Amano R.S., Sunden B. (Eds.) Computational Fluid Dynamics and Heat Transfer: Emerging Topics
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96 Computational Fluid Dynamics and Heat Transfer
b/C
a
= 0.639 b/C
a
= 1.460b/C
a
= 0.973b/C
a
= 0.973
(experiment)
TIF
Figure 3.22. Total pressure loss contour at x/C
a
=0.9.
0.55
0.60
b/C
a
= 0.639 b/C
a
= 0.973 b/C
a
= 1.460
0.60
0.80
0.75
0.75
0.70
0.65
0.55
Figure 3.23. Total pressure loss contour at x/C
a
=1.0.
Thisfigurealso showsthatthe cornervortexatthetipofthebladeis notverystrong
and cannot be clearly observed in the computations.
The total pressure losses C
po
in Figures. 19, 20, and 21 further confirm the
aforementioned conclusions that corner vortices occur on both the hub and
the casing suction-side corners. The computations for the case of b/C
a
=0.973
are compared with the experiment [44] and are shown in Figure 3.19. The mea-
suredC
po
valuesofthefirstlineintheexperimentarethesameasthecomputations.
Itisshownthatthe computationsareinfairagreementwiththeexperiments,except
attip andhub regionswherethe computationsshow alargervortexregion thanthat
shown by the experiment.
The influence of the losses due to the pitch–width variation can be seen by
comparingFigures3.22,23, and24fordifferentb/C
a
.Forthecasesofb/C
a
=0.973
and 1.46, the high-loss regions from both tip and hub corners near the suction side
are developed. These losses are caused due to the corner vortices and the suction-
side pressure characteristics. The end wall boundary layer is very thin near the
pressure side within the blade passage. The pressure-side boundary layer and the
suction-side boundary layer meet after the flow passes the blade trailing edge, as
shown in Figure 3. 20. It is also shown that the total pressure losses C
po
increases
withtheincreaseinb/C
a
.Thelosscontourshowsthatthesecondaryflowisstronger
forlargerb/C
a
,anditdevelopsfaster.Thisisbecauseforlargeb/C
a
,theflowcontrol
capacity become worse than that for small b/C
a
. The secondary vortex is easy to
Sunden ch003.tex 27/8/2010 18: 35 Page 97
CFD for industrial turbomachinery designs 97
b/C
a
= 0.639 b/C
a
= 0.973 b/C
a
= 1.460
Figure 3.24. Total pressure loss contour at x/C
a
=1.1.
b/C
a
= 0.639 b/C
a
= 1.460b/C
a
= 0.973
0.02
0.01
0.01
0.01
0.11
0.11
0.12
0.12
0.01
0.03
0.02
0.08
0.08
0.08
0.08
0.08
0.02
0.08
0.06
0.05
0.05
0.03
0.07
0.07
0.06
0.06
0.06
0.06
0.01
0.02
0.02
0.02
0.05
0.01
0.01
0.03
0.03
0.08
0.08
0.09
0.09
0.09
0.04
0.1
0.1
+
4
0.2
0.05
0.07
0.07
0.04
0.04
Figure 3.25. Blade-to-blade Mach number contour at 0.28% height.
develop in the blade channel. For the smallest b/C
a
, the two passage vortices occur
in the upper and lower parts of the blade passage closer to the suction side of the
blade without strong interactions. With the increase in the b/C
a
, the two vortices
start interacting with each other. Owing to the occurrence of the passage vortices,
and their interactions for the large b/C
a
cases, the secondary flow is very strong.
The strong three-dimensional effects dominate the whole passage flow for large
b/C
a
. However, for smaller b/C
a
, it has been found that the flow configuration is
different from those for larger b/C
a
cases. The two vortices occur from lower and
upper parts of the suction side, and they are more confined in the end wall region,
and there remains a two-dimensional flow pattern for a wide blade height range.
The blade-to-blade Mach number contours for the hub boundary layer region
and the pitchandtip boundary layer regions are shown in Figures 3.25, 26, and 27,
respectively, where the Mach number contours present different characteristics for
the boundary region and the main flow region. In the near-hub boundary region, a
smaller b/C
a
does not show a high Mach number region near the suction surf ace.
It seems that the flow acceleratessmoothly along the suction sidefor smaller b/C
a
.
For the cases of b/C
a
=0.973 and 1.460, a small region of a high Mach number
zone is observed close to the middle of the width in the suction side of the blade.
It is shown that a separation zone occurs and expands with the increase in b/C
a
.
