Article

Aerodynamic effects of forward blade skew in axial flow rotors of controlled vortex design

Abstract and Figures

Comparative studies have been carried out on two axial flow fan rotors of controlled vortex design (CVD), at their design flowrate, in order to investigate the effects of circumferential forward skew on blade aerodynamics. The studies were based on computational fluid dynamics (CFD), validated on the basis of global performance and hot wire flow field measurements. The computations indicated that the forward-skewed blade tip modifies the rotor inlet condition along the entire span, due to its protrusion to the relative inlet flow field. This leads to the rearrangement of spanwise blade load distribution, increase of losses along the dominant part of span, and converts the prescribed spanwise blade circulation distribution towards a free vortex flow pattern. Due to the above, reduction in both total pressure rise and efficiency was established. By moderation of the radial outward flow on the suction side, being especially significant for non-free vortex blading, forward sweep was found to be particularly useful for potential reduction of near-tip loss in CVD rotors. Application of reliable CFD-based design systems was recommended for systematic consideration and control of both load-and loss-modifying effects due to non-radial blade stacking.
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1011
Aerodynamic effects of forward blade skew in axial flow
rotors of controlled vortex design
JVad
,ARAKwedikha, Cs Horváth, M Balczó, M M Lohász, and T Régert
Department of Fluid Mechanics (DFM), Budapest University of Technology and Economics, Budapest, Hungary
The manuscript was received on 6 February 2007 and was accepted after revision for publication on 11 July 2007.
DOI: 10.1243/09576509JPE420
Abstract: Comparative studies have been carried out on two axial flow fan rotors of controlled
vortex design (CVD), at their design flowrate, in order to investigate the effects of circumferential
forward skew on blade aerodynamics. The studies were based on computational fluid dynamics
(CFD), validated on the basis of global performance and hot wire flow field measurements. The
computations indicated that the forward-skewed blade tip modifies the rotor inlet condition
along the entire span, due to its protrusion to the relative inlet flow field. This leads to the
rearrangement of spanwise blade load distribution, increase of losses along the dominant part of
span, and converts the prescribed spanwise blade circulation distribution towards a free vortex
flow pattern. Due to the above, reduction in both total pressure rise and efficiency was established.
By moderation of the radial outward flow on the suction side, being especially significant for non-
free vortex blading, forward sweep was found to be particularly useful for potential reduction of
near-tip loss in CVD rotors. Application of reliable CFD-based design systems was recommended
for systematic consideration and control of both load- and loss-modifying effects due to non-
radial blade stacking.
Keywords: axial flow turbomachinery, controlled vortex design, forward blade skew, forward
blade sweep, circumferential forward skew
1 INTRODUCTION
Rotors of axial flow turbomachines are often of ‘con-
trolled vortex’ design (CVD) [1]. This means that
contrarily to the classic free vortex concept prescribing
spanwise constant design blade circulation, the cir-
culation – and thus, the Euler work – increases along
the dominant part of the blade span in a prescribed
manner. CVD guarantees a better utilization of blade
sections at higher radii, i.e. it improves their contribu-
tion to the rotor performance. By this means, rotors
of high specific performance can be realized, i.e. rel-
atively high flow rate and total pressure rise can be
obtained even with moderate diameter, blade count,
and rotor speed [2,3]. CVD gives a means also for
reduction of hub losses by unloading the blade root
Corresponding author: Department of Fluid Mechanics (DFM),
Budapest University of Technology and Economics, Bertalan
Lajos u.4–6,Budapest H-1111, Hungary. email: vad@ara.bme.hu
[4], and offers a potential to avoid highly twisted blades
[5]. Furthermore, in multi stage machinery, it provides
a strategy to realize an appropriate rotor exit flow angle
distribution [1].
Blade sweep, dihedral, and skew are known as tech-
niques of non-radial blade stacking. A blade has sweep
and/or dihedral if the sections of a datum blade of
radial stacking line are displaced parallel and/or nor-
mal to the chord, respectively [6]. A blade is swept
forward if the sections of a radially stacked datum
blade are shifted parallel to their chord in such a way
that a blade section under consideration is upstream
of the neighbouring blade section at lower radius
[3]. A special combination of dihedral and forward
sweep is referred to as circumferential forward skew
(FSK) [7,8]. In this case, the datum blade sections are
shifted in the circumferential direction, towards the
direction of rotation. By this means, the axial exten-
sion of the unskewed (USK) datum blading can be
retained, the blade mechanics is expected to be more
favourable than in the case of forward sweep alone,
JPE420 ©IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy
1012 J Vad, ARAKwedikha, Cs Horváth, M Balczó, M M Lohász, and T Réger t
and the following aerodynamic benefits, dedicated to
the incorporated forward sweep, can be utilized.
The open literature suggests a general consensus
that forward sweep/skew gives potential for the follow-
ing advantages in the part load operational range (flow
rates lower than design): improvement of efficiency,
increase of total pressure peak, and extension of stall-
free operating range by improving the stall margin
[3,712]. Nevertheless, the research results are rather
diversified regarding the judgment of performance
and loss modifying effects of forward sweep/skew at
flow rates near the design point. In reference [6], it
is pointed out generally that forward sweep near the
tip, i.e. ‘positive sweep’, gives a potential for reduction
of near-tip losses. Based on reference [9], application
of near-tip FSW can be recommended for efficiency
improvement over the operational range near the
design point [3,7,8], suggest that the application of
forward sweep along the entire span is beneficial for
loss reduction and performance improvement. How-
ever, forward sweep reported in references [10] and
[11] and FSK in reference [4] were found to cause the
deterioration of efficiency near the design point. In
reference [12], the reduction of efficiency was estab-
lished for a forward-swept rotor over the dominant
part of the entire stall-free operational range. Back-
ward sweep was reported to be optimal in reference
[13] from the viewpoint of efficiency improvement.
