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Turbine performance studies for automotive turbochargers. Part
1: steady analysis
A. Romagnoli and R.F. Martinez-Botas*
Department of Mechanical Engineering Imperial College London
SW7 2AZ Exhibition Road London, UK
*Corresponding author
S. Rajoo Dept. Automotive Engineering
Faculty of Mechanical Engineering Universiti Teknologi
Malaysia
81310 Johor - Malaysia SYNOPSIS This paper presents the results
from an experimental investigation
conducted on different turbine designs for an automotive
turbocharger. The design progression was based on a commercial
nozzleless unit that was modified into a variable geometry single
and twin entry turbine. The main geometrical parameters were kept
constant for all the configurations and the turbine was tested
under steady and pulsating flow conditions (pulsating findings are
presented in an accompanying paper).
A significant depreciation in efficiency was measured between
the single and twin entry configuration due to the mixing effects.
The nozzleless unit provides the best compromise in terms of
performance at different speeds.
The twin entry turbine was also tested under partial and unequal
admissions. Based on the test results, a method to determine the
swallowing capacity under partial admission given the full
admission map is presented. The test results also showed that the
turbine swallowing capacity under unequal admission is linked to
the full admission case.
NOMENCLATURE
A Area, [m2] C Absolute velocity, [m/s] P Pressure, [Pa] SE
Single entry
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T Temperature, [K] TE Twin entry VR Velocity ratio
Mass flow rate, [Kg/s] r Radius, [m] Absolute flow angle, [deg]
Density, [Kg/m3] Subscript Azimuth angle 0 Total condition 1 Inner
limb/Inlet 2 Outer limb/Outlet atm Atmospheric ex Exit is
Isentropic pa Partial admission r Rotor te Twin entry un Unequal
admission
INTRODUCTION Increasing limitations on exhaust emissions and the
need to reduce fuel consumption have encouraged extensive use of
turbochargers in the automotive sector. The turbocharger turbines
comprise two main elements: the wheel and the stator (or volute).
The wheel can be either radial or mixed flow and its function is to
extract work from the exhaust gases. The main function of the
stator is to accelerate and distribute uniformly the flow around
the wheel. The most common configurations for the stator are
nozzleless, nozzled and twin entry. In a nozzleless turbine, the
volute is solely responsible for providing an adequate swirl and
consequently set the inlet flow angle for the rotor. In a nozzled
turbine, the volute is complimented with the downstream nozzle ring
in setting the flow characteristics into the rotor. In this case,
the volute is designed to provide uniform flow into the nozzle.
Additionally, in a variable geometry stator the volute-nozzle
coupling provides additional flexibility in adapting to the
incoming flow [1].
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Twin entry turbines are adopted for using the energy of
pulsating exhaust gases. Two banks of exhaust manifolds feed each
entry of the turbine so that the windmill is minimized as the mass
flow drops to zero. Spence et al. [2] carried out a performance
investigation on an equivalent swallowing capacity basis for three
different nozzleless and nozzled stators. The nozzleless
configuration revealed a better performance than the nozzled one.
This was attributed to different levels of roughness between the
stators. In the case by Baines and Lavy [3] the highest efficiency
was measured for the nozzled configuration. Capobianco and
Gambarotta [4] instead compared a single entry to a twin entry
turbine and found that, under full admission, the efficiency of the
twin entry turbine under is about 7% less.
The study reported here shows the performance for a design
progression from single to twin turbine. An evaluation of the
turbine efficiency and swallowing capacity was carried out on the
basis of the experimental results.
EXPERIMENTAL FACILITY The automotive research group at Imperial
College has actively been involved in the development and
understanding of pulsed flow turbines since the 1980's. The
turbocharger test facility was originally developed by Dale and
Watson [5] and extended by Baines et al. [6][7]. The experimental
facility available at Imperial College London is a simulated
reciprocating engine test bed for turbocharger research. The
facility can perform steady state testing in single and twin entry
turbines; it is also capable of carrying out unsteady tests [8][9].
The recent installation of an eddy current dynamometer enables
turbine testing within a large velocity ratio range [10][7]. The
test-rig is supplied by screw-type compressors, capable to
delivering air up to 1.2 kg/s mass flow rate at a maximum pressure
of 5 bars (absolute). For unsteady testing, an air pulse generator
is employed. It simulates experimentally the engine exhaust gas
pulsations by means of a set of counter rotating plates with
appropriately designed cut-outs. A variable speed D.C. motor
controls the rotating frequency of the chopper plates; hence the
frequency of the pulsation can be set [1].
