Effect of blade outlet angle on radial thrust of single-blade centrifugal pump

Transcription

1 IOP Conference Series: Earth and Environmental Science Effect of blade outlet angle on radial thrust of single-blade centrifugal pump To cite this article: Y Nishi et al 2012 IOP Conf. Ser.: Earth Environ. Sci View the article online for updates and enhancements. Related content - Investigations of internal turbulent flows in a low-head tubular pump and its performance predictions X L Tang, X S Chen, F J Wang et al. - Blade design loads on the flow exciting force in centrifugal pump Y Xu, A L Yang, D P Langand et al. - Performance and internal flow condition of mini centrifugal pump with splitter blades T Shigemitsu, J Fukutomi, K Kaji et al. This content was downloaded from IP address on 23/09/2018 at 23:51

2 Effect of blade outlet angle on radial thrust of single-blade centrifugal pump Y Nishi 1, J Fukutomi 2 and R Fujiwara 3 1 Department of Mechanical Engineering, Ibaraki University, Nakanarusawacho, Hitachi-shi, Ibaraki, , Japan 2 Institute of Technology and Science, The University of Tokushima, 2-1 Minamijosanjima-cho, Tokushima-shi, Tokushima, , Japan 3 Graduate School of Advanced Technology and Science, The University of Tokushima, 2-1 Minamijosanjima-cho, Tokushima-shi, Tokushima, , Japanre y-nishi@mx.ibaraki.ac.jp Abstract. Single-blade centrifugal pumps are widely used as sewage pumps. However, a large radial thrust acts on a single blade during pump operation because of the geometrical axial asymmetry of the impeller. This radial thrust causes vibrations of the pump shaft, reducing the service life of bearings and shaft seal devices. Therefore, to ensure pump reliability, it is necessary to quantitatively understand the radial thrust and clarify the behavior and generation mechanism. This study investigated the radial thrust acting on two kinds of single-blade centrifugal impellers having different blade outlet angles by experiments and computational fluid dynamics (CFD) analysis. Furthermore, the radial thrust was modeled by a combination of three components, inertia, momentum, and pressure, by applying an unsteady conservation of momentum to this impeller. As a result, the effects of the blade outlet angle on both the radial thrust and the modeled components were clarified. The total head of the impeller with a blade outlet angle of 16 degrees increases more than the impeller with a blade outlet angle of 8 degrees at a large flow rate. In this case, since the static pressure of the circumference of the impeller increases uniformly, the time-averaged value of the radial thrust of both impellers does not change at every flow rate. On the other hand, since the impeller blade loading becomes large, the fluctuation component of the radial thrust of the impeller with the blade outlet angle of 16 degrees increases. If the blade outlet angle increases, the fluctuation component of the inertia component will increase, but the time-averaged value of the inertia component is located near the origin despite changes in the flow rate. The fluctuation component of the momentum component becomes large at all flow rates. Furthermore, although the time-averaged value of the pressure component is almost constant, the fluctuation component of the pressure component becomes large at a large flow rate. In addition to the increase of the fluctuation component of this pressure component, because the fluctuation component of the inertia and momentum components becomes large (as mentioned above), the radial thrust increases at a large flow rate, as is the case for the impeller with a large blade outlet angle. Published under licence by Ltd 1

