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Journal of Mechanical Science and Technology 24 (10) (2010) 2007~2016

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-010-0705-9

The cavitation behavior with short length blades in centrifugal pump

Quangnha Thai and Changjin Lee* Department of Aerospace Information Engineering, Konkuk University, 1 Hwayang-dong, Gwangjin-gu, Seoul 143-701, Korea

(Manuscript Received September 3, 2009; Revised May 31, 2010; Accepted June 23, 2010)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract A CFD code with 2-D cascade model was developed to predict the cavitation behavior around the impeller blades of impeller in a cen-

trifugal pump. The governing equations are the two-phase Reynolds Averaged Navier-Stokes equations in a homogeneous form in which both liquid and vapor phases are treated as incompressible fluid. To close the model, a standard k- turbulence model is introduced. And the mass transfer rates between liquid and vapor phases are implemented as well. The validations are carried out by comparing with ref-erence data in impeller of a centrifugal pump impeller. The cavitation characteristics of current centrifugal pumps is tested at an on-design point (V=8 m/s) and two off-design points (V=20 m/s and V=30 m/s), respectively. The criteria of cavitation and flow instability around blades are presented. The results show that the current centrifugal pump can safely operate without cavitation at on-design point. Also, the simulation shows cavitation develops inhomogeneously among the blades at off-design points. Moreover, the effects of addi-tional blades in the impeller are studied as well. From the numerical results, it is expected that a half-length blade is the optimum configu-ration as additional blades in cavitation point of view.

Keywords: Cavitation; Half-length blade; 2-D cascade; Centrifugal pump; Impeller ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

Cavitation is a phenomenon in which liquid evaporates and vapor bubbles occur in the region where the pressure of the liquid falls off under vapor pressure. It is usually observed in high-speed fluid machinery such as propellers, pumps, and impeller blades where the flow accelerates and the pressure decreases. Cavitation can give rise to erosion damage, noise, vibration and hydraulic performance deterioration by periodic inception, growth, depletion of vapor bubbles. Specially, cavi-tation in a centrifugal pump reduces efficiency and causes pressure head damage. The understanding of cavitating flow is one of the common subjects for designers of high-speed fluid machinery. The flow in a centrifugal pump is intrinsically turbulent, 3-D and unsteady; sometimes cavitation appears. The design of centrifugal pump is mainly based on the steady-state theory, empirical correlation, combination of model test-ing, and engineering experiences. Over the last few years, however, with the development of the computer, there have been many researches on the centrifugal pump in numerical calculation. Croba et al. [1] considered a more realistic through 2-D, unsteady, incompressible and turbulent flow. Anagnostopoulos (2006) [2] simulated the 3-D turbulent flow

in a centrifugal pump impeller with Cartesian grid to represent an adequate accuracy for the complex geometry of the cen-trifugal pump impeller. Cheah et al. (2007) [3] simulated the complex internal flow in a centrifugal pump impeller with six twisted blades by using 3-D Navier-Stokes code with a stan-dard k- two-equation turbulence model. Different flow rates were specified at the inlet boundary to predict the characteris-tics of the pump such as impeller passage flow, flow separa-tion and pressure distribution.

As aforementioned, cavitation in an impeller is naturally a 3-D phenomenon. However, due to the quite intrinsic complex nature with phase change, a mathematical model and numeri-cal method are considerably difficult to establish. Generally, the pump is designed to operate with non-zero incidence angle at a nominal flow rate. Nevertheless, in the range of opera-tional conditions, the angle of attack of impeller blades re-mains very small, because of variable flow thread and the associated curvature of blades. The back flow at the inlet may happen sometimes but its not strong. So, the approach of a 2-D cascade can be adopted. The cavitation in a 2-D cascade calculation has been investigated by many researchers so far, instead of 3-D calculation. For example, Joussellin et al. [4] simulated rotating cavitation and alternate blade cavitation occurring four-blade cyclic cascade by applying 2-D unsteady numerical method incorporated with cavitation model by barotropic state law. Iga et al. [5] simulated propagating phe-nomena of cavitation, which corresponds to the rotating cavi-

