International Journal of Fluid Machinery and Systems Vol. 2, No. 1, January-March 2009
Original Paper
A Behavior of the Diffuser Rotating Stall in a Low Specific Speed Mixed-Flow Pump
Masahiro Miyabe
1, Akinori Furukawa
2, Hideaki Maeda
1, Isamu Umeki
1and Yoshinori Jittani
11
Department of Research and Development, Torishima Pump Mfg. Co., Ltd.
1-1-8, Miyata-cho, Takatsuki-shi, Osaka, 569-8660, Japan
2
Department of Mechanical Engineering Science, Kyushu University 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
Abstract
The flow instability in a low specific speed mixed-flow pump, having a positive slope of head-flow characteristics was investigated. Based on the static pressure measurements, it was found that a rotating stall in the vaned diffuser occurs at about 65% flow rate of best efficiency point (BEP). A dynamic Particle Image Velocimetry (DPIV) measurement and the numerical simulations were conducted in order to investigate the flow fields. As a result, the diffuser rotating stall was simulated even by Computational Fluid Dynamics (CFD) and the calculated periodic flow patterns agree well with the measured ones by DPIV. It is clarified that a periodical large scaled backflow, generated at the leading edge of the suction surface of the diffuser vane, causes the instability. Furthermore, the growth of the strong vortex at the leading edge of the diffuser vane induces the strong backflow from the diffuser outlet to the inlet. The scale of one stall cell is covered over four-passages in total thirteen vane-passages.
Keywords: Mixed flow pump, Flow instability, Vaned diffuser, Rotating stall, PIV, CFD
1. Introduction
A pump internal flow becomes much complicated in terms of time and space when a pump is operated at partial flow rate. In such a case, there appears a positive slope of head-flow characteristics and it causes the surge, vibrations and noise problems. A mixed flow pump with low specific speed of 0.853 (dimensionless) or 350 (m3/min, m, min-1) has been developed for the seawater desalination system. In the pump performance test, a positive slope of head-flow characteristics appears at about 65% flow rate of best efficiency point (BEP) and the vibration and noise increase with the flow rate. This result remarkably makes the operating range of this pump narrower. Thus, it is very important to predict the instability at the design stage and to survey preferable pump design parameters. In the authors’ conventional study, it was found that the unstable performance was caused by the rotating stall occurring in the vaned diffuser [1], [2]. There are a few studies on rotating stall in centrifugal pumps. Yoshida et al. [3] observed the rotating stall in a vaned diffuser.
The propagation speed is under 10 percent of the impeller rotational speed. They studied several types of vaned diffusers and reported that as the clearance between impeller and vaned diffuser was decreased, the rotating stall became weakened and the flow range of its occurrence diminished. Sano et al. [4] investigated several types of rotating stall in the impeller and vaned diffuser experimentally and numerically. They concluded that the flow instabilities in the vaned diffuser occur in the range with negative slope of the diffuser pressure performance. Hergt et al. [5], Eisele et al. [6] and Sinha et al. [7] made experimental observations of the internal flow in vaned diffusers at a low flow rate, but those investigations are not enough in spatial or temporal resolution. There are even few studies on rotating stall in mixed flow diffuser pumps. Kurokawa [8] measured time averaged internal flow with a Pitot tube at the exit of the impeller and the inlet of the diffuser vane. It was reported that the positive slope of pump performance curve was caused by a periodic strong reverse flow accompanied with a stall core, and the rotating stall was suppressed by a non-axisymmetric cut of the inlet of diffuser vanes. However this suppression method may not be employed in all cases, and the relationship between the rotating stall and the unsteady complex internal flow has not been clarified yet. In the case of mixed flow pump with a vaned diffuser, it is very important to consider three-dimensional unsteady flow. In the present paper, pressure fluctuations were measured with four pressure transducers and unsteady internal flow was measured with a Dynamic PIV [9] measurement system, both at the diffuser inlet and at the outlet. In addition, the flow fields were investigated in detail from numerical results with commercial Computational Fluid Dynamics (CFD) software. From these experimental and numerical results, the propagation mechanism of rotating stall, the cause of performance instabilities and the guideline of its restriction are discussed in detail.