The performance and loss modifying aspects of
forward sweep/skew, which are specific to the indi-
vidual case studies as the above literature overview
suggests, are closely related to the three-dimensional
(3D) features of the blade passage flow [12,14,15].
Such 3D flow features are especially characteristic
for rotors of CVD, due to the spanwise blade circu-
lation gradient and the resultant vorticity shed from
the blade [2]. Although a number of reports are avail-
able on forward-swept and FSK rotors of CVD, e.g.
[4,79,16], no special emphasis is given to simul-
taneous application of CVD and non-radial blade
stacking.
The current paper intends to present a case study
contributing to a more comprehensive understanding
of aerodynamic effects of FSK, CVD, and their combi-
nation, at the design flow rate. For this purpose, two
rotors of CVD, an USK and a FSK one, are aimed to
be compared qualitatively, by means of computational
fluid dynamics (CFD).
2 ROTORS OF CASE STUDY
Rotor FSK under present investigation operates in
the open-type low-speed wind tunnel facility of the
Hungarian Institute of Agricultural Engineering (IAE),
Gödöll˝o, Hungary. The facility and the related custom-
built fan were designed at DFM, and were produced
by Ventilation Works Ltd., Hungary in 2004. The com-
ponents and instrumentation of the facility being
relevant to the present study are shown schematically
in Fig. 1. The main fan characteristics are summarized
in Table 1. Geometrical details of the rotor and out-
let guide vane (OGV) blading are specified in Table 2.
FSK was applied to the rotor blades in order to extend
the stall-free operating range. A virtual image of FSK,
obtained from the CFD technique, and a front-view
photo are presented in Fig. 2. The rotor and OGV
blade sections have C4 profiles [5,17] of 10 per cent
maximum thickness along the entire span, with circu-
lar arc camber lines. Results for a constant rotational
speed of 416 r/min are reported herein. The Reynolds
number, calculated with the blade tip circumferential
speed, the tip chord and the kinematical viscosity of
air at 20 C is approximately 1.074 ×106. The Mach
number which was computed with the blade tip cir-
cumferential velocity and the speed of sound in air
at 20 C is 0.13, and therefore, the flow is considered
incompressible.
Rotor FSK was originated from the virtual rotor
USK of radial stacking line, by shifting the blade sec-
tions of USK in circumferential direction towards the
direction of rotation, without making any modifica-
tions to the USK blade section geometry and stagger
angle distribution. The blade trailing edges (TEs) of
both USK and FSK fit to planes normal to the axis
of rotation. The skew angle in Table 2 is defined as
the angle between radial lines fitted to the TEs of
the datum and the shifted blade sections. The skew
angle is zero at the hub and increases along the span.
By this means, it was intended to avoid any stacking
line blend points, for which increased losses may be
expected [11]. Near the hub, the rotor blade sections
Fig. 1 Experimental facility and instrumentation (the
supporting struts for the nose cone and the hub
are omitted for simplicity)
Table 1 Main fan characteristics
Casing diameter 2000 mm D0.33
Hub-to-tip ratio ν0.600 D M FSK 0.27
Rotor blade count N12
OGV blade count 11
Tip clearance τ0.036
Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE420 ©IMechE 2007
Aerodynamic effects of forward blade skew in axial flow rotors of CVD 1013
Table 2 Fan blading geometry
Rotor OGV
Fraction of span σ0 hub 0.25 0.50 mid 0.75 1.00 tip 0 hub 0.25 0.50 mid 0.75 1.00 tip
Solidity c/s1.38 1.01 0.89 0.80 0.72 1.93 1.50 1.32 1.19 1.18
Camber angle () 20.3 17.3 16.8 15.8 15.3 60.0 51.5 49.2 47.7 50.1
Stagger angle ()33.9 32.1 30.7 29.9 29.4 57.0 61.7 66.0 68.4 70.0
Skew angle () 0.0 0.0 0.3 1.6 3.5
Measured from circumferential direction.
Fig. 2 Virtual axonometric image and front-view photo
of FSK
are enlarged. This is favourable from the mechanical
point of view, and results in an aerodynamically ben-
eficial positive sweep and positive dihedral [6]atthe
blade root, as potential means of hub loss reduction.
In the following, ˆ denotes mass-averaging for ψid2 ,
ψ,ω, and ϕr, and area-averaging for ϕ. The USK rotor
is of CVD, i.e. the designed blade circulation increases
along the span, according to the following power
law [2,3]
ˆ
ψid 2 D(R)=ˆ
ψid 2 D ) ·R
νM
(1)
The CVD design concept was chosen in order to
make possible the preliminary design of each elemen-
tal blade cascade along the entire span using the same
cascade measurement data basis [17], and to reduce
blade twist and maintain chord length nearly constant
with span, for simplicity in manufacturing.