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TURBINE VOLUTE DESIGN The turbine used in the current study is a
mixed flow variable geometry designed at Imperial College [1]. The
design was based on a commercial nozzleless unit (HOLSET H3B) and
it aims for increased flexibility in the operating envelope of the
turbine. The turbine volute was manufactured in two halves allowing
a nozzle-ring and the divider to be inserted. Such an arrangement
of the turbine volute allows change between four turbine
configurations: single entry nozzleless, single entry nozzled, twin
entry nozzled and twin entry nozzleless. The main geometrical
parameters of the turbine arrangements remain the same.
where S is a constant (1)
(2) The volute design was carried out using the well established
mean
line analysis method [11][12]. The main assumptions for this
approach are: free vortex conditions in the volute and uniform flow
distribution around the volute periphery. This approach results in
two basic equations (1) & (2). Assuming incompressible flow and
rearranging Eq. (1) and (2) one obtains the A/r relation:
The equation above shows that the two critical parameters to
be
taken into account in the design of the volute are the cross
sectional area (A) and the correspondent centroid radius (r). In
order to distribute the mass uniformly around the circumference of
the rotor, the ratio between the area and the radius must be a
linear function of the azimuth angle. For a given mass flow rate
and density, the radial component of the velocity going into the
rotor is then fixed by the cross sectional area at the rotor inlet.
This means that the volute outlet angle is given by:
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In order to determine the volute exit flow angle, a simple
analysis was carried out using Eq. (1) to (4). A similar analysis
of the HOLSET 3HB turbine provided an exit flow angle of 68 with
respect to the radial direction. Hence a target range of 67 to 72
enveloping the HOLSET H3B value was chosen and the main geometrical
parameters (area and radius) calculated accordingly.
A similar approach was followed in the design of the divider for
the twin entry turbine. A solid modelling analysis was then carried
out in order to determine the best compromise between area
available to the flow and strength of the material. Amongst all the
possible solutions proposed, a tapered shape divider was chosen.
The final design of the single entry turbine together with the
turbine including the divider is shown in Figures 1 & 2.
Figure 1: Whole turbine stage Figure 2: Divider fitted in the in
single entry turbine
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STEADY TURBINE PERFORMANCE This paper reports performance
results from two single entry
configurations (nozzled and nozzleless volutes) previously
characterised at Imperial College [1][9][13]. These results are
complemented with data recently acquired for a variable geometry
twin entry mixed flow turbine. In this manner, a comprehensive
comparison of different configurations can be carried out. The
static efficiency (given as the ratio between the actual power and
the isentropic power) and the pseudo-dimensional mass flow
parameter have been plotted against the velocity ratio and the
pressure ratio respectively. The definition of these parameters can
be found below:
The turbines performance was assessed on an equivalent
geometry
basis. The design progression of the volute was aimed to
maintain the A/r, the exit flow angle and the shape of the
cross-section similar to the base line (HOLSET H3B). The turbine
wheel used for all the tests is of a mixed flow nature previously
designed at Imperial College by Abidat [14]. For consistency with
previously reported results, the wheel is referred to as rotor A.
The main geometrical parameters are given in Table 1 and more
details can be found in available literature [15][16].
Table 1 One-dimensional analysis of the advanced rotor A
Rotor Type A Inlet mean diameter (mm) 83.58 Number of blades
12
Exducer hub diameter (mm) 27.07 Exit mean blade angle -52
Inlet blade height (mm) 18.0 Inlet blade angle 20
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Figure 3: SE at 80% speed-Nozzled (60) vs. Nozzleless: a- ts vs.
VR & b-MFP vs. PR
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Figure 4: SE at 50% speed-Nozzled (60) vs. Nozzleless: a- ts vs.
VR & b-MFP vs. PR
Figures 3 & 4 show the performance parameters for a
nozzled
turbine at 600 vane angle (corresponding to the optimum vane
angle for this turbine) and a nozzleless equivalent (base line).
The figures show results for 50% and 80% of the design speed
testing which corresponds to 32000rpm and 48000rpm respectively.
