NUMERICAL AND EXPERIMENTAL INVESTIGATION OF CAVITATION IN ... · PDF fileNUMERICAL AND EXPERIMENTAL INVESTIGATION OF CAVITATION IN AXIAL PUMPS ... ch Ch a r c te is v lo y h = k

Eleventh International Water Technology Conference, IWTC11 2007 Sharm El-Sheikh, Egypt

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NUMERICAL AND EXPERIMENTAL INVESTIGATION OF

CAVITATION IN AXIAL PUMPS

Nabil H. Mostafa and Mohammed A. Boraey

Mechanical Power Engineering Department, College of Engineering

Zagazig University, Zagazig, 44519, Egypt. E-mail: [email protected]

ABSTRACT Axial pumps have a wide range of applications, and cavitation is one of the main causes of there performance degradation. So, the present study investigates experimentally and numerically the performance of cavitating axial pumps. In this study a three-dimensional Navier-Stokes code was used (CFDRC, 2004) to model the two-phase flow field around a four blades axial pump. The governing equations are discretized on a structured grid using an upwind difference scheme. The numerical simulation used the standard K-� turbulence model to account for the turbulence effect. The cavities shapes were determined over the blades. Also, the three-dimensional flow field around the cavitating impeller and the cavities vicinity was determined. The impeller diameter is 4 in. (101.6 mm). The computational grid elements were about 180,000 cells and distributed in sixteen domains. Reynolds number is about 333,000. The macroscopic behavior of the formation and transport of vapor bubbles is discussed with the effect of the Pressure, Velocity and Vorticity distribution. As observed experimentally the cavities formed around the blade tip at the suction side. The results were compared to a model impeller with Perspex glass casing. In the experimental part different photos were obtained using a stroboscopic light synchronized with the impeller rotational speed. The photos clarified the details of the formed cavities and showed a good agreement with the numerical simulation. The study showed that the cavitation model used by the CFD-ACE code is capable of predicting cavitation in rotating machines taking into consideration the slip speed factor (ratio between experimental rotating impeller speed and theoretical rotating frame speed). With slip speed factor 0.67, there is a good agreement between the experimental cavity shape and the numerically predicted one. Keywords: Cavitation, Axial Pump, CFD, Two Phase Flows and slip speed factor.


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NOMENCLATURE Ce, Cc Phase change rate coefficients CN Slip speed factor “ratio between impeller actual

rotational speed and theoretical rotating frame speed”

D Diameter of the pump impeller mm DH Diameter of the pump hub mm f Vapor mass fraction k Turbulence kinetic energy m2/s2 L Total length of the pump rotor mm Lc Chord length of the blade mm LI Total length of the impeller mm Ln Length of impeller nose mm Lp Projected length of the blade in the axial direction mm N Pump rotational speed r.p.m. P Fluid static pressure N/m2 psat Saturation pressure N/m2 P’turb The magnitude of pressure fluctuations N/m2 Pt Total pressure N/m2 Pv Vapor pressure N/m2 R Universal gas constant Nm/kg.K R Phase change rate Ren Reynolds number T Fluid temperature K �t Physical time step second u,v,w Fluid velocity components in x, y, z, respectively m/s V�

Velocity vector Vch Characteristic velocity Vch =�κ W Molecular weight kg/kg-mol

GREEK LETTERS αv Vapor volume fraction α g gas volume fraction β Rotor blade angle (angle between the axial direction

and the normal to blade) degree

Γ Effective exchange coefficient ρ The mixture density kg/m3 σ Cavitation number ((p∞-pv)/ (1/2ρlu2)) N/m

SUFFICES c Bubble reduction and collapse e Bubble generation and expansion Gas, G Gaseous phase L Liquid phase V Vapor phases


