International Journal of Scientific & Engineering Research, Volume 4, Issue 2, February -2013
ISSN 2229-5518
1
CFD analysis of flow through mixed flow
compressor under various operating conditions
D. Ramesh Rajakumar1 M.Govardhan2 S.Ramamurthy3
Abstract- Performance of mixed flow compressor with un-shrouded impeller strongly depends upon unsteady, asymmetrical flow fields in
the axial directions. The flow through the mixed flow compressor stage is complex due to three-dimensional shape of flow channel. A
three-dimensional turbulent flow through a single stage mixed flow compressor is numerically analyzed using commercial software to
understand the complex flow behavior inside the impeller channel and near the tip gap. The analysis showed scope for improvement in
design of the compressor for better performance in terms of efficiency and operating range.
Keywords-Mixed flow compressor, surge, stall, choke, CFD, tip Clearance, compressible flow, periodic, grids and jet-wake.
—————————— ——————————
1 INTRODUCTION
1.1 Motivation
Mixed flow Compressor stage is favored for applications in
small gas turbine engines as it provides smaller frontal area
and high thrust to weight ratio. The efficiency and
reliability of the compressor depends to a great extent on
flow behavior in its flow passage and flow near shroud (tip)
gap. It is well known that the interaction between mixed
flow impeller and diffuser substantially influences the flow
field and performance of both the components and thus the
entire compressor stage. It is therefore, necessary to study
and understand the complex flow field inside the flow
channel of the mixed flow compressor.
1.2 Background
Most of the pioneering works in design and analysis of
mixed flow compressor started in 1940s and 50s. Work
presented by Austin King et al. in 1942, was probably one
of the earliest works regarding mixed flow compressors [1].
They experimentally investigated a parallel cut-off mixed
flow impeller with several tip clearances to study the effect
of tip clearance.
Stanitz [4] described a method for design and analysis of
one-dimensional compressible flow in vane-less diffusers of
radial and mixed flow compressors including effects of
friction, heat transfer and area change. Hah et al. [3]
developed a fully elliptical three-dimensional viscous flow
analysis method with a finite volume relaxation procedure
to compute the flow inside the centrifugal impeller.
_______________________________________________
1Scientist,
National Trisonic Aerodynamic Facility
CSIR-National Aerospace Laboratories, Bangalore-India, 560017
E-mail:ramesh0102@yahoo.com
2Proffessor, Department of Mechanical Engineering, Indian Institute of
Technology Madras, Chennai, India, 600036.
3 Specialist Consultant, NCAD, CSIR-National Aerospace Laboratories
Bangalore- India, 560017
Ramamurthy and Murugesan [8] presented a method to
design centrifugal compressor geometry using analytical
approach to get optimum geometry. Patrik et al. [6] studied
the performance of eddy-viscosity, Baldwin-Lomax and
Chien k-ε, and low Reynolds number turbulence models
and applied to the simulation of a flow in the NASA lowspeed compressor. The k-ε prediction was better than the
other models. Pavel Simvnov et al. [7] have adopted
numerical simulation of three dimensional flow in a
centrifugal compressor stage with a diffuser of variable
geometry using the commercial ANSY CFX code. They
observed that the total pressure ratio distribution was not
favorable in case of larger radial gap. Predictions are very
close to the experimental results. Engine [2] described a
three dimensional CFD simulation of the flow field in three
different un shrouded centrifugal fan with varying tip
clearances from 5 mm to 30 mm. He used commercial CFD
code; fluent with k-ε two equation turbulence model in
order to study the effect of different tip clearances. Krain
and Hoffmann [5] have described the development of an
improved high pressure ratio centrifugal compressor using
analytical approach. A 3-D laser velocity meter was used to
probe the flow inside the channel. No specific literature is
available on flow simulation of mixed flow compressor. A
reliable prediction of the flow field in the mixed flow
compressor is regarded as a challenge.
1.3 Applications
Mixed flow compressors are used in engines installed in
short-range missiles, unmanned aerial vehicles, vehicles
used for reconnaissance and in helicopters.
These
compressors produce moderate stage pressure-ratios of the
order of 3.5 to 6 with the available materials like titanium
alloys.