For the nozzleless mixed flow turbine, the peak total to static
isentropic
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efficiency was 0.77 displaying a slight drop of 3 percentage
points at low velocity ratios (50%). Overall, the turbine exhibits
features common to mixed flow turbines [17]. The efficiency curves
remains fairly flat for velocity ratios near to peak. This is even
more evident at 50% speed where the efficiency drop, even at higher
velocity ratios, is
Figure 5: SE/TE at 80% speed-Different configurations: a- ts vs.
VR
& b-MFP vs. PR
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small. In the nozzle configuration, the peak efficiency was 0.81
at 80% speed (vane angle of 60). This represents an improvement of
4 percentage points at all low velocity ratios when compared to the
nozzleless case. The same improvement is not visible at the low
speed condition (50% speed) for which similar efficiencies were
found.
Figure 6: SE/TE at 50% speed-Different configurations: a- ts vs.
VR
& b-Mass vs. PR
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Interestingly, a significant shift of the efficiency curve
towards low velocity ratio can be seen in this case: the peak
efficiency velocity ratio shifts from 0.70 to 0.64. Such a shift is
significant for energy extraction, as in the real pulsating
condition of the turbine high efficiency at high pressure ratio
(low velocity ratio) is desired. One would thus presume that such a
performance curve would lead to greater pulse flow performance
[15][16][18]. At the present no data are available on support of
this assumption. However a preliminary comparison between the
pulsating flow performance for single entry nozzled and nozzleless
turbine is provided in Part Two of this paper [19].
In order to test a twin entry turbine, a divider was inserted
within the volute. The design took care to find the best compromise
between the strength of the divider and the area available to the
flow. The main geometrical parameters are the same as those of the
nozzled turbine except for the A/r that was reduced by 6%. Twin
entry turbines are usually adopted to isolate the gas flow from
each separate bank of manifolds. The turbine works under unequal
and/or partial admission conditions for most of its operation;
consequently, full admission does not replicate the working
conditions of the turbine under normal engine operating conditions.
Nevertheless, turbine maps are usually available only for full
admission conditions; therefore it seems logical to report tests
under full admission conditions for the twin entry geometry.
Figures 5 & 6 report the turbine efficiency under full
admission at 80% and 50% turbine speed. The presence of the divider
has a small detrimental effect on turbine efficiency; the peak
efficiency was found to be 0.79, which is slightly lower than that
measured in single entry. At high velocity ratios the turbine
performance shows an improvement of few percentage points with
respect to the single entry configuration at both 50% and 80%
speeds.
In order to characterize the effects of the vane angle, a set of
tests were carried out in the 70 and 40 vane angle range for both
types of entries (single and twin). The results are reported in
Figures 7 & 8. A slightly lower swallowing capacity was
measured for the twin entry turbine in comparison to the single
entry case for both 70 and 40 vane angle. This can be explained as
an effect of the divider within the volute that reduces the area
available to the flow. At 70 vane angle, no significant difference
in the peak efficiency value between the single and twin entry
configuration was measured. As the velocity
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ratio increases, the twin entry turbine performs better than the
single entry. The same conclusions can be reached for the 60 vane
angle (refer to Figure 5 & 6) but at 40 the results are
different, showing a
Figure 7: SE/TE at 80% speed - 70 vane angle: a- ts vs. VR &
b-MFP vs. PR
5% efficiency drop over the whole range of velocity ratios. The
mixing effect between the flows out of two limbs is considerable
and should be taken into account in design-phase.
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Figure 8: SE/TE at 80% speed - 40 vane angle: a- ts vs. VR &
b-MFP vs. PR
Figure 9 reports the single and twin entry performance
parameters
for 40, 60 and 70 vane angles at 80% speed. The single entry
configuration exhibits the best overall performance with a peak of
81% (60 vane angle 80% speed). At 40 vane angle an efficiency drop
of almost 25% and 20% was measured for the twin and single
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entry configuration in respect to the peak efficiency point (60
vane angle 80% speed). At 70 the peak efficiency for both the
single and twin entry turbine shows a shift in the velocity ratio
down to 0.57. On the mass flow side, the swallowing capacity at 70
is much lower than that measured at 60 and 40 vane angle and, for
mid range pressure ratios, it is almost half than that measured at
40.
Figure 9: SE/TE at 80% speed - Different vane angles: a- ts vs.