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INTRODUCTION Axial pumps are used extensively in industry; however the research work about cavitation in axial pumps is limited. Most of the experiments were carried out on a single hydrofoil at varying incidence angles, cavitation numbers, and free stream temperatures, in order to investigate the characteristics of cavitation instabilities and the impact of thermal cavitation effects as in Cervone et al., (2006). An experimental and theoretical model was developed to describe the unsteady behavior of cavitation, including vapour cloud shedding around 3D- hydrofoils by Mostafa et al., (2000), Singhal et al., 2002 and Mostafa (2001). A limited number of studies tried to simulate the cavitation in axial pumps. An energy model was used to predict the cavitation erosion in centrifugal pumps, but it predicts the hydrodynamic aspect of cavitaion only (Mostafa, et al., 1990). Iga et al., (2004) studied numerically the cavitation stabilities through flat plate cascades, which similar to “forward rotating cavitation,” “rotating stall cavitation” and “cavitating surge” occurs in high speed rotating fluid machinery. These are presented numerically under three blades cyclic condition. Fukaya et al., (2003) predicted the cavitation performance of an axial pump, but the model used does not include a turbulence model. Watanable and Brennen (2003) investigated the unsteady dynamics and inherent instabilities of a cavitating propeller operating in a water tunnel. An experimental and theoretical investigation of a cavitating propeller in a uniform inflow is presented by Pereira et al., (2004). The flow field was investigated by imaging techniques to extract quantitative information on the cavitation; however it assumed an inviscid flow. In the present study, a numerical simulation was performed to simulate, the steady three-dimensional Navier-Stokes equations, behavior of a cavitating axial pump with special interest in the cavity geometry, the pressure and void fraction fields. Also, it includes the effects of turbulence and fluid viscosity. The cavity shape will be determined over the blades and the three-dimensional flow field around the cavitating propeller and in the wake will be calculated. The macroscopic behavior of vapor bubbles will be discussed with the effect of pressure, velocity and turbulent. Numerical results are verified experimentally. EXPERIMENTAL WORK A special axial pump test rig was used to study the cavitation behavior of the pump at different operating conditions. The experiments were carried out at the Hydraulic Laboratory in Zagazig University, Egypt. The test rig is a closed water cycle axial pump/ Kaplan turbine. The pump consists of a four-blade impeller. The skewed four-blade model impeller has a radius R = 0.05 m. The rotor blades angle can be adjusted as required from 0 to 30 degree. The impeller shaft is equipped with a rotary encoder to measure the rotational speed. The test rig allows the measurement of the flow rate


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and the pressure variation along the pump casing. Optical access to the pump section is possible through cylindrical Perspex casing. The photos were taken using a video camera with a speed of 30 fps and a stroboscopic light synchronized with the pump rotational speed. The photos showed the developed cavity along the blade leading edge in order to compare it with the numerical results. THEORETICAL BACKGROUND The basic approach is to use standard viscous flow, Navier-Stokes equations, with provisions for variable density and a conventional turbulence model, such as K-ε model. A numerical model previously developed by CFDRC to solve Navier- Stokes equations (Hinze, 1975). The mixture density (ρ) is a function of vapor mass fraction (f), which is computed by solving a transport equation simultaneously with the mass and momentum conservation equations. The ρ -f relationship is:

1

11ρρρ

fvf −+≡ (1)

In two-phase flows, the use of vapor volume fraction (α) is also quite common. Therefore, it is deduced from f as follows:

vf ρ

ρα = (2)

The transport equation for vapor is written as follows: cReRfVfVVf

t−+∇Γ•=•+ )()()(

�ρρ∂

∂ (3)

The expressions of Re and Rc have been derived from the reduced form of the Rayleigh-Plesset equation (Hammitt, 1980), which describes the dynamics of single bubble in an infinite liquid domain. The expressions for Re and Rc are: )1(

32 f

l

psatpvl

chVeCeR −

−= ρρρσ (4)

f

lsatpp

vlchV

cCcR ρρρσ−

=32 (5)

Cavitation normally takes place in the vicinity of low pressure (or locally high velocity) regions, where turbulence effects are quite significant. In particular, turbulent pressure fluctuations have significant effect on cavitating flows. The magnitude of