Received July 29 2008; revised January 13 2009; accepted for publication January 10 2009: Review conducted by Prof. Song Seung Jin.
2. Experimental setup, procedure and computational setup
2.1 Experimental apparatus and the geometry of the tested pump
As shown in Fig.1, the experimental apparatus mainly consists of 300mm-diameter pipes, a control valve, an electro-magnetic flow meter and a storage tank (volume is 1.6m3). A horizontal mixed flow pump with specific speed of 0.85 (dimensionless) or 350 (m3/min, m, min-1) is placed at the test section and it is coupled through a torque transducer to an induction motor, which is electronically controlled to maintain the rotational speed constant at any set value. In this study, the shaft rotational speed is kept constant at 900min-1. The pump performance is evaluated from shaft rotational speed, torque, flow rate, and the difference of static pressure between sections A and B in Fig. 1. The flow rate is adjusted with a control valve and is measured by an electro-magnetic flow meter. The mixed flow pump allows flow visualization as illustrated schematically in Fig. 2 and relevant details on the pump geometry are listed in Table 1. The impeller is a closed type which has six blades and the diffuser has thirteen vanes. The front shroud of the impeller is made of acrylic resin to allow visual access into the flow within the impeller. The distance, which is 0.28d2t, between the impeller outlet tip and the diffuser vane inlet tip is relatively large in order to keep the total head as low as possible at shut off operating point. The water jacket is equipped around the casing and is filled with water to restrain the reflection of laser on the acrylic resin. In addition, two pressure transducers having 6mm-diameter-throat are mounted circumferentially at 0.82b3 distance from the diffuser vane inlet tip on the casing wall to determine the number of rotating stall cell.
These taps are setup at the center of the diffuser passage X and Y in Figs. 10 and 11. Another two pressure transducers are placed at the outlet in the same passage to investigate the relationship of pressure fluctuations between the inlet and the outlet of the diffuser vane, as shown in Fig. 3.
Fig. 1 Experimental apparatus
Fig. 2 Sectional view of the tested pump Section B
Valve Torque
transducer
Motor Tested pump
Section A
Flow meter
Particle injector d=300mm
Inverter 2
2
6.7d 4d
Revolution counter
Tank
Table 1 Primary dimensions of the tested pump
Hub Tip Hub Tip
Impeller: Number of blades 6 Diffuser: Number of vanes 13 Inlet diameter(mm) 60.8 164 Inlet diameter (mm) 282.3 323.3 Outlet diameter (mm) 244 258.4 Outlet diameter (mm) 295.3 346.9 Inlet blade angle (°) 44.5 16.7 Inlet vane angle (°) 21.7 25.8 Outlet blade angle (°) 36.8 30.2 Outlet vane angle (°) 114.8 107.3
9d 2d
2d
d2t
Closed impeller Swirl stop
Transparent case Section I
Section II
Water jacket Vaned diffuser Pressure transducer
d d
0.59d2t
0.62d2t
2.2 PIV measurement system
The facility has been designed for measuring of unsteady flow through the transparent part of the impeller, the clearance between the impeller and the diffuser vanes, and the diffuser passages. Figure 3 shows the schematic view of the Dynamic PIV measurement system. A double-pulsed YLF (10mJ/pulse@1kHz) laser is used as a source of illumination. The beam is expanded to about a 1mm thick light sheet by an optical lens. In this study, the interval between the first pulse and the second one is 80μs and the cycle of double pulse is 2000μs. The flow is seeded using nylon powder, with a mean diameter of 50μm. The specific gravity of this particle is 1.03. A control system synchronizes the PIV system and the signal of a pressure transducer. The PIV measurement areas are shown in Fig .2 as Sections I and II. The images are recorded by a 1024x1024 pixels2, 1000frames/s digital high speed camera which has 2GB memories. Then, the images can be obtained during about 2 second, namely 1013 pair of images. Those images are analyzed with a commercial auto-correlation software. In this study, a recursive cross-correlation method is used for detecting the peak of correlation value. A 32x32 pixels2 of interrogation area is applied as the first processing pass and the 16x16 pixels2 of interrogation area is also applied as the last processing pass to eliminate the spurious vectors [10] . The Gaussian distribution is used for the sub-pixel analysis and no peak locking is confirmed by examining the histogram of the tracer movement distance.
