REGULAR PAPER

D. Tsugita • C. K. P. Kowshik • Y. Ohta

Visualization of rotating vortex in a centrifugalblower impeller

Received: 25 July 2011 / Accepted: 5 January 2012 / Published online: 2 February 2012� The Visualization Society of Japan 2012

Abstract Rotating instability, RI, is a well-known unsteady phenomenon occurring in the off-designoperation of various types of turbomachinery systems. However, the generation mechanism as well as itsunsteady characteristics, especially in the case of centrifugal machines, has not yet been investigated indetail. In the present paper, therefore, research attention is focused on an unsteady vortex rotating along theimpeller periphery, which is considered to be the cause of the RI, and its characteristics are investigated byexperiments and two kinds of CFD analyses. A significant amplitude increase within a frequency bandbelow the blade passing frequency is found to be caused by irregular change of the vortex rotating speed.

Keywords Centrifugal blower � Rotating instability � Rotating vortex � Correlation analysis

1 Introduction

Rotating instability (RI) is considered as one of the symptoms of unsteady phenomena, such as rotating stallor surge in various turbomachinery systems, and is observed prior to rotating stall as an amplitude increasein the power spectra of velocity fluctuation and/or radiated noise (Mathioudakis and Breugelmans 1985). Toenhance the stability operation range of the machine, a number of investigations have to be made to knowthe mechanism and characteristics of the RI.

In cases of axial flow compressors, the cause of RI may be restricted to an unsteady vortex travelling inthe vicinity of the blade tip region. Marz et al. (2002) presumed periodical interaction of the blade tip vortexwith the tip flow of the neighboring blade to be the reason for the origin of RI. However, Mailach et al.(2001) reported that the origin of RI may be the fluctuating vortices propagating in a circumferentialdirection along the rotor blade row and yielding a rotating structure with high mode orders. Nishioka et al.(2009) reported the relation between RI and the rotating stall in an axial blower. Interaction between theflow spillage below the blade tip and tip clearance flow makes the flow blockage in a rotor cascade, andbecomes the cause of a spike-initiated stall. Kikuta et al. (2009) suggested the influence of blade tip vortexbreakdowns as the origin of RI. And then, Dazin et al. (2008) reported that a similar unsteady phenomenonwas also seen in the case of a centrifugal pump using PIV measurements and numerical analyses. However,a few reports were made in cases of centrifugal machines, such as centrifugal compressors or blowers andthe occurrence of RI has not yet even been reported in centrifugal machines with shrouded impellers.

D. Tsugita � C. K. P. KowshikWaseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

Y. Ohta (&)Department of Applied Mechanics and Aerospace Engineering, Waseda University, Tokyo, JapanE-mail: yutaka@waseda.jp

J Vis (2012) 15:207–214DOI 10.1007/s12650-012-0124-3

In this paper, therefore, the cause of RI in a centrifugal blower with a shrouded impeller is investigatedby both experiments and numerical simulations. In the experiments, velocity fluctuation and sound pressurelevel are measured by hot-wire anemometer and condenser microphone, respectively. In the numericalstudy, the flow field is calculated by both steady and unsteady simulations. Research attention is focused onthe rotating vortices (Woisetschlager 2008) that are suspected to be the cause of RI, visualized usingQ-definition (Jeong and Hussain 1995).

2 Experimental procedure and numerical simulations

2.1 Experimental apparatus and measuring methods

The design performances of tested centrifugal blower and measuring methods are shown in Table 1 andFig. 1, respectively. The tested centrifugal blower is installed in an anechoic chamber to remove both motorand shaft bearing noise, and the background noise level is sufficiently lower than that of the blower noise.The blower volume flow rate is measured by an orifice flow meter and is controlled by the butterfly valve atthe outlet duct end. The sealing clearance Si between the inlet duct and impeller is set at 0.5 mm.