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pressure fluctuations is estimated by using the following empirical correlation (Pereira et al., 2004):

P’turb= 0.39 ρ k (6) The phase-change threshold pressure value is as: '5.0 turbpsatpvp += (7)

It is well known that cavitating flows are sensitive to the presence of non-condensable gases. In most liquids, there is a small amount of non-condensable gases present in dissolved and/or mixed state. For example, laboratory water generally has 15 ppm air dissolved in it. In other applications, e.g., marine propellers, etc., this amount may be considerably larger. In this model, the non-condensable gas is included by prescribing an estimated mass fraction at inlet. This value is held constant throughout the calculation domain. However, the corresponding density (and hence volume fraction) varies significantly with local pressure. The perfect gas law is used to account for the expansion (or compressibility) of gas; i.e.

RTWP

gas =ρ (8)

The calculation of mixture density (equation 1) is modified as:

l

gfvf

ggf

vvf

ρρρρ−−

++=11 (9)

We have the following expressions for the volume fractions of vapor (αv) and gas (αg):

vvfv ρρα = (10)

ggfg ρ

ρα = (11)

and,

gvl ααα −−=1 (12)

The combined volume fraction of vapor and gas (i.e., αv + αg) is referred to as the Void Fraction (α). In practical applications, for qualitative assessment of the extent and location of cavitation, contour maps of void fraction (α) are important to determine bubbles location and shape.


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NUMERICAL SIMULATION The numerical simulation was done using a three-dimensional Navier-Stokes code (CFDRC, 2004-1) to model the two phase flow field around a 3D impeller in a cavitating axial pump. This code employs a homogenous flow approach, also known as Equal-Velocity-Equal-Temperature (EVET) approach (CFDRC, 2004-2) and Fukaya, et al., (2003). The governing equations are discretized on a structured grid using an upwind difference scheme. The numerical simulation used the standard K-� turbulence model to account for the turbulence effect. The cavity shape was determined. Also, various variables were calculated, such as void fraction, mass fraction, pressure and velocity contours. It is clear that the full cavitaion model used in this simulation includes a lot of effects which were previously ignored in the previous studies, such as fluid viscosity, turbulence and the slip speed factor (ratio between actual and theoretical impeller rotating speed). BOUNDARY CONDITIONS In order to determine the three-dimensional flow field around the cavitating propeller and in the wake, the structured grid geometry of the impeller is constructed at three blade angles, 10o, 20o and 30o. The structured grids are consisted of about 180,000 cells. The structured grid ware used to reduce the numerical diffusion errors. In this case of a four-blade axial flow pump, sixteen blocks were used to generate the 3D impeller model as shown in figure (1). The propeller diameter is 4 in. (101.6 mm). Reynolds number is about 333,000. The computational time was about 6 hours, using single processor (Pentium IV CPU, 2.4 GHz, and 512 MB of RAM). RESULTS AND DISCUSSION The cavity shape was determined over the blades. Also, the macroscopic behavior of the formation and transport of vapor bubbles is discussed with the effect of the pressure, Velocity and turbulence. Figure (2) demonstrates the experimental pressure distributions at the casing along the axial direction at three blade angles, 10o, 20o and 30o. These results were obtained experimentally at an impeller speed of 3000 rpm. In order to simulate the rotation in the structured gird of the rotor, a rotating frame of the grid was assumed around the rotor axis. To match between the computed pressure distributions and the experimental pressure, the slip speed factor of the rotating frame is equal to 0.67. The cavitation exists only at condition of blade angle of 30o.


