In the last decade, there were a few papers studying cavitation inside a globe valve。 Palau-Salvador et al。 (2008) simulated fluid flows inside a globe valve, investigating the inception of cavitation in the valve。 They also explored the influences of two various plugs on cavitation inside the valve。 Numerical results showed that the plug with a smooth configuration reduced the occurrence of cavitation。 An et al。 (2008) numerically studied three dimensional turbulent flow flows through a globe valve。 They investigated the effect of four cages on the turbulent flow。 Flow coefficients and cavitation were presented in the  study  to  judge  which  cage is the optimal one for the globe  valve。

The aim of this study is to predict variation of cavitation in a globe valve numerically。 To control and to restrict the cavitation area, two cages are proposed to be installed inside the globe valve。 The influence of the cages on the fluid flow is explored in this study。 The cavitation model is included in the numerical model to observe the variation of cavitation inside the globe valve with or without the cages。

Mathematical Formulas and Numerical  Method

Fig。 1 presents the schematic of the studied flow field, including the globe valve and the piping system。 The nominal pipe diameter of the globe valve is 50。8 mm; so, the entrance length between inlet boundary and the globe valve is 1,100 mm (20D) in the numerical model。 The downstream length between the globe valve and the outlet boundary is 2,600 mm (50D)。 As previously mentioned, cav- itation and the resultant noise in the globe valve can be controlled by a cage。 In this study, two various cages are proposed to be in- stalled inside the globe valve in the numerical models: the one- stage perforated cage and the one-stage step cage as shown in Fig。 2。 These two cages are chosen to simulate and predict their capabil- ities to control cavitation。 The design of the one-stage perforated cage [Fig。 2(a)] is to use numerous smaller passageways where liquids are guided and forms various small jets。 The one-stage step cage [Fig。 2(b)] has the similar layout but with additional sudden contractions in the end of passageways。 Moreover, the globe valve without a cage is also considered in this study to find the influence of these two cages。 Two valve openings—full opening and half opening—are chosen in this study。 The valve opening is determined by h=h0, where h represents the distance between the bottoms of the plug and cage as shown in Fig。 1 and h0 is h in a fully open globe valve。 h0 is 19 mm in this study。 The differences among the three models are the primary issues to discover and discuss。    The

Fig。 1。 Schematic of the studied flow field including the globe valve and the piping system

Fig。 2。 Cages in the numerical models: (a) one-stage perforated cage;

(b) one-stage step cage

26 / JOURNAL OF ENERGY ENGINEERING © ASCE / MARCH  2013

configurations of three models are reconstructed using a computer- aided design (CAD) software。

where Vb  and Vl  = volumes of bubbles and liquids,   respectively。

Vf varies from 0 to 1。 Vb  can be determined by

Governing Equations

Fluid flow through the globe valve with different valve openings are simulated numerically。 The mixture, including liquid water and vapor, is considered as the working fluid in this study and assumed to be a Newtonian and compressible fluid。 The flow motion in the globe valve needs to obey the mass conservation and the momentum conservation during movement, so the governing equations include the continuity equation and the Navier-Stokes equations。 The corresponding Reynolds number  is

2。54 × 105, so the flow is turbulent in the piping system。 Conse- quently, a turbulence model has to be included in the mathematical model。