The characteristic curve of the tested blower in 2,000 min-1 is indicated in Fig. 2. The flow coefficient/ and total pressure-rise coefficient W used in the figure are defined as follows:

/ ¼ Q=pD2B2u2;w ¼ 2Pt=qu22 ð1Þ

where, q and u2 are air density and impeller tip speed, respectively.The occurrence of RI can easily be detected by unsteady measurements of impeller discharge velocity

and/or radiated noise level. A gradual decrease of the volume flow rate induces RI at / = 0.08, then rotatingstall occurs simultaneously with the disappearance of RI at / = 0.04. In the present experiment, therefore,

Table 1 Design performance of tested centrifugal blower

Shaft rotational speed (N) 3,000 min-1

Flow rate (Q) 50.0 m3 min-1

Total pressure rise (Pt) 2.94 kPaSpecific speed (ns) 332 min-1, m3 min-1, mGas horsepower (hp) 3.59 kWImpeller dimensions

Number of blades (Z) 12Inlet diameter (D1) 260 mmOutlet diameter (D2) 460 mmOutlet width (B2) 39.0 mmBlade shape NACA 65Sealing clearance (Si) 0.5 mm

Blower suction noise

measurements

1m

Impeller discharge flow measurements

CTA bridge(DANTEC 90C10)

Personal computer(DELL)

Condenser microphone(B&K 4133)

Conditioningamplifier

(B&K 2690)

FFT analyzer(ONO SOKKI

DS2100)

A/D converter

Hot-wire probeSplit-fiber probe

(DANTEC 55R56)

Photoelectric sensor(Omron E32-CC200)

SiEnlarged view

Fig. 1 Experimental apparatus and measuring system

208 D. Tsugita et al.

the blower operating point is set at N = 2,000 min-1 and / = 0.08, where RI appears most dominantly inthe power spectra of the velocity fluctuation.

The unsteady velocity of the impeller discharge flow was measured by two-dimensional hot-film probes(DANTEC 55R56, 55R57) inserted into positions A to D, as shown in Fig. 3. The sound pressure level ofthe blower-radiated noise was measured by a condenser microphone at a location 1 m apart from the inletbellmouth. Both measurements were conducted 32 times and then the ensemble averaged for each waveformusing a pulse trigger signal train generated by a photo-reflector equipped at the impeller periphery. Thesampling rates of velocity and sound pressure were set at 12 and 12.8 kHz, respectively.

2.2 Numerical methods

Steady numerical simulation of the inner flow field of the centrifugal blower casing was conducted using acommercial CFD code of STAR-CCM?� The whole blower system, including the inlet duct, impeller andscroll casing, was set as the computing region, as shown in Fig. 4a. The number of unstructured polyhedralgrids was 3.39 9 106 points in the whole blower system. Uniform non-pre-swirl inflow from a standardcondition [101.325 (kPa), 288.15 (K)] was assumed as the inlet boundary condition, and the static pressurewas specified at the outlet duct end. Three-dimensional RANS was adopted as governing equation, and eachequation was discretized by the finite volume method. Multi-interface advection and reconstruction solver(MARS ) (Chorin 1968) and a central difference scheme were adopted for the evaluation of convection anddiffusion terms, and a k-x SST turbulence model was utilized.

On the other hand, unsteady simulation using an in-house code was also conducted for comparison. Thenumber of computing cells was 5.14 9 106 points in total, as shown in Fig. 4b. The total pressure andtotal temperature were fixed with a Riemann invariant of one-dimensional characteristic waves to provide anon-reflecting condition at the inlet boundary (Ohta et al. 2010). A one-dimensional throttling model wasadopted at the outlet boundary to determine the blower operating point. The simulation was carried out bysolving the governing equations of a continuity equation, a three-dimensional unsteady compressible N–S

To

tal p

ress

ure

-ris

e co

effi

cien

tψ

00 0.1 0.15 0.2 0.25

Flow coefficient φ

1.2

0.8

0.4

0.05

f

f =0.22

φ=0.04Rotating

stall

1.0

0.6

0.2

φ=0.08Rotating

Instability

φ =0.22Design point

N=2000min-1

ExperimentCFD

Fig. 2 Characteristics of tested centrifugal blower

Cut off

163 deg

120 deg 76.3 deg

45.0 deg

CD

B

A

E

θ

210 deg

Fig. 3 Location of velocity measurement

Visualization of rotating vortex in a centrifugal blower impeller 209

equation, an energy equation and an equation of the state of an ideal gas. Numerical fluxes of the convectiveterms were evaluated by simple high-resolution upwind scheme (SHUS) (Steger and Warming 1981;Roe 1981), and were extended to a higher order by the monotone upwind scheme for conservative laws(MUSCL) interpolation (van Leer 1979). Lower/upper alternating direction implicit (LU-ADI) was used forthe time integration. For viscous terms, the fluxes were determined in a central differencing manner withGauss’s theorem. Both Coriolis and centrifugal forces were considered as inertial force terms. The Baldwin–Lomax turbulence model was adopted.