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Figure (3) represents the total pressure at blade angle of 30o, impeller running speed of 3000 rpm and slip speed factor of 0.67. Figures (3.a, 3.b and 3.c) show the total pressure contours in the suction side, pressure side and the rotor surface, respectively. Naturally, the minimum total pressures are located at the suction side. The total pressure varies from maximum to minimum in the suction side as demonstrated in the previous figures. In the same condition, figure (4) represents the static pressure contours. Figures (4.a, 4.b and 4.c) show the pressure contours in the suction side, pressure side and the rotor surface respectively. The minimum pressures are located at the suction side. Results indicate that the maximum energy loss occurs at the blade leading side. Also, figure (5) represents the vorticity in the previous condition. Figures (5.a, 5.b and 5.c) show the vorticity contours in the suction side, pressure side and the rotor surface respectively. The maximum vorticity is located at the suction side. The vorticity varies from maximum to minimum in the suction side as demonstrated in the previous figures. It indicates that the maximum energy loss occurs at the blade suction side. Both pressure drop and vortices cavitate the flow as indicated in figure (6). Figures (6.a, 6.b and 6.c) show iso-surface of the Vapor Volume fraction in the suction side, at α=25%, 50% and 75% respectively. The maximum Vapor Volume fractions are located at the suction side which matches with minimum pressure and maximums vortices locations. Figure (7) summarizes the contours of Vapor Volume fraction. Figure (8) demonstrates the void fraction contours (vapor and gas). Figures (8.a and 8.b) show the void fraction contours in the suction side, and the rotor surface, respectively. The void fraction contours are diffused more than the void vapor fraction contour. The void fraction contours are approximately similar to the density contours as shown in figure (9). Figure (10) demonstrates the calculated steady cavity for pump speed of 3000 rpm and slip speed factor of 0.67. In comparison with Figure (11), the experimental picture shows cavity shape and location are similar to the numerically predicted one. SUMMARY AND CONCLUSIONS An experimental and numerical study was performed to investigate the cavitation in axial pumps. The numerical simulation was done using a commercial CFD code called CFD-ACE which uses the "The full cavitaion model" to predict the cavitaion in axial pumps. The experimental work was done using a test rig designed for cavitation study. In order to simulate the rotation in the computational domain of the rotor, a rotating frame of reference is assumed around the rotor axis with the slip speed factor (ratio between impeller actual rotational speed and theoretical rotating frame speed) should be determined experimentally. The steady cavitation model used by the CFD-ACE code is capable of predicting cavitation in rotating machines with taking into consideration the slip speed factor. With slip speed factor of 0.67, there is a good agreement between the experimental cavity shape and the numerically predicted one.


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The maximum energy loss occurs at blade suction side. Both pressure drop and vortices cavitate the flow. So, the maximum Vapor Volume fraction is located at the suction side which matches the minimum pressure and maximum vorticity locations. REFERENCES 1- Cerone, A., Bramanti, C., Rapposelli, E., and Agostino, L., March 2006 "Thermal

Cavitation Experiments on a NACA 0015 Hydrofoil" Transactions of the ASME, Journal of Fluids Engineering, Vol. 128, pp. 326-331.

2- CFD-ACE V2004 User Manual – Volume 1, May 1, 2004 3- CFD-ACE V2004 Modules Manual – Volume 1, May 1, 2004. 4- Fukaya, M., Okamura, T., Tamura, Y., Matsumoto, Y., November 1-4, 2003

"Prediction of Cavitation Performance of Axial Flow Pump by Using Numerical Cavitating Flow Simulation with Bubble Flow Model" Fifth International Symposium on Cavitation, Osaka, Japan.

5- Hammitt, F. G., 1980, "Cavitation and Multiphase Flow Phenomena" McGraw-Hill International Book Co., New York.

6- Hinze, J.O., 1975, "Turbulence" McGraw-Hill Book Co., Second Edition. 7- Iga, Y., Nohmi, M., Goto, A., Ikohagi, T., May 2004, "Numerical Analysis of

Cavitation Instabilities Arising in the Three-Blade Cascade” Transactions of the ASME, Journal of Fluids Engineering, Vol. 126, pp. 419-429.

8- Mostafa, N. H., Rayan, M. A., and Mahgob, M. M., 1990, "Energetic model for Cavitation Erosion Prediction in Centrifugal Pump Impeller" Proceeding of ASME/CSME Cavitation and Multiphase Flow Forum, Toronto, Canada. pp. 133-138.