Fig. 3 Schematic view of DPIV measurement system 2.3 Computational model
In the present study, a commercial software package (SCRYU/Tetra Ver.6) was used for the calculation. The transport equations are discretized using a finite-volume method. The code solves the Reynolds-averaged Navier-Stokes equations with a standard k-ε turbulence model. The logarithmic-law of wall function was also used to simulate boundary layers. Fig. 4 shows the computational domain and mesh, respectively. The clearance of 1mm between the impeller front shroud and the casing was included, but the balance holes were not included in the numerical setup. About three million unstructured meshes were used and 4-layer prism mesh was generated at the clearance. Mass-averaged flow rate was set at the inlet boundary and constant static pressure was assumed on the outlet boundary. The time step for unsteady calculation is 1.0x10-4 [s]. The calculation of 667steps corresponds to one revolution of the impeller. Calculations of six flow rate points (φ=0.132, 0.092, 0.087, 0.079, 0.069, 0.016) were carried out and the final condition of each case was given as the initial condition of the following calculation. Firstly, a calculation at BEP was conducted and then the flow rate was decreased accordingly. Basically, the calculations were conducted at least 4,000 steps (t*=6.0) and some cases at partial flow rate were implemented over 13,000 steps (t*=19.5) in order to obtain a quasi-periodic solution.
Fig. 4 Computational domain and mesh Synchronizer
Amplifier
Data recorder
Trigger
Optical lens Fiber
cable
YLF laser Water jacket
Flow
Particle tracer Pressure transducer
Camera PC
Data
5d
Stationary region Stationary region
6d
Rotational region
d d
3. Results and discussions
3.1 Pump characteristics and static pressure fluctuations
A performance curve of the tested pump is presented in Fig. 5. Calculated total head and shaft power, evaluated by averaging the flow field during 1 revolution of the impeller, are also plotted in Fig. 5. At flow conditions below φ=0.087, there is a steep change in the slope of the curve due to the diffuser rotating stall. From the engineering point of view, the CFD results agree well with the measured ones, although the predicted head is little higher. CFD predicted a stall at a flow rate ratio of 60%, which is 5%
lower than the measured value. This discrepancy may be caused by the following: (1) Mesh resolution, (2) Turbulence model.
Typical pressure signals in the diffuser passage under conditions of no-stall and stall are shown in Figs. 6 and 7(a) respectively. In the stalled condition at φ=0.069, pressure signals are analyzed by FFT as shown in Fig. 7(b), and it is found that the fundamental frequency is f*=0.083 and the amplitude is higher than that at the blade passing frequency. Based on the time lag of the two pressure signals mounted on the casing wall of the adjacent diffuser passage and the results obtained by DPIV, it is confirmed that the diffuser rotating stall occurs and the number of the stall cell is one, and the propagating direction of the stall cell is the same as that of impeller rotation. The cause of the onset of a diffuser rotating stall is closely related to the backflow at the vaned diffuser hub-side and it is investigated by using CFD in the reference [12].