VR &
b-MFP vs. PR
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Figure 10: SE/TE at 80% speed-Same swallowing capacity: a- ts
vs. VR b-MFP vs. PR
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Figure 11: TE partial admission 80% speed - 60 Vane angle: a- ts
vs. VR b-MFP vs. PR
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Figure 12: TE partial admission 50% speed - 60 Vane angle: a- ts
vs. VR b-MFP vs. PR
In order to complete the analysis an assessment of turbine
efficiency on an equivalent swallowing capacity basis was also
carried at 80% speed. In order to let more mass flow to go through,
the vanes were open at 40. As the vanes open, they produce a
deviation from the optimum incidence condition leading to an
increase in losses. This is clearly visible in Figure 10 where
there is a detrimental effect of vane opening to meet the same
swallowing capacity.
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As it was previously stated, the twin entry turbocharger always
exhibits an imbalance of flow conditions between the two entries,
caused by the manifold arrangement; the twin entry turbine was also
tested under partial admission conditions for the optimum (60) vane
angle. The importance of partial admission conditions becomes
apparent when evaluating aerodynamic losses and translating these
into the real pulsating operation of the turbocharger.
Figures 11 & 12 report the turbine efficiency at 80% and 50%
speed under full and partial admission condition; where partial is
meant to be the condition in which one entry does not flow at all
while the other flows (labelled as outer open in the figure). These
tests are repeated by reversing entry that flows (labelled as inner
open on the figures), one can thus see the effect of the chosen
entry to flow. Independent the entry that has flow, a large fall in
efficiency is measured, the drop is as large as 20 percentage
points at 80% speed and 24 percentage points at 50% speed. The peak
efficiency point for either inner or outer limb fully open is the
same at both speeds, which is 61% and 53% for 80% and 50% speed
respectively. Nevertheless the inner limb seems to perform better
than the outer limb; note the mass flow in both limbs is the same.
This is not a new finding, it is the consequence of the different
paths taken by the flow for a given shroud curvature.
Figure 13: Mass flow prediction under partial admission - 50%
speed - 60 vane angle
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Figure 14: Mass flow prediction under partial admission - 80%
speed - 60 vane angle
As previously mentioned, turbine maps are usually provided under
full admission conditions and so far no method has been proposed
for evaluating the mass flow parameter under partial admission
given a full admission mass flow curve. Here a simple method is
proposed. Figures 13 & 14 report the swallowing capacity for
the twin entry turbine under full admission conditions for both 50%
and 80% speeds. It can be seen that by simply halving the mass flow
measured under full admission, the corresponding partial admission
is not reached. In fact by following this simple approach, one
would be treating the turbine as a single entry turbine with half
the passage area and thus, it does not take account for the
interaction existing between the two limbs. Furthermore, even
though in partial-admission conditions no air flows at the inlet of
one of the entries, stagnant air at atmospheric pressure is still
present within in the non-flow limb and leakages into that entry
from the flowing side can occur. The general expression for the
mass flow parameter is given by Eq. (7). For a twin entry turbine
the mass flow parameter is calculated as a mass-averaged mass flow
parameter where an area averaged pressure is used:
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By blanking off entry 2 (thus = 0) the total mass flow rate
= , leading to:
The total pressure P02 is near atmospheric as there is no
dynamic head to be taken into account and neglecting the
centrifugal head imposed by the rotor (which is small in any case).
The mass flow parameter calculated by mean of Eq. (10) is given in
Figures 13 & 14. The mass flow prediction from the full entry
maps is much improved for both speeds. At high pressure ratios the
newly predicted mass flow matches that measured experimentally
while at low pressure ratios the simple approach are less accurate.
This can be explained if we consider that at low pressure ratios,
the total pressure in the flow-limb is similar to atmospheric and
hence the denominator of Eq. (10) does not change significantly
when the term P02/2 is added.
The above discussion centred on what is commonly called partial
admission where one port is completely closed; here we report
results from the partial and full flow cased. These are labelled as
unequal admission cases and one of the questions relates to how the
steady tests under unequal admission should be carried out. For the
purpose of this research, the unequal admission condition was
obtained by keeping constant the pressure ratio in one limb and let
the other change in order to match the selected speed (seen in the
line labels of Figure 15 as Outer followed by the pressure ration
kept constant in that entry). Other approaches are possible such as
reported by Capobianco and Gambarotta [4] that performed a set of
unequal cases by keeping the mass flow ratio between the two limbs
constant.