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98 Computational Fluid Dynamics and Heat Transfer
b/C
a
= 0.639 b/C
a
= 0.973 b/C
a
= 1.460
0.9
0.1
0.04
0.07
0.12
0.11
0.05
0.08
0.11
0.1
0.09
0.09
0.1
0.05
0.05
0.03
0.07
0.03
0.04
0.05
0.01
0.02
0.03
0.04
0.06
0.02
0.01
0.07
0.05
0.11
0.1
0.09
0.02
0.08
0.05
0.
8
Figure 3.26. Blade-to-blade Mach number contour at 50% height.
b/C
a
= 0.639 b/C
a
= 0.973 b/C
a
= 1.460
0.02
0.03
0.5
0.2
0.06
0.3
0.4
0.7
0.11
0.24
0.13
0.11
0.12
0.04
0.1
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.7
0.08
0.06
0.1
0.1
0.02
0.05
0.02
0.6
0.7
0.05
0.03
0.03
0.09
0.09
0.09
0.09
0.1
0.03
0.11
0.2
0.2
0.1
0.8
0.2
0.1
0.11
0.2
0.1
0.08
0.09
0.1
1
2
Figure 3.27. Blade-to-blade Mach number contour at 99.72% height.
The results show that the blade-to-blade Mach number gradient along the turbine
axial direction increases with the increase in b/C
a
.
The blade-to-blade static pressure coefficient contours near the hub, pitch, and
tip are shown in Figures 3.28, 29, and 30, respectively. It is shown that, due to
thestrongsecondary-flow effect, theminimumpressureoccursinthepassageaway
fromthebladesurface.Alsonotethat,withtheincreaseinb/C
a
,theflowaccelerates
faster in the leading edge region. A clear low-pressure zone occurs on the suction
sideof thebladefor allthe different pitch–widthcases when aflow separationzone
on the blade suction surface.
Figures 3.31, 32, and 33 show the contours of the blade-to-blade total pressure
coefficient distributions in the hub boundary (0.28% height), pitch (50% height),
and tip boundary (99.72% height) regions, respectively. The losses for different
b/C
a
,theplotsstartwiththesamelevelatthesamebladelocation.Thetotalpressure
losses are much larger in hub and tip boundary regions than in the midspan for all
cases. In general, small b/C
a
has small losses for all flow regions. For the smaller
b/C
a
, a small zone of high loss extending from trailing edge can be observed only
Sunden ch003.tex 27/8/2010 18: 35 Page 99
CFD for industrial turbomachinery designs 99
b/C
a
= 0.639 b/C
a
= 0.973 b/C
a
= 1.460
Figure 3.28. Blade-to-blade static pressure coefficient contour at 0.28% height.
−0.8
−0.8
−0.8
−0.8
−0.8
−1
−0.8
−0.8
−0.1
−1
−1.1
−0.9
−0.8
−0.7
−0.6
−0.5
−0.2
−0.3
−0.4
−0.7
−0.7
−0.7
−0.6
−0.6
−0.5
−0.5
−0.4
−0.4
−0.2
−0.3
−0.2
−0.1
−0.1
−1
−0.1
−0.9
−0.9
−0.9
−0.9
−0.9
−0.9
−0.9
−0.9
−1.4
−1.5
−1.4
−1.7
−1.5
−11
−11
−
1.1
−1.7
−1.4
−1.2
−1.3
−1.1
−1.1
−0.1
−0.1
−0.3
−0.4
−0.7
−0.6
−1
−1
−0.09
−0.9
−1
−0.8
−0.08
−0.5
−0.3
−1.8
−1.4
−1.3
−1.3
−1.1
−0.1
−1.2
−1.2
b/C
a
= 0.639 b/C
a
= 0.973 b/C
a
= 1.460
Figure 3.29. Blade-to-blade static pressure coefficient contour at 50% height.
b/C
a
= 0.973
−
+
1
−0.1
−0.2
−0.3
−0.4
−0.5
−0.6
−0.8
−0.7
−0.7
−0.9
−0.8
−0.9
−0.8
−0.8
−
+
0.7
−1
−1.1
−1.1
−1
b/C
a
= 0.639
−0.4
−0.1
−0.6
−0.5
−0.6
−0.6
−0.7
−0.8
−0.7
−0.6
−0.6
−0.6
−0.6
−0.7
−0.8
−0.7
−0.6
−0.6
−0.2
−0.1
−0.5
−0.4
−0.3
b/C
a
= 1.46
−0.3
−0.1
−0.2
−0.3
−0.5
−0.1
−0.8
−0.1
−0.6
−0.8
−0.7
−0.9
−0.8
−
+
4
−1.1
−1.9
−1.8
−1.6
−1.5−1.7
−1.1
−1
−1
−1
−1.3
−1.5
−1.1
−1.6
−1.9
−1.9
Figure 3.30. Blade-to-blade static pressure coefficient contour at 97.72 height.