3 EXPERIMENTS
The experimental facility at IAE is not a test rig dedi-
cated for turbomachinery R&D; the FSK rotor under
investigation is its auxiliary unit. Consequently, the
facility is in absence of instrumentation expected in
turbofan studies. Nevertheless, it had been equipped
with an ad hoc, on-site measurement setup (Fig. 1),
in order to establish an experimental database for
validation of the CFD tool.
Characteristic curve and efficiency measurements
were carried out on the fan stage. The flow rate was
measured using the inlet bellmouth as an inlet cone,
calibrated on the basis of detailed velocity measure-
ments made in the test section. The total pressure
rise was considered as the difference of static pres-
sures measured downstream of the OGV and upstream
of the rotor in the annulus of constant cross-section
(equal upstream and downstream dynamic pressures
were assumed in the annulus). The differential pres-
sures playing role in the flow rate and total pressure
rise measurements were determined using Betz liquid
micromanometers. The constancy of rotor speed was
checked by means of a laser stroboscope.
The overall efficiency ηwas established as the ratio
between aerodynamic performance (product of vol-
ume flow rate and total pressure rise) and electric
power input to the frequency converter, measured by
a clamp meter. Although ηinevitably includes the
losses of the speed control unit, the electric motor, the
belt drive, and the bearings, it gives basic qualitative
information on the energetic behaviour of the fan.
Detailed flow velocity measurements were carried
out at the near-peak-efficiency point of =0.33, cor-
responding to the design flowrate. The velocity field
was measured using hot wire anemometry, in constant
temperature anemometer (CTA) mode, by means of a
DANTEC 9055P0511 type cross wire probe connected
to DISA 55M type CTA bridges equipped with servo
loop.The mobile CTA system is outlined in Fig. 1. vx1as
well as vx2and vu2 were measured along the radial span
having an axial position of 74.5 and 126.6 per cent
midspan axial chord, respectively, where the zero axial
position indicates the leading edge (LE) at midspan.
The radial traverses were carried out from 0.025 S
to 0.975 S, with resolution of 0.025 S. The sampling
rate provided 120 measurement readings per blade
passage at each radius along the circumference. The
measurements were taken at each radial position cov-
ering the progress of each blade passage 104 times. For
the CTA-based data presented herein, the velocity dis-
tributions representing the individual blade passages
have been circumferentially averaged.
Table 3 summarizes the pessimistically estimated
relative standard uncertainty of the measurement-
based quantities presented in the paper, at 95 per cent
confidence level, listing the most significant uncer-
tainty sources. The uncertainty analysis has been
carried out using the ‘root sum square’ method, follow-
ing the methodology in reference [12]. Any subvalue
JPE420 ©IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy
1014 J Vad, ARAKwedikha, Cs Horváth, M Balczó, M M Lohász, and T Réger t
Table 3 Experimental uncertainty
Quantity Source of uncertainty U(%)
/DUncertainty of inlet cone calibration ±1.5
Variation of operating state ±1.0
Uncertainty of differential pressure measurement ±0.5
/DOverall ±2.0
/DVariation of operating state ±1.0
Uncertainty of differential pressure measurement ±0.5
/DOverall ±1.2
η/η
DUncertainty of volume flowrate ±2.0
Uncertainty of total pressure rise ±1.2
Uncertainty of electric power measurement ±1.0
η/η
DOverall ±2.5
σUncertainty of measurement of endwall relative position ±0.5
ˆϕ1,ˆϕ2,ˆ
ψid Uncertainty of adjusted volume flowrate ±2.0
Angular misalignment ±2.0
Temperature and pressure variation ±1.4
Uncertainty of velocity calibration ±1.4
Linearization error; voltage signal processing and A/D board resolution limits ±0.7
ˆϕ1,ˆϕ2,ˆ
ψid Overall ±3.5
of Uin the table is not necessarily the error due to the
related uncertainty source in itself but the uncertainty
propagating due to this error (e.g. the Usubvalue
specified for the differential pressure measurement
for /Dis not the measurement uncertainty of the
manometer in itself). The overall uncertainties of the
quantities presented herein are taken as the square
root of sum of squares of Usubvalues. The uncertainty
is generally higher than expected in turbomachinery
studies [8], due to the ad hoc measuring technique
and to the non-laboratory environmental conditions.
The overall measurement uncertainty ranges are indi-
cated by error bars in the diagrams in the vicinity of
the measurement data points.
4 CFD TECHNIQUE
The flow fields in USK and FSK were simulated by
means of the commercially available finite-volume
CFD code FLUENT [18]. Referring to references [7], [8],
[16], and [19] reporting on computations for swept and
leaned fan and compressor rotors, the standard kε
turbulence model [20] has been used. The enhanced
wall treatment of FLUENT was applied, incorporat-
ing a blended model [21] between the two-layer
model and the logarithmic law of the wall. Among the
two-equation turbulence modelling options built into
FLUENT, this technique was found to give the most
reasonable agreement with the measurement results
presented later.
Taking the periodicity into consideration, the com-
putations regarded one blade pitch only. A typical
computational domain is presented in Fig. 3. The
domains extend to approximately 8 and 3.5 midspan
axial chord lengths upstream and downstream of the
rotor blading in the axial direction, respectively. The
Fig. 3 Computational domain for FSK (the casing is
hidden for clarity)
inlet face is a sector of the circular duct with 30central
angle. Downstream of the inlet face, sectors of the
steady inlet cone and the rotating hub with one blade
in the middle of the domain are included for both types
of blading.