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2 OBJECTIVES
3 GEOMETRIC MODELING AND MESHING
In this work, computational investigations are carried out
to get the stage performance map with tip clearance of 0.5
mm for different operating speeds and mass flow rates
covering the complete operating range from choke to surge.
The computational simulations are done at five different
speeds. Mixed flow impeller was designed for 2.72 kg/s
and static to total pressure ratio of 3.8 with design speed of
39836 rpm. The complex flow inside the impeller channel is
studied at different flow conditions. Specifications of the
mixed flow compressor are shown in Table 1.
3.1 Modeling
2
Figure-1 shows the CAD model of compressor stage
designed and generated in solid works CAD package. As
the domain is axi-symmetric, a single channel consisting of
one main blade and one splitter blade is considered for flow
analysis. A vane-less space is provided downstream of the
impeller is also considered.
TABLE 1
Specifications of mixed flow impeller
Impeller inlet parameter
Value
d1it
Impeller inlet tip diameter
d1ih
Impeller inlet hub diameter
N
Impeller rotational speed
(m)
(m)
(RPM)
0.156
0.0625
39836
Hub–to–tip diameter ratio
d1ih d1it
0.40
Relative blade angle at tip
β1it
61.8
Relative blade angle at hub
(deg)
β1ih
(deg)
Impeller exit parameter
Impeller exit tip diameter
d2it
(m)
d 2ih
Impeller exit hub diameter
(m)
Impeller exit blade height
b2i (m)
Relative blade angle at tip
β 2itI
Relative blade angle at hub
Absolute flow angle
α2it
β 2ihI
(deg)
0.253
0.239
0.0141
(deg)
(deg)
Fig.1. CAD model of mixed flow impeller
36.7
58.5
46.8
70
Impeller domain is generated using Gambit turbo tool preprocessor. Turbo tool was used for constant tip clearance
configuration of 0.5 mm. The flow domain is divided into
multiple volumes to form cube like structure so as to fit
hexahedral element. Meshing was carried out using
Gambit preprocessor. Hexahedral mesh elements were
used in all volumes except near the clearance region over
the main blade and splitter blade. Grid independence study
was done for 62349 and 127150 elements with zero tip
clearance and result is shown in Fig.2. The result shows that
number of elements beyond one lakh has no influence on
the performance of compressors. However, higher elements
are considered for analysis due to zero skewed elements.
3.2 computational methodology
Impeller main blades
11
Impeller splitter blades
11
For the present work, computations were performed using
commercial code namely Fluent. A 3D viscous flow
through impeller was analyzed. Segregated solver is used.
The numerical fluxes are estimated with first order upwind
scheme.
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International Journal of Scientific & Engineering Research, Volume 4, Issue 2, February -2013
ISSN 2229-5518
magnitude from its initial value and the integrated
residuals of all the variables were reduced by six orders of
magnitude, the solution was considered as converged. The
mass flow summary, the residual history of the variables
and the monitor point values were used to judge the
convergence behavior of the theoretical analyzed results.
The mass imbalance was checked after the solution was
converged. In all the cases the observed imbalance in mass
flow rate was as low as 0.001%.
3.3 Boundary Conditions
Figure 4 shows the flow domain along with boundary
conditions assigned in the present analysis. Inlet boundary
conditions used were total pressure, total temperature, and
absolute flow angle.
Fig.2. Grid independence study
For the present analysis there are 1080292 elements are
used. The mesh geometry is shown in Fig.3. Table 2, below
gives the elements in different regions.
TABLE 2
Number of elements at domain
Fluid
volume
Surface
mesh
Solid mesh
size
Number
of cells
Shroud
clearance
Pave
Hex/cooper
1
63362
impeller
pave
Tet/hybrid
3
1016930
total
1080292
The distribution of these quantities was assumed constant
throughout inlet boundary and hence single value was
given. At exit, static pressure (sometimes termed as
backpressure) was specified. Periodic boundary conditions
were imposed on side faces of tip clearance, upstream and
downstream of the impeller blade. The shroud casing was
considered stationary. Hub surface and blades of impeller
were specified as rotating frame.