Fig. 5 Pump performance curve Fig. 7(b) Power spectrum in stalled condition
Fig. 6 Static pressure fluctuation in no-stall condition
Fig. 7(a) Static pressure fluctuation in stalled condition
-0.4 -0.2 0.0 0.2 0.4
0 5 10 15 20
t*(=tΩ /2 π ) Δψs
Ps (Meas.) Ps (Calc.) PIV (Meas.) -0.4
-0.2 0.0 0.2 0.4
0 20 40 60 80 100
t*(=tΩ/2π) Δψs
-0.4 -0.2 0.0 0.2 0.4
0 20 40 60 80 100
t*(=tΩ/2π) Δψs
0.0 0.4 0.8 1.2
0.00 0.05 0.10 0.15 0.20
φ
ψ, τ
0.0 0.4 0.8 1.2 1.6
η∗
ψ (Meas.) ψ (Calc.) τ (Meas.) τ (Calc.) η* (Meas.) η* (Calc.)
Fig. 8 Relationship between static pressure signal and internal flow patterns at the inlet of Passage Y
Fig. 9 Comparison of static pressure fluctuation between experiment and CFD
φ=0.069, 1cell
-0.4 -0.2 0.0 0.2 0.4
0 5 10 15 20
t*(=tΩ/2π) Δψs
Ps Ps
Meas.
Calc.
φ=0.016, 2cells, at Passage Y (c) (d)
(e)
φ=0.069, 1cell φ=0.092, no-stall
Meas.
Calc.
(a)
(b)
0.00 0.05 0.10 0.15
0 1 2 3 4 5 6 7
f*(=2πf/Ω)
Vr
Rotating stall f*=0.083
Blade passing
3.2 Comparison of flow fields between the measured results and the calculated ones
Figure 8 shows the relationship between measured static pressure and internal flow patterns at the inlet of the vaned diffuser atφ=0.069. The static pressure fluctuation calculated by CFD is also depicted in Fig. 8. As for the PIV measurements, the vertical axis indicates flow conditions as follows. The outward flow condition is defined as +0.2, blockaded condition as 0, and backflow condition as -0.2. The symbols of (a)-(e) correspond to the Figs.10-13(a)-(e), respectively.
Figure 9 shows the comparison of static pressure fluctuation between experiment and CFD at φ=0.016. In authors' previous studies, it is experimentally confirmed that when the flow rate was further reduced, the propagation speed of stall cell increased and the number of stall cell eventually changed from 1 into 2 at φ=0.042. The diffuser rotating stall occurred even at shut off operating point and the number of the stall cell was two [1], [2].
The pressure fluctuation calculated by CFD agrees very well with the measured one except for the rotating stall propagation speed. The propagation speed calculated by CFD is about 10 to 20% higher than that of the measured one. The calculated vortex size might be smaller than the measured one and CFD might underestimate the head loss.
Maps of instantaneous velocity vectors and static pressure contours in flow fields near the inlet and the outlet of the diffuser calculated by CFD are shown in Figs. 10(a)-(e) and Figs. 12(a)-(e) respectively. Results of measured velocity by DPIV are also shown in Figs. 11(a)-(e) for the inlet flow field of Section I, and in Figs. 13(a)-(e) for the outlet field of Section II. Each non- dimensional time t* in the figure corresponds to the horizontal axis of Fig. 8. The scale of the velocity vector is expressed in the lower left of each figure.
3.3 Propagation mechanism of diffuser rotating stall and loss analysis
In this paragraph, firstly, the propagation mechanism of rotating stall will be discussed based on both the measured results and calculated ones. After that, the cause of a head-flow characteristic instability will be discussed to analyze the head loss based on the calculated results.
At partial flow rates, the flow separates from the suction surface at the leading edge of the diffuser vane casing side, the internal flow becomes non-axisymmetric and a strong unsteady vortex is generated at a diffuser inlet passage. The vortex rapidly develops toward the inlet of the diffuser vane, and a three-dimensional stall cell structure is generated [11]. Then, it disturbs the outward flow entering into the inlet of the diffuser vane and static pressure reaches its minimum due to the vortex core, which condition is found at (b) in Fig.8, and vector maps are displayed as Passage Y of Figs. 10(b) and 11(b). At the time t*=10.68, the flow at the outlet is stagnated as found in the vector maps in Figs. 11(b) and 12(b). In condition (c) in Fig. 8, the adverse static pressure gradient along the meridional direction is abruptly increased due to a strongly developed vortex at the diffuser vane inlet.