3 1. Introduction A single-blade centrifugal pump can form a large passed particle size (the minimum particle size for the flow channel in a pump). Thus, it is commonly used as a sewage pump. However, the impeller is geometrically asymmetrical, and the axially asymmetrical volute casing is also installed in the impeller perimeter. Therefore, pressure distribution of the impeller circumference becomes non-uniform, and a large radial thrust arises during operation [1,2]. This radial thrust causes vibrations of the pump shaft, reducing the service life of bearings and shaft seal devices. Therefore, to improve pump reliability, it is extremely important to quantitatively understand this radial thrust and clarify its behavior and generation mechanism. For radial thrust on single-blade centrifugal pumps, studies have been conducted to understand the effects of the number of blades [1,3], blade angle distributions [4], casings [1,4], and the relationship with pressure distributions on the blade surfaces [2]. However, details of the behavior and generation mechanism of the radial thrust in a single-blade centrifugal pump are not yet clearly understood. The authors proposed a design method for a single-blade centrifugal impeller, and investigated the performance characteristics and radial thrust of a single-blade centrifugal impeller, which was designed based on the design method by experiments and computational fluid dynamics (CFD) analysis [5]. Furthermore, radial thrust components acting on the impeller were modeled by the law of conservation of unsteady momentum, and the effects of these components on the radial thrust were clarified [6]. In this study, we designed an impeller that enlarged only the blade outlet angle to the single-blade centrifugal impeller used. In addition, the radial thrust which acts on the impeller from which a blade outlet angle differs was investigated by an experiment and a CFD analysis. Furthermore, the radial thrust component that acts on an impeller is modeled, and the effect of the blade outlet angle on the radial thrust and its components was clarified. 2. Experimental apparatus and method Figure 1 shows a schematic diagram of two kinds of test impellers with different blade outlet angles; their technical specifications are given in Table 1. TYPE A is an impeller of β b2 =8, and is designed based on a design method proposed in a previous report [5]. TYPE B is an impeller for which the only change was the blade outlet angle of 16, as it was made using the same meridian flow channel as TYPE A. Figs. 2 and 3 show the blade angle distribution and blade loading distribution to the dimensionless meridian plane distance m/m 2 on a central stream line of TYPE A and TYPE B. As shown in Fig. 2, TYPE A and TYPE B both have blade inlet angles of 13, and are smoothly changed to the value of each blade outlet angle. As a result, as shown in Fig. 3, for the blade loading distribution, both impellers are aft-loading. Figure 4 shows a schematic diagram of the experimental apparatus. The experiment was conducted using a rotational speed of n = 1740 min -1, and the flow rate Q was measured with an electromagnetic flow meter. The total head H was determined by measuring the static pressure using small-straingauge-type pressure transducers attached to the static pressure holes before and after the pump. The shaft power L was determined by separately measuring the rotational speed n with an electromagnetic pickup, and the driving torque T was measured with a torsion-bar-type torque detector. In the coordinate system shown in Fig. 5, the directions parallel and perpendicular to the volute casing were defined as the X- and Y-axes, respectively. With the impeller phase angle θ0 taken in an anticlockwise direction from the X-axis, the position at which the blade outlet end passes the X-axis (the position shown in Fig. 5) was defined as θ0 = 0. Eight points for measuring pressure fluctuations were located 10-mm outward from the impeller outlet, as shown in Fig. 5, at intervals of 45, starting at θ = 22.5 in the anticlockwise direction, with θ = 0 set on the X-axis. When the blade outlet end was at θ0 = 0, a trigger signal was generated and the measurement of pressure fluctuation was synchronized with the rotation of the impeller. 2

4 Table 1 Specifications of test impellers Section A-A (TYPE A) Section A-A (TYPE B) Fig. 1 Test impellers TYPE A TYPE B 67 mm Impeller suction diameter D 0 Impeller inner diameter D 1 58 mm Impeller outer diameter D mm Blade inlet width b 1 56 mm Blade outlet width b 2 56 mm Blade inlet angle β b1 13 Bl d tl t l β TYPE A TYPE B Design value(type A) Design value(type B) Finite number of blades(type A) Finite number of blades(type B) β b 12 8 d(rv u )/dm Inlet m/m 2 Outlet Inlet m/m 2 Outlet Fig. 2 Blade angle distributions Fig. 3 Blade loading distributions The measurement of radial thrust by the X-Y load cell included in the bearing perimeter was synchronized with the rotation of the impeller. A strain gauge was mounted on the X-Y load cell in the four-active-gauge method. The dynamic calibration method [7] was adopted for calibration. To calibrate the relationship between the output voltage and force, a known centrifugal force was applied in air on the calibration disk with a mass equal to the impeller mass minus the buoyancy acting on the impeller. The test impeller and the calibration disk were in dynamic balance. The influence of heat on the bearing section was nullified using a measuring method in which the pump was stopped for a short time of about 15 seconds under thermally stable conditions to adjust the zero point, and was immediately brought back to operation under the same conditions [8]. Flow control valve Measurement point Test pump Torque meter Tachometer Motor Tank Flow meter Pressure taps Fig. 4 Experimental apparatus Fig. 5 Measurement points 3

