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

R E G UL A R P A P E R

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

Visualization of rotating vortex in a centrifugal blower impeller

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

Abstract Rotating instability, RI, is a well-known unsteady phenomenon occurring in the off-design operation of various types of turbomachinery systems. However, the generation mechanism as well as its unsteady characteristics, especially in the case of centrifugal machines, has not yet been investigated in detail. In the present paper, therefore, research attention is focused on an unsteady vortex rotating along the impeller periphery, which is considered to be the cause of the RI, and its characteristics are investigated by experiments and two kinds of CFD analyses. A significant amplitude increase within a frequency band below 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 stall or surge in various turbomachinery systems, and is observed prior to rotating stall as an amplitude increase in the power spectra of velocity fluctuation and/or radiated noise (Mathioudakis and Breugelmans 1985). To enhance the stability operation range of the machine, a number of investigations have to be made to know the mechanism and characteristics of the RI. In cases of axial flow compressors, the cause of RI may be restricted to an unsteady vortex travelling in the vicinity of the blade tip region. Ma¨rz et al. (2002) presumed periodical interaction of the blade tip vortex with 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 circumferential direction 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 the flow spillage below the blade tip and tip clearance flow makes the flow blockage in a rotor cascade, and becomes the cause of a spike-initiated stall. Kikuta et al. (2009) suggested the influence of blade tip vortex breakdowns as the origin of RI. And then, Dazin et al. (2008) reported that a similar unsteady phenomenon was 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 and the occurrence of RI has not yet even been reported in centrifugal machines with shrouded impellers.

D. Tsugita  C. K. P. Kowshik Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555, Japan Y. Ohta (&) Department of Applied Mechanics and Aerospace Engineering, Waseda University, Tokyo, Japan E-mail: [email protected]

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In this paper, therefore, the cause of RI in a centrifugal blower with a shrouded impeller is investigated by both experiments and numerical simulations. In the experiments, velocity fluctuation and sound pressure level are measured by hot-wire anemometer and condenser microphone, respectively. In the numerical study, the flow field is calculated by both steady and unsteady simulations. Research attention is focused on the rotating vortices (Woisetschlager 2008) that are suspected to be the cause of RI, visualized using Q-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 and Fig. 1, respectively. The tested centrifugal blower is installed in an anechoic chamber to remove both motor and 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 at the 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=pD2 B2 u2 ; 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 rotating stall occurs simultaneously with the disappearance of RI at / = 0.04. In the present experiment, therefore, Table 1 Design performance of tested centrifugal blower 3,000 min-1 50.0 m3 min-1 2.94 kPa 332 min-1, m3 min-1, m 3.59 kW

Shaft rotational speed (N) Flow rate (Q) Total pressure rise (Pt) Specific speed (ns) Gas horsepower (hp) Impeller dimensions Number of blades (Z) Inlet diameter (D1) Outlet diameter (D2) Outlet width (B2) Blade shape Sealing clearance (Si)

12 260 mm 460 mm 39.0 mm NACA 65 0.5 mm Personal computer (DELL) Impeller discharge flow measurements

A/D converter

Photoelectric sensor (Omron E32-CC200)

CTA bridge (DANTEC 90C10) Hot-wire probe Split-fiber probe (DANTEC 55R56)

1m Enlarged view Si Condenser microphone (B&K 4133) Conditioning amplifier (B&K 2690)

FFT analyzer (ONO SOKKI DS2100)

Fig. 1 Experimental apparatus and measuring system

Blower suction noise measurements

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the blower operating point is set at N = 2,000 min-1 and / = 0.08, where RI appears most dominantly in the 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 of the blower-radiated noise was measured by a condenser microphone at a location 1 m apart from the inlet bellmouth. Both measurements were conducted 32 times and then the ensemble averaged for each waveform using a pulse trigger signal train generated by a photo-reflector equipped at the impeller periphery. The sampling 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 a commercial CFD code of STAR-CCM?Ò The whole blower system, including the inlet duct, impeller and scroll casing, was set as the computing region, as shown in Fig. 4a. The number of unstructured polyhedral grids was 3.39 9 106 points in the whole blower system. Uniform non-pre-swirl inflow from a standard condition [101.325 (kPa), 288.15 (K)] was assumed as the inlet boundary condition, and the static pressure was specified at the outlet duct end. Three-dimensional RANS was adopted as governing equation, and each equation 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 and diffusion 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. The number of computing cells was 5.14 9 106 points in total, as shown in Fig. 4b. The total pressure and total temperature were fixed with a Riemann invariant of one-dimensional characteristic waves to provide a non-reflecting condition at the inlet boundary (Ohta et al. 2010). A one-dimensional throttling model was adopted at the outlet boundary to determine the blower operating point. The simulation was carried out by solving the governing equations of a continuity equation, a three-dimensional unsteady compressible N–S