Then it causes a strong backflow in the whole area of one diffuser passage, as found from the velocity vector maps in Passage Y of Figs. 10-13(c). The outward flow at the outlet of the impeller is considerably influenced by this strong backflow and the loss of total pressure is increased. The backflow itself recovers static pressure in the diffuser passage. The circumferential component of the velocity from the impeller outlet is decreased due to strong backflow. Besides, the meridional velocity is even greatly decreased. Therefore, the flow incident angle becomes so large at the leading edge of the adjacent diffuser vane and a strong vortex is generated at the suction surface of the vaned diffuser inlet. Moreover, it seems that a stall cell propagates toward the adjacent passage in condition (d) of Fig. 8, as found from the vector maps in Passage Y of Figs. 10(d) and 11(d).
The static pressure takes its maximum when the backflow reaches the vaned diffuser inlet. At that moment, the stall cell has already shifted toward the adjacent passage. Thus, stagnation is caused by the impinging between backflow and outward flow from the impeller as an equilibrium boundary, and the static pressure reaches its maximum in condition (e) of Fig.8, as seen from the vector maps in Passage Y of Figs. 10(e) and 11(e). The flow at the outlet is also stagnated as shown in the vector maps in Figs.
12(e) and 13(e). The equilibrium boundary, which is formed by the stagnation mentioned above, is moved to downstream by the outward flow, and then the internal flow is gradually improved in condition (a) in Fig.8, and as shown in the vector maps in Passage Y of Figs. 10-13(a). It is experimentally clarified that the stall core covers one passage and the total of the backflow area and the blockaded area covers three passages based on the number of PIV picture frames and dimensionless frequency (f*=0.083) . In addition, the same results are obtained by CFD as shown in Figs. 14(a) and (b).
Moreover, as the flow rate is further decreased, the propagation speed of stall cell increases and the number of stall cell eventually changes from 1 into 2 at φ=0.042 due to the increase of circumferential component of absolute velocity at the impeller outlet. Figs. 15(a) and (b) show the calculated flow field at φ=0.016 and two stall cells can be confirmed. It is also clarified that each stall cell covers one passage and the total of the backflow area and the blockaded area covers three passages as well as the case of one stall cell.
Figure 16 shows total head coefficient (Ψ), impeller head coefficient (Ψi), diffuser pressure coefficient (Ψd), and the dimensionless circumferential component of absolute velocity at impeller outlet (Vθ2*) and at the vaned diffuser inlet (Vθ3*). It is found that Ψd and Vθ3* are steeply decreased with the occurrence of rotating stall. However, Ψi and Vθ2* are not largely changed. In the stalled condition, the circumferential velocity at the inlet of the diffuser vane is considerably reduced due to the backflow, accompanied by a rotating stall core. As a result, the rotating stall occurs in the range with negative slope of diffuser pressure performance Ψd as well as in reference [2]. Besides, the head loss increases at the clearance between the impeller and the diffuser vane. Therefore, pump characteristic instability is caused by the abrupt increase of head loss at the vaned diffuser inlet.
Our future work is to restrict the strong vortices at the vaned diffuser inlet and the backflow from the vaned diffuser outlet by optimizing the diffuser vane loading distributions.