Fig.4. Flow domain and BCS
4.0 RESULTS AND DISCUSSIONS
Fig.3. Typical mesh of the
computational domain
The continuity equation, which governs mass conservation,
is used to determine the pressure field in the pressurebased method. Turbulence is modeled using standard k-ε
model. When the integrated residual of the pressure
correction equation was reduced by four orders of
4.1 Performance characteristics
The performance of the compressor estimated for various
operating speeds with 0.5mm tip clearance from the CFD
code is shown in Fig.5. The performance of the impeller
was obtained for five speeds, which includes 60%, 75%,
90%, 100% and 105% of the design speed. At each speed
the complete impeller operating range (choke to surge) was
obtained. The total to total pressure ratio is plotted against
mass flow parameter for different operating speeds. It is
observed from this figure that at design speed compressor
shows choke mass flow rate of 3.29 kg/s whereas the
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surging mass flow rate is around 2.39 kg/s. The impeller
design mass flow rate at the design speed is 2.73 kg/sec.
Hence compressor at design speed has roughly about 37%
surge margin. The estimated pressure ratio (4.50) is slightly
lower than design pressure ratio (4.55) due to the
inaccuracy in the loss models used in the design. The
performance at speed higher than design speed shows a
maximum mass flow rate that can be allowed through the
impeller is 2% of design mass flow rate.
The isentropic efficiency of the impeller was estimated from
the impeller total to total pressure ratio and total to total
temperature ratio for 0.5mm tip clearance at different
speeds. The variation of impeller isentropic efficiency for
different speeds that were considered in Fig. 5 is shown in
Fig. 6. The peak efficiency of the impeller for various
speeds is around 91%, which corresponds to flow having
zero incidence at impeller inlet. The impeller design
efficiency is 93.8%. On either side of the peak efficiency
point the impeller efficiency drops. The sharp drop in
efficiency is noticed towards choking side. The lowest
efficiency value which corresponds to unstable operating
point at different speeds increases with increase in speed.
4
This compressor was tested in closed circuit compressor
test rig with vane-less configuration up to 32000 rpm. Vane
less diffuser outlet static pressure and impeller inlet static
pressure were measured for different mass flow conditions
The measured stage pressures are plotted against measured
mass flow for five different speeds. Through Fluent code,
for these speeds and inlet flow conditions the outlet
pressure and mass flow through the compressor are
estimated. The estimated pressure ratio from CFD is plotted
against mass flow rate and compared with experimental
values for different speeds.
The performance graph
obtained is shown in Fig.7.
Fig.7.Comparison of performance
It is observed from this figure that the agreement between
CFD and experimental results is good at all speeds.
Estimated mass flow is 7.8 % (average) lower than the
measured mass flow due to blockage is not considered in
the design . This is attributed to small error in mass flow
measurement in experimental investigations.
.
Fig.5. Impeller pressure ratio
4.2 Blade loading
To study the variation of static pressure on the blade
suction and pressure surfaces, different operating point at
29000 rpm is selected and these points are indicated in
figure 9 as A, B, C, D, E and F. These operating points were
selected such that they are close to surge, design and choke
conditions. These points on the graph are represented as A,
C and F. At these selected points the variation of static
pressure along the blade surface length is shown in Figs.
10a, 10b and 10c.
The local static pressure is normalized with inlet total
pressure. The local surface distance is normalized with
total surface distance. In each figure, the static pressure
variation at three different locations namely, hub, mean
and tip section are shown.
Fig.6. Impeller efficiency
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5
Fig.9. Operating points for flow studies
Fig.10c. Blade static pressure variation
At the surge point there is drop in blade loading. At each
station, the area under pressure distribution curve is higher
at the tip section compared to hub section. This behavior is
not seen at the surge flow rate. Hence the tip section is
highly loaded as the work done is highest at tip section. It is
also observed that the static pressure across the blade
length increases uniformly from inlet to outlet indicating
continuous pressure rise. This behavior is observed at all
locations except at choke mass flow.
4.3 Flow angle variations
Fig.10a.Blad static pressure variation
It is observed that a cross over occurs in static pressure
distribution curves at choke flow rate, indicating reduction
in blade loading. As the mass flow rate is reduced, the
pressure distribution curve improves and blade loading
increases.