5 3. Method and analysis conditions In this study, we used the FLUENT 6.3 general-purpose analysis code. Three-dimensional unsteady flow analysis was conducted giving consideration to the mutual interference of the impeller and the volute casing. In this analysis, the standard wall function was used to handle regions near wall surfaces, and the standard k ε model was adopted as the turbulent flow model. The computational domain comprises a suction pipe, an impeller, a volute casing, and a discharge pipe, as shown in Fig. 6. The total number of elements of TYPE A and TYPE B reached about 900,000. In this study, the gaps between the impeller and the volute casing were not modeled. The inlet and outlet of the computational domain were the suction pipe inlet and the discharge pipe outlet, respectively. For boundary conditions, the mass flow rate was given to the inlet boundary, and a gauge pressure of 0 Pa was given to the outlet boundary. The same angular velocity as in the experimental conditions was given to the fluid domain of the impeller in a rotational coordinate system. The impeller surface and the rear and front shroud walls were defined in a relative coordinate system. The suction pipe, volute casing, and discharge pipe were defined on a fixed wall in an absolute coordinate system. To bond the outlet of the suction pipe to the suction inlet of the impeller, and the outlet of the impeller to the inlet of the volute casing, the sliding mesh method [9] was used. Impeller 0.8 TYPE A(Exp.) TYPE B(Exp.) TYPE A(Cal.) TYPE B(Cal.) Design point Discharge pipe Outlet boundary ψ η Volute casing Suction pipe λ Inlet boundary Fig. 6 Computational domain and grids φ Fig. 7 Performance curves 4. Experimental and analytical results and discussion 4.1 Performance characteristics The experimental value and CFD analysis value of a performance curve for TYPE A and TYPE B are shown in Fig. 7. The design point of the impeller of TYPE A is also shown in Fig. 7. If the experimental values of the head coefficient ψ of TYPE A and TYPE B are compared, both values of ψ are in general agreement at the shut-off flow rate. However, if the flow rate coefficient φ becomes larger than 0.005, ψ for TYPE B is large. This is because the blade outlet angle of TYPE B is large, which is because of the increase in vu2, i.e., the theoretical pump head. The experimental value and CFD analysis value of ψ for TYPE A are in good agreement. In addition, with respect to the ψ of TYPE B, although the CFD analysis value is slightly higher than the experimental value, both are qualitatively in agreement. Neither of the head curves of TYPE A and TYPE B have a positively sloped instability characteristic. With respect to the experimental value of the shaft power coefficient λ, λ of TYPE A and TYPE B are mostly in agreement at the shut-off flow rate. λ of TYPE B becomes large according to the increase of the above-mentioned theoretical pump head with an increase of the flow rate. For the CFD analysis value, this tendency is realized. With respect to the experimental value of the pump efficiency η, the best efficiency point flow rates for TYPE A and TYPE B are almost the same. The maximum 4

6 efficiency value of TYPE B has improved from 62.4% of TYPE A to 63.4%, and η of TYPE B is high at a large flow rate. In the CFD analysis value, η of TYPE B is similarly higher than that of TYPE A from the best efficiency point flow rate to a large flow rate. Therefore, the experimental value and CFD analysis value are qualitatively in agreement. In addition, because the impeller and the volute casing do not match well, the best efficiency point flow rate of TYPE A is a large flow rate from the design flow rate φ = [5,6]. 4.2 Comparison of Radial Thrust Radial thrust can be expressed as a vector sum of the averaged component (time-averaged value) and the fluctuating component [1,2,7]. This study defines the vector difference between the radial thrust F and its averaged component Fav as the fluctuating component ΔF, which is discussed below. The time-averaged value fav of the radial thrust and the root mean square value of the fluctuation component Δf that were acquired in an experiment and CFD analysis are shown in Fig. 8. Here, the radial thrust of the CFD analysis value was calculated by integrating with the pressure and wall shearing stress that act on the blade surface. The experimental values of fav for TYPE A and TYPE B are in general agreement at every flow rate. Both experimental fav values are a minimum in the φ = neighborhoods, and become large as the flow rate subsequently becomes small or large. The time-averaged pressure distribution of Fig. 9 shows that CP of TYPE B is higher than that of TYPE A with an increase in flow rate as with the head coefficient. However, CP of TYPE B is uniformly higher than that of TYPE A at every flow rate. Therefore, it is thought that the time-averaged value of the radial thrust of both impellers does not change at every flow rate. The CFD analysis value of fav is a minimum for < φ < However, the tendency that becomes large at small or large flow rates is the same as that of the experimental value. Since this has the large width of a volute casing to this impeller, a best efficiency point flow rate becomes a large flow rate from the design flow rate φ = However, since the angle of divergence of a volute casing is small (as shown in Fig. 5), uniform pressure in the direction of the circumference is obtained for < φ < Therefore, it is believed that the time-averaged value of radial thrust is also a minimum there. On the other hand, the experimental values for TYPE A and TYPE B are almost the same about the root mean square value of Δf in the domain where the flow rate is smaller than φ = However, in the domain where the flow rate is larger than φ = 0.019, the root mean square value of Δf for TYPE B is larger than that of TYPE A. This tendency is also the same at the CFD analysis value. From the above-mentioned discussion, it can be said that the qualitative tendency of the obtained radial thrust in this CFD analysis is sufficient f av (TYPE A, Exp.) f av (TYPE B, Exp.) Δf(TYPE A, Exp.) Δf(TYPE B, Exp.) f av (TYPE A, Cal.) f av (TYPE B, Cal.) Δf(TYPE A, Cal.) Δf(TYPE B, Cal.) φ=0.008(type A) φ=0.019(type A) φ=0.030(type A) φ=0.047(type A) φ=0.008(type B) φ=0.019(type B) φ=0.030(type B) φ=0.047(type B) f C P φ θ[deg] Fig. 8 Comparison of radial thrusts Fig. 9 Time-averaged pressure distributions (Exp.) 5