At the inlet face, a swirl-free uniform axial inlet con-
dition corresponding to the actual flow rate has been
prescribed. The inlet turbulence intensity has been
set to 1 per cent, and the casing diameter was taken
as the hydraulic diameter for the calculation of the
turbulence length scale. Utilizing the features of the
annular cascade configuration, boundary conditions
of periodicity were applied. A zero diffusion flux con-
dition has been used for all flow variables at the outlet
boundary (outflow condition in FLUENT [18]).
Taking [19,22] as preliminary references, structured
hexahedral mesh has been developed for the entire
computational domain. This meshing technique is felt
promising from the viewpoint of computational accu-
racy. Furthermore, it offers a means to reduce the
computational cost by moderating the cell number.
About 50 per cent of the cells are located in the
refined domain in the vicinity of the blade. Taking
up the challenge of the relatively complicated blade
geometry, due to skew above midspan and LE sweep
Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE420 ©IMechE 2007
Aerodynamic effects of forward blade skew in axial flow rotors of CVD 1015
Fig. 4 Finer mesh for FSK near the LE, TE, and tip
near the hub, the domain consists of 31 blocks. Fig. 4
shows representative segments and views of the mesh
for FSK near the LE, TE, and tip. An O-type mesh topol-
ogy has been built around the LE and TE, while H-type
topology is applied to the entire rotor blade passage.
Figure 5 presents a detail of the mesh topology in the
tip clearance region.
The equiangle skewness of a cell is defined as the
maximum value of the ratio of actual and possibly
highest deviation from the optimum angle, consider-
ing each vertex [18]. The grid design ensures that 99 per
cent of the cells have equiangle skewness less than 0.7,
and the maximum skewness value is 0.82. The highest
skewness values appear near the LE and TE. Over the
dominant part of the SS and PS, the skewness is less
than 0.25.
During the computations, the majority of y+values
fell within the range of 30–100, fulfilling the require-
ments of the applied wall law. The discretization of the
convective momentum and turbulent quantity fluxes
were carried out by the Quadratic Upstream Inter-
polation for Convective Kinematics (QUICK) method.
Fig. 5 Mesh topology in the tip clearance region
Typical computations required approximately 3000
iterations. The solutions were considered converged
when the scaled residuals [18] of all equations were
resolved to levels of order of magnitude of 106.
4.1 Grid sensitivity studies
Four discretization levels were used for the compu-
tation. Taking the ‘coarse’ mesh consisting of about
204.000 hexahedral cells as a basis, nearly uniform
refinement in axial, pitchwise, and spanwise direc-
tions resulted in the ‘mid’, ‘finer, and ‘finest’ meshes
(about 301.000, 494.000, and 694.000 cells, respec-
tively). The finer mesh, forming the basis of CFD
results presented in the paper, consists of 45 nodes
along the span. Clearance meshes resolved in span-
wise direction by 5, 9, and 17 nodes were tested, taking
the finer mesh as a basis. Application of nine nodes
in the clearance was concluded to be necessary, but
further refinement was found to be needless for the
fidelity of the numerical solution. For the finer mesh,
the outer domain (H-mesh) consists of 203, 27, and
54 grid nodes in axial, circumferential, and spanwise
directions, respectively.
The ideal total pressure rise was found to be the most
sensitive indicator of dependence of the numerical
solution on discretization. Figure 6 presents the ˆ
ψid 2
data computed for FSK at the design flow rate using
the four discretization levels. The grid-independency
of results based on the finer mesh is achieved on an
acceptable level from the aspect of present studies.
The computational data presented from this point
onwards are based on the finer mesh numerical
results.
4.2 Validation analyses
Figure 7 shows the measured spanwise ˆϕ1,ˆ
ψid 2, and
ˆϕ2distributions established on the basis of CTA mea-
surement data for the design point. The experimental
data are compared in the figure with the distributions
Fig. 6 Influence of overall mesh refinement on the
numerical solution
JPE420 ©IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy
1016 J Vad, ARAKwedikha, Cs Horváth, M Balczó, M M Lohász, and T Réger t
Fig. 7 Measured and computed flow details for FSK.
Black dots: measurements, lines: CFD
computed for FSK at the axial positions of the
measurements.
The ˆϕ1diagrams show the approximate realization
of the uniform axial rotor inlet condition used in
blade design. The computed ˆϕ1data fall below the
measured values near the hub, and the related ‘dis-
placement effect’ results in increased computed axial
velocity above midspan. The discrepancy of the near-
hub data is dedicated to the difference between the
realized and modelled inlet geometries, with special
regard to the inlet cone shape. Although the simula-
tion considers an inlet nose cone with smooth surface,
the inlet cone has eventually been assembled from
conical segments, as seen in Fig. 2, for manufacturing
simplification being accepted for industrial fans. The
edges appearing at the connection of the segments
act as turbulence generators, refreshing the hub inlet
boundary layer otherwise being thickened.