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Figure 15: Twin entry - Mass flow in unequal admission - 80%
speed - 60 vane angle
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Figure 16: Twin entry - Mass flow in unequal admission - 50%
speed
- 60 vane angle
Here the tests were carried at 80% and 50% speed and the results
shown in Figures 15 & 16. The trends are similar to those
measured under full admission; this is more evident as the pressure
ratio and the turbine speed increase. For instance at 80% and
pressure ratio 1.9 the mass flow curve follows very closely the
full admission curve. As already mentioned, the unequal admission
condition is somewhat difficult to analyse and published research
does not provide much
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insight. Given the similarity between the mass flow curves, we
tried to understand whether or not a common correlation exists
between the full and unequal admission condition. Given the mass
flow curves in Figures 15 & 16, in order to proceed with the
analysis, the ratio between the unequal admission flow and that in
the flow-limb was calculated. The same was done for the pressure
ratios.
Figure 17: Swallowing capacity under unequal admission Different
test conditions
The results of such an approach are shown in Figure 17, this
figure
includes all the test conditions shown in Figures 15 & 16.
It was found that all the points collapse into a single curve
following an exponential trend. This suggests that a unique
correlation links the mass flows between the two limbs. In fact if
we develop the expressions for the Expansion Ratio and the Mass
Flow Parameter Ratio we obtain Eq. (11) & (12). These equations
show that the ratio of Expansion Ratio corresponds to the pressure
ratio between the inner and outer limbs and that Mass Flow
Parameter Ratio is a function of both K and the mass flow ratio in
both limbs.
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Figure 17 shows that Eq. (12) follows an exponential trend and
hence for a given pressure ratio and mass flow in one limb, the
mass flow in the other limb is uniquely defined. In other words,
since the full admission maps are usually available, given the mass
flow and the pressure ratio in one limb, it is possible to define
the mass flow and pressure ratio in the other limb such that their
combination corresponds to any point of the full admission curve.
This could be significant as it could contribute to developing a
tool to generate unequal admission maps from a full admission map.
However, it is still necessary to carry out limited testing to
ascertain the constants A and B. The collection of a sufficient
large database will eventually indicate if there are some
commonalities that can be taken into account in order to find what
are the parameters affecting A and B.
CONCLUSIONS The current paper discusses the progressive
evaluation of different turbine designs from nozzleless to twin
entry. The base turbine design is a commercial nozzleless unit,
from which the single entry nozzled turbine was designed and
progressively redesigned to twin entry. The evaluation shown in the
paper covers the steady flow conditions with discussion on full,
partial and unequal admissions.
The nozzled single entry turbine (a with a 60 degree vane angel)
was found to perform better than the corresponding nozzleless
configuration. In twin entry mode the insertion of the divider was
found not to be detrimental to the overall performance; it showed
improvement at high velocity ratios.
As the vanes open (40), a large drop in efficiency occurred
between the single and twin entry turbine. The mixing effects were
evaluated to account for as much as 5% in efficiency loss over the
whole range of velocity ratios. On the other hand, as the vanes
close (70), no difference in efficiency was measured between the
single and twin entry configurations. The peak efficiency is
slightly lower than that measured at 60 vane angle with a
significant shift in the velocity ratio from 0.67 to 0.57.
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The efficiency of the turbines at equivalent swallowing capacity
under steady flow was found to be decreasing from nozzleless to
twin entry design configurations. At velocity ratio of 0.67, the
single entry nozzled turbine efficiency is 16% lower than the
nozzleless, meanwhile the twin entry turbine is 21% lower than the
single entry.
The paper also presents a method to calculate the partial
admission swallowing capacity of a twin entry turbine from the full
admission map. This is particularly beneficial as an engine
developer will only generally have the full admission map in a twin
entry turbine, and it is accepted that the turbine operates in
partial admission in most cases. The test results also revealed
that the mass flows between limbs are correlated by an exponential
manner.
ACKNOWLEDGEMENTS
The authors would like to acknowledge Ricardo plc, Ford Motor
Company Ltd and University of Brighton. This consortium along with
Imperial College are part of funded program (TSB) named VERTIGO
(Virtual Emission Research Tools and Integration).