(a) t*= 8.10
(a) t*= 8.10
(b) t*=10.68 (b) t*=10.68
(c) t*=11.40 (c) t*=11.40
(d) t*=12.00 (d) t*=12.00
(e) t*=12.75 (e) t*=12.75
Fig. 10 Calculated flow fields in the diffuser Fig. 11 Measured flow fields in the diffuser inlet region at φ=0.069 inlet region at φ=0.069
0.6u2t
0.6u2t
0.6u2t
0.6u2t
0.6u2t
Passage X Passage Y
Passage X Passage Y
Passage X
Passage X
Passage X Passage Y
Passage Y
Passage Y Passage X
Passage Y
0.6u2t
0.6u2t
Passage Y Passage X
Passage Y Passage X ψ
0.6u2t
Passage Y Passage X
Passage X Passage Y
ψ
ψ 0.6u2t
0.6u2t
ψ1.0
0.8 0.6 Ψs
1.0 0.8 0.6 1.0 0.8 0.6 1.0 0.8 0.6 1.0 0.8 0.6
Ψs Ψs Ψs Ψs
(a) t*= 8.10
(a) t*= 8.10
(b) t*=10.68 (b) t*=10.68
(c) t*=11.40 (c) t*=11.40
(d) t*=12.00 (d) t*=12.00
Fig. 12 Calculated flow fields in diffuser Fig. 13 Measured flow fields in diffuser outlet region (Passage Y) at φ=0.069 outlet region (Passage Y) at φ=0.069
0.6u
0.6u2t
0.6u2t
0.6u2t
ψ
ψ
0.6u2t 0.6u2t
0.6u2t
0.6u2t
ψ Ψs
Ψs Ψs Ψs
(e) t*=12.75 (e) t*=12.75
Fig. 12 Calculated flow fields in diffuser Fig. 13 Measured flow fields in diffuser outlet region (Passage Y) at φ=0.069 outlet region (Passage Y) at φ=0.069
(a) Instantaneous static pressure contour map
Fig. 14 Calculated flow fields at φ=0.069, t*=10.75
Fig. 15 Calculated flow fields at φ=0.016, t*=18.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0.00 0.05 0.10 0.15 0.20
φ Ψ, Ψi , Ψd , Vθ 2* , Vθ 3*
(b) Instantaneous velocity vectors 1.1
0.8 0.5 Ψs
Ψ (Meas.) Ψ (Calc.) Ψi (Calc.) Ψd (Calc.) Vθ2∗ (Calc.) Vθ3∗ (Calc.)
(a) Instantaneous static pressure contour map Ψs
(b) Instantaneous velocity vectors 0.6u2t
0.6u2t
1.1 0.8 0.5
Back flow
Vortex core Blockaded
Outward flow
Vortex core Back flow Blockaded Outward flow
Vortex core Ψs
Fig. 16 Loss analysis
4. Conclusions
[1] CFD is able to predict the positive slope of a head-flow characteristic.
[2] The instantaneous velocity vectors calculated by CFD qualitatively agree well with the measured ones by DPIV.
[3] The flow instability is caused by the vortex developed at the leading edge casing corner of the diffuser vane and the vortex induces backflow from the vaned diffuser outlet.
[4] It is clarified experimentally and numerically that the scale of a stall is about a four-passage expansion of total thirteen-passage in the vaned diffuser.
[5] Pump characteristic instability is caused by the sudden increase of head loss at the vaned diffuser inlet.
Acknowledgement
The authors would like to thank Torishima Pump Mfg. Co., Ltd. for permission to present this paper.
Nomenclature
b d f f*
H L n Ns
ωs ps
pt
Q t t*
u Vr
Passage width [m]
Diameter [m]
Frequency [1/s]
Nondimensional frequency =2πf/Ω Total head [m]
Shaft Power [kW]
Number of rotating stall cells Specific speed [m3/min, m, min-1] Nondimensional specific speed Static pressure [Pa]
Total pressure [Pa]
Flow rate [m3/min]
Time [s]
Nondimensional time=tΩ/2π Peripheral velocity [m/s]
Root mean square value of a signal [V]
Vθ
Vθ2*
Vθ3*
φ η η∗ ρ τ Ψ Ψd
Ψi Ψs ΔΨs
Ω
Circumferential velocity [m/s]
= Vθ2/u2t
= Vθ3/u2t
Flow coefficient=Q/60/πb2d2tu2t
Efficiency=φΨ/τ Efficiency ratio=η/ηbep Fluid density [kg/m3]
Shaft power coefficient=2L/(ρu2t3πb2d2t) Total head coefficient=2gH/u2t2
Diffuser outlet static to diffuser inlet static pressure coefficient=2(ps4-ps3)/ρu2t2
Impeller outlet total to impeller inlet total pressure coefficient=2(pt2-pt2)/ρu2t2
Static pressure coefficient=2ps/ρu2t2
Fluctuation of static pressure coefficient Impeller rotational speed [rad/s]
References
[1] Miyabe, M., Maeda, H., Umeki, I., and Jittani, Y., 2006, “Unstable Head-Flow Characteristic Generation Mechanism of a Low Specific Speed Mixed Flow Pump,” Journal of Thermal Science, Vol.15, No.2, pp. 115-120.