This paper was recommended for publication in revised form by Associate EditorWon-Gu Joo

*Corresponding author. Tel.: +82 2 450 3533, Fax: +82 2 444 6106 E-mail address: cjlee@konkuk.ac.kr

KSME & Springer 2010

2008 Q. Thai and C. Lee / Journal of Mechanical Science and Technology 24 (10) (2010) 2007~2016

tation through three-blade cyclic cascade and discussed the difference of the results obtained in different conditions at the inlet boundary. And the collaborative work of French re-searchers [6, 7] carried out the numerical and experimental analysis about cavitation behavior of four-blade inducer using a 2-D model of unsteady cavitating flow in a blade cascade.

For the reduction of computing time and analysis in design, the 2-D cascade looks like a new technique to 3-D calculation of cavitation analysis. Based on the prediction of 2-D cascade, a clearer understanding can be expected for 3-D cavitation. This is the reason why the present paper would like to simu-late cavitation around pump blades by using the 2-D cascade. We are interested in simulating the cavitation behavior around blades of impeller in centrifugal pump. The main objective is to establish the criterion of cavitation inception, the influence of the interaction among cavitations in flow passages. And, the effect of additional blades in impeller of centrifugal pump is also investigated by evaluating the characteristics of cavita-tion including the area of cavitation region and the fluctuation of mass flow rate. The benefits and disadvantages when put-ting the additional blades will be discussed in this study as well.

2. Governing equations and numerical procedure

2.1 Governing equations

The vapor-liquid flow is described by a single-fluid model which is treated as a homogeneous bubble-liquid mixture. The set of governing equations under single-fluid model comprises the conservative form of Reynolds-averaged Navier-Stokes equations, the k- two-equation turbulence closure and a transport equation for the liquid volume fraction. The continu-ity, momentum and liquid volume fraction equations are writ-ten in Cartesian coordinate system as follows:

. 0m mV S

dV v ndSt

+ =

r r (1)

dVbdSnTdSnvvdVvt V mSS mV m +=+ rrrrrrr .. (2)

( ) + +=+

VSl

Vl dVmmdSnvdVt

&&rr

. (3)

where

( ) ( )

+

++

++=

i

j

j

itij

j

jtij x

uxu

xu

pT 32

The constitutive relations for the density and dynamic vis-

cosity of the mixture are:

( )lvllm += 1 and ( )lvllm +== 1

And the turbulent viscosity is defined as follows:

2kCm

t =

2.2 Cavitation model

Cavitation terms, based on Kunz et al.s model [8], are used in this study. The evaporation and condensation rates are giv-en as follows:

[ ]

=

tU

ppMINCmll

vlvdest

2

21

,0

&

( )

+ =t

Cm

l

llvprod

12

&

where Cprod = 9x105, Cdest = 3x104, t = 1

2.3 Numerical procedure

The discretization of the governing Eqs. (1), (2), (3) is done by using finite volume method. And the collocated grid sys-tem is used to allocate velocity components and dependent variables. The convective and diffusive terms are differenced by upwind scheme and central scheme, respectively. The solu-tion of pressure and velocity may show an unphysical oscilla-tion due to the use of collocated grid system and should be treated by using interpolation in the momentum equation to avoid oscillation. Details of the numerical description can be found in the reference [9].

2.4 2-D cascade and boundary condition

Analyzing the flow field data will provide deep insights into the flow mechanism. 2-D cascade flow was adopted as the methodology for flow analysis in this study. The 2-D blade-to-blade cascade was drawn by cutting the 3-D inducer geometry at constant radius equal to 70% of the tip radius as shown in Fig. 1. Details are found in the reference [10]. The axial flow entrance combines the rotational speed of the blades and will result in the relative velocity between flow and blades. In the present 2-D calculation, the blades are considered stationary and the relative flow comes to blades with a certain angle of attack. The boundary conditions used in the present simula-tions includes inflow, outflow, non-slip, and periodic bound-ary condition. At the inle