Authors 2010 REFERENCES 1 Srithar, R., Steady and Pulsating
Performance of a Variable
Geometry Mixed Flow Turbocharger Turbine, Thesis (PhD). Imperial
College of Science, Technology, and Medicine, University of London,
England, 2007.
2 Spence, S.W.T., Rosborough, R.S.E., Artt. D., McCullogh, G.,
A
direct performance comparison of vaned and vaneless stators for
radial turbines, Journal of Turbomachinery, ASME Vol.129, pp. 53,
January 2007.
3 Baines, N. C., Lavy, M., Flows in Vaned and Vaneless Stators
of
Radial Inflow Turbocharger Turbines, Institution of Mechanical
Engineers Turbochargers and Turbocharging Conference, Paper No.
C405/005, pp. 712, 1990.
-
10.1243/17547164C0012010034
456
4 Capobianco, M., Gambarotta, A., Performance of a twin-entry
automotive turbocharger turbine. ASME Paper 93- ICE-2, 1993.
5 Dale, A., and Watson, D., Vaneless radial turbocharger turbine
performance, 110/86. Turbocharging and turbochargers, IMechE,
3rd:65:76, 1986.
6 Baines, N.C., Hajilouy-Benisi, A., and Yeo, J.H., The pulse
flow performance and modelling of radial inflow turbines,
c484/006/94. IMechE, pages 209:219, 1994.
7 Szymko, S., The Development of an Eddy Current Dynamometer
forEvaluation of Steady and Pulsating Turbocharger Turbine
Performance, Thesis (Ph.D.), Imperial College London, UK, 2006.
8 Arcoumanis, C., Hakeem, I., Khezzar, L. and Martinez-Botas,
R.F. Performance of a Mixed Flow Turbocharger Turbine Under
Pulsating Flow Conditions, Transc ASME 95-GT-210, 1995.
9 Karamanis, N., Martinez-Botas, R.F., Mixed-Flow Turbines
for
Automotive Turbochargers: Steady and unsteady Performance,
IMechE Int. J. Engine Research, Vol 3 No.3, 2002.
10 Szymko, S., Martinez-Botas, R.F., Pullen, K. R., McGlashan,
N.R.
and Chen, H., A High-Speed, Permanent Magnet Eddy-Current
Dynamometer for Turbocharger Research 7th Int. Conf on
Turbochargers and Turbocharging, Proc. of the IMechE, paper
C602-026, 2002.
11 Watson, N., Janota, M.S., Turbocharging the Internal
Combustion Engine, London: The Maxmillan Press Ltd, 1982.
12 Japikse, D., and Baines, N.C., Introduction to
Turbomachinery,
Concept ETI Inc., USA and Oxford University Press, Oxford,
1994.
13 Szymko, S., Martinez-Botas, R.F. and Pullen, K.R.
Experimental Evaluation of Turbocharger Turbine Performance under
Pulsating
-
10.1243/17547164C0012010034
457
Flow Conditions, Proc. of ASME Turbo Expo, GT 2005-68878,
2005.
14 Abidat, M., Design and Testing of a Highly Loaded Mixed Flow
Turbine, Thesis (PhD.), Imperial College of Science, Technology,
and Medicine, University of London, England, 1991.
15 Karamanis, N., Inlet and exit flow characteristics of mixed
flow
turbines in advanced automotive turbocharging, Thesis (Ph.D.),
Imperial College London, UK, 2000.
16 Hakeem, I., Steady and Unsteady Performance of Mixed Flow
Turbines forAutomotive Turbochargers, Thesis (Ph.D.), Imperial
College of Science, Technology, and Medicine, University of London,
England, 1995.
17 Srithar, R., Martinez-Botas, R.F., Mixed flow turbine
research: a review, Journal of turbomachinery, ASME Vol.130, Issue
4, October 2008.
18 Palfreyman, D., Aerodynamics of a mixed flow turbocharger
turbine under steady and pulse flow conditions: A numerical study,
Thesis (Ph,D.), Imperial College London, UK, 2004.
19 Romagnoli, A., Rajoo, S. and Martinez-Botas, R.F., Turbine
performance studies for automotive turbochargers Part two: unsteady
analysis, 9th Int. Conf. on Turbocharging and Turbochargers, Instn.
of Mech. Engrs, London, 2009.