Content uploaded by Máté Márton Lohász

Author content

All content in this area was uploaded by Máté Márton Lohász

Content may be subject to copyright.

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

[3,7–12]. 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.

[4,7–9,16], 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(ν ) ·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 η∗was 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 η∗inevitably 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 k−ε

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 30◦central

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 10−6.

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

sCL≈2ˆ

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, 30◦FSK)

studied in references [7] and [8] involving standard

k−εmodelling. 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

[10–12], 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

[7–9]. 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 22◦and

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.

REFERENCES

1 Gallimore, S. J., Bolger, J. J., Cumpsty,N. A.,Taylor, M. J.,

Wright, P. I., and Place, J. M. M. The use of sweep and

dihedral in multistage axial ﬂow compressor blading –

parts I and II. ASME, J. Turbomach., 2002, 124, 521–541.

2 Vad, J. and Bencze, F. Three-dimensional ﬂow in axial

ﬂow fans of non-free vortex design. Int. J. HeatFluid Flow,

1998, 19, 601–607.

3 Corsini, A. and Rispoli, F. Using sweep to extend the

stall-free operational range in axial fan rotors. Proc. Instn

Mech. Engrs, Part A: J. Power and Energy, 2004, 218,

129–139.

4 Meixner, H. U. Vergleichende LDA-Messungen an

ungesichelten und gesichelten Axialventilatoren. Disser-

tation Universität Karlsruhe, VDI-Verlag, Reihe 7: Strö-

mungstechnik, No. 266, Düsseldorf, 1995.

5 Lakshminarayana, B. Fluid dynamics and heat trans-

fer of turbomachinery, 1996 (John Wiley & Sons, Inc.,

New York, USA).

6 Clemen, C. and Stark, U. Compressor blades with sweep

and dihedral: a parameter study. In Proceedings of 5th

European Conference onTurbomachinery Fluid Dynam-

ics and Thermodynamics, Prague, 2003, pp. 151–161.

7 Beiler, M. G. Untersuchung der dreidimensionalen

Strömung durch Axialventilatoren mit gekrümmten

Schaufeln. Doctoral Dissertation, Universität-

GH-Siegen, VDI Verlag Düsseldorf, Reihe 7:

Strömungstechnik, Nr. 298, 1996.

8 Beiler, M. G. and Carolus, T. H. Computation and mea-

surement of the ﬂow in axial ﬂow fans with skewed

blades. ASME, J. Turbomach., 1999, 121, 59–66.

9 Yamaguchi, N., Tominaga, T., Hattori, S., and

Mitsuhashi, T. Secondary-loss reduction by forward-

skewing of axial compressor rotor blading. In Proceed-

ings of Yokohama International Gas Turbine Congress,

Yokohama, 1991, pp. II.61–II.68.

10 Rohkamm, H., Wulff, D., Kosyna, G., Saathoff, H., Stark,

U., Gümmer,V., Swoboda, M., and Goller, M. The impact

of rotor tip sweep on the three-dimensional ﬂow in a

highly-loaded single-stage low-speed axial compressor:

part II – test facility and experimental results. In 5th Euro-

pean Conference on Turbomachinery Fluid Dynamics

and Thermodynamics, Prague, 2003, pp. 175–185.

11 Clemen,C.,Gümmer,V., Goller,M., Rohkamm, H., Stark,

U., and Saathoff, H. Tip-aerodynamics of forward-swept

rotor blades in a highly-loaded single-stage axial-ﬂow

low-speed compressor. In 10th International Symposium

on Transport Phenomena and Dynamics of Rotating

Machinery (ISROMAC10), Honolulu, 2004, paper no. 027,

available in CD-ROM.

12 Vad,J., Kwedikha, A. R. A., and Jaberg, H. Effects of blade

sweep on the performance characteristics of axial ﬂow

turbomachinery rotors. Proc. IMechE,Part A: J. Power and

Energy, 2006, 220, 737–751.

13 Jang, C.-M., Samad, A., and Kim, K.-Y. Optimal design

of swept, leaned and skewed blades in a transonic axial

compressor. ASME paper GT2006-90384, 2006.

14 Vad, J., Kwedikha, A. R. A., and Jaberg, H. Inﬂuence

of blade sweep on the energetic behavior of axial ﬂow

turbomachinery rotors at design ﬂow rate. ASME paper

GT2004-53544, 2004.

JPE420 ©IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy

1022 J Vad, ARAKwedikha, Cs Horváth, M Balczó, M M Lohász, and T Réger t

15 Vad, J. Analytical modeling of radial ﬂuid migration in

the boundary layer of axial ﬂow turbomachinery blades.

ASME paper GT2006-90523, 2006.

16 Govardhan, M., Krishna Kumar, O. G., and Sitaram, N.

Computational study of the effect of sweep on the

performance and ﬂow ﬁeld in an axial ﬂow compressor

rotor. Proc. IMechE, Part A: J. Power and Energy, 2007,

221, 315–329.

17 Wallis, R. A. Axial ﬂow fans and ducts, 1983 (John Wiley

& Sons, NewYork).

18 Fluent 6.2.16 user’s guide, 2004 (Fluent Inc., Lebanon,

NH, USA).

19 Benini, E. and Biollo, R. On the aerodynamics of swept

and leaned transonic compressor rotors. ASME paper

GT2006-90547, 2006.

20 Launder, B. E. and Spalding, D. B. Lectures in math-

ematical models of turbulence, 1972 (Academic Press,

London).

21 Kader, B. Temperature and concentration proﬁles in

fully turbulent boundary layers. Int. J. Heat Mass Transf.,

1993, 24, 1541–1544.

22 Wu, Y., Chu, W., Lu, X., and Zhu, J. Behavior of tip

leakage ﬂow in an axial compressor rotor. ASME paper

GT2006-90399, 2006.

23 Vad, J., Kwedikha, A. R. A., and Horváth, Cs. Combined

effects of controlled vortex design and forward blade

skew on the three-dimensional ﬂow in axial ﬂow rotors.

In Conference on Modelling Fluid Flow (CMFF’06),

Budapest, 2006, pp. 1139–1146.

APPENDIX 1

Notation

cblade chord

CLblade lift coefﬁcient

Cplocal static pressure coefﬁcient

=(p−¯

p1)/(ρu2

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 =(dt−dh)/2

trotor tip clearance

uref reference velocity =dtπn

Urelative standard experimental

uncertainty

vﬂow velocity in the absolute frame of

reference

w∞relative free-stream velocity

y+wall normal cell size (in wall units)

ptlocal total pressure rise

ηglobal total efﬁciency

η∗overall 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/(ρuref 2/2)

ψid local ideal total pressure rise coef-

ﬁcient =ptid/(ρ 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=ηptid =pt2 −pt1 =p2+ρv2

2

2−p1+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

dr−ρvx1

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

dRη−ψid 2

2R2=2ϕ2

dϕ2

dR−ϕ1

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