined by Balje (1981) and Kun & Sentz (1985), which are
based on the well known “similarity principles”. The similarity laws state that for given Reynolds number, Mach number and
Specific heat ratio of the working fluid, to achieve optimized geometry for maximum efficiency, two dimensionless parameters:
specific speed and specific diameter uniquely determine the major dimensions of the wheel and its inlet and exit velocity triangles.
Specific speed (
Q
n
Δ
1
32
Q
s n ) and specific diameter (
s d ) are defined as:
Specific speed
()4
3
3
3
s in
s
h
−
(
=
ω
(1)
Specific diameter
)
3
4
hD
d
s in
s
−
Δ×
=
(2)
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Ghosh / International Journal of Engineering, Science and Technology, Vol. 2, No.1, 2010, pp. 175191
177
In the definition of
s n and
s d the volumetric flow rate
3
Q is that at the exit of the turbine wheel. Kun and Sentz (1985),
however suggest two empirical factors
QkQ
1
/k
ex
ρρ =
h
=Δ
−
3
The factors
rise in temperature and density in the diffuser as shown in Figure 2. Following the suggestion of Kun and Sentz (1985),
03. 1
. The factor
ex
Q/Q3
stage, where as
3
Q and
3
ρ
condition of the turbine wheel can be calculated from equations (3) and (4) respectively. If the guess value is correct, then
ρ should give a turbine exit velocity
3
C that satisfies the velocity triangle as described in equation (13); otherwise the iteration
process is repeated with a new guess value of
Q determines turbine exit velocity uniquely. The thermodynamic
relations for reversible isentropic flow in the diffuser are,
2
3
033
hh
−=
1 k and
2 k for evaluating
3
Q and
s
h3, which define
s n and
s d .
ex3=
and
(
in
h
02
(3)
(4)
(5)
13
)
exs
h
sin
k
−
1 k and
2
k account for the difference between the states ‘3’ and ‘ex’ caused by pressure recovery and consequent
2
k value is
1 k represents the ratio
are unknown. By taking a guess value of
, which is also equal to
3 ex/ρρ
. The value of
ex
Q and
ex
ρ
are known at this
ρ ) at the exit
1 k , the volume flow rate (
3
Q ) and the density (
3
3
Q and
3
1 k . The value of
3
ex
hh
003=
,
ex
ss =
3
and
2
C
Figure 2: State points of turboexpander
Using the property tables, the value of
initial values of
3
ρ is within the prescribed limit, the iteration is converges. Since the change in entropy in the diffuser is small
compared to the total entropy change, assumption of isentropic flow will lead to very little error. The estimation
deviate appreciably, if the expansion of fluid from ‘in’ to ‘ex’ is nonisentropic. With this assumption, the value of
to be 1.11, starting with the initial guess value of 1.02. A flow chart for determining the value of
For estimating the thermodynamic properties at different states along the flow passage, the software package ALLPROPS 4.2
available from the University of Idaho, Moscow (Lemmon et al., 1995) is used. Table 3 represents the thermodynamic states at the
inlet of the nozzle and the exit of the diffuser according to input specifications. The exit state has two different columns, one is
isentropic expansion and other is with isentropic efficiency of 75%.
Using data from Table 3,
.
10 26.23
−
×===
ex
ρ
86. 5
3
===
k
−
×==
ex
QkQ
3
ρ can be estimated from
3
s and
3
h . When the difference between the calculated and
1 k does not
1 k is estimated
1 k is described in the Figure 9.
3
3
1097. 3
86 . 5
−
×
tr
ex
m
Q
m3/s
27. 5
11. 1
1
ex
ρ
ρ
kg/m3
(6)
3
13
1042 . 4
m3/s
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Ghosh / International Journal of Engineering, Science and Technology, Vol. 2, No.1, 2010, pp. 175191
178
()
39861107 .38 03. 1
3
,, 0
h
23
=××=−=Δ
−
sexinsin
hkh
J/kg
From Balje (1981) the peak efficiency of a radial inflow turbine corresponds to the values of:
54 . 0
=
s n
and
4 . 3
=
s
d
Substituting these values in equations (1) and (2) respectively, yields
Rotational speed
22910
=
ω
rad/s = 2,18,775 r/min,
Wheel diameter
mmD0 . 16
.