The rotor inlet axial velocity underpredicted by CFD
leads to higher flow incidence and blade load (lift)
below midspan. Considering nearly unchanged free-
stream relative velocity w, the increased blade lift of
an elemental cascade leads to increased outlet swirl
and ideal total pressure rise, according to the following
classic approximate relationship [5,11,17], assuming
swirl-free inlet far upstream
c
sCL2ˆ
vu2
ˆ
w
(2)
Just the opposite tendency, i.e. decreased incidence,
lift, outlet swirl, and ideal total pressure rise is expected
above midspan where the rotor inlet axial velocity
is overpredicted in comparison with the measure-
ments. The trends explained above appear in the
ˆ
ψid 2 plots where the computed data are higher and
lower than the measurement-based ones below and
above midspan, respectively. The ‘theoretical’ ˆ
ψid 2
distributions specified in Fig. 7, calculated from 20
to 80 per cent span using the model described in
Appendix 2, correlate fairly well with the CFD as
well as with the measurement-based ˆ
ψid 2 diagrams.
This confirms the physical relevance and consistency
of both the measured and computed ˆϕ1,ˆ
ψid 2, and ˆϕ2
data sets.
Besides the above described incidence effect,
another reason for the discrepancies above midspan,
especially near the tip, is the limited capability of the
applied turbulence model. However, even with the
presence of the incidence effect, the relative differ-
ences between the computed and measured ˆ
ψid 2 and
ˆϕ2data reported here do not exceed, up to 90 per
cent span, the maximum differences valid for a rep-
resentative forward-skewed fan (AV30N fan, 30FSK)
studied in references [7] and [8] involving standard
kεmodelling. It should be noted that the validity of
the CFD technique in references [7] and [8] has been
accepted for widespread investigation of CVD rotors
with non-radial blade stacking.
All of the qualitative features judged to be essential
for the validity of the CFD tool on the basis of refer-
ence [3] – i.e. the overturning (increased ˆ
ψid 2)near the
rotating hub; the spanwise increase of ideal total pres-
sure rise, fitting to the CVD concept [2]; the peak in
ˆ
ψid 2 near the blade tip due to the presence of high-
loss fluid; and the decrease of swirl near the casing
due to the underturning effect of the stationary cas-
ing wall and the leakage flow – are resolved by the
computation.
The validity of the CFD method enables the rep-
resentation of the following trends observed in the
measured ˆϕ2data: axial velocity reduction near the
blade root due to the hub boundary layer; increasing
Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE420 ©IMechE 2007
Aerodynamic effects of forward blade skew in axial flow rotors of CVD 1017
axial velocity along the dominant part of span, due to
the CVD concept [2,16]; and velocity defect near the
casing, due to the presence of high-loss fluid as well
as the casing boundary layer and leakage flow. The ˆϕ2
values below midspan and the predicted location and
value of maximum axial velocity are in fair agreement
with the experiments.
The measured and computed characteristic and effi-
ciency curves are shown in Fig. 8. CFD has been
calculated on the basis of the difference between
the computed mass-averaged static pressures at the
rotor outlet and inlet CTA measurement locations in
the annulus. The total pressure and flow coefficient
data are normalized by the corresponding values of
the measured FSK design point (D M FSK =0.27, D=
0.33). ηCFD was calculated as the product of com-
puted global total pressure rise and volume flow rate
data divided by the computed shaft power input. The
efficiency data have been normalized by appropriate
reference values taken at the design flow rate. Polyno-
mial trend lines have been fitted to the data points in
the figure.
The [D,D M FSK] design point and the slope of
the M FSK() curve near the design flow rate are
fairly well captured by the simulation. The measured
and computed trends of efficiency variance from the
Fig. 8 Measured and computed global performance
curves
design point towards moderately lower flow rates are
also in fair agreement.
5 COMPARATIVE SURVEY
5.1 Comparison of USK and FSK performance
curves
Figure 8 offers a comparison between the performance
curves computed for USK and FSK. Despite the limited
capability of the applied turbulence model at lower
flow rates, the computed () curves represent the
following well-known qualitative features dedicated
to forward sweep/skew: (a) if no blade correction is
applied for retaining the original Euler work, is
reduced near the design flow rate [4,7,8,12,14,16],
(b) the total pressure peak is shifted towards lower flow
rates, and (c) is improved at flow rates considerably
lower than the stall margin of the rotor with radially
stacked blades [3,11]. The computed η() plots show
that the deterioration of total efficiency is less drastic
for FSK when throttling from the design flowrate.
The total efficiency computed for FSK at the design
point falls below the value for USK. This observa-
tion, fitting to former experiences in references [4] and
[1012], is the aspect provoking the discussion in the
following sections.
5.2 Design flowrate: pitchwise averaged data
Figure 9 presents the spanwise distribution of pitch-
wise averaged values for the dimensionless rotor inlet
and outlet axial velocities as well as radial velocity,
ideal total pressure rise, and total pressure loss coeffi-
cient at the outlet. The inlet (‘1’) and outlet (‘2’) planes
have the axial position of 20.0 and 113.0 per cent
midspan axial chord, respectively, where the zero axial
position indicates the LE at midspan.
As the figure suggests, the applied blade skew has
an influence on the rotor inlet flow field: the inlet axial
velocity for FSK is increased near the tip and is reduced
at lower radii, as can be observed for FSK rotors in ref-
erence [4]. The outlet axial velocity is increased below
midspan for FSK. The difference in radial rearrange-
ment of fluid for USK and FSK, i.e. radially inward
dominant flow for FSK [4,7], is visible on the outlet
radial velocity plots. As the ideal total pressure rise
and axial velocity plots show, FSK performs increased
and decreased Euler work compared to USK below and
above midspan, respectively. Such trend appears in
reference [7] as well (AV30N fan). The Euler work at
the tip is reduced due to non-radial blade stacking, as
was observed in [11].
