Keywords

1 Introduction

Hydraulic driven shiplift (HDSL) is a new attempt on high dam navigation technology in the world. It mainly uses water power as the lifting power and security measure. The ship reception chamber moves with the rise and fall of the buoys in the vertical shafts, which are driven by the filling and emptying system. When the ship chamber load is changed, the submerged depth of the buoys will have a corresponding change to make the ship chamber reach a new equilibrium between chamber and buoys, and solve the serious leakage problem in ship chamber, which is an incomparable technical advantage than traditional electric driven shiplift (Hu 2011). It is especially suitable for high dam navigation, and has a broad application prospect. Jinghong shiplift is the first HDSL in the world (Fig. 1).

The filling and emptying system of HDSL is similar to the electric drive system of traditional shiplift, which is the source of power. Its running speed and acceleration are controlled through the precise regulation of water flow. Hence, the performance of the valve plays an important role in the safety and stability of HDSL.

Cavitation is a transition phase between liquid and cavitation bubbles which occur within low pressure zone and crush with pressure recovery (Pan et al. 2013). Cavitation is a very common hydraulic phenomenon in hydraulic machinery such as propellers (Pennings et al. 2016), venturi tubes (Bertoldi et al. 2015), vane pumps (Li 2016), and control valves (Hubballi et al. 2013). Studies of valve cavitation always focus on noise, vibration, and performance reduction (Shirazi et al. 2012). Most research still relies on experiments (Long et al. 2018) with a variety of measurement methods such as high-speed photography (Wang et al. 2015), PIV (Kravtsova et al. 2014), probes (Pham et al. 1999), and observation window (Osterman et al. 2009). With the fast development of CFD (computational fluid dynamics), numerical simulations have also been used to study cavitation inside the valves and other situations beyond the capability of experiments (Liu et al. 2006).

Cavitation should be controlled for the safety and efficiency of HDSL. Based on the mechanism of cavitation, the cavitation defense measures for control valves are mainly divided into two categories: aeration (Tomov et al. 2015) and structure optimization (Gholami et al. 2015). Chern studied the globe valve with or without a cage by cavitation model (Chern et al. 2004). The results indicated that the cage could limit the cavitation to the vicinity of cage and prevent cavitation to erode valve body and downstream pipe. Hubballi performed analytic and experimental research by using cavitation index to predict the cavitation effects for hydraulic control valves. Jo made a numerical study for reducing cavitation in butterfly valve (Jo et al. 2013), and the perforated plate was thought to be effective to suppress the cavitation inside of the pipe. Gholami studied the needle valve by 3-D numerical simulation. A circular row of vanes was used at the end section of the needle valve. From their study, they concluded that cavitation was suppressed, but the flow coefficient also was decreased. Lee made a shape design of bottom plug used in a 3-way reversing valve to minimize the cavitation effect (Lee et al. 2016). Han selected three kinds of typical structures of poppet valves to research (Han et al. 2017). The results revealed that two-stage throttle valve (TS valve) can effectively suppress the occurrence of cavitation while the flow force of TS valve was much bigger than other valves.

Fig. 1.
figure 1

Jinghong HDSL perspective view.

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The present researches about industrial valve cavitation, mainly concentrate on the cavitation mechanism and the structure optimization of valve. In the conditions of high pressure and large flow rate, there have few researches about useful measures which can be applied to practical engineering for efficiently restraining cavitation. In the current research, experimental study on abrupt expansion pipe behind plunger valve was carried out, the flow regime and cavitation phenomena were observed through glass tube, and the influence rules of abrupt-expansion on the hydraulic characteristics of valve were analyzed.

2 Materials and Methods

In this paper, as seen in Fig. 2, the test valve is a plunger valve, DN = 150 mm, the type of sleeve is SZ20–30% (made by VAG Germany). The experiments were carried out in the multi-functional cavitation experiment hall of Nanjing Hydraulic Research Institute (Nanjing, China). This laboratory is automated with the automatic control of pumps, valves, pressure and flow monitoring. The maximum capacity of water pressure supply system is 1.5MPa and the maximum flow rate is 0.15m3/s. The experimental model is mainly composed by test valve and glass pipe (Fig. 3).

The influence rules of hydraulic characteristics of valve with abrupt-expansion were observed in this study. It mainly includes the properties of flow capacity, wall pressure characteristics and cavitation characteristics. The representative parameters are as follows: flow coefficient (μ), pressure characteristics of pipe after valve including time-average pressure (Pta) and fluctuating pressure (Prms) and cavitation index (K). The main physical quantities required to be observed are as follows: flow rate (Q), cavitation noise, wall pressure, upstream steady pressure (Pu) and downstream steady pressure (Pd). The locations of the sensors are shown in Fig. 4.