Sunden ch003.tex 27/8/2010 18: 35 Page 100
100 Computational Fluid Dynamics and Heat Transfer
1.4
1.4
1.3
1.2
1.5
1.5
1.5
1.5
1.3
1.5
1+7
1.4
1.3
1.4
1.5
1.4
1.7
1.6
1.1
1.3
1.6
1.6
1.6
0.9
0.7
0.5
0.4
0.5
0.
6
0.9
0.3
.9
1.3
1.4
1.3
1.3
1.3
b/C
a
= 0.639
0.8
0.9
1.1
1.2
1.5
1
.5
1.5
1
1.5
1.7
1.5
1.5
1.3
1
.1
1.5
1.6
1.6
1.5
1.5
1.5
1.5
1.7
1.8
1.6
1.9
1.7
1.7
0.7
0.7
0.7
1.3
1.5
1.5
1.5
1.5
1.5
1.5
1.4
1
b/C
a
= 0.973
0.8
2.2
2.3
2.4
2.5
2
2
2
1.5
1.8
1.6
1.6
1.7
1.7
1.7
1.4
1.4
1.4
1
2.4
2.5
2.3
2.2
2.2
2.5
2.4
2.7
1.5
1.1
1.3
1.3
1.5
1.5
1.6
1.4
1.5
1.7
1.9
0.9
0.9
1.8
1.4
1.1
1.1
b/C
a
= 1.460
Figure 3.31. Blade-to-blade total pressure loss at 0.28% height.
1.4
1.5
1.5
1.6
1.1
1.4
1.2
1.2
1.1
1.1
1.6
1.2
1.3
1.3
1.3
1.1
0.8
0.9
0.8
0.9
0.9
0.6
1
0.9
0.6
0.9
0.6
0.9
0.8
0.7
1
1.2
1+8
1
1
1
1
1
1
1
1
1.1
0.6
0.6
0.6
+
1
1
1
0.8
0.8
0.8
0.8
0.7
0.9
1+1
20.4
.4
3
2
2
9
3
1
1
1
1
1
2
9
1
2
1
1
1
2
2
22
3
3
1
1
1
0.8
0.8
0.2
2.2
3.5
b/C
a
= 0.639 b /C
a
= 0.973 b/C
a
= 1.460
Figure 3.32. Blade-to-blade total pressure loss at 50% height.
b/C
a
= 0.639
b/C
a
= 0.973 b/C
a
= 1.460
1.7
1.1
1.1
2.2
1.3
1.9
1.6
1.8
1.3
1.2
1.1
1.1
1
1.3
2.2
1.9
1.7
2.4
1.2
1.3
2.4
2.4
2.4
1.3
1.3
1.3
1.3
.8
0.8
0.7
1.8
1.1
1.3
1.4 1.7
1.6
1.1
1.3
1.6
1.7
1.4
0.1
1.2
123
1.7
1.2
1.2
1.2
1.1
0.7
1.2
1.3
0.6
1.8
0.6
0.7 0.8
0.8
0.9
0.9
0.8
0.9
1
.3
1
.2
1
.1
1.1
Figure 3.33. Blade-to-blade total pressure loss at 99.72% height.
Sunden ch003.tex 27/8/2010 18: 35 Page 101
CFD for industrial turbomachinery designs 101
on the tip boundary. Foralarger b/C
a
, there appears a high-loss zone starting from
the trailing edge extending to the upstream of the suction side of the blade.
3.9.2 Flow around centrifuge compressors scroll tongue
Centrifugal compressors utilizeradial change across the impeller toraise gas com-
pressor.Acentrifugal compressor allowsmore diffusionwithin the impellerblades
to raise pressure; thus, centrifugal compressor can produce higher specific work
transfer withinone stagecompared toan axial compressor.Although theefficiency
ofcentrifugal compressoris lower thanthatof axialcompressor atlargevolumetric
flow rate, centrifugal compressor has many applications for moderate- and small-
flow gas compressions. A centrifugal compressor has a shorter axial length with
wider operating range than axial compressors to get the same discharge pressure.
An increasedefficiencyof centrifugalcompressors has beenthe traditional empha-
sis ofthe compressordesign. However, anincreasing operating rangeand part load
efficiency have become more important. Many efforts have been made in research
field to optimize different component of the compressor stage [45–51].