Figure 9 presents also the ˆ
ψid 2 D and ˆϕ2D distribu-
tions that were determined as outlined in Appendix 2.
These distributions indicate the increase of ˆ
ψid 2 D and
JPE420 ©IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy
1018 J Vad, ARAKwedikha, Cs Horváth, M Balczó, M M Lohász, and T Réger t
Fig. 9 Pitchwise averaged data. White dots: USK, black
dots: FSK
ˆϕ2D along the span due to the CVD concept. They
served as a basis for the preliminary design of the rotor
blade sections further from the annulus walls. Con-
sidering the non-uniformity of CFD-predicted axial
rotor inlet condition, which differs from that used
in the design concept, the agreement between the
design and USK distributions is fair farther from
the endwalls. However, increased discrepancy can be
observed between the design and FSK distributions.
Although the total pressure loss is reduced near the
tip, it is increased over the dominant part of span due
to skew. The same tendency was reported in reference
[11] for a rotor with forward sweep at the tip.
The above tendencies will be explained in the fol-
lowing section, by means of analysis of the detailed
flow field. Rotor inlet and outlet flow maps will be pre-
sented. Furthermore, the flow field will be surveyed at
20 and 90 per cent span, being two representative loca-
tions where significant differences occur in the fluid
mechanical behaviour of USK and FSK (Fig. 9).
5.3 Design flowrate: pitchwise resolved data
Figure 10 presents the maps of ideal total pressure rise,
axial and radial velocities, and total pressure loss coef-
ficient at the rotor outlet. The regions downstream of
the SS and PS, separated by the blade wake zone, are
indicated by appropriate labels. These data reflects
the trends seen in Fig. 9. For USK, spanwise increase
of ψid 2 dominates along the span, according to the
CVD concept based on equation (1). The spanwise
gradient of Euler work and blade circulation results
in increasing axial velocity along the dominant part of
the span according to the physical concept described
in Appendix 2, and in vortices shed from the TE. The
TE shed vorticity induces radially inward and outward
flow on the PS and SS, respectively, as observed also in
references [2] and [3].
Circumferential FSK causes substantial changes in
the 3D blade passage flow structure.The spanwise gra-
dient of ψid 2 is reduced for FSK, for reasons explained
later. This trend was observed also in references [4]
and [7]. Based on the physical principle expressed in
equation (7) in Appendix 2, the moderation of span-
wise ψid 2 gradient causes the moderation of spanwise
variance of ϕ2. The theoretical ˆϕ2plots in Fig. 9, com-
posed as described in Appendix 2, and correlating
fairly well with the CFD data, justify this physical trend.
The reduction of d ˆϕ2/dRcorresponds to an increase
and a decrease of ϕ2below and above midspan,
respectively, as was found also in references [4] and
[79]. According to continuity, this yields the domi-
nance of inward flow in terms of pitchwise averaged
radial velocity (negative ˆϕr2 values for FSK in Fig. 9),
corresponding to the amplification and the attenua-
tion of radially inward and outward flow on the PS
and SS, respectively. The moderation of d ˆ
ψid 2/dR,
Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE420 ©IMechE 2007
Aerodynamic effects of forward blade skew in axial flow rotors of CVD 1019
Fig. 10 Outlet flow maps. Left column: USK, right
column: FSK
i.e. reduction of spanwise blade circulation gradient,
results in the attenuation of TE shed vorticity [2,5]
for FSK, also contributing to the moderation of radial
outward flow on the SS.
The mechanism by which FSK attenuates the SS
radial outward flow is demonstrated in Fig. 11. Due to
FSK, the isobars in the decelerating region are inclined
‘more forward’ for FSK than for USK. Therefore, the
local radial outward flow is moderated, the flow is
guided ‘more inward’ for FSK on the SS. Such radial
flow controlling effect has been described qualitatively
in reference [9].
The moderation of d ˆ
ψid 2/dRdetected for FSK is
explained as follows. Figure 12 shows the axial velocity
and ideal total pressure rise maps at the rotor inlet.
The upstream regions where the forward effect of SS
Fig. 11 Distribution of static pressure coefficient Cpon
the SS Left: USK, right: FSK
and PS phenomena can be detected are indicated
by appropriate labels. A zone of pronounced suc-
tion effect can be observed upstream of the SS of
the near-tip region of FSK, indicated by increased
axial velocity and counter-swirl compared with USK.
Upstream of the PS of FSK, locally reduced axial veloc-
ity and increased swirl appear, compared with USK.
Pitchwise-averaging points out that ˆϕ1(Fig. 9) and
the Euler work are higher for FSK near the tip at the
rotor inlet. This is suggested also by the generally
increased ψid and ϕdata near the FSK LE in Fig. 13.