3 Results and discussion

3.1 Generation mechanism and cause of rotating instability

The power spectra of impeller discharge velocity and radiated sound pressure when the blower rotationalspeed is changed by 100 min-1 within the range between N = 1,900 and 2,100 min-1 are shown in Fig. 5.Red dashed lines in the figure indicate a half frequency of the fundamental blade passing frequency (BPF).The peak frequencies of the bandwidth growth on the power spectra of velocity fluctuations are differentfrom those of the sound pressure. The peak frequency of the velocity fluctuation is lower, but that of thesound pressure is higher than half of the fundamental BPF shown by red dashed lines in the figure. As theimpeller rotational speed increases, the peak frequencies will also increase correspondingly, as typicallyshown in Fig. 6. The ordinate axis in Fig. 6 indicates the frequency ratio of RI to the fundamental BPF. Asone can see from the figure, both frequencies exist almost in a symmetrical position to half of the funda-mental BPF. Accordingly, there may have existed a certain regularity between the generation mechanism ofthe noise component induced by RI and corresponding flow fields.

Grids for unsteady calculation.(b)Grids for steady calculation.(a)

Impeller 1.67 106 pointsCasing 1.72 106 points

Total 3.39 106 points

Impeller 2.84 106 pointsCasing 2.45 106 points

Total 5.29 106 points

Fig. 4 Computational grids

0.4

0.5

0

0.3

0.2

0.1

100

0

80

60

40

20

So

un

d p

ress

ure

leve

l dB

Vel

oci

ty f

luct

uat

ion

m/s

Frequency Hz

φ=0.08

φ=0.22

RI

(a) N = 1900 min-1.

0 100 300 400 500200

1stBPF1stBPF/2

RI

RI

(c) N = 2100 min-1.

RI

RI

(b) N = 2000 min-1.

RI

(Mea

suri

ng

lo

cati

on

: C

)

0 100 300 400 500200 0 100 300 400 500200

Fig. 5 Power spectra of velocity fluctuation and sound pressure

210 D. Tsugita et al.

The former result can easily be explained by considering the unsteady vortex travelling along theimpeller periphery, as schematically shown in Fig. 7. When the rotating speed of the vortex is assumed to be45% of the impeller rotating speed, a discrete frequency component of 45% of the fundamental BPF can beobserved by unsteady velocity measurement. On the other hand, since the impeller rotating speed relative tothe rotating vortex is almost 55% in a vortex frozen frame, interaction between the vortex and the impellerdischarge flow may happen at the frequency of 55% of the fundamental BPF. The bandwidth growth of thesound pressure appearing at almost 55% of the fundamental BPF may be due to the interaction, and the RInoise is found to be generated by the interaction between the rotating vortex and the impeller discharge flow.

3.2 Unsteady behavior of rotating vortices

The power spectra of velocity fluctuation measured at points A to D along the impeller periphery are shownin Fig. 8. The bandwidth growth considered to be generated by RI appears remarkably in the power spectraon a frequency a little lower than half of the BPF. Since the bandwidth growth enclosed with red dashedcircles in Fig. 8 was not measured at the locations such as point E, the unsteady vortex may initiate aroundmeasuring location A and seems to become large while rotating along the impeller periphery. The effects ofRI are significant, as typically shown in the power spectra measured at locations B and C in the figure.However, the vortex seems to attenuate rapidly and be eliminated in a short time by contracted flow as itapproaches the cut-off of the scroll.

In the present experiment, the local speed of the rotating vortex is experimentally measured using cross-correlation analysis. The cross-correlation coefficient Sxy used in the analysis is defined as follows:

Rotating speed N min-1

Fig. 6 Comparison of peak frequencies of velocity fluctuation and sound pressure

0.45ωω [rad/s]

Absolute frame

0.45ω [rad/s]

ω [rad/s]

Velocitymeasuring point

0.55ω [rad/s]

Relative frame Impellerdischarge flow

Fig. 7 Unsteady behavior of vortices rotating around the impeller periphery and interaction with impeller discharge flow

0 100 300 400 500200

0.4

0.5

0

0.3

0.2

0.1

Frequency Hz

Vel

oci

ty f

luct

uat

ion

m/s

RIRIRIRI

(a)

RIRI

1stBPF1stBPF φ =0.08φ =0.22

0 100 300 400 500200 0 100 300 400 500200 0 100 300 400 500200

(b) (c) (d)

Fig. 8 Power spectra of velocity fluctuation at each measuring point (N = 2,000 min-1)

Visualization of rotating vortex in a centrifugal blower impeller 211

SxyðsÞ ¼R

3TrevðUxðtÞ � Ux;aveðtÞÞðUyðt þ sÞ � Uy;aveðt þ sÞÞdt

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR3TrevðUxðtÞ � Ux;aveðtÞÞ2dt

R3TrevðUyðt þ sÞ � Uy;aveðt þ sÞÞ2dt

q ; ð2Þ

where, Trev and Ux in the equation are impeller revolution time and instantaneous velocity fluctuationmeasured at location x, respectively. Subscript ave denotes the time-averaged velocity.