Fig.10b. Blade static pressure variation
The flow angles at impeller exit was estimated from CFD
results at 29000 rpm for three operating points A, C and F
as indicated in Fig.9. The meridional plane considered is
slightly away from the impeller exit. These angles being
calculated from the local values of velocities namely U, W
and C. The local position of each velocity vector at impeller
exit is being captured by local co-ordinates. The relative
flow angle and absolute flow angle variation with respect
to normalized arc length at three span wise location at
impeller exit are shown in Figs. 11a-11d. The spanwise
locations being taken one at mid wall (50% of blade height)
and one at very close to the shroud wall (95% of blade
height). The variation of flow angles at shroud wall
represents the tip clearance effects.
The relative flow angle variation at impeller exit at 95% of
blade height is shown in Fig.11a.The locations of pressure
and suction surface of the adjacent blades are indicated as
PS and SS in this Figure. It is observed that very close to
the blade locations the relative flow angle drops at
operating points A and C where as in the blade passage the
flow angles are higher than the blade angle. The design
blade outlet angle at shroud is 58.5 deg. At operating point
A, the flow angle is higher than blade angle by about 8
degrees and at design point the flow angle is slightly higher
than the blade angle. The difference in the flow angle and
the blade angle represents the slip. It shows the slip
increases from operating point C to A. At the operating
point it is observed that the flow angle is lower than the
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International Journal of Scientific & Engineering Research, Volume 4, Issue 2, February -2013
ISSN 2229-5518
blade angle by about 8 deg. However it is seen from
Fig.11b, the absolute flow angle decreases from surge point
to choke point. This is because as the operating points
moves from A to F the mass flow rate increases and the
pressure ratio drops. The reduction in pressure ratio
indicate the drop in work done by the impeller, hence the
tangential component of absolute velocity at impeller exit
reduces. As the mass flow increases, the meridional
component of absolute velocity increases. The combined
effect is reduction in absolute flow angle at operating point
F. The variation in absolute flow angle is very predominant
as the mass flow rate is increased. This will have a large
effect on the diffuser producing large negative incidence.
The typical change in flow angle at the blade locations will
have large influence on the diffuser flow as the number of
diffuser blades are fraction of number of impeller blades.
The flow angle variation very close to the blades is very
large due to the tip leakage flows, which is not observed at
50 % of blade height.
Figures 11c-11d represents flow angle variation at impeller
exit at 50% of the blade height for same operating points
considered in the previous case. Here the relative flow
angle variation with respect to operating point shows the
flow angle increases with decrease in mass flow rate. But
the average value of flow angle is higher than the blade
angle at operating points A and C.
The design blade angle at 50% of blade height is 52.6 deg.
The absolute flow angles remain constant over the blade
pitch for a given operating point except close to the blade
locations. The variation in the flow angle near the blade
locations are smaller than the variation at 95% of the blade
height, indicating the influence of tip clearance flow is
marginally felt.
Fig. 11c. Relative flow angle at 50%
blade height for outlet of impeller
Fig. 11a.Relative flow angle at 95%
blade height for outlet of impeller
Fig.11d. Absolute flow angle at 50%
blade height for impeller outlet
Fig. 11b. Absolute flow angle at 95%
blade height for impeller outlet
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4.5 Relative Mach number and velocity variation in
flow channel
To study the flow behavior inside the impeller channel,
different meridional planes namely Inlet, P1, P2, P3, P4, P5,
P6 and outlet are considered. Among these planes, four
planes namely P1, P4, P6 and impeller outlet planes are
used to represent the variations of relative velocities for
clarity. The representation of the planes is shown in Figure
12a and the relative Mach number plot for different flow
conditions at the different planes is shown in Figure 12b. It
is observed from Fig.12b that the relative Mach number at
impeller outlet is uniform and increase from surge to choke
flow conditions. At inlet plane, the relative Mach Number
for each flow condition increases from hub to tip as the
blade speed increases and inlet absolute velocity is axial
and uniform. Within the blade channel, at plane P4 and P6,
the relative velocity is not uniform.
Fig.13a.Relative velocity variation at operating point -C
In this figure relative velocity is being plotted over two
blade pitch so that at any location within the blade channel
one main blade and one splitter blade are present. In each
figure P and S represents pressure and suction surfaces of
the adjacent blades and hub and shroud locations are also
marked.
Fig. 12a. Meridional planes
Fig.13b.Relative velocity variation at operating point –A
It is observed for the impeller outlet plane the relative
velocity decreases from suction surface to pressure surface
at all meridional locations except at shroud region
indicating the flow behaves like a potential flow. It is also
seen that the relative velocity in the circumferential as well
as in the meridional directions remains constant and do not
show any variation. However the magnitude of the relative
velocity increases from surge to choke operating point. It is
also seen that there is no jet-wake pattern indicated in some
of the literatures.