Power produced
()
hhmP
ex0in
=−=
&
Tip speed
22
= DU
ω
Spouting velocity
h2C
in0
Δ=
U
(7)
2=
()
KW
9 . 0h
m/s
h
183
η
=
m
&
2
exs 0in
=−
28 ./
20.278
exs
=
−
m/s and (9)
Velocity ratio
66. 0
0
2=
C
According to Whitfield and Baines (1990), the velocity ratio
0
2C
U
in a radial inflow turbine generally remains within 0.66 and
0.70. The ratio of exit tip diameter to inlet diameter should be limited to a maximum value of 0.70 (Dixon, 1978; Rohlik, 1968) to
avoid excessive shroud curvature. Corresponding to the peak efficiency point (Kun and Sentz, 1985):
676 . 0DD
2
tip
8 .10
=
tip
D
mm
Table 3: Thermodynamic states at inlet and exit of prototype turbine
Inlet isentropic exit state (ex,s)
Pressure (bar) 6 1.50
Temperature (K) 122 81.72
Density (kg/m3) 17.78 6.55
Enthalpy (kJ/kg) 119.14 80.44
Entropy (kJ/kg.K) 5.339 5.339
Balje (1981) prescribes values for the hub ratio
tip
D/
=λ
against
recommendation for radial flow machines. In axial flow and large radial flow turbines, a small hub ratio would lead to large blade
height, with associated machining difficulties and vibration problems. But in a small radial flow machine, a lower hub ratio can be
adopted without any serious difficulty and with the benefit of a larger cross section and lower fluid velocity. According to Rohlik
(1968), the exit hub to tip diameter ratio should maintained above a value of 0.4 to avoid excessive hub blade blockage and energy
loss. Kun and Sentz (1985) have taken a hub ratio of 0.35 citing mechanical considerations.
425./
==
tiphub
DD
λ
6 . 4
=
hub
D
mm
There are different approaches for choosing the number of blades, the most common method is based on the concept of ‘slip’, as
applied to centrifugal compressors (Rohlik, 1968; Stewart and Glassman, 1973; Jadeja et al., 1985). Denton (1996) has given same
guidance on the choice of number of blades by ensuring that the flow is not stagnant on the pressure surface. For small turbines,
the hub circumference at exit and diameter of milling cutters available determine the number of blades. In this design the number
of blades (Ztr) are chosen to be 10, and the thickness of the blades to be 0.6 mm throughout.
From geometrical considerations:
(
mean
β
sin24
==
ξ
(10)
Actual exit state (ex)
1.50
89.93
5.86
90.11
5.452
hub D
s n and
s d for axial flow turbines, but makes no specific
(11)
)
()
hubtiptr tr
hubtip
DDtZ
DDA
π
22
3
−
−−=
(12)
(8)
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Ghosh / International Journal of Engineering, Science and Technology, Vol. 2, No.1, 2010, pp. 175191
179
()
(
(
sin
)
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
−
−−==
mean
β
)
hub
hubtiptr
2
tr
hubtip
DDtZ
DDCCAQ
π
4
22
3333
(13.a)
()
3
22
33
24
W
DDtZ
DDCQ
tip trtr
hubtip
×
−
−−=
π
(13.b)
2
U
2
C
2
W
θ
θ
3
C
3
W
3
U
Direction of rotation
Z
r
β
(a) Inlet velocity triangle in the rθ plane (b) Exit velocity triangle in the θ z plane.
Figure 3: Inlet and exit velocity triangles of the turbine wheel
From the velocity triangle in Figure 3
()
hubtipmean
mean
β
DD
C
+
U
C
==
ω
3
, 3
3
4
tan
(14)
For a given value of
mean relative velocity angle
U
3
Q as given by equation (6), equations (13) and (14) are solved simultaneously for exhaust velocity
β
, giving:
3
C and
mean
°=
=
=
1 .
6 . 45
/90
/ 2 .88
m
3
3
mean
β
mean
sC
sm
(15)
In summary, the major dimensions for our prototype turbine have been computed as follows:
Rotational speed: N = 22910 rad/s = 218,775 rpm
Wheel diameter:
2
D = 16.0 mm
Eye tip diameter:
tip
D
= 10.8 mm
Eye hub diameter:
hub
D
= 4.6 mm
Number of blades:
tr
Z = 10
Thickness of blades tr t
4. Design of diffuser
For the purpose of design, the diffuser can be seen as an assembly of three separate sections operating in series – a converging
section or shroud, a short parallel section and finally the diverging section. The converging portion of the diffuser acts as a casing
to the turbine. The straight portion of the diffuser helps in reducing the nonuniformity of flow, and in the diverging section, the
pressure recovery takes place.
The geometrical specifications of the diffuser have chosen somewhat arbitrarily. Diameter of diffuser inlet is equal to diameter of
the turbine inlet. Diameter of throat of diffuser is dependent on the shroud clearance. The recommended clearance is 2% of the exit
(16)
= 0.6 mm