[2] Miyabe, M., Furukawa, A., Maeda, H., Umeki, I., and Jittani, Y., 2006, "Unstable Performance of a Low Specific Speed Mixed Flow Pump (in Japanese)," Trans. JSME, Vol.72, No.722, pp. 2481-2487.
[3] Yoshida, Y., Murakami, Y., Tsurusaki, T., and Tsujimoto, Y., 1991, “Rotating Stalls in Centrifugal Impeller/Vaned diffuser Systems,” Proceedings of the First ASME/JSME Joint Fluids Engineering, Conference, Portland, FED-107, pp. 125-130.
[4] Sano, T., Yoshida, Y., Tsujimoto, Y., and Matsushima, T., 2002, “Numerical Study of Rotating Stall in a Pump Vaned Diffuser, ” ASME Journal of Fluids Engineering, Vol.124, pp. 363-370.
[5] Hergt, P., and Starke, J., 1985, "Flow Patterns Causing Instabilities in the Performance Curves of Centrifugal Pumps with Vaned Diffusers," Proceedings of the Second International Pump Symposium. pp. 67-75.
[6] Eisele, K., Zhang, Z., Casey, M. V., Gülich, J., and Schachenmann, A., 1997, “Flow Analysis in a Pump Diffuser-Part1 LDA and PTV Measurements of the Unsteady Flow,” ASME Journal of Fluids Engineering, Vol.119, pp. 968-977.
[7] Sinha, M., Pinarbashi, A., and Katz, J., 2001, “The Flow Structure During Onset and Developed States of Rotating Stall with a Vaned Diffuser of a Centrifugal Pump,” ASME Journal of Fluids Engineering, Vol.123, pp. 490-499.
[8] Kurokawa, J., 1988, “Performance Curve Instability of a Diffuser Pump at Low Flow-Rates (in Japanese),” Trans. JSME, Vol.54, No.508, pp. 3449-3456.
[9] Hayami, H., Okamoto, K., Aramaki, S., and Kobayashi, T., 2003, “Development of a New Dynamic PIV System,” Proc. of the 7th International Symposium of Fluid Control, Measurement and Visualization, Sorrento, pp. 1-6.
[10] Hart, D.P., 2000, “Super-Resolution PIV by Recursive Local-Correlation,” Journal of Visualization, 3-2, pp. 187-194.
[11] Inoue, M., Kuroumaru, M., Tanino, T., and Furukawa, M., 2000, “Propagation of Multiple Short-Length-Scale Stall Cells in an Axial Compressor Rotor,” ASME Journal of Turbomachinery, Vol.122, pp. 45-54.
[12] Miyabe, M., Furukawa, A., Maeda, H., Umeki, I., and Jittani, Y., 2008, "On Improvement of Characteristic Instability and Internal Flow in Mixed Flow Pumps," Journal of Fluid Science and Technology, Vol.3, No.6, pp. 732-743.
Subscripts 1=impeller inlet 2=impeller outlet 3=diffuser inlet 4=diffuser outlet h=hub side
t=tip side or casing side
Ψs ΔΨs
Ω