7 (a) TYPE A (b) TYPE B Fig. 10 Changes of radial thrust (CFD) The Lissajous figures of the radial thrust obtained by CFD analysis for TYPE A and TYPE B are shown in Figs. 10(a) and 10(b), respectively. In Figs. 10(a) and 10(b), the values of radial thrust at θ0 = 0, 90, 180, and 270 are denoted by,,, and, respectively, and the time-averaged values for radial thrust are denoted using the same notation system. These notational conventions are adopted in the illustrations below. The time-averaged value for the radial thrust of TYPE A and TYPE B is located mainly at the origin at φ = and φ = 0.030, respectively. If the flow rate decreases, it will move to the +Y axis direction, or if the flow rate increases, it will move to the -Y axis direction. As shown in Fig. 9, CP for both TYPE A and TYPE B are almost constant in the direction of the circumference at φ = and φ = 0.030, respectively. However, this is because CP near the winding start of the volute is low at the small flow rate φ = 0.008, and CP near the winding end of the volute becomes high at the large flow rate φ = On the other hand, when consideration is given to the fluctuation component Δf, TYPE B is larger than TYPE A at φ Also, the difference of TYPE B and TYPE A is larger as the flow rate increases. Theoretical blade loading with a finite number of blades on the central stream line from the blade inlet to the exit is also shown in Fig. 3. Here, a calculation of theoretical blade loading with a finite number of blades uses the time-averaged value of the slip factor k in the CFD analysis at φ = Since both the theoretical blade loading of TYPE A and TYPE B decrease rapidly near the blade exit under the influence of the slip, they are middle loads. Since TYPE B becomes large for this middle load, and the theoretical radial thrust with a finite number of blades of TYPE B (which is integrated with this) also becomes large, it is believed that the fluctuation component Δf of TYPE B became large. 4.3 Comparison of radial thrust components In this section, using the following methods, the radial thrust components for TYPE A and TYPE B are modeled, and each component is compared. Based on the law of conservation of unsteady momentum, the radial thrust F that acts on the blade pressure surfaces, blade suction surfaces, and inner shroud surfaces are modeled by the following equation. F F F F (1) I M P 6

8 Here, FI denotes the inertia component [N], FM denotes the momentum component [N], and FP denotes the pressure component [N]. Radial thrust by shearing stress is ignored. The x- and y-components of the inertia component FI, which is a force generated by the change of momentum of the impeller per unit time, are given by the following equations. F Ix F Iy dvx dv (2) V dt dv y dv (3) V dt Here, V denotes the inspection volume, i.e., the volume of the flow channel in the impeller [m3]. The x- and y-components of the momentum component FM, which is a force generated by the difference between the momentum flowing out of the impeller outlet per unit time and the momentum flowing in from the impeller suction inlet per unit time, are given by the following equations. F Mx vx2vr 2dA v x0v a0da (4) A0 F My v y2v r 2dA v y0v a0da (5) A0 The x- and y-components of the pressure component FP, which is a force resulting from the pressure acting on the fluid on the inspection surface, are given by the following equations. F P cos da (6) Px Py 2 F P sin da (7) 2 Using the above equations, the x- and y-components of the radial thrust acting on the impeller are given by the following equations. F F x y dvx dv v x2vr 2dA v x0v a0da P2 cosda V dt A0 (8) dv y dv v y2vr 2dA v y0v a0da P2 sinda V dt A0 (9) Fig. 11(a) and 11(b) compares the Lissajous figures of TYPE B for F obtained by component analysis and direct integration at φ = and φ = Here, in calculating the pressure component FP of the component analysis value, the static pressure of the wall surface on the shroud side was used as the static pressure at the impeller outlet, with the static pressure assumed to be constant in the direction of the width. Although for the direction of the fluctuation component Δf, there is a small difference between the component analysis value and the direct integration value (CFD analysis value), they are in good agreement. It appears that the reason why the CFD analysis value differs slightly from the component analysis value is the absence of the effect of shearing stress and the effect of the width- 7