A frequency of no less than 300 Hz of each velocity fluctuation data was cut-off by low-pass filter, andcross-correlation analysis was conducted. A typical example of cross-correlation analysis using velocityfluctuation signals measured at position A and C is indicated in Fig. 9. Tbp in the figure represents theinterval of blade passing time. Many continuous peaks recognized in the cross-correlation data suggest theexistence of continuous vortices passing through measurement locations A and C. The time duration, TAC, ofthe rotating vortex travelling from location A to C can be determined from the waveform as the nearest peakof 45% the 1st BPF. The time interval, Tvor, expresses the spatial as well as temporal interval of vorticestravelling around the impeller periphery one after another. Then, the rotating speed, ax, of the vortextravelling from location A to C can be calculated as hAC=TAC, where, hAC is the angle made by locations Aand C, x means the impeller rotating speed and a is the ratio of the vortex speed to the impeller rotatingspeed x. In the correlation analysis, 2,000 data samples were used to calculate the cross-correlation.

Distributions of the vortex rotating speed obtained from cross-correlation analyses of 2,000 data samplesare shown in Fig. 10. In the figure, the rotating speeds calculated at four sections between locations A–B, B–C, C–D and A–D are shown for reference. The obtained vortex speeds once become slower betweenlocations B and C (42.27% of the 1st BPF), then faster again when they approach the cut-off of the scroll(45.18% of the 1st BPF at section C–D). This tendency largely depends on the scale of the rotating vortex, inwhich the vortex becomes larger between locations B and C, and the scale becomes smaller again when itapproaches the cut-off of the scroll. The averaged rotating speed between locations A and D is about 44%,and matches well with the measured data of the power spectra already shown in Fig. 5. From the correlationanalyses of both the velocity fluctuation and radiated noise, the bandwidth growth on the power spectra isfound to be caused by an irregular change of the vortex rotating speed along the impeller periphery.

3.3 Visualization of rotating vortex by CFD

The structure of the rotating vortex is visualized using Q-definition, as shown in Fig. 11. In the figure, thecontour of the Q value is colored by non-dimensional helicity. When the flow coefficient is / = 0.22, thedesign point, the impeller discharge flow seems to be stable and an unusual vortex is not recognized in

0.5

Cro

ss-c

orr

elat

ion

coef

fici

ent

Sxy

-0.50

Non-dimensional time-delay ττ/Tbp

)( 3−vorT )(3

vorT)(2vorT)(1

vorT)( 2−vorT )( 1−

vorT12

TAC

6

0

Fig. 9 Cross-correlation analysis to determine the rotating speed of vorticies

A-D

43.95%

0

50

40

30

20

10

C-D

45.18%

Nu

mb

er o

f sa

mp

ling

dat

a

Rotating speed (vs 1stBPF) %

B-C 42.27%

5525 35 45

44.23%A-B

5525 35 45 5525 35 45 5525 35 45

Fig. 10 Distribution of vortex rotating speed (N = 2,000 min-1)

212 D. Tsugita et al.

the impeller periphery. On the other hand, when the volume flow rate is reduced to / = 0.08, an unstablevortex, as shown by the dashed red circles in figures (b) and (c) grows up. According to the velocity vectorshown in figure (d), the vortex seems to initiate around the hub surface of the blade suction side, and is muchsignificant toward the shroud side of the impeller. This numerical result agreed well with the experimentaldata in which the frequency of RI in the impeller discharge velocity dominates around the shroud side of theimpeller. At present, the detailed mechanism of the vortex is not fully understood, but the impeller sepa-ration vortex generated around the suction surface at a low-volume flow-rate condition is considered to bethe cause of the vortex.

