Turbulence  Kinetic Energy

In theory, the eddy motion in a turbulent flow relies on the energy supplied by the mean flow (Tennekes and Lumely 1972)。 The dis- tribution of turbulence kinetic energy, k, is worthy of investigation。

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Fig。 4。 Flow patterns in fully open globe valves at t ¼ 10 s: (a) without a cage; (b) one-stage perforated cage; (c) one-stage step cage

For the region where k is very large, the mean flow provides more energy to the eddy motion at this region。 Figs。 6 and 7 show contours of k in fully and half-open conditions。 It is clear that the distributions of k in the globe valves without and with the cages are very different。 In Fig。 6(a), the high turbulence kinetic energy occurs at the bottom of the globe valve without a cage and the downstream region。 In terms of Figs。 6(b and c), high turbulence kinetic energy contours are found at the exits of the flow passages inside the cages。 In particular, the intensity of k in the vicinity of the exits of the one-stage step cage is very strong as shown in Fig。 6(c)。 However, both results in the globe valves with a cage show that k is milder in the downstream region than that  without a cage。

When the valve opening decreases, the contours of k vary a little (Fig。 7)。 The intensity of k is increased in the globe valve without a cage as shown in Fig。 7(a)。 The high turbulence kinetic energy appears not only at the bottom of the valve and the downstream region but also the bottom of the plug。 Meanwhile, Figs。 7(b and c) describe k as much smaller than in the globe valve without a cage。 In addition, k, which varies from 100 to 600 and is

located in the downstream of the globe valve with the one-stage perforated cage, is smaller than that with the one-stage step cage。 According to results, most turbulence kinetic energy happens inside the valve body when the cage is installed in the globe valve。 The intensity of k is especially very large below the bottom of the plug。

Prediction of Cavitation

In this study, cavitation distributions are the most important results to analyze and discover regions of cavitation in the globe valves。 Vf varying from 0 to 1 is used to observe cavitation in the globe valves。 Generally, the criterion of Vf to judge whether or not cavitation occurs at each computational cell is 0。5。 When Vf is higher than 0。5 at a computational cell, it represents that this cell contains significant vapor and cavitation occurs。 Fig。 8 shows con- tours and 3D isosurfaces of Vf of 0。5 at the fully open globe valves with and without  the  cages。  Distributions  of  vapor  at the globe valves with and without the cages are very different。 Fig。 8(a) shows that vapor appears in the vortices inside the globe

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Fig。 5。 Flow patterns in half-open globe valves at t ¼ 10 s: (a) without a cage; (b) one-stage perforated cage; (c) one-stage step cage

valve without a cage。 Also, vapor occurs in the downstream re- circulation。 Furthermore, when those two cages are  installed, Figs。 8(b and c) depict that vapor does not appear in the previous regions。 Instead, vapor primarily congregates at the exits of flow passages of the cages。 Moreover, the region of cavitation in the one-stage perforated cage is smaller than that in the one-stage step cage。 Nevertheless, both results show that less vapor occurs in the downstream region when the cages are installed at the globe valve。 In terms of the prediction of cavitation, the two cages can gather most of the vapor in the vicinity of exits and then  protect the valve body。

Fig。 9 demonstrates contours and iso-surfaces of Vf of 0。5 for half-open globe valves without and with the cages。 In Fig。 9(a), although the cavitation distribution is almost the same with the result at the fully open valve, cavitation occurrence in the down- stream region becomes smaller。 The results of Figs。 9(b and c) show that the cavitation occurs when the vortex inside the valve becomes serious as the valve opening decreases。 Cavitation can be observed especially clearly in the results of the globe valve with the one-stage