Total pressure-rise coefficient ψ

1.2

1.0

0.8

φ =0.08 Rotating Instability

0.6

φ =0.22

Design f =0.22 point

0.4

φ =0.04 f Rotating stall

0.2

0

N =2000min-1 Experiment CFD

0.05

0

0.1

0.15

0.2

Flow coefficient φ Fig. 2 Characteristics of tested centrifugal blower

B 120 deg

C

76.3 deg

D

Cut off

45.0 deg

A 163 deg

E 210 deg

Fig. 3 Location of velocity measurement

θ

0.25

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equation, an energy equation and an equation of the state of an ideal gas. Numerical fluxes of the convective terms 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 for the time integration. For viscous terms, the fluxes were determined in a central differencing manner with Gauss’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 rotational speed 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 different from those of the sound pressure. The peak frequency of the velocity fluctuation is lower, but that of the sound pressure is higher than half of the fundamental BPF shown by red dashed lines in the figure. As the impeller rotational speed increases, the peak frequencies will also increase correspondingly, as typically shown in Fig. 6. The ordinate axis in Fig. 6 indicates the frequency ratio of RI to the fundamental BPF. As one can see from the figure, both frequencies exist almost in a symmetrical position to half of the fundamental BPF. Accordingly, there may have existed a certain regularity between the generation mechanism of the noise component induced by RI and corresponding flow fields.

Impeller 1.67 106 points Casing 1.72 106 points Total 3.39 106 points

Impeller 2.84 106 points Casing 2.45 106 points Total 5.29 106 points

(a) Grids for steady calculation.

(b) Grids for unsteady calculation.

Velocity fluctuation m/s Sound pressure level dB (Measuring location: C)

Fig. 4 Computational grids 0.5 1stBPF/2

0.4

RI

0.3

1stBPF

RI

RI

0.2 0.1 0 100

φ=0.08

RI

80

RI

RI

60 40

φ=0.22

20 0 0

100

200

300

400 500

0

100

200

300

400 500

0

100

200

300

400 500

Frequency Hz

(a) N = 1900 min-1.

(b) N = 2000 min-1.

Fig. 5 Power spectra of velocity fluctuation and sound pressure

(c) N = 2100 min-1.

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The former result can easily be explained by considering the unsteady vortex travelling along the impeller periphery, as schematically shown in Fig. 7. When the rotating speed of the vortex is assumed to be 45% of the impeller rotating speed, a discrete frequency component of 45% of the fundamental BPF can be observed by unsteady velocity measurement. On the other hand, since the impeller rotating speed relative to the rotating vortex is almost 55% in a vortex frozen frame, interaction between the vortex and the impeller discharge flow may happen at the frequency of 55% of the fundamental BPF. The bandwidth growth of the sound pressure appearing at almost 55% of the fundamental BPF may be due to the interaction, and the RI noise 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 shown in Fig. 8. The bandwidth growth considered to be generated by RI appears remarkably in the power spectra on a frequency a little lower than half of the BPF. Since the bandwidth growth enclosed with red dashed circles in Fig. 8 was not measured at the locations such as point E, the unsteady vortex may initiate around measuring location A and seems to become large while rotating along the impeller periphery. The effects of RI 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 it approaches the cut-off of the scroll. In the present experiment, the local speed of the rotating vortex is experimentally measured using crosscorrelation 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

0.45 ω [rad/s]

Absolute frame

Velocity measuring point

Impeller discharge flow

Relative frame

0.45 ω [rad/s]

ω [rad/s]

0.55 ω [rad/s]

Velocity fluctuation m/s

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

0.5 0.4 0.3

(a)

1stBPF

(b)

(c)

(d) RI

RI

φ =0.08 φ =0.22

RI

0.2 0.1 0

0 100 200 300 400 500

0 100 200 300 400 500

0 100 200 300 400 500

Frequency Hz

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

0 100 200 300 400 500

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R

3Trev ðUx ðtÞ  Ux;ave ðtÞÞðUy ðt þ sÞ  Uy;ave ðt þ sÞÞdt ffi; Sxy ðsÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R 2 R 2 ðU ðtÞ  U ðtÞÞ dt ðU ðt þ sÞ  U ðt þ sÞÞ dt x x;ave y y;ave 3Trev 3Trev