9 direction distribution of the static pressure at the impeller outlet. In addition, in other flow rates for TYPE B, the component analysis value and the CFD analysis value are in good agreement. It was confirmed that the component analysis value and the CFD analysis value are also in good agreement for TYPE A [6]. Below, each component of TYPE A and TYPE B is therefore examined in detail. The inertia component fi of TYPE A and TYPE B that was determined in the CFD analysis is shown in Fig. 12(a) and 12(b), respectively. With respect to the time-averaged value of the inertia component, TYPE A and TYPE B are located mainly at the origin, despite changes in the flow rate. The magnitude of ΔfI for TYPE A decreases slightly with an increase in the flow rate. On the other hand, if the magnitude of ΔfI for TYPE B changes from φ = to φ = 0.019, it will become small, but if the flow rate subsequently increases, it will become a little large. With respect to the size of the fluctuation component ΔfI, TYPE B is larger at every flow rate because vu of TYPE B is large and the unsteadiness of the flow is strong. With respect to the direction of the fluctuation component ΔfI, it is located in almost the same direction as the same impeller. That is, it rarely changes with flow rates. Next, the momentum component fm of TYPE A and TYPE B that was found in the CFD analysis is shown in Fig. 13(a) and 13(b), respectively. The time-averaged value of the momentum component of TYPE B is slightly larger than that of TYPE A. At a small flow rate φ = 0.008, the time-averaged value of TYPE A and TYPE B changes in direction at the winding start of the volute. On the other hand, at a large flow rate φ = 0.047, the time-averaged value of TYPE A and TYPE B changes in a direction opposite to the discharge port. Although the fluctuation component ΔfM of the momentum component is small compared with other components, it will become large if the flow rate decreases. With respect to the size of the fluctuation component ΔfM, TYPE B is larger than TYPE A. This is considered to be due to the influence of vu2 of TYPE B being larger than that of TYPE A. The pressure component fp of TYPE A and TYPE B that was obtained in the CFD analysis is shown in Fig. 14(a) and 14(b), respectively. At φ = and φ = 0.030, the time-averaged value of the pressure component of TYPE A and TYPE B is located mainly at the origin, as was the case with the CFD analysis value of the radial thrust shown in Fig. 10(a) and 10(b), respectively. If the flow rate decreases, it will move in the +Y axis direction, and if the flow rate increases, it will move in the -Y axis direction. This shows that the pressure component is dominant in the time-averaged value of the radial thrust. The time-averaged values of the pressure component of TYPE A and TYPE B show an almost same value at every flow rate. This is because the CP distribution of TYPE B is uniformly higher than that of TYPE A, as mentioned above. On the other hand, the size of ΔfP is the same as that indicated by the tendency of Fig. 10(a) and 10(b), except for φ = and φ = 0.019, which are the opposite. Also, the size of ΔfP becomes large as the flow rate increases. Moreover, although ΔfP has a value that is close to the fluctuation component of the inertia component at φ = 0.008, at every flow rate, ΔfP is the largest when compared with other components. When ΔfP of TYPE A and TYPE B are compared, at the small flow rate φ = 0.008, both have almost the same size, but at the large flow rate, TYPE B is larger than TYPE A at φ 0.019, as in Fig. 10(a) and 10(b). Therefore, it is understood that the influence of the pressure component on the fluctuation component of the radial thrust is also significant. As mentioned above, although the pressure components of TYPE A and TYPE B are almost the same size at a small flow rate, because the inertia component and momentum component of TYPE B are larger than those of TYPE A, the total radial thrust also becomes large. From the best efficiency point flow rate to a large flow rate, although the time-averaged values of the pressure components of TYPE A and TYPE B are generally in agreement, the fluctuation component of the pressure component of TYPE B is much larger than that of TYPE A. Furthermore, the fluctuation component of the inertia component of TYPE A becomes small as the flow rate increases. However, although the fluctuation component of the inertia component of TYPE B rarely changes at small flow rates and the best efficiency point flow rate, it will become large if the flow rate becomes large. Therefore, the total radial thrust of TYPE B becomes much larger than that of TYPE A. 8