An industrial centrifugal compressor stage consists of three main components:
a rotating impeller, vaned or vaneless diffusers, and a scroll or collector as shown
inFigure 3.34.The impelleradds work togas by increasingits angularmomentum.
Gas static pressure and velocity increase after passing through the impeller.Vaned
andvanelessdiffusersconvertkineticenergyintostaticpressurebydeceleratingthe
fluid.Ascrollisusedforcollectinggasfromdiffuseranddeliveringittoapplication
systemor next stage.The scrollisthe lastcomponentin thecompressionprocess in
asingle-stage compressor.Gasleavesimpeller withlogarithmicspiral shapedue to
the rotation of the impeller.A scroll has two functions: to collect and transport the
fluid into downstream system and to raise the static pressure by converting kinetic
energy into potential energy (static pressure). A scroll design is complicated due
to the effect of the strong three-dimensional swirl flow. Typically, a scroll design
Diffuser
Impeller
Scroll
Figure 3.34. Centrifugal compressor.
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102 Computational Fluid Dynamics and Heat Transfer
Sharp tongue
Leading edge
Scroll discharge
Leading edge
Scroll
(a) (b)
Figure 3.35. (a) Sharp tongue. (b) Scroll tongue structures.
is based on the two-dimensional analysis. Traditionally the emphasis on the scroll
design is mainly on collection and less on diffusion function. Diffusion inside of
scrollismoreeffectiveforthekineticenergyassociatedwiththetangentialvelocity;
this is accomplished by increasing cross-sectional area from scroll tongue to exit,
creating a conical diffuser. But there is an efficiency loss caused by the inability of
the scroll to convert portion of the kinetic energy due to the radial component of
fluid velocity out of the diffuser.This effect is compounded when a vaned diffuser
is used, as vanes create a more radial flow at the vaned diffuser exit. Typically,
thereis atradeoffbetweenthe increasedrecoveryofvaned diffuserand thereduced
recovery of scroll; a different solidity vaned diffuser is used to meet performance
and operating range requirements.
Atascroll tongueasshownin Figure3.35, theflowencountersadividing plane,
so-called tongue, above which the flow exits the compressor and below which the
flowreentersthescroll.Thetongueofascrollislocatedata360degreepoint,corre-
spondingto thejoint ofscrollsmallest area,largestarea,and exit cone.The leading
edge of thescroll tongue is analogous to that ofan airfoil; a sharp leadingedgehas
alessblockageeffectbutissensitivetotheangleofattackasshowninFigure3.35a,
whileawell-roundedleadingedgeisinsensitivetotheflowincidencebuthasalarger
blockage effect as shown in Figure 3.35b. A sharp tongue is very sensitive to the
flowincidence,andcausesaflowseparationatoff-designflows.Themanufacturing
process is very difficult for the construction of a sharp tongue.A rounded tongue,
however, has a larger blockage area than a sharp tongue, which may reduce effi-
ciencyatdesignpoint.Withtheunderstandingoftheinfluenceofthetongue,acom-
pressor with higher efficiency and wider stable operating region can be designed.
For obtaining a better off-design performance, the research on a scroll tongue
was designed with a large cutback angle as shown in Figure 3.35b, which allows
recirculation of about 25% of the stage discharge mass flow inside of the scroll.
Little research has been done to understand flows inside of a scroll, especially
inthetonguearea[52–54].Recentresearch[55–59]foundthatagood scrolldesign
could improve the compressor performance and the operating range. Most scroll
Sunden ch003.tex 27/8/2010 18: 35 Page 103
CFD for industrial turbomachinery designs 103
Figure 3.36. Calculation meshes.
studies have been performed on existing geometries and can be categorized into
twogroups:scrollflowstructureinvestigations[52–55]andflowinteractionstudies
between the scroll and the impeller [55–59]. Large portions of the scroll studies
wereperformedforpumps.Thereislittleinformationavailableforthescrolldesign
and the scroll parametric influencesonthe compressor performance. Recent pump
scrollstudies[59]showedthatthetongueshapeimpactshead,pressurefluctuations,
and noise in a centrifugal pump. Irabu et al. [60] studied the water flow patterns
aroundapumptongueatsmallflows.Thestudyfoundthatflowseparationsoccurred
from both upper and lower surfaces of the tongue, and fur ther reported the flow
field influence due to different tongue geometries and focused on the detailed flow
analysis besides performance test on a large cutback tongue scroll.