This shows the geometry of the
meridional shape plays an important role in generating
such (jet-wake) flow.
Fig.12b.Relative Mach number contours
The variations of relative velocity normalized with respect
to tip speed for the impeller outlet plane at different
operating points are shown in Figs.13a-13c.
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8
7 NOMENCLATURES
C
absolute velocity (m/s)
P
pressure (Pa)
W
relative velocity (m/s)
U
impeller tip velocity (m/s)
Mass flow parameter = m √ (T01/ T01ref) / (P01/ P01ref)
y/t
normalized distance from suction to pressure surface
z/b normalized distance from hub to
shroud
Greek symbols
α
β
absolute flow angle( deg.)
relative flow angle(deg.)
Subscripts
1
impeller inlet
Fig.13c.Relative velocity variation at operating point- F
It is inferred that typical flow pattern namely jet-wake as
observed in radial flow impellers are absent in the case of
mixed flow impellers.
2
3
o
s
impeller outlet
diffuser outlet
total quantity
static quantity
8 REFERENCES
5 CONCLUSIONS
There is close match between experimental and CFD
results. The estimated pressure ratio (4.50) is slightly lower
than design pressure ratio (4.55) due to the inaccuracy in
the loss models used in the design. The performance at
speed higher than design speed (105%) shows a maximum
mass flow rate that can be allowed through the impeller is
2% of design mass flow rate. The compressor at design
speed has roughly about 37% surge margin.
The surface pressure distribution indicate the blade loading
increases from hub to shroud at a given mass flow rate and
the blade loading increases as the operating point moves
from choke to surge. The local static pressure on the blade
surface increases from inlet to outlet showing continuous
pressure rise.
Flow angle at impeller outlet is uniform from hub to shroud
at design point and shows variations at choke and surge
flow conditions. Velocity
within
the
channel is
uniform and the conventional jet-wake pattern is not
observed in mixed flow compressor that is prominent in
radial compressor.
[1]
Austin King, J. and Edward, G.,1942. “Performance
Characteristics of Mixed flow impeller and vaned diffuser with
several modifications”, NACA-WR-E197.
[2]
Engin T., 2008. ”study of tip clearance effects in centrifugal fns
with unshrouded impellers using computational fluid dynamics”.
Proc.IMech vol.220 partA: J. power and energy, pp599-610.
[3]
Hah, C., 1988. “Application of viscous flow computations for the
aerodynamic performance of a backswept impeller at various
operating conditions”, J. of turbomachinery, Tran. of ASME,
vol. 110, pp 303-311.
[4]
John D. Stanitz,, 1952. “One Dimensional compressible flow in
Vanless Diffusers of radial and Mixed-flow centrifugal
compressors including Effects of friction heat transfer and area
change.” NACA TN 2610.
[5]
Krain.H and Hoffmann.B,, 2008. ”Flow study of a Redesigned
H- Pressure-Ratio Centrifugal Compressor”, J. of propulsion
and Power, Vol.24, No.5, pp.1117-1123.
[6]
Patrik, Rautaheimo, P., and Salminen, J., 2003. “Numerical
simulation of the flow in the NASA low-speed centrifugal
compressor”, International Jl. of turbo and jet engines, Vol. 20,
pp 155-170.
[7]
Pavel E. Smirnov and Thorsten Hansen., 2007. “ Numerical
simulation of turbulent flows in centrifugal compressors stages
with different radial gaps”, proceedings of GT2007-27376,
ASME Turbo Expo 2007, power for land , sea and air, may
14-17,Montreal, Canada, pp1-10.
[8]
Ramamurthy, S. and Murugesan, K., 1996. “An analytic
approach to design centrifugal impeller geometry”, Proceedings
of NCABE 96.
6 ACKNOWLEDGEMENTS
The authors would like to thank The Director –NAL for the
his approval for publishing this paper and V. Nagarajan ,
HOD, NTAF, Mr.M.N. Varadarajan, Janakirama Reddy,
Rajesh Yemandi of CLOCTER for their valuable support
during the experiments.
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