The reason for the above-mentioned is that the near-
tip part of the forward-skewed blade protrudes into
the upstream relative flow field, and carries out work
in advance compared to the blade sections at lower
radii. According to the conservation of mass at the pre-
scribed design flowrate, increase of inlet axial velocity
near the tip results in the reduction of inlet axial veloc-
ity at lower radii of FSK, as was already indicated in
Fig. 9. The reduced axial velocity results in increased
flow incidence angle, manifesting itself in increased
lift, i.e. increased depression and overpressure on the
SS and PS, respectively. This is illustrated in the Cp
Fig. 12 Inlet flow maps. Left column: USK, right
column: FSK
JPE420 ©IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy
1020 J Vad, ARAKwedikha, Cs Horváth, M Balczó, M M Lohász, and T Réger t
Fig. 13 Flow characteristics at 90 per cent span
plots of Fig. 14. As equation (2) suggests, the higher lift
being valid for FSK at lower radii potentially leads to
increased Euler work and blade section performance.
Indeed, as Fig. 14 indicates, FSK performs higher ideal
total pressure rise and axial velocity at lower radii,
compared with USK, as was suggested already in Fig. 9.
Figure 13 shows increased loss on the SS of FSK
near the tip, for the following presumed reason. Cir-
cumferential FSK results in positive sweep [6] near
the tip, with leakage loss-reducing effects anticipated,
but inevitably also in negative dihedral, i.e. acute
angle between the suction surface and the casing
wall. As presumed on the basis of reference [6], nega-
tive dihedral results in increased near-tip and leakage
losses. The unfavourable effect of negative dihedral
appears to dominate over the favourable effect of pos-
itive sweep from the viewpoint of losses near the tip,
although the tip sweep angle is considerably larger
than the tip dihedral angle (approximately 22and
13, respectively).
As the ω2plots in Fig. 10 suggest, blade sections of
FSK away from the tip also have increased loss on the
SS. This is mainly due to the increased flow incidence
Fig. 14 Flow characteristics at 20 per cent span
angle and the resultant higher adverse pressure gradi-
ent. The increase of losses further from the endwalls
in a rotor of forward-swept tip was also discussed in
reference [11] to the unfavourable conditions in the
SS boundary layer.
6 SUMMARY AND CONCLUSIONS
Comparative CFD studies have been carried out on
two rotors – USK and FSK – at the design flow rate,
in order to investigate the aerodynamic effects of
CVD and circumferential FSK, without geometrical
correction of the elemental blade cascades of the
skewed blading. Preliminary studies were published in
reference [23].The results are summarized as follows.
1. The studies indicated that the circumferentially
forward-skewed blade tip carries out work on the
incoming fluid in advance compared with the blade
sections at lower radii, due to its protrusion into
the upstream relative flow field. This results in
increased and decreased inlet axial velocities near
the tip and at lower radii, respectively.
Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE420 ©IMechE 2007
Aerodynamic effects of forward blade skew in axial flow rotors of CVD 1021
2. The decreased axial velocity at lower radii leads to
increased incidence, lift, and blade performance.
Such uploading below midspan, coupled with
unloading above midspan due to sweep, reduces
the spanwise gradient of Euler work. Consequently,
the blade circulation and axial velocity distribution
prescribed along the span by the CVD concept
tends towards that of a free vortex flow pattern. This
results in the decrease of global ideal total pressure
rise.
3. Increased total pressure loss was found along the
dominant portion of the span of FSK. This was
dedicated to (a) the negative dihedral near the
tip, always incorporated by circumferential FSK,
and (b) predominantly due to the off-design cas-
cade conditions at lower radii, i.e. increased flow
incidence due to the tip forward effect, and the
related higher SS adverse pressure gradients. Due
to the reduced global ideal total pressure rise and
increased losses, the global total pressure rise and
total efficiency of FSK were found to be reduced
compared with the USK rotor.
4. For rotors of CVD, the radial outward flow on the
SS is intensified in comparison with free vortex
rotors, due to the vortices shed from the TE in
accordance with the spanwise increasing blade cir-
culation. This suggests that in CVD bladings, the SS
boundary layer fluid has increased inclination to
migrate outward and to accumulate near the tip. As
the present studies indicated, forward sweep atten-
uates the radial outward flow on the SS. This yields
that the application of forward sweep for potential
reduction of near-tip loss is especially welcome for
CVD rotors.
5. The present study, supplemented with literature
data cited in the introduction, suggests that appli-
cability of ad hoc blade stacking techniques is
doubtful in the achievement of efficiency gain
and prescribed performance at the design flow
rate. Instead, application of reliable CFD-based
design systems [13] is recommended for systematic
consideration and control of both load- and loss-
modifying effects due to non-radial blade stacking.
ACKNOWLEDGEMENTS
This work has been supported by the Hungarian
National Fund for Science and Research under con-
tracts No. OTKA T 043493 and K63704, and, on the
behalf of Cs. Horváth, out of the József Öveges Pro-
gram HEF_06_3 (BMEGPK06). Gratitude is expressed
to Prof László Fenyvesi and Mr József Deákvári, Hun-
garian IAE, Gödöll˝o, for contributing to the measure-
ments, and to Mr Lóránt Farkas, Szell˝oz˝oM˝uvek Kft.
(Ventilation Works Ltd), for consultation.