Turbulencemodelingandturbulencemodelselectionsarecriticaltotheaccuracy
of the flow field simulations.A larger number of CFD codes for a turbomachinery
analysisusethezeroequationturbulencemodel[1,2].Mostcalculationsshowedthat
zeroequationturbulencemodelsgavereasonableresultsforflowcalculations.Some
researchershavedemonstratedthatotherturbulencemodelscanalsobeusedtogain
reasonableresults[61,62]. Somecomparisons fordifferent turbulencemodelshave
beenpresented[63]. Different turbulencemodelsshoweddifferentadvantages.For
theflowinsideofthecentrifugalcompressorandscroll, differentturbulencemodels
also had been used for flow calculations. There are very limited publications that
address the comparisons of different turbulence models.
Two types of tongues, a sharp tongue (r/b
2
=0) and arounded tongue
(r/b
2
=0.3), were investigated. The calculation meshes are shown in Figure 3.36.
TheCFDstudiesforbothtongueshapeswereperformedbyusingthezero-equation
turbulence model for comparisons of the tongue shape impacts. The CFD analysis
was also performed for rounded shape tongue volute by using the k-ε turbulence
modeltoinvestigatethemodeleffectsoftheturbulenceequations intheCFDsimu-
lations. Inthecurrentstudy, sixflowrateswerecalculated forvoluteswithdifferent
tongues to provide the performance information. The computed performances for
a round tongue with two different turbulence models are shown in Figure 3.37.
Sunden ch003.tex 27/8/2010 18: 35 Page 104
104 Computational Fluid Dynamics and Heat Transfer
φ/φ
0
ψ,η
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.6 0.8 1 1.2 1.4
Algebraic
Algebraic
Experiment
Experiment
K-E
K-E
Figure 3.37. Comparison of the performance curves.
The calculations using the different turbulence models did not produce significant
differences in the results of performance. The results from both two turbulence
models are in good agreement with the experimental data. The calculations show
that only at the flow coefficient near choke, more choke margin occurred than
the experimental data. The calculations also show that the two-equation turbu-
lencemodelsgive slightly higherefficiencyat designflow pointcomparedwith the
zero-equation turbulence model. Furthermore, the k-ε turbulence equations pre-
dicted a lower head coefficient at a larger flow and a lower flow compared with the
zero-equation turbulence model.
However, the rounded tongue has less advantage over the sharp tongue when
a compressor operates at a design flow rate. This is because when a compressor
operates at around the design flow condition, the flow near the sharp tongue area
has little incidence and the flow passes the sharp tongue smoothly. Therefore, the
sharptongueproducessmallblockage,whereastheroundedtongueproduceslarger
blockagewhenthe compressoroperates nearthe designflowcondition.Asa result,
at the design flow condition, the rounded tongue has less pressure recovery when
compared with the sharp tongue case. However, when a compressor operates at
a flow rate larger than the design flow rate, a scroll tongue encounters a positive
incidence. Because a rounded tongue is not sensitive to the flow incidence, inci-
dence losses for a rounded tongue are smaller than those for a sharp tongue. The
rounded tongueproduces betterpressure recovery thanthe sharp tongue.Whenthe
compressor operates at a low flow rate, the advantages of the sharp tongue reduce
withdecreaseintheflowrate. Becausethetonguenegativeincidenceincreaseswith
the decrease in compressor flow rate, the sharp tongue blockage increases faster
thantheroundedtongueblockage.Figure3.40showsthenondimensionalturbulent
Sunden ch003.tex 27/8/2010 18: 35 Page 105
CFD for industrial turbomachinery designs 105
1.040
1.045
1.050
0 50 100 150 200 250 300 350
Circumferential angle (deg)
Cp
Cp volute inlet hub (experimental)
Cp volute inlet hub (Algebraic model)
Cp volute inlet hub (K-E model)
Figure 3.38. Static pressure distribution along volute inlet hub wall.
0.6
0.55
0.5
0.6 0.8 1 1.2 1.4
0.45
0.4
0.35
ψ
r/b
2
= 0.3
r/b
2
= 0.0
φ/φ
0
Figure 3.39. Performance characteristic.
viscosity(µ
T
/µ)distributions obtainedbyemployingthek-ε turbulenceequations.
It can be seen that, for a lower flow rate and design flow rate cases, the turbu-
lent viscosity is uniformly distributed excepted near the tongue area. For the lower
flow rate, wecanseeahigherturbulencelevel behind the diffuser vane.Therefore,
inaflowratenearsurgeanddesign,thezero-equationturbulencemodelcanprovide
a reasonable prediction of flow characteristics.