9- Mostafa, N. H., Nayfeh, A., Vlachos, P., and Telionis, D., January 2001 "Cavitating Flow Over a Projectile" AIAA Aerospace Sciences Meeting, AIAA-2001-1041, Reno, Nevada.

10- Mostafa, N. H., June 2001 "Computed Transient Supercavitating Flow Over A Projectile" Mansoura Engineering Journal, Vol. 26, No. 2, pp. 79-91.

11- Pereira, F., Salvatrore, F. and Felice, F., July 2004 "Measurement and Modeling of Propeller Cavitation in Uniform Inflow" Transactions of the ASME, Journal of Fluids Engineering, Vol. 126, pp. 671-679.

12- Singhal, A. K., Athavale, M. M., Li, H., Jiang, Y., September 2002 "Mathematical Basis and Validation of the Full Cavitation Model" Journal of Fluids Engineering, Vol. 124, pp. 617-624.

13- Watanable S. and Brennen, C., March 2003 "Dynamics of Cavitating Propeller in a Water Tunnel" Transactions of the ASME, Journal of Fluids Engineering, Vol. 125, pp. 283-292.


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Fig. (1) The structured grid for the axial Pump model.

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 4 9 12 14 18 22

Axial Distance of Pressure Tappings Points on Casing (cm)

P (B

ar)

Rotor Angle =10

Rotor Angle =20

Rotor Angle =30

Q=21 L/S

Q=19 L/S

Q=10 L/S

Impeller Nose Blade Inlet

Mid Blade

Blade Exit

Diffuser Inlet

Diffuser ExitPump Inlet

Fig. (2) Experimental pressure distribution at the casing along the axial direction.


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Fig. (3.a) Total Pressure contours at Suction

side at 3000 rpm and CN=0.67.

Fig. (4.a) Static Pressure contours at Suction

side at 3000 rpm and CN=0.67

Fig. (3.b) Total pressure contours at Pressure

side at 3000 rpm and CN=0.67.

Fig. (4.b) Static pressure contours at Pressure side at 3000 rpm and CN=0.67.

Fig. (3.c) Total pressure contours around the Rotor at 3000 rpm and CN=0.67.

Fig. (4.c) Static pressure contours around the Rotor at 3000 rpm and CN=0.67.


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Fig.(5.a) Vorticity contours at Suction Side at 3000 rpm and CN=0.67.

Fig. (6.a) Iso-surface of Vapor Volume fraction (αααα=25%) at Suction Side at 3000 rpm and

CN=0.67.

Fig. (5.b) Vorticity contours at Pressure Side at 3000 rpm and CN=0.67.

Fig. (6.b) Iso-surface of Vapor Volume fraction (αααα=50%) at Suction Side at 3000 rpm and

CN=0.67.

Fig. (5.c) Vorticity contours around the Rotor surface at 3000 rpm and CN=0.67.

Fig. (6.c) Iso-surface of Vapor Volume fraction

(αααα=75%) at Suction Side at 3000 rpm and CN=0.67.


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Fig. (7) Vapor volume fraction contours at

suction side at 3000 rpm and CN=0.67.

Fig. (9) Density contours at suction side

at 3000 rpm and CN=0.67.

Fig. (8.a) Volume Fraction contours at suction side at 3000 rpm and CN=0.67.

Fig. (10) Computational Cavity at

3000 rpm and CN=0.67.

Fig. (8.b) Volume fraction contours around the Rotor at 3000 rpm and CN=0.67.

Fig. (11) Experimental Cavity at 3000 rpm.

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NUMERICAL AND EXPERIMENTAL INVESTIGATION OF CAVITATION IN ... · PDF fileNUMERICAL AND EXPERIMENTAL INVESTIGATION OF CAVITATION IN AXIAL PUMPS ... ch Ch a r c te is v lo y h = k