Fig. 2.
figure 2

(a) Perspective view of plunger valve; (b) Picture of plunger valve.

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Fig. 3.
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Experimental setup.

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Fig. 4.
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Sensor layout (mm).

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In this research, the experimental studies of three kinds of abrupt-expansions were investigated. The specific dimensions of parameters were shown in Table 1, and the definition of expansion ratio (R) was shown in Eq. 1. ID and OD denote the inside diameter and outside diameter of glass pipe.

Table 1. Experiment content.
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$$ R{ = }\frac{{A_{1} }}{{A_{2} }} $$
(1)

A1 denotes the reference section area of abrupt-expansion (m2); A2 denotes the reference section area of pipe (m2).

3 Results and Discussion

3.1 Flow Phenomena

The typical cavitation phenomena of plunger valve are shown in Fig. 5. The cavitation appearances in three types of abrupt-expansions are same. It is mainly misty cavitation. Due to the particular structure of plunger valve, the misty cavitation can be combined into vortex rope cavitation at opening degree of 0.3. Enlarging of the abrupt-expansion size, a thickness of water cushion is added between the cavitation and the pipe wall. For R = 1.00, the pipe is filled with misty cavitation, the collapse of bubbles will directly erode the pipe wall. For R = 2.15, the pipe is basically filled with misty cavitation, but occasionally there is a layer of water cushion between bubbles and pipe wall. For R = 4.00, there is a stable water cushion between cavitation and pipe wall. The process of bubble collapse is confined within the water body, so the impact of collapse on pipe can be buffered, and the pipe vibration and cavitation damage could be reduced significantly.

Fig. 5.
figure 5

Cavitation phenomena.

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3.2 Flow Coefficient

In this research, μ is defined as follow:

$$ \mu = \frac{Q}{{A\sqrt {2\frac{{(P_{u} - P_{d} )}}{\rho }} }} = \frac{1}{{\sqrt {1 + \sum \zeta } }} $$
(2)

A denotes the reference section area (m2); ρ denotes the density of water; g denotes the acceleration of gravity; ∑ζ denotes the resistance of the test system. Figure 6 and Table 2 show the difference of μ for various R.

Fig. 6.
figure 6

Flow coefficient for various R.

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Table 2. Flow coefficient for various R.
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From the definition of μ, it can be said that flow loss is the root cause of the change of μ. The resistance of the test system is composed with valve resistance (ζv) and abrupt-expansion resistance (ζe). The ζe includes resistance of the expansion section (ζex), resistance along the expansion body (ζλ) and resistance of the contraction section (ζc), and shown as follows:

$$ \sum {\zeta = \zeta_{v} + \zeta_{e} = \zeta_{v} + (\zeta_{ex} + \zeta_{\lambda } + \zeta_{c} } ) $$
(3)

Because the l/d of abrupt-expansion is large enough (Du et al. 2015),

ζλ is small and it can be negligible. Therefore, ζe can be simplified as:

$$ \zeta_{e} \approx \zeta_{ex} + \zeta_{c} $$
(4)

Section 1 and 2 were defined as shown in Fig. 7. Because the two sections were in the same elevation, so there was no need to consider the potential energy. The relationship of R and ζc could be analyzed by theoretical method as follows:

Fig. 7.
figure 7

Abrupt-contraction section.

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The Bernoulli’s equation considered flow loss:

$$ \frac{{v_{1}^{2} }}{2g} + \frac{{p_{1} }}{\rho g} = \frac{{v_{2}^{2} }}{2g} + \frac{{p_{2} }}{\rho g} + \zeta_{c} \frac{{v_{2}^{2} }}{2g} $$
(5)

The continuity equation:

$$ A_{1} v_{1} = A_{2} v_{2} $$
(6)

The simultaneous solution of Eq. (1)–(6):

$$ \mu = \frac{1}{{\sqrt {1 + \frac{{R^{2} }}{{R^{2} - 1}}\zeta_{c} } }} $$
(7)

In the same way, the influence of R on ζex can be analyzed, and combined with Eq. 7:

$$ \mu = \frac{1}{{\sqrt {1 + \frac{{R^{2} }}{{R^{2} - 1}}\zeta_{e} } }} $$
(8)