10 (a) φ = (b) φ = Fig. 11 Lissajous figures of radial thrust (TYPE B) (a) TYPE A (a) TYPE A (a) TYPE A (b) TYPE B (b) TYPE B (b) TYPE B Fig. 12 Inertia component (CFD) Fig. 13 Momentum component (CFD) Fig. 14 Pressure component (CFD) 5. Conclusion 9

11 Our study on the radial thrust of two kinds of impellers with different blade outlet angles yielded the following results: (1) An impeller with a blade outlet angle of 16 degrees has a total head higher than an impeller with a blade outlet angle of 8 degrees at a large flow rate. However, since the pressure of the circumference of an impeller with a blade outlet angle of 16 degrees increases uniformly, the time-averaged values of the radial thrust of the impeller whose blade outlet angles are 16 degrees and 8 degrees are mostly in agreement at every flow rate. (2) For the impeller with a large blade outlet angle, the blade loading becomes large, and the fluctuation component of the radial thrust therefore increases. This tendency becomes significant at a large flow rate. (3) If the fluctuation component of the inertia component increases the blade outlet angle, it will increase, but the time-averaged value of the inertia component is located mainly at the origin despite changes in the flow rate. (4) The time-averaged value of the momentum component will become slightly large if the blade outlet angle is increased, and the fluctuation component of the momentum component also becomes large at every flow rate. (5) Even if the time-averaged value of the pressure component increases the blade outlet angle, it rarely changes, but it exhibits the same actions as the time-averaged value of the radial thrust. The fluctuation component of the pressure component becomes large at large flow rates. In addition, since the fluctuation component of the inertia component and the momentum component also becomes large, for the impeller with a large blade outlet angle, the radial thrust increases at a large flow rate. Nomenclature A b C P D F f g H L m n P Area of the impeller [m 2 ] Blade width [m] Pressure coefficient (=(P-P s )/(ρu 2 2 /2)) Blade diameter [m] Radial thrust [N] Radial thrust coefficient (=F/(ρu 2 2 b 2 r 2 /2)) Gravitational acceleration [m/s 2 ] Total head [m] Shaft power [W] meridian plane distance [m] Rotational speed [min -1 ] Static pressure [Pa] P s Q r u v β b η λ ρ φ ψ Static pressure at suction side reference position[pa] Flow rate [m 3 /s] Impeller radius [m] Circumferential velocity [m/s] Absolute velocity [m/s] Blade angle [deg] Pump efficiency (=ρgqh/l) Shaft power coefficient (=L/(ρπD 2 b 2 u 2 3 /2)) Fluid density [kg/m 3 ] Flow rate coefficient (=Q/(πD 2 b 2 u 2 )) Head coefficient (=H/(u 2 2 /2g)) Subscripts 0, 1, 2 a r Impeller suction inlet, Blade inlet, Blade outlet Axial component Radial component u x y Circumferential component x component y component References [1] Okamura T 1979 Transactions of the Japan Society of Mechanical Engineers, Series B 45 (398): (in Japanese) [2] Aoki M 1984 Transactions of the Japan Society of Mechanical Engineers, Series B 50 (451): (in Japanese) [3] Benra F K, Dohmen H J and Schneider O 2003 Calculation of hydrodynamic forces and flow induced vibrations of centrifugal sewage water pumps 4th ASME/JSME Joint Fluids Engineering Conference Paper FEDSM Honolulu Hawaii USA [4] Benra F K, Dohmen H J and Sommer M 2006 Experimental investigation of hydrodynamic forces for different configurations of single-blade centrifugal pumps The 11th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC-11), Honolulu, Hawaii, USA. [5] Nishi Y. Fujiwara R and Fukutomi J 2009 Journal of Fluid Science and Technology 4 (3):

12 [6] Nishi Y, Fukutomi J and Fujiwara R 2011 International Journal of Fluid Machinery and Systems 4 (4): [7] Tanaka K, Arai M, Ikeo S and Matsumoto Y 1989 Turbomachinery 17 (4): (in Japanese) [8] Ishida I 2002 Turbomachinery 30 (12): (in Japanese) [9] Fluent User s Manual 2006: 9-30 (in Japanese) 11