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APPENDIX 1
Notation
cblade chord
CLblade lift coefficient
Cplocal static pressure coefficient
=(p¯
p1)/u2
ref /2)
ddiameter
Mexponent in the design power law,
equation (1)
nrotor speed
Nrotor blade count
pstatic pressure
rradius =d/2
Rdimensionless radius =r/rt
sblade spacing (blade pitch) =dπ/N
Sblade span =(dtdh)/2
trotor tip clearance
uref reference velocity =dtπn
Urelative standard experimental
uncertainty
vflow velocity in the absolute frame of
reference
wrelative free-stream velocity
y+wall normal cell size (in wall units)
ptlocal total pressure rise
ηglobal total efficiency
ηoverall efficiency
νhub-to-tip ratio =dh/dt
ρfluid density
σfraction of span (radial distance from
the hub divided by S)
τrelative tip clearance =t/S
ϕlocal axial flow coefficient =vx/uref
ϕrlocal radial flow coefficient =vruref
global flow coefficient (annulus area-
averaged axial velocity divided by uref )
global total pressure coefficient
(annulus mass-averaged total
pressure rise divided by ρuref 2/2)
ψlocal total pressure rise coefficient
=pt/uref 2/2)
ψid local ideal total pressure rise coef-
ficient =ptid/ u2
ref /2)=2Rvu/uref
(from the Euler equation of turboma-
chines, considering swirl-free inlet far
upstream)
ωtotal pressure loss coefficient
=ψid ψ
Subscripts and superscripts
CFD based on CFD data
D design; at the design flow rate
FSK circumferentially forward-skewed
blading
h hub
id ideal (inviscid)
M based on measurement data
r radial coordinate
t blade tip
u tangential coordinate
USK unskewed blading
xaxial coordinate
1 rotor inlet plane
2 rotor exit plane
ˆpitchwise averaged value
passage-averaged value
APPENDIX 2
Calculation of approximate theoretical spanwise
distributions of flow characteristics
Pitchwise averaged quantities are considered herein.
The superscript ˆhas been omitted for simplicity.
At a given radius, the total pressure rise realized by
the rotor is
pt=ηptid =pt2 pt1 =p2+ρv2
2
2p1+ρv2
1
2
(3)
Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE420 ©IMechE 2007
Aerodynamic effects of forward blade skew in axial flow rotors of CVD 1023
The following simplifying assumptions are taken.
1. The flow is incompressible, i.e. ρ=constant.
2. Although the local total efficiency in equation (3)
varies along the span, it is assumed to be constant
farther from the endwalls at the design flowrate, on
the basis of measurement data in [12].
3. The inlet swirl is neglected, i.e. vul=0, and the
streamlines are parallel upstream of the rotor,
i.e. the normal component of Euler equation
in the natural coordinate system reads p1(r)=
constant.
4. The radial velocity components are neglected, i.e.
v2
1=v2
x1and v2
2=v2
x2+v2
u2.
Taking the radial derivative of equation (3), and
applying the above simplifications, reads
ηd(ptid)
dr=dp2
dr+ρvx2
dvx2
dr+ρvu2
dvu2
drρvx1
dvx1
dr
(4)
The Euler equation of turbomachines for swirl-free
inlet is as follows
ptid =ρuvu2 (5)
According to the Euler equation, dp2/dris expressed as
dp2
dr=ρv2
u2
r(6)
Substituting equations (5) and (6) to equation (4),
rearranging, and putting into a dimensionless form
reads
dψid 2
dRηψid 2
2R2=2ϕ2
dϕ2
dRϕ1
dϕ1
dR(7)
When determining the theoretical ψid 2(R)distribu-
tions in Fig. 7, the measured as well as the computed
ϕ1(R)and ϕ2(R)distributions were approximated as
linear functions from 20 to 80 per cent span, using the
least squares method. This provided for local approx-
imate data of ϕ1,dϕ1/dR,ϕ2, and dϕ2/dRto be substi-
tuted into equation (7). The differential equation (7)
was solved for ψid 2(R)numerically for the spanwise
region of axial velocity linearization, retaining the
computed ψid 2 data at midspan as boundary condi-
tion. For determination of the theoretical ϕ2(R)distri-
butions in Fig. 9, the ϕ1(R)and ψid 2(R)distributions
were linearized, and equation (7) was solved numer-
ically, retaining the computed ϕ2data at midspan as
boundary condition. η=0.90 was set for each case as
representative value, based on reference [12].
The ψid2 D(R)and ϕ2D(R)distributions shown in Fig. 9
were determined on the basis of equations (1) and
(7), but assuming uniform axial inlet condition, apply-
ing empirical corrections considering the spanwise
change of efficiency and the blockage due to the annu-
lus wall boundary layers, and taking the prescribed D
and Ddata as integral conditions.
JPE420 ©IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy
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... Furthermore, the increase in the stall margin of the impeller due to the forward-skewed blades is greater than that of the backward-skewed blades. Vad et al. [5] designed circumferentially skewed blades of an axial fan, and their experimental results showed that the forward-skewed blades enhance the performance of blades by increasing the axial velocity near the tip and by reducing the axial velocity near the lower half of the blade. However, both the total pressure rise and the efficiency decrease. ...
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... The peak load of the fan blades is reduced, as the fan-blade leading edge is no longer centric, which leads to weaker interaction forces of the fan blade with the inflow [9,10]. The type of skew also changes the loading along the fan span: forward skew is known to decrease the blade loading in the tip region and backward skew to increase the loading [11][12][13][14][15]. Additionally, fan-blade skew leads to a reduction of turbulence ingestion noise compared with fans without any fan-blade skew [4,[16][17][18]. ...
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