ð2Þ

where, Trev and Ux in the equation are impeller revolution time and instantaneous velocity fluctuation measured 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, and cross-correlation analysis was conducted. A typical example of cross-correlation analysis using velocity fluctuation signals measured at position A and C is indicated in Fig. 9. Tbp in the figure represents the interval of blade passing time. Many continuous peaks recognized in the cross-correlation data suggest the existence of continuous vortices passing through measurement locations A and C. The time duration, TAC, of the rotating vortex travelling from location A to C can be determined from the waveform as the nearest peak of 45% the 1st BPF. The time interval, Tvor, expresses the spatial as well as temporal interval of vortices travelling around the impeller periphery one after another. Then, the rotating speed, ax, of the vortex travelling from location A to C can be calculated as hAC =TAC , where, hAC is the angle made by locations A and C, x means the impeller rotating speed and a is the ratio of the vortex speed to the impeller rotating speed 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 samples are 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 between locations 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, in which the vortex becomes larger between locations B and C, and the scale becomes smaller again when it approaches 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 correlation analyses of both the velocity fluctuation and radiated noise, the bandwidth growth on the power spectra is found 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, the contour of the Q value is colored by non-dimensional helicity. When the flow coefficient is / = 0.22, the design point, the impeller discharge flow seems to be stable and an unusual vortex is not recognized in

Cross-correlation coefficient Sxy

TAC 0.5

0

(1) (2) (3 ) Tvor Tvor Tvor

( −3 ) ( −2 ) ( −1) Tvor Tvor Tvor -0.5

0

6

12

Non-dimensional time-delay τ /Tbp

Number of sampling data

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

50 40

A-B

B-C

44.23%

C-D

42.27%

A-D

45.18%

30

43.95%

20 10 0 25

35

45

55

25

35

45

55

25

35

45

Rotating speed (vs 1stBPF) %

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

55

25

35

45

55

Visualization of rotating vortex in a centrifugal blower impeller

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(b) Front view ( φ =0.08 )

(c) Side view ( φ =0.08 )

1 0 -1

(a) Front view ( φ =0.22 )

Non-dimensional helicity

the impeller periphery. On the other hand, when the volume flow rate is reduced to / = 0.08, an unstable vortex, as shown by the dashed red circles in figures (b) and (c) grows up. According to the velocity vector shown in figure (d), the vortex seems to initiate around the hub surface of the blade suction side, and is much significant toward the shroud side of the impeller. This numerical result agreed well with the experimental data in which the frequency of RI in the impeller discharge velocity dominates around the shroud side of the impeller. At present, the detailed mechanism of the vortex is not fully understood, but the impeller separation vortex generated around the suction surface at a low-volume flow-rate condition is considered to be the cause of the vortex. The result of the unsteady CFD is also shown in Fig. 12. A number of vortices rotating along the impeller periphery can be recognized and were generated near position E and eliminated around position D

(d) Velocity vectors( φ =0.08 )

(c) t =7.81Tbp

(d) t =11.7Tbp

0

(b) t =3.91Tbp

-1

(a) t =0

Non-dimensional helicity

1

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

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

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in the figure. The calculated rotating speed from the CFD result was almost 40% of the impeller speed, as expected from the experimental results. As mentioned above, the hypothesis of the rotating vortex as the origin of RI in the shrouded centrifugal impeller 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 both experiments and numerical simulations. Detailed measurements of the impeller discharge velocity and the blower-radiated noise enabled us to present a rotating instability model in which the origin is considered to be an unsteady vortex rotating continuously along the impeller periphery. Furthermore, the characteristics of the rotating vortex were confirmed by utilizing correlation analyses, and also visualization of the rotating vortex 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 power spectra of the impeller discharge velocity as well as that of the generated noise. However, their frequencies are different from each other. 2. The cause of the rotating instability can be explained by considering the unsteady vortex which rotates along the impeller periphery. The rotating instability noise is found to be generated by the interaction between the vortex and the impeller discharge flow. 3. The bandwidth growth of the power spectra of the impeller discharge velocity caused by RI is mainly due to the irregular change of the vortex rotating speed. The rotating speed changes with locations, and decreases with the growth of the vortex scale. The averaged rotating speed is about 44% of the impeller speed. 4. The mechanism as well as the rotating characteristics of the vortex is visualized using two kinds of numerical simulations. According to the numerical results, the vortex seems to initiate at the hub surface on the suction side of the impeller and gets big toward the shroud side. This unsteady vortex is confirmed to be the origin of rotating instability in the case of a shrouded impeller. The detailed structure and rotating mechanism of the unsteady vortex must be further investigated.

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