The result of the unsteady CFD is also shown in Fig. 12. A number of vortices rotating along theimpeller periphery can be recognized and were generated near position E and eliminated around position D

(b) Front view ( φ=0.08 )

(c) Side view ( φ=0.08 )

(a) Front view ( φ=0.22 )

(d) Velocity vectors( φ=0.08 )

1-1No

n-d

imen

sio

nal

hel

icit

y

0

Fig. 11 Visualization of rotating vortex structure by steady calculation (N = 2,000 min-1)

(a) t =0

(c) t =7.81Tbp

(b) t =3.91Tbp

(d) t =11.7Tbp

1-1

No

n-d

imen

sio

nal

hel

icit

y

0

Fig. 12 Visualization of rotating vortex by unsteady calculation (N = 2,000 min-1)

Visualization of rotating vortex in a centrifugal blower impeller 213

in the figure. The calculated rotating speed from the CFD result was almost 40% of the impeller speed, asexpected from the experimental results.

As mentioned above, the hypothesis of the rotating vortex as the origin of RI in the shrouded centrifugalimpeller is numerically certified by the visualization method as well as by correlation analysis.

4 Concluding remarks

Rotating instability occurring in a centrifugal blower with a shrouded impeller was investigated by bothexperiments and numerical simulations. Detailed measurements of the impeller discharge velocity and theblower-radiated noise enabled us to present a rotating instability model in which the origin is considered tobe an unsteady vortex rotating continuously along the impeller periphery. Furthermore, the characteristics ofthe rotating vortex were confirmed by utilizing correlation analyses, and also visualization of the rotatingvortex by two kinds of numerical simulations was carried out.

The findings can be summarized as follows:

1. Rotating instability of a shrouded centrifugal impeller appears as a bandwidth growth in the powerspectra of the impeller discharge velocity as well as that of the generated noise. However, theirfrequencies are different from each other.

2. The cause of the rotating instability can be explained by considering the unsteady vortex which rotatesalong the impeller periphery. The rotating instability noise is found to be generated by the interactionbetween the vortex and the impeller discharge flow.

3. The bandwidth growth of the power spectra of the impeller discharge velocity caused by RI is mainlydue to the irregular change of the vortex rotating speed. The rotating speed changes with locations, anddecreases with the growth of the vortex scale. The averaged rotating speed is about 44% of the impellerspeed.

4. The mechanism as well as the rotating characteristics of the vortex is visualized using two kinds ofnumerical simulations. According to the numerical results, the vortex seems to initiate at the hub surfaceon the suction side of the impeller and gets big toward the shroud side. This unsteady vortex isconfirmed to be the origin of rotating instability in the case of a shrouded impeller. The detailedstructure and rotating mechanism of the unsteady vortex must be further investigated.

References

Chorin AJ (1968) Numerical solution of the Navier–Stokes equations. Math Comput 22:745–762Dazin A, Coutier-Delgosha O et al (2008) Rotating instability in the vaneless diffuser of a radial flow pump. J Therm Sci

17(4):368–374Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 286:69–94Kikuta H, Furukawa M et al (2009) ‘‘Effect of tip clearance on rotating stall inception in an axial flow compressor rotor’’. Proc.

of JSME Fluid Engineering Conference 2009, pp 377–378 (in Japanese)Mailach R, Lehmann I, Vogeler K (2001) Rotating instabilities in an axial compressor originating from the fluctuating blade tip

vortex. Trans ASME J Turbomach 123:453–460Marz J, Hah C, Neise W (2002) An experimental and numerical investigation into the mechanism of rotating instability. Trans

ASME J Turbomach 124:367–375Mathioudakis K, Breugelmans FAE (1985) Development of small rotating stall in a single stage axial compressor, ASME paper

no. 85-GT-227Nishioka T, Kanno T, Hayami H (2009) Effect of rotor tip leakage flow on spike-type stall inception. Trans

JSME(B) 73(732):71–77 (in Japanese)Ohta Y, Goto T, Outa E (2010) Unsteady behavior and control of diffuser leading-edge vortex in a centrifugal compresser.

Proc. of ASME Turbo Expo, GT-22394Roe PL (1981) Approximate Riemann solvers, parameter vectors and difference schemes. J Comp Phys 43:357–372Steger JL, Warming RF (1981) Flux vector splitting of the inviscid gas dynamic equations with application to finite-difference

methods. J Comp Phys 40:263–293van Leer B (1979) Towards the ultimate conservative difference scheme, a second order sequel to Godunov’s method. J Comp

Phys 32:101–136Woisetschlager J (2008) Experimental and numerical flow visualization in a transonic turbine. J Visualization 11(1):95–102

214 D. Tsugita et al.