The empirical formulas of ζex and ζc are as (Li et al. 2006):

$$ \zeta_{ex} = (1 - \frac{1}{R})^{2} $$
(9)
$$ \zeta_{c} = 0.5(1 - \frac{1}{R}) $$
(10)

μ parameter can be obtained as:

$$ \mu = \frac{1}{{\sqrt {1 + \frac{{R^{2} }}{{R^{2} - 1}}\zeta_{e} } }} = \frac{1}{{\sqrt {1 + (1.5 - \frac{2.5}{{R + 1}})} }} $$
(11)

The impact of R on ζe shows in Fig. 8: with the increase of R, ζe is increasing, and μ is reducing, but the reducing extent is dropped. For R = 3, ζe ≈ 0.9; for R = 8, ζe is only 1.2. It can be seen that, when R increases to a certain extent, the further enlargement of R will not have a significant effect on ζe. Because the abrupt expansion pipe wall is too far from the mainstream to make a significant impact.

Fig. 8.
figure 8

Relationship of R and ζe.

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Based on Eq. 11, the formula of μ on the whole test section with R could be obtained:

$$ \mu = \frac{1}{{\sqrt {1 + \zeta_{v} + 1.5 - \frac{2.5}{{R + 1}}} }} $$
(12)

The comparison between theoretical value and measured data of μ is shown in Fig. 9.

Fig. 9.
figure 9

Comparison of theoretical value and measured data.

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It can be seen that the measured data are in good agreement with the theoretical values. Based on the results of above analysis, the variation law of μ can be fully explained.

For n = 0.1–0.5, the variations of μ are very small. Because of ζv is much bigger than ζe. The influence of abrupt-expansion could be neglected. For n = 0.6–1.0, with the increase of n, the ζv declined dramatically, and the influence of abrupt-expansion increased remarkably. For R has increased from 2.15 to 4.00, the decrease of μ was 5%, which shown in both of theoretical and experimental results.

3.3 Pressure Characteristics

Figure 10 shows the pressure characteristics for various R values of typical condition. For R increased from 1.00 to 2.15, Pta increased and its maximum promotion was 20 kPa; Prms near valve port decreased significantly and the drop was 2 kPa; For R increased from 2.15 to 4.00, the change of Pta and Prms were very small.

Fig. 10.
figure 10

Pressure characteristics for various R of typical condition. (a) Time-average pressure for various R; (b) Fluctuating pressure for various R.

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Combined with pictures of cavitation phenomena, there is a layer of water subfill between pipe wall and mainstream, which is beneficial to increase the Pta after valve, the collapsing of cavitation can be limited within the water body and the Prms can be reduced significantly. After the stable water cushion is formed, the further increase of R, which means the further increase of the thickness of water cushion, has marginal effect on the pressure characteristics of pipe wall.

3.4 Noise Characteristics

As shown in Fig. 11, For R increased from 1.00 to 2.15, time-average sound pressure (SP) dropped rapidly by about 30 Pa, the sound pressure level (SPL) decreased about 40 db in the dominant frequency (6 kHz), and cavitation had been significantly inhibited. For R increased from 2.15 to 4.00, SP and SPL changed slightly. The comparisons of cavitation noise characteristics for various R values in different working conditions are shown in Table 3, it is indicated that when the stable water cushion is formed, the further increase of R wouldn’t increase the cavitation suppression effect obviously.

Fig. 11.
figure 11

Noise characteristics for various R of typical condition. (a) Sound pressure for various R; (b) Sound pressure level for various R.

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Table 3. Cavitation noise characteristics (CNC) under different R.
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4 Conclusions

  1. (1)

    Abrupt-expansion reduced the discharge capability of valve. For n = 0.1–0.5, the influence was very small. Because of ζv was much bigger than ζe. The influence of abrupt-expansion could be neglected. For n = 0.6–1.0, the influence increased remarkably, because ζv decreased with n obviously. The variation of μ for various R values was smaller for R increased from 2.15 to 4.00, because ζe decreased slightly with the further increase of R.

  2. (2)

    Abrupt-expansion could improve the pressure characteristics on pipe wall behind valve and inhibit cavitation significantly. There was a layer of water subfill between the wall of abrupt-expansion and mainstream, which could increase the Pta, limit the collapse of cavitation and reduce the Prms significantly.

  3. (3)

    In order to minimize the influence on the flow coefficient and ensure the formation of stable water cushion, it is suggested that the expansion ratio for this type of abrupt-expansion is suitable for 3.00.